summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/generic/pgf/version-for-tex4ht/en/pgfmanualse3.html
blob: d3a305f8a11fb512b59f234d4b0ab89c13602857 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"  
  "http://www.w3.org/TR/html4/loose.dtd">  
<html > 
<head><title>3 Tutorial: A Picture for Karl&#8217;s Students</title> 
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> 
<meta name="generator" content="TeX4ht (http://www.cis.ohio-state.edu/~gurari/TeX4ht/mn.html)"> 
<meta name="originator" content="TeX4ht (http://www.cis.ohio-state.edu/~gurari/TeX4ht/mn.html)"> 
<!-- html --> 
<meta name="src" content="pgfmanual.tex"> 
<meta name="date" content="2005-10-23 18:34:00"> 
<link rel="stylesheet" type="text/css" href="pgfmanual.css"> 
</head><body 
>
   <div class="crosslinks"><p class="noindent">[<a 
href="pgfmanualse4.html" >next</a>] [<a 
href="pgfmanualse2.html" >prev</a>] [<a 
href="pgfmanualse2.html#tailpgfmanualse2.html" >prev-tail</a>] [<a 
href="#tailpgfmanualse3.html">tail</a>] [<a 
href="pgfmanual.html#pgfmanualse3.html" >up</a>] </p></div>
   <h3 class="sectionHead"><span class="titlemark">3   </span> <a 
 id="x4-220003"></a>Tutorial: A Picture for Karl&#8217;s Students</h3>
<!--l. 3--><p class="noindent">This tutorial is intended for new users of <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&nbsp;and Ti<span 
class="cmti-10">k</span>Z. It does not give an exhaustive account of all the features of
Ti<span 
class="cmti-10">k</span>Z&nbsp;or <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>, just of those that you are likely to use right away.
<!--l. 7--><p class="indent">   Karl is a math and chemistry high-school teacher. He used to create the graphics in his worksheets and exams
using <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span 
class="E">E</span>X</span></span>&#8217;s <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{picture}</span></span></span> environment. While the results were acceptable, creating the graphics often turned out
to be a lengthy process. Also, there tended to be problems with lines having slightly wrong angles and circles also
seemed to be hard to get right. Naturally, his students could not care less whether the lines had the exact right
angles and they find Karl&#8217;s exams too difficult no matter how nicely they were drawn. But Karl was never entirely
satisfied with the result.
<!--l. 17--><p class="indent">   Karl&#8217;s son, who was even less satisfied with the results (he did not have to take the exams, after all), told Karl
that he might wish to try out a new package for creating graphics. A bit confusingly, this package seems to have two
names: First, Karl had to download and install a package called <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>. Then it turns out that inside this package
there is another package called Ti<span 
class="cmti-10">k</span>Z, which is supposed to stand for &#8220;Ti<span 
class="cmti-10">k</span>Z&nbsp;ist <span 
class="cmti-10">kein </span>Zeichenprogramm.&#8221; Karl
finds this all a bit strange and Ti<span 
class="cmti-10">k</span>Z&nbsp;seems to indicate that the package does not do what he needs.
However, having used <span 
class="cmcsc-10"><small 
class="small-caps">G</small><small 
class="small-caps">N</small><small 
class="small-caps">U</small> </span>software for quite some time and &#8220;<span 
class="cmcsc-10"><small 
class="small-caps">G</small><small 
class="small-caps">N</small><small 
class="small-caps">U</small> </span>not being Unix,&#8221; there seems to
be hope yet. His son assures him that Ti<span 
class="cmti-10">k</span>Z&#8217;s name is intended to warn people that Ti<span 
class="cmti-10">k</span>Z&nbsp;is not a
program that you can use to draw graphics with your mouse or tablet. Rather, it is more like a &#8220;graphics
language.&#8221;
<!--l. 33--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.1   </span> <a 
 id="x4-230003.1"></a>Problem Statement</h4>
<!--l. 35--><p class="noindent">Karl wants to put a graphic on the next worksheet for his students. He is currently teaching his students about sine
and cosine. What he would like to have is something that looks like this (ideally):
<!--l. 40--><p class="noindent"><object data="pgfmanual-5.svg" width="465.67824pt" height="269.39056pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>
                                                                                         
                                                                                         
<!--l. 115--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.2   </span> <a 
 id="x4-240003.2"></a>Setting up the Environment</h4>
<!--l. 117--><p class="noindent">In Ti<span 
class="cmti-10">k</span>Z, to draw a picture, at the start of the picture you need to tell <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;or <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span 
class="E">E</span>X</span></span>&nbsp;that you want to start a
picture. In <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span 
class="E">E</span>X</span></span>&nbsp;this is done using the environment <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{tikzpicture}</span></span></span>, in plain <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;you just use <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikzpicture</span></span></span>
to start the picture and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\endtikzpicture</span></span></span> to end it.
<!--l. 123--><p class="noindent">
   <h5 class="subsubsectionHead"><span class="titlemark">3.2.1   </span> <a 
 id="x4-250003.2.1"></a>Setting up the Environment in <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span 
class="E">E</span>X</span></span></h5>
<!--l. 125--><p class="noindent">Karl, being a <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span 
class="E">E</span>X</span></span>&nbsp;user, thus sets up his file as follows:
<!--l. 127--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-4-" ><colgroup id="TBL-4-1g"><col 
id="TBL-4-1"></colgroup><tr  
 valign="baseline" id="TBL-4-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-4-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\documentclass{article}</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;say</span>
<br><span 
class="cmtt-8">\usepackage{tikz}</span>
<br><span 
class="cmtt-8">\begin{document}</span>
<br><span 
class="cmtt-8">We</span><span 
class="cmtt-8">&nbsp;are</span><span 
class="cmtt-8">&nbsp;working</span><span 
class="cmtt-8">&nbsp;on</span>
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}.</span>
<br><span 
class="cmtt-8">\end{document}</span></div>                                                                                                </td></tr></table> </td>
</tr></table></div>
<!--l. 139--><p class="indent">   When executed, that is, run via <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pdflatex</span></span></span> or via <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">latex</span></span></span> followed by <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">dvips</span></span></span>, the resulting will contain something
that looks like this:
<!--l. 142--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-5-" ><colgroup id="TBL-5-1g"><col 
id="TBL-5-1"><col 
id="TBL-5-2"></colgroup><tr  
 valign="baseline" id="TBL-5-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-5-1-1"  
class="td11">  &nbsp;We are working on<object data="pgfmanual-6.svg" width="85.75821pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>.&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-5-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">We</span><span 
class="cmtt-8">&nbsp;are</span><span 
class="cmtt-8">&nbsp;working</span><span 
class="cmtt-8">&nbsp;on</span>
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}.</span></div>                                                                                            </td></tr></table> </td>
</tr></table></div>
<!--l. 150--><p class="indent">   Admittedly, not quite the whole picture, yet, but we do have the axes established. Well, not quite, but we have
the lines that make up the axes drawn. Karl suddenly has a sinking feeling that the picture is still some way
off.
<!--l. 155--><p class="indent">   Let&#8217;s have a more detailed look at the code. First, the package <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">tikz</span></span></span> is loaded. This package is a so-called
&#8220;frontend&#8221; to the basic <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&nbsp;system. The basic layer, which is also described in this manual, is somewhat
more, well, basic and thus harder to use. The frontend makes things easier by providing a simpler
syntax.
<!--l. 161--><p class="indent">   Inside the environment there are two <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> commands. They mean: &#8220;The path, which is specified following the
command up to the semicolon, should be drawn.&#8221; The first path is specified as <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(-1.5,0)</span><span 
class="cmtt-10">&nbsp;--</span><span 
class="cmtt-10">&nbsp;(0,1.5)</span></span></span>,
which means &#8220;a straight line from the point at position (<span 
class="cmsy-10">-</span>1<span 
class="cmmi-10">.</span>5<span 
class="cmmi-10">,</span>0) to the point at position (0<span 
class="cmmi-10">,</span>1<span 
class="cmmi-10">.</span>5).&#8221;
Here, the positions are specified within a special coordinate system in which, initially, one unit is
1cm.
<!--l. 169--><p class="indent">   Karl is quite pleased to note that the environment automatically reserves enough space to encompass the
picture.
<!--l. 173--><p class="noindent">
   <h5 class="subsubsectionHead"><span class="titlemark">3.2.2   </span> <a 
 id="x4-260003.2.2"></a>Setting up the Environment in Plain <span class="TEX">T<span 
class="E">E</span>X</span></h5>
<!--l. 175--><p class="noindent">Karl&#8217;s wife Gerda, who also happens to be a math teacher, is not a <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span 
class="E">E</span>X</span></span>&nbsp;user, but uses plain <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;since she
prefers to do things &#8220;the old way.&#8221; She can also use Ti<span 
class="cmti-10">k</span>Z. Instead of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\usepackage{tikz}</span></span></span> she has to
write <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\input</span><span 
class="cmtt-10">&nbsp;tikz.tex</span></span></span> and instead of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\begin{tikzpicture}</span></span></span> she writes <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikzpicture</span></span></span> and instead of
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\end{tikzpicture}</span></span></span> she writes <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\endtikzpicture</span></span></span>.
<!--l. 182--><p class="indent">   Thus, she would use:
                                                                                         
                                                                                         
<!--l. 183--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-6-" ><colgroup id="TBL-6-1g"><col 
id="TBL-6-1"></colgroup><tr  
 valign="baseline" id="TBL-6-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-6-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmsltt-10x-x-80">%%</span><span 
class="cmsltt-10x-x-80">&nbsp;Plain</span><span 
class="cmsltt-10x-x-80">&nbsp;TeX</span><span 
class="cmsltt-10x-x-80">&nbsp;file</span>
<br><span 
class="cmtt-8">\input</span><span 
class="cmtt-8">&nbsp;tikz.tex</span>
<br><span 
class="cmtt-8">\baselineskip=12pt</span>
<br><span 
class="cmtt-8">\hsize=6.3truein</span>
<br><span 
class="cmtt-8">\vsize=8.7truein</span>
<br><span 
class="cmtt-8">We</span><span 
class="cmtt-8">&nbsp;are</span><span 
class="cmtt-8">&nbsp;working</span><span 
class="cmtt-8">&nbsp;on</span>
<br><span 
class="cmtt-8">\tikzpicture</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">\endtikzpicture.</span>
<br><span 
class="cmtt-8">\bye</span></div>                                                                                                          </td></tr></table> </td>
</tr></table></div>
<!--l. 197--><p class="indent">   Gerda can typeset this file using either <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pdftex</span></span></span> or <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">tex</span></span></span> together with <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">dvips</span></span></span>. Ti<span 
class="cmti-10">k</span>Z&nbsp;will automatically discern
which driver she is using. If she wishes to use <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">dvipdfm</span></span></span> together with <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">tex</span></span></span>, she either needs to modify the file
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pgf.cfg</span></span></span> or can write <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\def\pgfsysdriver{pgfsys-dvipdfm.def}</span></span></span> somewhere <span 
class="cmti-10">before </span>she inputs <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">tikz.tex</span></span></span> or
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pgf.tex</span></span></span>.
<!--l. 207--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.3   </span> <a 
 id="x4-270003.3"></a>Straight Path Construction</h4>
<!--l. 209--><p class="noindent">The basic building block of all pictures in Ti<span 
class="cmti-10">k</span>Z&nbsp;is the path. A <span 
class="cmti-10">path </span>is a series of straight lines and curves that are
connected (that is not the whole picture, but let us ignore the complications for the moment). You
start a path by specifying the coordinates of the start position as a point in round brackets, as in
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(0,0)</span></span></span>. This is followed by a series of &#8220;path extension operations.&#8221; The simplest is <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">--</span></span></span>, which we used
already. It must be followed by another coordinate and it extends the path in a straight line to this new
position. For example, if we were to turn the two paths of the axes into one path, the following would
result:
<!--l. 220--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-7-" ><colgroup id="TBL-7-1g"><col 
id="TBL-7-1"><col 
id="TBL-7-2"></colgroup><tr  
 valign="baseline" id="TBL-7-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-7-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-7.svg" width="85.75821pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-7-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span></div>                                                       </td></tr></table> </td>
</tr></table></div>
<!--l. 224--><p class="indent">   Karl is a bit confused by the fact that there is no <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{tikzpicture}</span></span></span> environment, here. Instead, the little
command <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikz</span></span></span> is used. This command either takes one argument (starting with an opening brace as in
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikz{\draw</span><span 
class="cmtt-10">&nbsp;(0,0)</span><span 
class="cmtt-10">&nbsp;--</span><span 
class="cmtt-10">&nbsp;(1.5,0)}</span></span></span>, which yields <object data="pgfmanual-8.svg" width="43.0791pt" height="1.0pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>) or collects everything up to the next semicolon and
puts it inside a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{tikzpicture}</span></span></span> environment. As a rule of thumb, all Ti<span 
class="cmti-10">k</span>Z&nbsp;graphic drawing commands must occur
as an argument of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikz</span></span></span> or inside a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{tikzpicture}</span></span></span> environment. Fortunately, the command <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> will only be
defined inside this environment, so there is little chance that you will accidentally do something wrong
here.
<!--l. 237--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.4   </span> <a 
 id="x4-280003.4"></a>Curved Path Construction</h4>
<!--l. 239--><p class="noindent">The next thing Karl wants to do is to draw the circle. For this, straight lines obviously will not do. Instead, we need
some way to draw curves. For this, Ti<span 
class="cmti-10">k</span>Z&nbsp;provides a special syntax. One or two &#8220;control points&#8221; are needed. The
math behind them is not quite trivial, but here is the basic idea: Suppose you are at point <span 
class="cmmi-10">x </span>and the first control
point is <span 
class="cmmi-10">y</span>. Then the curve will start &#8220;going in the direction of&nbsp;<span 
class="cmmi-10">y </span>at&nbsp;<span 
class="cmmi-10">x</span>,&#8221; that is, the tangent of the
curve at <span 
class="cmmi-10">x </span>will point toward&nbsp;<span 
class="cmmi-10">y</span>. Next, suppose the curve should end at <span 
class="cmmi-10">z </span>and the second support point
is <span 
class="cmmi-10">w</span>. Then the curve will, indeed, end at <span 
class="cmmi-10">z </span>and the tangent of the curve at point <span 
class="cmmi-10">z </span>will go through
<span 
class="cmmi-10">w</span>.
<!--l. 250--><p class="indent">   Here is an example (the control points have been added for clarity):
                                                                                         
                                                                                         
<!--l. 251--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-8-" ><colgroup id="TBL-8-1g"><col 
id="TBL-8-1"><col 
id="TBL-8-2"></colgroup><tr  
 valign="baseline" id="TBL-8-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-8-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-9.svg" width="61.30548pt" height="32.85274pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-8-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw</span><span 
class="cmtt-8">&nbsp;[gray]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(2pt)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(1,1)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(2pt)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(2,1)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(2pt)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(2,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(2pt);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;controls</span><span 
class="cmtt-8">&nbsp;(1,1)</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;(2,1)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;(2,0);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 261--><p class="indent">   The general syntax for extending a path in a &#8220;curved&#8221; way is <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">..</span><span 
class="cmtt-10">&nbsp;controls</span></span></span> <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">first control point</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">and</span></span></span> <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">second</span>
<span 
class="cmti-10">control point</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">..</span></span></span> <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">end point</span><span 
class="cmsy-10">&gt;</span>. You can leave out the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">and</span></span></span> <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">second control point</span><span 
class="cmsy-10">&gt;</span>, which causes the first one to be used
twice.
<!--l. 267--><p class="indent">   So, Karl can now add the first half circle to the picture:
<!--l. 269--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-9-" ><colgroup id="TBL-9-1g"><col 
id="TBL-9-1"><col 
id="TBL-9-2"></colgroup><tr  
 valign="baseline" id="TBL-9-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-9-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-10.svg" width="85.75821pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-9-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1,0)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;controls</span><span 
class="cmtt-8">&nbsp;(-1,0.555)</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;(-0.555,1)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;(0,1)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;controls</span><span 
class="cmtt-8">&nbsp;(0.555,1)</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;(1,0.555)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;(1,0);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 278--><p class="indent">   Karl is happy with the result, but finds specifying circles in this way to be extremely awkward. Fortunately,
there is a much simpler way.
<!--l. 282--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.5   </span> <a 
 id="x4-290003.5"></a>Circle Path Construction</h4>
<!--l. 284--><p class="noindent">In order to draw a circle, the path construction operation <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">circle</span></span></span> can be used. This operation is followed by a radius
in round brackets as in the following example: (Note that the previous position is used as the <span 
class="cmti-10">center </span>of the
circle.)
<!--l. 289--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-10-" ><colgroup id="TBL-10-1g"><col 
id="TBL-10-1"><col 
id="TBL-10-2"></colgroup><tr  
 valign="baseline" id="TBL-10-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-10-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-11.svg" width="20.4pt" height="20.4pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-10-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(10pt);</span></div>                                                                              </td></tr></table> </td>
</tr></table></div>
<!--l. 293--><p class="indent">   You can also append an ellipse to the path using the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">ellipse</span></span></span> operation. Instead of a single radius you can
specify two of them, one for the <span 
class="cmmi-10">x</span>-direction and one for the <span 
class="cmmi-10">y</span>-direction, separated by <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">and</span></span></span>:
<!--l. 298--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-11-" ><colgroup id="TBL-11-1g"><col 
id="TBL-11-1"><col 
id="TBL-11-2"></colgroup><tr  
 valign="baseline" id="TBL-11-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-11-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-12.svg" width="40.4pt" height="20.4pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-11-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;ellipse</span><span 
class="cmtt-8">&nbsp;(20pt</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;10pt);</span></div>                                                                    </td></tr></table> </td>
</tr></table></div>
<!--l. 302--><p class="indent">   To draw an ellipse whose axes are not horizontal and vertical, but point in an arbitrary direction (a &#8220;turned
ellipse&#8221; like <object data="pgfmanual-13.svg" width="12.4573pt" height="9.28381pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>) you can use transformations, which are explained later. The code for the little ellipse is
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikz</span><span 
class="cmtt-10">&nbsp;\draw[rotate=30]</span><span 
class="cmtt-10">&nbsp;(0,0)</span><span 
class="cmtt-10">&nbsp;ellipse</span><span 
class="cmtt-10">&nbsp;(6pt</span><span 
class="cmtt-10">&nbsp;and</span><span 
class="cmtt-10">&nbsp;3pt);</span></span></span>, by the way.
<!--l. 309--><p class="indent">   So, returning to Karl&#8217;s problem, he can write <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span><span 
class="cmtt-10">&nbsp;(0,0)</span><span 
class="cmtt-10">&nbsp;circle</span><span 
class="cmtt-10">&nbsp;(1cm);</span></span></span> to draw the circle:
<!--l. 312--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-12-" ><colgroup id="TBL-12-1g"><col 
id="TBL-12-1"><col 
id="TBL-12-2"></colgroup><tr  
 valign="baseline" id="TBL-12-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-12-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-14.svg" width="85.75821pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-12-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table>
                                                                                         
                                                                                         
</div>
<!--l. 321--><p class="indent">   At this point, Karl is a bit alarmed that the circle is so small when he wants the final picture to
be much bigger. He is pleased to learn that Ti<span 
class="cmti-10">k</span>Z&nbsp;has powerful transformation options and scaling
everything by a factor of three is very easy. But let us leave the size as it is for the moment to save some
space.
<!--l. 330--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.6   </span> <a 
 id="x4-300003.6"></a>Rectangle Path Construction</h4>
<!--l. 332--><p class="noindent">The next things we would like to have is the grid in the background. There are several ways to produce it. For
example, one might draw lots of rectangles. Since rectangles are so common, there is a special syntax for them: To
add a rectangle to the current path, use the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">rectangle</span></span></span> path construction operation. This operation should
be followed by another coordinate and will append a rectangle to the path such that the previous
coordinate and the next coordinates are corners of the rectangle. So, let us add two rectangles to the
picture:
<!--l. 341--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-13-" ><colgroup id="TBL-13-1g"><col 
id="TBL-13-1"><col 
id="TBL-13-2"></colgroup><tr  
 valign="baseline" id="TBL-13-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-13-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-15.svg" width="85.75821pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-13-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(0.5,0.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-0.5,-0.5)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(-1,-1);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 351--><p class="indent">   While this may be nice in other situations, this is not really leading anywhere with Karl&#8217;s problem: First, we
would need an awful lot of these rectangles and then there is the border that is not &#8220;closed.&#8221;
<!--l. 355--><p class="indent">   So, Karl is about to resort to simply drawing four vertical and four horizontal lines using the nice <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span>
command, when he learns that there is a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">grid</span></span></span> path construction operation.
<!--l. 361--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.7   </span> <a 
 id="x4-310003.7"></a>Grid Path Construction</h4>
<!--l. 363--><p class="noindent">The <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">grid</span></span></span> path operation adds a grid to the current path. It will add lines making up a grid that fills the rectangle
whose one corner is the current point and whose other corner is the point following the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">grid</span></span></span> operation. For
example, the code <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikz</span><span 
class="cmtt-10">&nbsp;\draw[step=2pt]</span><span 
class="cmtt-10">&nbsp;(0,0)</span><span 
class="cmtt-10">&nbsp;grid</span><span 
class="cmtt-10">&nbsp;(10pt,10pt);</span></span></span> produces <object data="pgfmanual-16.svg" width="10.4pt" height="10.4pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>. Note how the optional
argument for <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> can be used to specify a grid width (there are also <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">xstep</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">ystep</span></span></span> to define the steppings
independently). As Karl will learn soon, there are <span 
class="cmti-10">lots </span>of things that can be influenced using such
options.
<!--l. 374--><p class="indent">   For Karl, the following code could be used:
<!--l. 376--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-14-" ><colgroup id="TBL-14-1g"><col 
id="TBL-14-1"><col 
id="TBL-14-2"></colgroup><tr  
 valign="baseline" id="TBL-14-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-14-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-17.svg" width="85.75821pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-14-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
<!--l. 385--><p class="indent">   Having another look at the desired picture, Karl notices that it would be nice for the grid to be more subdued.
(His son told him that grids tend to be distracting if they are not subdued.) To subdue the grid, Karl adds two more
options to the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> command that draws the grid. First, he uses the color <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">gray</span></span></span> for the grid lines. Second, he
reduces the line width to <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">very</span><span 
class="cmtt-10">&nbsp;thin</span></span></span>. Finally, he swaps the ordering of the commands so that the grid is drawn first
and everything else on top.
<!--l. 394--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-15-" ><colgroup id="TBL-15-1g"><col 
id="TBL-15-1"><col 
id="TBL-15-2"></colgroup><tr  
 valign="baseline" id="TBL-15-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-15-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-18.svg" width="85.75821pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-15-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 404--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.8   </span> <a 
 id="x4-320003.8"></a>Adding a Touch of Style</h4>
<!--l. 406--><p class="noindent">Instead of the options <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">gray,very</span><span 
class="cmtt-10">&nbsp;thin</span></span></span> Karl could also have said <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">style=help</span><span 
class="cmtt-10">&nbsp;lines</span></span></span>. <span 
class="cmti-10">Styles </span>are predefined sets of
options that can be used to organize how a graphic is drawn. By saying <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">style=help</span><span 
class="cmtt-10">&nbsp;lines</span></span></span> you say
&#8220;use the style that I (or someone else) has set for drawing help lines.&#8221; If Karl decides, at some later
point, that grids should be drawn, say, using the color <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">blue!50</span></span></span> instead of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">gray</span></span></span>, he could say the
following:
<!--l. 413--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-16-" ><colgroup id="TBL-16-1g"><col 
id="TBL-16-1"></colgroup><tr  
 valign="baseline" id="TBL-16-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-16-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v"><br><span 
class="cmtt-8">\tikzstyle</span><span 
class="cmtt-8">&nbsp;help</span><span 
class="cmtt-8">&nbsp;lines=[color=blue!50,very</span><span 
class="cmtt-8">&nbsp;thin]</span>
</div>                                                                                                              </td></tr></table> </td>
</tr></table>
</div>
<!--l. 416--><p class="indent">   Alternatively, he could have said the following:
<!--l. 417--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-17-" ><colgroup id="TBL-17-1g"><col 
id="TBL-17-1"></colgroup><tr  
 valign="baseline" id="TBL-17-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-17-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v"><br><span 
class="cmtt-8">\tikzstyle</span><span 
class="cmtt-8">&nbsp;help</span><span 
class="cmtt-8">&nbsp;lines+=[color=blue!50]</span>
</div>                                                                                                              </td></tr></table> </td>
</tr></table>
</div>
<!--l. 420--><p class="indent">   This would have added the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">color=blue!50</span></span></span> option. The <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">help</span><span 
class="cmtt-10">&nbsp;lines</span></span></span> style would now contain <span 
class="cmti-10">two </span>color options,
but the second would override the first.
<!--l. 424--><p class="indent">   Using styles makes your graphics code more flexible. You can change the way things look easily in a consistent
manner.
<!--l. 427--><p class="indent">   To build a hierarchy of styles you can have one style use another. So in order to define a style <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">Karl's</span><span 
class="cmtt-10">&nbsp;grid</span></span></span> that
is based on the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">grid</span></span></span> style Karl could say
<!--l. 430--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-18-" ><colgroup id="TBL-18-1g"><col 
id="TBL-18-1"></colgroup><tr  
 valign="baseline" id="TBL-18-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-18-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikzstyle</span><span 
class="cmtt-8">&nbsp;Karl's</span><span 
class="cmtt-8">&nbsp;grid=[style=help</span><span 
class="cmtt-8">&nbsp;lines,color=blue!50]</span>
<br><span 
class="cmtt-8">...</span>
<br><span 
class="cmtt-8">\draw[style=Karl's</span><span 
class="cmtt-8">&nbsp;grid]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(5,5);</span></div>                                                                    </td></tr></table> </td>
</tr></table></div>
<!--l. 436--><p class="indent">   You can also leave out the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">style=</span></span></span>. Thus, whenever Ti<span 
class="cmti-10">k</span>Z&nbsp;encounters an options that it does not know about, it
will check whether this option happens to be the name of a style. If so, the style is used. Thus, Karl could also have
written:
<!--l. 440--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-19-" ><colgroup id="TBL-19-1g"><col 
id="TBL-19-1"></colgroup><tr  
 valign="baseline" id="TBL-19-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-19-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikzstyle</span><span 
class="cmtt-8">&nbsp;Karl's</span><span 
class="cmtt-8">&nbsp;grid=[help</span><span 
class="cmtt-8">&nbsp;lines,color=blue!50]</span>
<br><span 
class="cmtt-8">...</span>
<br><span 
class="cmtt-8">\draw[Karl's</span><span 
class="cmtt-8">&nbsp;grid]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(5,5);</span></div>                                                                          </td></tr></table> </td>
</tr></table></div>
<!--l. 446--><p class="indent">   For some styles, like the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">very</span><span 
class="cmtt-10">&nbsp;thin</span></span></span> style, it is pretty clear what the style does and there is no need to say
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">style=very</span><span 
class="cmtt-10">&nbsp;thin</span></span></span>. For other styles, like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">help</span><span 
class="cmtt-10">&nbsp;lines</span></span></span>, it seems more natural to me to say <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">style=help</span><span 
class="cmtt-10">&nbsp;lines</span></span></span>. But,
mainly, this is a matter of taste.
<!--l. 452--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.9   </span> <a 
 id="x4-330003.9"></a>Drawing Options</h4>
                                                                                         
                                                                                         
<!--l. 454--><p class="noindent">Karl wonders what other options there are that influence how a path is drawn. He saw already that the
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">color=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">color</span><span 
class="cmsy-10">&gt; </span>option can be used to set the line&#8217;s color. The option <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">draw=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">color</span><span 
class="cmsy-10">&gt; </span>does nearly the same, only it sets
the color for the lines only and a different color can be used for filling (Karl will need this when he fills the arc for
the angle).
<!--l. 461--><p class="indent">   He saw that the style <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">very</span><span 
class="cmtt-10">&nbsp;thin</span></span></span> yields very thin lines. Karl is not really surprised by this and neither is he
surprised to learn that <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thin</span></span></span> yields thin lines, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thick</span></span></span> yields thick lines, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">very</span><span 
class="cmtt-10">&nbsp;thick</span></span></span> yields very thick lines,
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">ultra</span><span 
class="cmtt-10">&nbsp;thick</span></span></span> yields really, really thick lines and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">ultra</span><span 
class="cmtt-10">&nbsp;thin</span></span></span> yields lines that are so thin that low-resolution printers
and displays will have trouble showing them. He wonders what gives lines of &#8220;normal&#8221; thickness. It turns out that
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thin</span></span></span> is the correct choice. This seems strange to Karl, but his son explains him that <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span 
class="E">E</span>X</span></span>&nbsp;has two commands
called <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\thinlines</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\thicklines</span></span></span> and that <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\thinlines</span></span></span> gives the line width of &#8220;normal&#8221; lines,
more precisely, of the thickness that, say, the stem of a letter like &#8220;T&#8221; or &#8220;i&#8221; has. Nevertheless, Karl
would like to know whether there is anything &#8220;in the middle&#8221; between <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thin</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thick</span></span></span>. There is:
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">semithick</span></span></span>.
<!--l. 476--><p class="indent">   Another useful thing one can do with lines is to dash or dot them. For this, the two styles <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">dashed</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">dotted</span></span></span>
can be used, yielding <object data="pgfmanual-19.svg" width="10.4pt" height="1.0pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> and <object data="pgfmanual-20.svg" width="10.4pt" height="1.0pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>. Both options also exist in a loose and a dense version, called <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">loosely</span><span 
class="cmtt-10">&nbsp;dashed</span></span></span>,
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">densely</span><span 
class="cmtt-10">&nbsp;dashed</span></span></span>, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">loosely</span><span 
class="cmtt-10">&nbsp;dotted</span></span></span>, and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">closely</span><span 
class="cmtt-10">&nbsp;dotted</span></span></span>. If he really, really needs to, Karl can also define much
more complex dashing patterns with the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">dash</span><span 
class="cmtt-10">&nbsp;pattern</span></span></span> option, but his son insists that dashing is to be used with
utmost care and mostly distracts. Karl&#8217;s son claims that complicated dashing patterns are evil. Karl&#8217;s students do
not care about dashing patterns.
<!--l. 489--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.10   </span> <a 
 id="x4-340003.10"></a>Arc Path Construction</h4>
<!--l. 491--><p class="noindent">Our next obstacle is to draw the arc for the angle. For this, the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">arc</span></span></span> path construction operation is useful,
which draws part of a circle or ellipse. This <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">arc</span></span></span> operation must be followed by a triple in rounded
brackets, where the components of the triple are separated by colons. The first two components are
angles, the last one is a radius. An example would be <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(10:80:10pt)</span></span></span>, which means &#8220;an arc from 10
degrees to 80 degrees on a circle of radius 10pt.&#8221; Karl obviously needs an arc from 0<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup> to 30<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup>. The
radius should be something relatively small, perhaps around one third of the circle&#8217;s radius. This gives:
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(0:30:3mm)</span></span></span>.
<!--l. 502--><p class="indent">   When one uses the arc path construction operation, the specified arc will be added with its starting point at the
current position. So, we first have to &#8220;get there.&#8221;
<!--l. 506--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-20-" ><colgroup id="TBL-20-1g"><col 
id="TBL-20-1"><col 
id="TBL-20-2"></colgroup><tr  
 valign="baseline" id="TBL-20-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-20-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-21.svg" width="85.75821pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-20-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 516--><p class="indent">   Karl thinks this is really a bit small and he cannot continue unless he learns how to do scaling. For this, he can
add the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">[scale=3]</span></span></span> option. He could add this option to each <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> command, but that would be
awkward. Instead, he adds it to the whole environment, which causes this option to apply to everything
within.
                                                                                         
                                                                                         
<!--l. 522--><p class="noindent"><div class="obeylines-v"></div><object data="pgfmanual-22.svg" width="256.47464pt" height="256.47464pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-21-" ><colgroup id="TBL-21-1g"><col 
id="TBL-21-1"></colgroup><tr  
 valign="baseline" id="TBL-21-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-21-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table>
</div>
<!--l. 532--><p class="indent">   As for circles, you can specify &#8220;two&#8221; radii in order to get an elliptical arc.
<!--l. 535--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-22-" ><colgroup id="TBL-22-1g"><col 
id="TBL-22-1"><col 
id="TBL-22-2"></colgroup><tr  
 valign="baseline" id="TBL-22-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-22-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-23.svg" width="99.98462pt" height="57.30548pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-22-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikz</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:315:1.75cm</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;1cm);</span></div>                                                               </td></tr></table> </td>
</tr></table></div>
<!--l. 540--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.11   </span> <a 
 id="x4-350003.11"></a>Clipping a Path</h4>
<!--l. 542--><p class="noindent">In order to save space in this manual, it would be nice to clip Karl&#8217;s graphics a bit so that we can focus on the
&#8220;interesting&#8221; parts. Clipping is pretty easy in Ti<span 
class="cmti-10">k</span>Z. You can use the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\clip</span></span></span> command clip all subsequent
drawing. It works like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span>, only it does not draw anything, but uses the given path to clip everything
subsequently.
<!--l. 549--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-23-" ><colgroup id="TBL-23-1g"><col 
id="TBL-23-1"><col 
id="TBL-23-2"></colgroup><tr  
 valign="baseline" id="TBL-23-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-23-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-24.svg" width="102.4309pt" height="81.09004pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-23-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.1,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1.1,0.75);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 560--><p class="indent">   You can also do both at the same time: Draw <span 
class="cmti-10">and </span>clip a path. For this, use the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> command and add the
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">clip</span></span></span> option. (This is not the whole picture: You can also use the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\clip</span></span></span> command and add the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">draw</span></span></span>
option. Well, that is also not the whole picture: In reality, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> is just a shorthand for <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\path[draw]</span></span></span>
                                                                                         
                                                                                         
and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\clip</span></span></span> is a shorthand for <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\path[clip]</span></span></span> and you could also say <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\path[draw,clip]</span></span></span>.) Here is an
example:
<!--l. 568--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-24-" ><colgroup id="TBL-24-1g"><col 
id="TBL-24-1"><col 
id="TBL-24-2"></colgroup><tr  
 valign="baseline" id="TBL-24-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-24-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-25.svg" width="102.83093pt" height="102.83093pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-24-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip[draw]</span><span 
class="cmtt-8">&nbsp;(0.5,0.5)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(.6cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 580--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.12   </span> <a 
 id="x4-360003.12"></a>Parabola and Sine Path Construction</h4>
<!--l. 582--><p class="noindent">Although Karl does not need them for his picture, he is pleased to learn that there are <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parabola</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">sin</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">cos</span></span></span>
path operations for adding parabolas and sine and cosine curves to the current path. For the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">parabola</span></span></span> operation,
the current point will lie on the parabola as well as the point given after the parabola operation. Consider the
following example:
<!--l. 589--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-25-" ><colgroup id="TBL-25-1g"><col 
id="TBL-25-1"><col 
id="TBL-25-2"></colgroup><tr  
 valign="baseline" id="TBL-25-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-25-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-26.svg" width="28.85274pt" height="28.85274pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> &nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-25-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1,1)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;parabola</span><span 
class="cmtt-8">&nbsp;(1,1);</span></div>                                                      </td></tr></table> </td>
</tr></table></div>
<!--l. 593--><p class="indent">   It is also possible to place the bend somewhere else:
<!--l. 595--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-26-" ><colgroup id="TBL-26-1g"><col 
id="TBL-26-1"><col 
id="TBL-26-2"></colgroup><tr  
 valign="baseline" id="TBL-26-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-26-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-27.svg" width="6.4pt" height="16.4pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> &nbsp; </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-26-1-2"  
class="td11"> <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\draw[x=1pt,y=1pt]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;parabola</span><span 
class="cmtt-8">&nbsp;bend</span><span 
class="cmtt-8">&nbsp;(4,16)</span><span 
class="cmtt-8">&nbsp;(6,12);</span></div>                                                   </td></tr></table> </td>
</tr></table></div>
<!--l. 599--><p class="indent">   The operations <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">sin</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">cos</span></span></span> add a sine or cosine curve in the interval [0<span 
class="cmmi-10">,<img 
src="cmmi10-19.gif" alt="p" class="10x-x-19" />/</span>2] such that the previous
current point is at the start of the curve and the curve ends at the given end point. Here are two
examples:
<!--l. 603--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-27-" ><colgroup id="TBL-27-1g"><col 
id="TBL-27-1"><col 
id="TBL-27-2"></colgroup><tr  
 valign="baseline" id="TBL-27-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-27-1-1"  
class="td11">  &nbsp;A sine <object data="pgfmanual-28.svg" width="7.15971pt" height="4.70554pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> curve.&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-27-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v"><br><span 
class="cmtt-8">A</span><span 
class="cmtt-8">&nbsp;sine</span><span 
class="cmtt-8">&nbsp;\tikz</span><span 
class="cmtt-8">&nbsp;\draw[x=1ex,y=1ex]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;sin</span><span 
class="cmtt-8">&nbsp;(1.57,1);</span><span 
class="cmtt-8">&nbsp;curve.</span>
</div>                                                                                                              </td></tr></table> </td>
</tr></table>
</div>
<!--l. 607--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-28-" ><colgroup id="TBL-28-1g"><col 
id="TBL-28-1"><col 
id="TBL-28-2"></colgroup><tr  
 valign="baseline" id="TBL-28-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-28-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-29.svg" width="27.43887pt" height="9.01108pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> &nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-28-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\draw[x=1.57ex,y=1ex]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;sin</span><span 
class="cmtt-8">&nbsp;(1,1)</span><span 
class="cmtt-8">&nbsp;cos</span><span 
class="cmtt-8">&nbsp;(2,0)</span><span 
class="cmtt-8">&nbsp;sin</span><span 
class="cmtt-8">&nbsp;(3,-1)</span><span 
class="cmtt-8">&nbsp;cos</span><span 
class="cmtt-8">&nbsp;(4,0)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0,1)</span><span 
class="cmtt-8">&nbsp;cos</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;sin</span><span 
class="cmtt-8">&nbsp;(2,-1)</span><span 
class="cmtt-8">&nbsp;cos</span><span 
class="cmtt-8">&nbsp;(3,0)</span><span 
class="cmtt-8">&nbsp;sin</span><span 
class="cmtt-8">&nbsp;(4,1);</span></div>                                   </td></tr></table> </td>
</tr></table></div>
<!--l. 614--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.13   </span> <a 
 id="x4-370003.13"></a>Filling and Drawing</h4>
<!--l. 616--><p class="noindent">Returning to the picture, Karl now wants the angle to be &#8220;filled&#8221; with a very light green. For this he uses <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\fill</span></span></span>
instead of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span>. Here is what Karl does:
                                                                                         
                                                                                         
<!--l. 620--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-29-" ><colgroup id="TBL-29-1g"><col 
id="TBL-29-1"><col 
id="TBL-29-2"></colgroup><tr  
 valign="baseline" id="TBL-29-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-29-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-30.svg" width="102.4309pt" height="81.09004pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-29-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.1,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1.1,0.75);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\fill[green!20!white]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,0);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 631--><p class="indent">   The color <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">green!20!white</span></span></span> means 20% green and 80% white mixed together. Such color expression are possible
since <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&nbsp;uses Uwe Kern&#8217;s <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">xcolor</span></span></span> package, see the documentation of that package for details on color
expressions.
<!--l. 636--><p class="indent">   What would have happened, if Karl had not &#8220;closed&#8221; the path using <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">--(0,0)</span></span></span> at the end? In this case, the path
is closed automatically, so this could have been omitted. Indeed, it would even have been better to write the
following, instead:
<!--l. 640--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-30-" ><colgroup id="TBL-30-1g"><col 
id="TBL-30-1"></colgroup><tr  
 valign="baseline" id="TBL-30-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-30-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v"><br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\fill[green!20!white]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
</div>                                                                                                              </td></tr></table> </td>
</tr></table>
</div>
<!--l. 643--><p class="indent">   The <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">--cycle</span></span></span> causes the current path to be closed (actually the current part of the current path) by smoothly
joining the first and last point. To appreciate the difference, consider the following example:
<!--l. 648--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-31-" ><colgroup id="TBL-31-1g"><col 
id="TBL-31-1"><col 
id="TBL-31-2"></colgroup><tr  
 valign="baseline" id="TBL-31-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-31-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-31.svg" width="90.35823pt" height="45.17911pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-31-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[line</span><span 
class="cmtt-8">&nbsp;width=5pt]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1,1)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(2,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3,1)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\useasboundingbox</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;make</span><span 
class="cmsltt-10x-x-80">&nbsp;bounding</span><span 
class="cmsltt-10x-x-80">&nbsp;box</span><span 
class="cmsltt-10x-x-80">&nbsp;higher</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 656--><p class="indent">   You can also fill and draw a path at the same time using the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\filldraw</span></span></span> command. This will first draw the path,
then fill it. This may not seem too useful, but you can specify different colors to be used for filling and for stroking.
These are specified as optional arguments like this:
<!--l. 662--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-32-" ><colgroup id="TBL-32-1g"><col 
id="TBL-32-1"><col 
id="TBL-32-2"></colgroup><tr  
 valign="baseline" id="TBL-32-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-32-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-32.svg" width="102.4309pt" height="81.09004pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-32-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.1,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1.1,0.75);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20!white,</span><span 
class="cmtt-8">&nbsp;draw=green!50!black]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 676--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.14   </span> <a 
 id="x4-380003.14"></a>Shading</h4>
<!--l. 678--><p class="noindent">Karl briefly considers the possibility of making the angle &#8220;more fancy&#8221; by <span 
class="cmti-10">shading </span>it. Instead of filling the with a
uniform color, a smooth transition between different colors is used. For this, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\shade</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\shadedraw</span></span></span>, for shading
and drawing at the same time, can be used:
                                                                                         
                                                                                         
<!--l. 684--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-33-" ><colgroup id="TBL-33-1g"><col 
id="TBL-33-1"><col 
id="TBL-33-2"></colgroup><tr  
 valign="baseline" id="TBL-33-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-33-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-33.svg" width="99.5846pt" height="28.45274pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-33-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikz</span><span 
class="cmtt-8">&nbsp;\shade</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(2,1)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(3,0.5)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(.5cm);</span></div>                                                  </td></tr></table> </td>
</tr></table></div>
<!--l. 687--><p class="indent">   The default shading is a smooth transition from gray to white. To specify different colors, you can use
options:
<!--l. 690--><p class="noindent"><div class="obeylines-v"></div><object data="pgfmanual-34.svg" width="270.30106pt" height="30.05275pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-34-" ><colgroup id="TBL-34-1g"><col 
id="TBL-34-1"></colgroup><tr  
 valign="baseline" id="TBL-34-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-34-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[rounded</span><span 
class="cmtt-8">&nbsp;corners,ultra</span><span 
class="cmtt-8">&nbsp;thick]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\shade[top</span><span 
class="cmtt-8">&nbsp;color=yellow,bottom</span><span 
class="cmtt-8">&nbsp;color=black]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;+(2,1);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\shade[left</span><span 
class="cmtt-8">&nbsp;color=yellow,right</span><span 
class="cmtt-8">&nbsp;color=black]</span><span 
class="cmtt-8">&nbsp;(3,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;+(2,1);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\shadedraw[inner</span><span 
class="cmtt-8">&nbsp;color=yellow,outer</span><span 
class="cmtt-8">&nbsp;color=black,draw=yellow]</span><span 
class="cmtt-8">&nbsp;(6,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;+(2,1);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\shade[ball</span><span 
class="cmtt-8">&nbsp;color=green]</span><span 
class="cmtt-8">&nbsp;(9,.5)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(.5cm);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table>
</div>
<!--l. 699--><p class="indent">   For Karl, the following might be appropriate:
<!--l. 701--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-35-" ><colgroup id="TBL-35-1g"><col 
id="TBL-35-1"><col 
id="TBL-35-2"></colgroup><tr  
 valign="baseline" id="TBL-35-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-35-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-35.svg" width="102.4309pt" height="81.09004pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-35-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.1,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1.1,0.75);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\shadedraw[left</span><span 
class="cmtt-8">&nbsp;color=gray,right</span><span 
class="cmtt-8">&nbsp;color=green,</span><span 
class="cmtt-8">&nbsp;draw=green!50!black]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 713--><p class="indent">   However, he wisely decides that shadings usually only distract without adding anything to the
picture.
<!--l. 717--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.15   </span> <a 
 id="x4-390003.15"></a>Specifying Coordinates</h4>
<!--l. 719--><p class="noindent">Karl now wants to add the sine and cosine lines. He knows already that he can use the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">color=</span></span></span> option to set the
lines&#8217;s colors. So, what is the best way to specify the coordinates?
<!--l. 723--><p class="indent">   There are different ways of specifying coordinates. The easiest way is to say something like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(10pt,2cm)</span></span></span>. This
means 10pt in <span 
class="cmmi-10">x</span>-direction and 2cm in <span 
class="cmmi-10">y</span>-directions. Alternatively, you can also leave out the units as in <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(1,2)</span></span></span>, which
means &#8220;one times the current <span 
class="cmmi-10">x</span>-vector plus twice the current <span 
class="cmmi-10">y</span>-vector.&#8221; These vectors default to 1cm in the
<span 
class="cmmi-10">x</span>-direction and 1cm in the <span 
class="cmmi-10">y</span>-direction, respectively.
<!--l. 730--><p class="indent">   In order to specify points in polar coordinates, use the notation <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(30:1cm)</span></span></span>, which means 1cm in direction 30
degree. This is obviously quite useful to &#8220;get to the point (cos30<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup><span 
class="cmmi-10">,</span>sin30<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup>) on the circle.&#8221;
<!--l. 735--><p class="indent">   You can add a single <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">+</span></span></span> sign in front of a coordinate or two of them as in <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">+(1cm,0cm)</span></span></span> or <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">++(0cm,2cm)</span></span></span>. Such
coordinates are interpreted differently: The first form means &#8220;1cm upwards from the previous specified position&#8221;
and the second means &#8220;2cm to the right of the previous specified position, making this the new specified position.&#8221;
For example, we can draw the sine line as follows:
                                                                                         
                                                                                         
<!--l. 742--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-36-" ><colgroup id="TBL-36-1g"><col 
id="TBL-36-1"><col 
id="TBL-36-2"></colgroup><tr  
 valign="baseline" id="TBL-36-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-36-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-36.svg" width="102.4309pt" height="81.09004pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-36-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.1,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1.1,0.75);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20,draw=green!50!black]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[red,very</span><span 
class="cmtt-8">&nbsp;thick]</span><span 
class="cmtt-8">&nbsp;(30:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(0,-0.5);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 755--><p class="indent">   Karl used the fact sin30<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup> = 1<span 
class="cmmi-10">/</span>2. However, he very much doubts that his students know this, so it
would be nice to have a way of specifying &#8220;the point straight down from <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(30:1cm)</span></span></span> that lies on the
<span 
class="cmmi-10">x</span>-axis.&#8221; This is, indeed, possible using a special syntax: Karl can write <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(30:1cm</span><span 
class="cmtt-10">&nbsp;|-</span><span 
class="cmtt-10">&nbsp;0,0)</span></span></span>. In general, the
meaning of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">p</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">&nbsp;|-</span><span 
class="cmtt-10">&nbsp;</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">q</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">)</span></span></span> is &#8220;the intersection of a vertical line through <span 
class="cmmi-10">p </span>and a horizontal line through
<span 
class="cmmi-10">q</span>.&#8221;
<!--l. 763--><p class="indent">   Next, let us draw the cosine line. One way would be to say <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(30:1cm</span><span 
class="cmtt-10">&nbsp;|-</span><span 
class="cmtt-10">&nbsp;0,0)</span><span 
class="cmtt-10">&nbsp;--</span><span 
class="cmtt-10">&nbsp;(0,0)</span></span></span>. Another way is the
following: we &#8220;continue&#8221; from where the sine ends:
<!--l. 767--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-37-" ><colgroup id="TBL-37-1g"><col 
id="TBL-37-1"><col 
id="TBL-37-2"></colgroup><tr  
 valign="baseline" id="TBL-37-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-37-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-37.svg" width="102.4309pt" height="81.09004pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-37-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.1,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1.1,0.75);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20,draw=green!50!black]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[red,very</span><span 
class="cmtt-8">&nbsp;thick]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(30:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(0,-0.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[blue,very</span><span 
class="cmtt-8">&nbsp;thick]</span><span 
class="cmtt-8">&nbsp;(30:1cm)</span><span 
class="cmtt-8">&nbsp;++(0,-0.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,0);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 781--><p class="indent">   Note the there is no <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">--</span></span></span> between <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(30:1cm)</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">+(0,-0.5)</span></span></span>. In detail, this path is interpreted as follows: &#8220;First,
the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(30:1cm)</span></span></span> tells me to move by pen to (cos30<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup><span 
class="cmmi-10">,</span>1<span 
class="cmmi-10">/</span>2). Next, there comes another coordinate specification, so I
move my pen there without drawing anything. This new point is half a unit down from the last position, thus it is at
(cos30<sup ><span 
class="cmsy-7"><span class="htf-cmbx">o</span></span></sup><span 
class="cmmi-10">,</span>0). Finally, I move the pen to the origin, but this time drawing something (because of the
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">--</span></span></span>).&#8221;
<!--l. 789--><p class="indent">   To appreciate the difference between <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">+</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">++</span></span></span> consider the following example:
<!--l. 792--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-38-" ><colgroup id="TBL-38-1g"><col 
id="TBL-38-1"><col 
id="TBL-38-2"></colgroup><tr  
 valign="baseline" id="TBL-38-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-38-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-38.svg" width="71.53185pt" height="28.85274pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-38-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\def\rectanglepath{--</span><span 
class="cmtt-8">&nbsp;++(1cm,0cm)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;++(0cm,1cm)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;++(-1cm,0cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;\rectanglepath;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(1.5,0)</span><span 
class="cmtt-8">&nbsp;\rectanglepath;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 800--><p class="indent">   By comparison, when using a single <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">+</span></span></span>, the coordinates are different:
                                                                                         
                                                                                         
<!--l. 802--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-39-" ><colgroup id="TBL-39-1g"><col 
id="TBL-39-1"><col 
id="TBL-39-2"></colgroup><tr  
 valign="baseline" id="TBL-39-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-39-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-39.svg" width="71.53185pt" height="28.85274pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-39-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\def\rectanglepath{--</span><span 
class="cmtt-8">&nbsp;+(1cm,0cm)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(1cm,1cm)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(0cm,1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;\rectanglepath;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(1.5,0)</span><span 
class="cmtt-8">&nbsp;\rectanglepath;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 811--><p class="indent">   Naturally, all of this could have been written more clearly and more economically like this (either with a single of
a double <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">+</span></span></span>):
<!--l. 813--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-40-" ><colgroup id="TBL-40-1g"><col 
id="TBL-40-1"><col 
id="TBL-40-2"></colgroup><tr  
 valign="baseline" id="TBL-40-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-40-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-40.svg" width="71.53185pt" height="28.85274pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-40-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;+(1,1)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(1.5,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;+(1,1);</span></div>                                                 </td></tr></table> </td>
</tr></table></div>
<!--l. 819--><p class="indent">   Karl is left with the line for tan<span 
class="cmmi-10"><img 
src="cmmi10-b.gif" alt="a" class="10x-x-b" /></span>, which seems difficult to specify using transformations and polar
coordinates. For this he needs another way of specifying coordinates: Karl can specify intersections of lines as
coordinates. The line for tan<span 
class="cmmi-10"><img 
src="cmmi10-b.gif" alt="a" class="10x-x-b" /> </span>starts at (1<span 
class="cmmi-10">,</span>0) and goes upward to a point that is at the intersection of a
line going &#8220;up&#8221; and a line going from the origin through <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(30:1cm)</span></span></span>. The syntax for this point is the
following:
<!--l. 827--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-41-" ><colgroup id="TBL-41-1g"><col 
id="TBL-41-1"></colgroup><tr  
 valign="baseline" id="TBL-41-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-41-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v"><br><span 
class="cmtt-8">\draw[very</span><span 
class="cmtt-8">&nbsp;thick,orange]</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(intersection</span><span 
class="cmtt-8">&nbsp;of</span><span 
class="cmtt-8">&nbsp;1,0--1,1</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;0,0--30:1cm);</span>
</div>                                                                                                              </td></tr></table> </td>
</tr></table>
</div>
<!--l. 831--><p class="indent">   In the following, two final examples of how to use relative positioning are presented. Note that
the transformation options, which are explained later, are often more useful for shifting than relative
positioning.
<!--l. 836--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-42-" ><colgroup id="TBL-42-1g"><col 
id="TBL-42-1"><col 
id="TBL-42-2"></colgroup><tr  
 valign="baseline" id="TBL-42-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-42-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-41.svg" width="71.53185pt" height="31.01779pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-42-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=0.5]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(90:1cm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(90:360:1cm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(60:5pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(30:1cm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(30:90:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(3,0)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;+(0:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(72:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(144:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(216:1cm)</span><span 
class="cmtt-8">&nbsp;--</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;+(288:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 848--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.16   </span> <a 
 id="x4-400003.16"></a>Adding Arrow Tips</h4>
<!--l. 850--><p class="noindent">Karl now wants to add the little arrow tips at the end of the axes. He has noticed that in many plots, even in
scientific journals, these arrow tips seem to missing, presumably because the generating programs cannot produce
them. Karl thinks arrow tips belong at the end of axes. His son agrees. His students do not care about arrow
tips.
<!--l. 856--><p class="indent">   It turns out that adding arrow tips is pretty easy: Karl adds the option <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">-&gt;</span></span></span> to the drawing commands for the
axes:
                                                                                         
                                                                                         
<!--l. 859--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-43-" ><colgroup id="TBL-43-1g"><col 
id="TBL-43-1"><col 
id="TBL-43-2"></colgroup><tr  
 valign="baseline" id="TBL-43-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-43-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-42.svg" width="102.4309pt" height="145.96184pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-43-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.1,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1.1,1.51);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20,draw=green!50!black]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[red,very</span><span 
class="cmtt-8">&nbsp;thick]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(30:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;+(0,-0.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[blue,very</span><span 
class="cmtt-8">&nbsp;thick]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(30:1cm)</span><span 
class="cmtt-8">&nbsp;++(0,-0.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[orange,very</span><span 
class="cmtt-8">&nbsp;thick]</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(intersection</span><span 
class="cmtt-8">&nbsp;of</span><span 
class="cmtt-8">&nbsp;1,0--1,1</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;0,0--30:1cm);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 874--><p class="indent">   If Karl had used the option <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">&lt;-</span></span></span> instead of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">-&gt;</span></span></span>, arrow tips would have been put at the beginning of the path. The
option <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">&lt;-&gt;</span></span></span> puts arrow tips at both ends of the path.
<!--l. 878--><p class="indent">   There are certain restrictions to the kind of paths to which arrow tips can be added. As a rule of thumb, you can
add arrow tips only to a single open &#8220;line.&#8221; For example, you should not try to add tips to, say, a rectangle or a
circle. (You can try, but no guarantees as to what will happen now or in future versions.) However,
you can add arrow tips to curved paths and to paths that have several segments, as in the following
examples:
<!--l. 886--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-44-" ><colgroup id="TBL-44-1g"><col 
id="TBL-44-1"><col 
id="TBL-44-2"></colgroup><tr  
 valign="baseline" id="TBL-44-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-44-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-43.svg" width="71.53188pt" height="10.4pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-44-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;[&lt;-&gt;]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(180:30:10pt);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;[&lt;-&gt;]</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5cm,10pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(2cm,0pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(2.5cm,10pt);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 893--><p class="indent">   Karl has a more detailed look at the arrow that Ti<span 
class="cmti-10">k</span>Z&nbsp;puts at the end. It looks like this when he zooms it: <object data="pgfmanual-44.svg" width="10.0pt" height="4.30554pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>.
The shape seems vaguely familiar and, indeed, this is exactly the end of <span class="TEX">T<span 
class="E">E</span>X</span>&#8217;s standard arrow used in something
like <span 
class="cmmi-10">f</span> : <span 
class="cmmi-10">A </span><span 
class="cmsy-10"><img 
src="cmsy10-21.gif" alt="--&gt;" class="10x-x-21" /> </span><span 
class="cmmi-10">B</span>.
<!--l. 901--><p class="indent">   Karl likes the arrow, especially since it is not &#8220;as thick&#8221; as the arrows offered by many other packages.
However, he expects that, sometimes, he might need to use some other kinds of arrow. To do so, Karl
can say <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">&gt;=</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">right arrow tip kind</span><span 
class="cmsy-10">&gt;</span>, where <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">right arrow tip kind</span><span 
class="cmsy-10">&gt; </span>is a special arrow tip specification. For
example, if Karl says <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">&gt;=stealth</span></span></span>, then he tells Ti<span 
class="cmti-10">k</span>Z&nbsp;that he would like &#8220;stealth-fighter-like&#8221; arrow
tips:
<!--l. 909--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-45-" ><colgroup id="TBL-45-1g"><col 
id="TBL-45-1"><col 
id="TBL-45-2"></colgroup><tr  
 valign="baseline" id="TBL-45-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-45-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-45.svg" width="71.93187pt" height="11.19998pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-45-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[&gt;=stealth]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;[-&gt;]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(180:30:10pt);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;[&lt;&lt;-,very</span><span 
class="cmtt-8">&nbsp;thick]</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5cm,10pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(2cm,0pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(2.5cm,10pt);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 916--><p class="indent">   Karl wonders whether such a military name for the arrow type is really necessary. He is not really mollified when
his son tells him that Microsoft&#8217;s PowerPoint uses the same name. He decides to have his students discuss this at
some point.
<!--l. 921--><p class="indent">   In addition to <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">stealth</span></span></span> there are several other predefined arrow tip kinds Karl can choose from, see Section&nbsp;<a 
href="pgfmanualse14.html#x15-16000014.1">14.1<!--tex4ht:ref: section-library-arrows --></a>.
Furthermore, he can define arrows types himself, if he needs new ones.
<!--l. 929--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.17   </span> <a 
 id="x4-410003.17"></a>Scoping</h4>
<!--l. 931--><p class="noindent">Karl saw already that there are numerous graphic options that affect how paths are rendered. Often, he would like
to apply certain options to a whole set of graphic commands. For example, Karl might wish to draw three paths
                                                                                         
                                                                                         
using a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thick</span></span></span> pen, but would like everything else to be drawn &#8220;normally.&#8221;
<!--l. 937--><p class="indent">   If Karl wishes to set a certain graphic option for the whole picture, he can simply pass this option to the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikz</span></span></span>
command or to the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{tikzpicture}</span></span></span> environment (Gerda would pass the options to <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\tikzpicture</span></span></span>).
However, if Karl wants to apply graphic options to a local group, he put these commands inside a
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{scope}</span></span></span> environment (Gerda uses <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\scope</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\endscope</span></span></span>). This environment takes graphic options as
an optional argument and these options apply to everything inside the scope, but not to anything
outside.
<!--l. 946--><p class="indent">   Here is an example:
<!--l. 948--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-46-" ><colgroup id="TBL-46-1g"><col 
id="TBL-46-1"><col 
id="TBL-46-2"></colgroup><tr  
 valign="baseline" id="TBL-46-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-46-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-46.svg" width="86.95824pt" height="30.05275pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-46-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[ultra</span><span 
class="cmtt-8">&nbsp;thick]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\begin{scope}[thin]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1,1);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(2,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(2,1);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\end{scope}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(3,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3,1);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 959--><p class="indent">   Scoping has another interesting effect: Any changes to the clipping area are local to the scope. Thus, if you say
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\clip</span></span></span> somewhere inside a scope, the effect of the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\clip</span></span></span> command ends at the end of the scope. This is useful since
there is no other way of &#8220;enlarging&#8221; the clipping area.
<!--l. 965--><p class="indent">   Karl has also already seen that giving options to commands like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> apply only to that command. In turns
out that the situation is slightly more complex. First, options to a command like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span></span></span> are not really
options to the command, but they are &#8220;path options&#8221; and can be given anywhere on the path. So,
instead of <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw[thin]</span><span 
class="cmtt-10">&nbsp;(0,0)</span><span 
class="cmtt-10">&nbsp;--</span><span 
class="cmtt-10">&nbsp;(1,0);</span></span></span> one can also write <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span><span 
class="cmtt-10">&nbsp;(0,0)</span><span 
class="cmtt-10">&nbsp;[thin]</span><span 
class="cmtt-10">&nbsp;--</span><span 
class="cmtt-10">&nbsp;(1,0);</span></span></span> or
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span><span 
class="cmtt-10">&nbsp;(0,0)</span><span 
class="cmtt-10">&nbsp;--</span><span 
class="cmtt-10">&nbsp;(1,0)</span><span 
class="cmtt-10">&nbsp;[thin];</span></span></span>; all of these have the same effect. This might seem strange since in the last case, it
would appear that the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thin</span></span></span> should take effect only &#8220;after&#8221; the line from (0<span 
class="cmmi-10">,</span>0) to (1<span 
class="cmmi-10">,</span>0) has been draw. However,
most graphic options only apply to the whole path. Indeed, if you say both <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thin</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">thick</span></span></span> on the same path, the
last option given will &#8220;win.&#8221;
<!--l. 979--><p class="indent">   When reading the above, Karl notices that only &#8220;most&#8221; graphic options apply to the whole path. Indeed, all
transformation options do <span 
class="cmti-10">not </span>apply to the whole path, but only to &#8220;everything following them on the path.&#8221; We
will have a more detailed look at this in a moment. Nevertheless, all options given during a path construction apply
only to this path.
<!--l. 988--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.18   </span> <a 
 id="x4-420003.18"></a>Transformations</h4>
<!--l. 990--><p class="noindent">When you specify a coordinate like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(1cm,1cm)</span></span></span>, where is that coordinate placed on the page? To determine the
position, Ti<span 
class="cmti-10">k</span>Z, <span class="TEX">T<span 
class="E">E</span>X</span>, and <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">D</small><small 
class="small-caps">F</small> </span>or PostScript all apply certain transformations to the given coordinate in order to
determine the finally position on the page.
<!--l. 996--><p class="indent">   Ti<span 
class="cmti-10">k</span>Z&nbsp;provides numerous options that allow you to transform coordinates in <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&#8217;s private coordinate system. For
example, the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">xshift</span></span></span> option allows you to shift all subsequent points by a certain amount:
<!--l. 1001--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-47-" ><colgroup id="TBL-47-1g"><col 
id="TBL-47-1"><col 
id="TBL-47-2"></colgroup><tr  
 valign="baseline" id="TBL-47-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-47-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-47.svg" width="2.4pt" height="14.62636pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> &nbsp; </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-47-1-2"  
class="td11"> <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,0.5)</span><span 
class="cmtt-8">&nbsp;[xshift=2pt]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,0.5);</span></div>                                                   </td></tr></table> </td>
</tr></table></div>
<!--l. 1005--><p class="indent">   It is important to note that you can change transformation &#8220;in the middle of a path,&#8221; a feature that is
not supported by <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">D</small><small 
class="small-caps">F</small></span>&nbsp;or PostScript. The reason is that <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&nbsp;keeps track of its own transformation
matrix.
<!--l. 1010--><p class="indent">   Here is a more complicated example:
<!--l. 1011--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-48-" ><colgroup id="TBL-48-1g"><col 
id="TBL-48-1"><col 
id="TBL-48-2"></colgroup><tr  
 valign="baseline" id="TBL-48-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-48-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-48.svg" width="41.38083pt" height="41.38083pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-48-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[even</span><span 
class="cmtt-8">&nbsp;odd</span><span 
class="cmtt-8">&nbsp;rule,rounded</span><span 
class="cmtt-8">&nbsp;corners=2pt,x=10pt,y=10pt]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=examplefill]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1,1)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[xshift=5pt,yshift=5pt]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1,1)</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;[rotate=30]</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(-1,-1)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(2,2);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
<!--l. 1019--><p class="indent">   The most useful transformations are <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">xshift</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">yshift</span></span></span> for shifting, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">shift</span></span></span> for shifting to a given point as in
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">shift={(1,0)}</span></span></span> or <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">shift={+(0,0)}</span></span></span> (the braces are necessary so that <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;does not mistake the comma for
separating options), <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">rotate</span></span></span> for rotating by a certain angle (there is also a <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">rotate</span><span 
class="cmtt-10">&nbsp;around</span></span></span> for rotating around a
given point), <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">scale</span></span></span> for scaling by a certain factor, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">xscale</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">yscale</span></span></span> for scaling only in the <span 
class="cmmi-10">x</span>- or <span 
class="cmmi-10">y</span>-direction
(<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">xscale=-1</span></span></span> is a flip), and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">xslant</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">yslant</span></span></span> for slanting. If these transformation and those that I have not
mentioned are not sufficient, the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">cm</span></span></span> option allows you to apply an arbitrary transformation matrix. Karl&#8217;s students,
by the way, do not know what a transformation matrix is.
<!--l. 1034--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.19   </span> <a 
 id="x4-430003.19"></a>Repeating Things: For-Loops</h4>
<!--l. 1036--><p class="noindent">Karl&#8217;s next aim is to add little ticks on the axes at positions <span 
class="cmsy-10">-</span>1, <span 
class="cmsy-10">-</span>1<span 
class="cmmi-10">/</span>2, 1<span 
class="cmmi-10">/</span>2, and 1. For this, it would be nice to
use some kind of &#8220;loop,&#8221; especially since he wishes to do the same thing at each of these positions.
There are different packages for doing this. <span class="LATEX">L<span class="A">A</span><span class="TEX">T<span 
class="E">E</span>X</span></span>&nbsp;has its own internal command for this, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pstricks</span></span></span>
comes along with the powerful <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\mulitdo</span></span></span> command. All of these can be used together with <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&nbsp;and
Ti<span 
class="cmti-10">k</span>Z, so if you are familiar with them, feel free to use them. <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>&nbsp;introduces yet another command,
called <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span>, which I introduced since I could never remember the syntax of the other packages.
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> is defined in the package <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pgffor</span></span></span> and can be used independently of <span 
class="cmcsc-10"><small 
class="small-caps">P</small><small 
class="small-caps">G</small><small 
class="small-caps">F</small></span>. Ti<span 
class="cmti-10">k</span>Z&nbsp;includes it
automatically.
<!--l. 1048--><p class="indent">   In its basic form, the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> command is easy to use:
<!--l. 1049--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-49-" ><colgroup id="TBL-49-1g"><col 
id="TBL-49-1"><col 
id="TBL-49-2"></colgroup><tr  
 valign="baseline" id="TBL-49-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-49-1-1"  
class="td11">  &nbsp;<span 
class="cmmi-10">x </span>= 1, <span 
class="cmmi-10">x </span>= 2, <span 
class="cmmi-10">x </span>= 3, &nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-49-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v"><br>
<span 
class="cmtt-8">\foreach</span><span 
class="cmtt-8">&nbsp;\x</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{1,2,3}</span><span 
class="cmtt-8">&nbsp;{$x</span><span 
class="cmtt-8">&nbsp;=\x$,</span><span 
class="cmtt-8">&nbsp;}</span></div>                                                                            </td></tr></table> </td>
</tr></table>
</div>
<!--l. 1053--><p class="indent">   The general syntax is <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">variable</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">&nbsp;in</span><span 
class="cmtt-10">&nbsp;{</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">list of values</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">}</span><span 
class="cmtt-10">&nbsp;</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">commands</span><span 
class="cmsy-10">&gt;</span>. Inside the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">commands</span><span 
class="cmsy-10">&gt;</span>, the
<span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">variable</span><span 
class="cmsy-10">&gt; </span>will be assigned to the different values. If the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">commands</span><span 
class="cmsy-10">&gt; </span>do not start with a brace, everything up to the
next semicolon is used as <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">commands</span><span 
class="cmsy-10">&gt;</span>.
<!--l. 1059--><p class="indent">   For Karl and the ticks on the axes, he could use the following code:
<!--l. 1061--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-50-" ><colgroup id="TBL-50-1g"><col 
id="TBL-50-1"><col 
id="TBL-50-2"></colgroup><tr  
 valign="baseline" id="TBL-50-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-50-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-49.svg" width="102.4309pt" height="145.96184pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-50-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.1,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(1.1,1.51);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20,draw=green!50!black]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\x</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1cm,-0.5cm,1cm}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(\x,-1pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(\x,1pt);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\y</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1cm,-0.5cm,0.5cm,1cm}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(-1pt,\y)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1pt,\y);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 1078--><p class="indent">   As a matter of fact, there are many different ways of creating the ticks. For example, Karl could have put the
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span><span 
class="cmtt-10">&nbsp;...;</span></span></span> inside curly braces. He could also have used, say,
<!--l. 1081--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-51-" ><colgroup id="TBL-51-1g"><col 
id="TBL-51-1"></colgroup><tr  
 valign="baseline" id="TBL-51-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-51-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\foreach</span><span 
class="cmtt-8">&nbsp;\x</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,-0.5,1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[xshift=\x</span><span 
class="cmtt-8">&nbsp;cm]</span><span 
class="cmtt-8">&nbsp;(0pt,-1pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0pt,1pt);</span></div>                                                                </td></tr></table> </td>
</tr></table></div>
<!--l. 1086--><p class="indent">   Karl is curious what would happen in a more complicated situation where there are, say, 20 ticks. It seems
bothersome to explicitly mention all these numbers in the set for <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span>. Indeed, it is possible to use <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">...</span></span></span> inside
                                                                                         
                                                                                         
the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> statement to iterate over a large number of values (which must, however, be dimensionless real
numbers) as in the following example:
<!--l. 1093--><p class="noindent"><div class="obeylines-v"></div><object data="pgfmanual-50.svg" width="279.23653pt" height="23.16183pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-52-" ><colgroup id="TBL-52-1g"><col 
id="TBL-52-1"></colgroup><tr  
 valign="baseline" id="TBL-52-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-52-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\x</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{1,...,10}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(\x,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(0.4cm);</span></div>                                                                          </td></tr></table> </td>
</tr></table>
</div>
<!--l. 1098--><p class="indent">   If you provide <span 
class="cmti-10">two </span>numbers before the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">...</span></span></span>, the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> statement will use their difference for the
stepping:
<!--l. 1101--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-53-" ><colgroup id="TBL-53-1g"><col 
id="TBL-53-1"><col 
id="TBL-53-2"></colgroup><tr  
 valign="baseline" id="TBL-53-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-53-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-51.svg" width="57.30548pt" height="2.4pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> &nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-53-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\tikz</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\x</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,-0.5,...,1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(\x</span><span 
class="cmtt-8">&nbsp;cm,-1pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(\x</span><span 
class="cmtt-8">&nbsp;cm,1pt);</span></div>                                                                     </td></tr></table> </td>
</tr></table></div>
<!--l. 1106--><p class="indent">   We can also nest loops to create interesting effects:
<!--l. 1108--><p class="noindent"><div class="obeylines-v"></div><object data="pgfmanual-52.svg" width="341.8329pt" height="142.6637pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-54-" ><colgroup id="TBL-54-1g"><col 
id="TBL-54-1"></colgroup><tr  
 valign="baseline" id="TBL-54-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-54-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\x</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{1,2,...,5,7,8,...,12}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\y</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{1,...,5}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(\x,\y)</span><span 
class="cmtt-8">&nbsp;+(-.5,-.5)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;++(.5,.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(\x,\y)</span><span 
class="cmtt-8">&nbsp;node{\x,\y};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;}</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table>
</div>
<!--l. 1119--><p class="indent">   The <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> statement can do even trickier stuff, but the above gives the idea.
<!--l. 1125--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.20   </span> <a 
 id="x4-440003.20"></a>Adding Text</h4>
<!--l. 1127--><p class="noindent">Karl is, by now, quite satisfied with the picture. However, the most important parts, namely the labels, are still
missing!
<!--l. 1130--><p class="indent">   Ti<span 
class="cmti-10">k</span>Z&nbsp;offers an easy-to-use and powerful system for adding text and, more generally, complex shapes to a
picture at specific positions. The basic idea is the following: When Ti<span 
class="cmti-10">k</span>Z&nbsp;is constructing a path and
encounters the keyword <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> in the middle of a path, it reads a <span 
class="cmti-10">node specification</span>. The keyword <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> is
typically followed by some options and then some text between curly braces. This text is put inside a
normal <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;box (if the node specification directly follows a coordinate, which is usually the case,
Ti<span 
class="cmti-10">k</span>Z&nbsp;is able to perform some magic so that it is even possible to use verbatim text inside the boxes)
and then placed at the current position, that is, at the last specified position (possibly shifted a bit,
according to the given options). However, all nodes are drawn only after the path has been completely
drawn/filled/shaded/clipped/whatever.
<!--l. 1144--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-55-" ><colgroup id="TBL-55-1g"><col 
id="TBL-55-1"><col 
id="TBL-55-2"></colgroup><tr  
 valign="baseline" id="TBL-55-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-55-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-53.svg" width="102.17403pt" height="57.30548pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object> &nbsp; </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-55-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v"><br>
<span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(2,2);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0.5,0.5)</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;[fill=examplefill]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{Text</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;\verb!node</span><span 
class="cmtt-8">&nbsp;1!}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,1.5)</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;{Text</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;\verb!node</span><span 
class="cmtt-8">&nbsp;2!};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
<!--l. 1153--><p class="indent">   Obviously, Karl would not only like to place nodes <span 
class="cmti-10">on </span>the last specified position, but also to the left or the
right of these positions. For this, every node object that you put in your picture is equipped with
several <span 
class="cmti-10">anchors</span>. For example, the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">north</span></span></span> anchor is in the middle at the upper end of the shape, the
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">south</span></span></span> anchor is at the bottom and the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">north</span><span 
class="cmtt-10">&nbsp;east</span></span></span> anchor is in the upper right corner. When you
given the option <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">anchor=north</span></span></span>, the text will be placed such that this northern anchor will lie on the
current position and the text is, thus, below the current position. Karl uses this to draw the ticks as
follows:
<!--l. 1164--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-56-" ><colgroup id="TBL-56-1g"><col 
id="TBL-56-1"><col 
id="TBL-56-2"></colgroup><tr  
 valign="baseline" id="TBL-56-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-56-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-54.svg" width="102.43085pt" height="145.96184pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-56-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.6,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(0.6,1.51);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,style=help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20,draw=green!50!black]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\x</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,-0.5,1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(\x</span><span 
class="cmtt-8">&nbsp;cm,1pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(\x</span><span 
class="cmtt-8">&nbsp;cm,-1pt)</span><span 
class="cmtt-8">&nbsp;node[anchor=north]</span><span 
class="cmtt-8">&nbsp;{$\x$};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\y</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,-0.5,0.5,1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(1pt,\y</span><span 
class="cmtt-8">&nbsp;cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(-1pt,\y</span><span 
class="cmtt-8">&nbsp;cm)</span><span 
class="cmtt-8">&nbsp;node[anchor=east]</span><span 
class="cmtt-8">&nbsp;{$\y$};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 1180--><p class="indent">   This is quite nice, already. Using these anchors, Karl can now add most of the other text elements. However,
Karl thinks that, though &#8220;correct,&#8221; it is quite counter-intuitive that in order to place something <span 
class="cmti-10">below </span>a given point,
he has to use the <span 
class="cmti-10">north </span>anchor. For this reason, there is an option called <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">below</span></span></span>, which does the same as
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">anchor=north</span></span></span>. Similarly, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">above</span><span 
class="cmtt-10">&nbsp;right</span></span></span> does the same as <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">anchor=south</span><span 
class="cmtt-10">&nbsp;east</span></span></span>. In addition, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">below</span></span></span> takes an
optional dimension argument. If given, the shape will additionally be shifted downwards by the given
amount. So, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">below=1pt</span></span></span> can be used to put a text label below some point and, additionally shift it 1pt
downwards.
<!--l. 1192--><p class="indent">   Karl is not quite satisfied with the ticks. He would like to have 1<span 
class="cmmi-10">/</span>2 or <img 
src="pgfmanual9x.gif" alt="12"  class="frac" align="middle"> shown instead of 0<span 
class="cmmi-10">.</span>5, partly
to show off the nice capabilities of <span class="TEX">T<span 
class="E">E</span>X</span>&nbsp;and Ti<span 
class="cmti-10">k</span>Z, partly because for positions like 1<span 
class="cmmi-10">/</span>3 or <span 
class="cmmi-10"><img 
src="cmmi10-19.gif" alt="p" class="10x-x-19" /> </span>it is
certainly very much preferable to have the &#8220;mathematical&#8221; tick there instead of just the &#8220;numeric&#8221;
tick. His students, on the other hand, prefer 0<span 
class="cmmi-10">.</span>5 over 1<span 
class="cmmi-10">/</span>2 since they are not too fond of fractions in
general.
<!--l. 1200--><p class="indent">   Karl now faces a problem: For the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> statement, the position <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\x</span></span></span> should still be given as <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">0.5</span></span></span> since
Ti<span 
class="cmti-10">k</span>Z&nbsp;will not know where <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\frac{1}{2}</span></span></span> is supposed to be. On the other hand, the typeset text should really be
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\frac{1}{2}</span></span></span>. To solve this problem, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> offers a special syntax: Instead of having one variable <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\x</span></span></span>, Karl can
specify two (or even more) variables separated by a slash as in <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\x</span><span 
class="cmtt-10">&nbsp;/</span><span 
class="cmtt-10">&nbsp;\xtext</span></span></span>. Then, the elements in the set over
which <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\foreach</span></span></span> iterates must also be of the form <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">first</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">/</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">second</span><span 
class="cmsy-10">&gt;</span>. In each iteration, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\x</span></span></span> will be set to <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">first</span><span 
class="cmsy-10">&gt; </span>and
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\xtext</span></span></span> will be set to <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">second</span><span 
class="cmsy-10">&gt;</span>. If no <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">second</span><span 
class="cmsy-10">&gt; </span>is given, the <span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">first</span><span 
class="cmsy-10">&gt; </span>will be used again. So, here is the new code for the
ticks:
                                                                                         
                                                                                         
<!--l. 1212--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-57-" ><colgroup id="TBL-57-1g"><col 
id="TBL-57-1"><col 
id="TBL-57-2"></colgroup><tr  
 valign="baseline" id="TBL-57-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-57-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-55.svg" width="102.43085pt" height="145.96184pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-57-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-0.6,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(0.6,1.51);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,style=help</span><span 
class="cmtt-8">&nbsp;lines]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20,draw=green!50!black]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0);</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\x/\xtext</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,</span><span 
class="cmtt-8">&nbsp;-0.5/-\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(\x</span><span 
class="cmtt-8">&nbsp;cm,1pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(\x</span><span 
class="cmtt-8">&nbsp;cm,-1pt)</span><span 
class="cmtt-8">&nbsp;node[anchor=north]</span><span 
class="cmtt-8">&nbsp;{$\xtext$};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\y/\ytext</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,</span><span 
class="cmtt-8">&nbsp;-0.5/-\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;0.5/\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(1pt,\y</span><span 
class="cmtt-8">&nbsp;cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(-1pt,\y</span><span 
class="cmtt-8">&nbsp;cm)</span><span 
class="cmtt-8">&nbsp;node[anchor=east]</span><span 
class="cmtt-8">&nbsp;{$\ytext$};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 1228--><p class="indent">   Karl is quite pleased with the result, but his son points out that this is still not perfectly satisfactory: The grid
and the circle interfere with the numbers and decrease their legibility. Karl is not very concerned by this (his
students do not even notice), but his son insists that there is an easy solution: Karl can add the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">[fill=white]</span></span></span>
option to fill out the background of the text shape with a white color.
<!--l. 1236--><p class="indent">   The next thing Karl wants to do is to add the labels like sin<span 
class="cmmi-10"><img 
src="cmmi10-b.gif" alt="a" class="10x-x-b" /></span>. For this, he would like to place a label &#8220;in the
middle of line.&#8221; To do so, instead of specifying the label <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span><span 
class="cmtt-10">&nbsp;{$\sin\alpha$}</span></span></span> directly after one of the endpoints of
the line (which would place the label at that endpoint), Karl can give the label directly after the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">--</span></span></span>,
before the coordinate. By default, this places the label in the middle of the line, but the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pos=</span></span></span> options
can be used to modify this. Also, options like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">near</span><span 
class="cmtt-10">&nbsp;start</span></span></span> and <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">near</span><span 
class="cmtt-10">&nbsp;end</span></span></span> can be used to modify this
position:
<!--l. 1248--><p class="noindent"><div class="obeylines-v"></div><object data="pgfmanual-56.svg" width="341.43292pt" height="85.35818pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-58-" ><colgroup id="TBL-58-1g"><col 
id="TBL-58-1"></colgroup><tr  
 valign="baseline" id="TBL-58-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-58-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\clip</span><span 
class="cmtt-8">&nbsp;(-2,-0.2)</span><span 
class="cmtt-8">&nbsp;rectangle</span><span 
class="cmtt-8">&nbsp;(2,0.8);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[step=.5cm,gray,very</span><span 
class="cmtt-8">&nbsp;thin]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20,draw=green!50!black]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0mm)</span><span 
class="cmtt-8">&nbsp;arc</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0:30:3mm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;cycle;</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0)</span><span 
class="cmtt-8">&nbsp;coordinate</span><span 
class="cmtt-8">&nbsp;(x</span><span 
class="cmtt-8">&nbsp;axis);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5)</span><span 
class="cmtt-8">&nbsp;coordinate</span><span 
class="cmtt-8">&nbsp;(y</span><span 
class="cmtt-8">&nbsp;axis);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[very</span><span 
class="cmtt-8">&nbsp;thick,red]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(30:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;node[left=1pt,fill=white]</span><span 
class="cmtt-8">&nbsp;{$\sin</span><span 
class="cmtt-8">&nbsp;\alpha$}</span><span 
class="cmtt-8">&nbsp;(30:1cm</span><span 
class="cmtt-8">&nbsp;|-</span><span 
class="cmtt-8">&nbsp;x</span><span 
class="cmtt-8">&nbsp;axis);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[very</span><span 
class="cmtt-8">&nbsp;thick,blue]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(30:1cm</span><span 
class="cmtt-8">&nbsp;|-</span><span 
class="cmtt-8">&nbsp;x</span><span 
class="cmtt-8">&nbsp;axis)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;node[below=2pt,fill=white]</span><span 
class="cmtt-8">&nbsp;{$\cos</span><span 
class="cmtt-8">&nbsp;\alpha$}</span><span 
class="cmtt-8">&nbsp;(0,0);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[very</span><span 
class="cmtt-8">&nbsp;thick,orange]</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;[right=1pt,fill=white]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{$\displaystyle</span><span 
class="cmtt-8">&nbsp;\tan</span><span 
class="cmtt-8">&nbsp;\alpha</span><span 
class="cmtt-8">&nbsp;\color{black}=</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\frac{{\color{red}\sin</span><span 
class="cmtt-8">&nbsp;\alpha}}{\color{blue}\cos</span><span 
class="cmtt-8">&nbsp;\alpha}$}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(intersection</span><span 
class="cmtt-8">&nbsp;of</span><span 
class="cmtt-8">&nbsp;0,0--30:1cm</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;1,0--1,1)</span><span 
class="cmtt-8">&nbsp;coordinate</span><span 
class="cmtt-8">&nbsp;(t);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(t);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\x/\xtext</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,</span><span 
class="cmtt-8">&nbsp;-0.5/-\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(\x</span><span 
class="cmtt-8">&nbsp;cm,1pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(\x</span><span 
class="cmtt-8">&nbsp;cm,-1pt)</span><span 
class="cmtt-8">&nbsp;node[anchor=north,fill=white]</span><span 
class="cmtt-8">&nbsp;{$\xtext$};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\y/\ytext</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,</span><span 
class="cmtt-8">&nbsp;-0.5/-\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;0.5/\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(1pt,\y</span><span 
class="cmtt-8">&nbsp;cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(-1pt,\y</span><span 
class="cmtt-8">&nbsp;cm)</span><span 
class="cmtt-8">&nbsp;node[anchor=east,fill=white]</span><span 
class="cmtt-8">&nbsp;{$\ytext$};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table>
</div>
<!--l. 1276--><p class="indent">   You can also position labels on curves and, by adding the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">sloped</span></span></span> option, have them rotated such that they
match the line&#8217;s slope. Here is an example:
                                                                                         
                                                                                         
<!--l. 1280--><p class="noindent"><div class="obeylines-v"></div><object data="pgfmanual-57.svg" width="341.83292pt" height="45.52199pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-59-" ><colgroup id="TBL-59-1g"><col 
id="TBL-59-1"></colgroup><tr  
 valign="baseline" id="TBL-59-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-59-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;controls</span><span 
class="cmtt-8">&nbsp;(6,1)</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;(9,1)</span><span 
class="cmtt-8">&nbsp;..</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[near</span><span 
class="cmtt-8">&nbsp;start,sloped,above]</span><span 
class="cmtt-8">&nbsp;{near</span><span 
class="cmtt-8">&nbsp;start}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node</span><span 
class="cmtt-8">&nbsp;{midway}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[very</span><span 
class="cmtt-8">&nbsp;near</span><span 
class="cmtt-8">&nbsp;end,sloped,below]</span><span 
class="cmtt-8">&nbsp;{very</span><span 
class="cmtt-8">&nbsp;near</span><span 
class="cmtt-8">&nbsp;end}</span><span 
class="cmtt-8">&nbsp;(12,0);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table>
</div>
<!--l. 1289--><p class="indent">   It remains to draw the explanatory text at the right of the picture. The main difficulty here lies in limiting the
width of the text &#8220;label,&#8221; which is quite long, so that line breaking is used. Fortunately, Karl can use the option
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">text</span><span 
class="cmtt-10">&nbsp;width=6cm</span></span></span> to get the desired effect. So, here is the full code:
<!--l. 1295--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-60-" ><colgroup id="TBL-60-1g"><col 
id="TBL-60-1"></colgroup><tr  
 valign="baseline" id="TBL-60-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-60-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}[scale=3,cap=round]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Local</span><span 
class="cmsltt-10x-x-80">&nbsp;definitions</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\def\costhirty{0.8660256}</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Colors</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\colorlet{anglecolor}{green!50!black}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\colorlet{sincolor}{red}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\colorlet{tancolor}{orange!80!black}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\colorlet{coscolor}{blue}</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;Styles</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{axes}=[]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{important</span><span 
class="cmtt-8">&nbsp;line}=[very</span><span 
class="cmtt-8">&nbsp;thick]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{information</span><span 
class="cmtt-8">&nbsp;text}=[rounded</span><span 
class="cmtt-8">&nbsp;corners,fill=red!10,inner</span><span 
class="cmtt-8">&nbsp;sep=1ex]</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmsltt-10x-x-80">%</span><span 
class="cmsltt-10x-x-80">&nbsp;The</span><span 
class="cmsltt-10x-x-80">&nbsp;graphic</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[style=help</span><span 
class="cmtt-8">&nbsp;lines,step=0.5cm]</span><span 
class="cmtt-8">&nbsp;(-1.4,-1.4)</span><span 
class="cmtt-8">&nbsp;grid</span><span 
class="cmtt-8">&nbsp;(1.4,1.4);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;circle</span><span 
class="cmtt-8">&nbsp;(1cm);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\begin{scope}[style=axes]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(-1.5,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(1.5,0)</span><span 
class="cmtt-8">&nbsp;node[right]</span><span 
class="cmtt-8">&nbsp;{$x$}</span><span 
class="cmtt-8">&nbsp;coordinate(x</span><span 
class="cmtt-8">&nbsp;axis);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;]</span><span 
class="cmtt-8">&nbsp;(0,-1.5)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0,1.5)</span><span 
class="cmtt-8">&nbsp;node[above]</span><span 
class="cmtt-8">&nbsp;{$y$}</span><span 
class="cmtt-8">&nbsp;coordinate(y</span><span 
class="cmtt-8">&nbsp;axis);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\x/\xtext</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,</span><span 
class="cmtt-8">&nbsp;-.5/-\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[xshift=\x</span><span 
class="cmtt-8">&nbsp;cm]</span><span 
class="cmtt-8">&nbsp;(0pt,1pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(0pt,-1pt)</span><span 
class="cmtt-8">&nbsp;node[below,fill=white]</span><span 
class="cmtt-8">&nbsp;{$\xtext$};</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\foreach</span><span 
class="cmtt-8">&nbsp;\y/\ytext</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;{-1,</span><span 
class="cmtt-8">&nbsp;-.5/-\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;.5/\frac{1}{2},</span><span 
class="cmtt-8">&nbsp;1}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[yshift=\y</span><span 
class="cmtt-8">&nbsp;cm]</span><span 
class="cmtt-8">&nbsp;(1pt,0pt)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(-1pt,0pt)</span><span 
class="cmtt-8">&nbsp;node[left,fill=white]</span><span 
class="cmtt-8">&nbsp;{$\ytext$};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\end{scope}</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\filldraw[fill=green!20,draw=anglecolor]</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(3mm,0pt)</span><span 
class="cmtt-8">&nbsp;arc(0:30:3mm);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(15:2mm)</span><span 
class="cmtt-8">&nbsp;node[anglecolor]</span><span 
class="cmtt-8">&nbsp;{$\alpha$};</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[style=important</span><span 
class="cmtt-8">&nbsp;line,sincolor]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(30:1cm)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;node[left=1pt,fill=white]</span><span 
class="cmtt-8">&nbsp;{$\sin</span><span 
class="cmtt-8">&nbsp;\alpha$}</span><span 
class="cmtt-8">&nbsp;(30:1cm</span><span 
class="cmtt-8">&nbsp;|-</span><span 
class="cmtt-8">&nbsp;x</span><span 
class="cmtt-8">&nbsp;axis);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[style=important</span><span 
class="cmtt-8">&nbsp;line,coscolor]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(30:1cm</span><span 
class="cmtt-8">&nbsp;|-</span><span 
class="cmtt-8">&nbsp;x</span><span 
class="cmtt-8">&nbsp;axis)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;node[below=2pt,fill=white]</span><span 
class="cmtt-8">&nbsp;{$\cos</span><span 
class="cmtt-8">&nbsp;\alpha$}</span><span 
class="cmtt-8">&nbsp;(0,0);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[style=important</span><span 
class="cmtt-8">&nbsp;line,tancolor]</span><span 
class="cmtt-8">&nbsp;(1,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;node[right=1pt,fill=white]</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;$\displaystyle</span><span 
class="cmtt-8">&nbsp;\tan</span><span 
class="cmtt-8">&nbsp;\alpha</span><span 
class="cmtt-8">&nbsp;\color{black}=</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\frac{{\color{sincolor}\sin</span><span 
class="cmtt-8">&nbsp;\alpha}}{\color{coscolor}\cos</span><span 
class="cmtt-8">&nbsp;\alpha}$}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(intersection</span><span 
class="cmtt-8">&nbsp;of</span><span 
class="cmtt-8">&nbsp;0,0--30:1cm</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;1,0--1,1)</span><span 
class="cmtt-8">&nbsp;coordinate</span><span 
class="cmtt-8">&nbsp;(t);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(t);</span>
<br>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[xshift=1.85cm]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[right,text</span><span 
class="cmtt-8">&nbsp;width=6cm,style=information</span><span 
class="cmtt-8">&nbsp;text]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;The</span><span 
class="cmtt-8">&nbsp;{\color{anglecolor}</span><span 
class="cmtt-8">&nbsp;angle</span><span 
class="cmtt-8">&nbsp;$\alpha$}</span><span 
class="cmtt-8">&nbsp;is</span><span 
class="cmtt-8">&nbsp;$30^\circ$</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;the</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;example</span><span 
class="cmtt-8">&nbsp;($\pi/6$</span><span 
class="cmtt-8">&nbsp;in</span><span 
class="cmtt-8">&nbsp;radians).</span><span 
class="cmtt-8">&nbsp;The</span><span 
class="cmtt-8">&nbsp;{\color{sincolor}sine</span><span 
class="cmtt-8">&nbsp;of</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;$\alpha$},</span><span 
class="cmtt-8">&nbsp;which</span><span 
class="cmtt-8">&nbsp;is</span><span 
class="cmtt-8">&nbsp;the</span><span 
class="cmtt-8">&nbsp;height</span><span 
class="cmtt-8">&nbsp;of</span><span 
class="cmtt-8">&nbsp;the</span><span 
class="cmtt-8">&nbsp;red</span><span 
class="cmtt-8">&nbsp;line,</span><span 
class="cmtt-8">&nbsp;is</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\[</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;{\color{sincolor}</span><span 
class="cmtt-8">&nbsp;\sin</span><span 
class="cmtt-8">&nbsp;\alpha}</span><span 
class="cmtt-8">&nbsp;=</span><span 
class="cmtt-8">&nbsp;1/2.</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;By</span><span 
class="cmtt-8">&nbsp;the</span><span 
class="cmtt-8">&nbsp;Theorem</span><span 
class="cmtt-8">&nbsp;of</span><span 
class="cmtt-8">&nbsp;Pythagoras</span><span 
class="cmtt-8">&nbsp;...</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;};</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
                                                                                         
                                                                                         
<!--l. 1358--><p class="noindent">
   <h4 class="subsectionHead"><span class="titlemark">3.21   </span> <a 
 id="x4-450003.21"></a>Nodes</h4>
<!--l. 1360--><p class="noindent">Placing text at a given position is just a special case of a more general underlying mechanism. When you say
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\draw</span><span 
class="cmtt-10">&nbsp;(0,0)</span><span 
class="cmtt-10">&nbsp;node{text};</span></span></span>, what actually happens is that a rectangular node, anchored at its center, is put at
position (0<span 
class="cmmi-10">,</span>0). On top of the rectangular node the text <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">text</span></span></span> is drawn. Since no action is specified for the rectangle
(like <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">draw</span></span></span> or <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">fill</span></span></span>), the rectangle is actually discarded and only the text is shown. However, by adding
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">fill</span></span></span> or <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">draw</span></span></span>, we can make the underlying shape visible. Furthermore, we can <span 
class="cmti-10">change </span>the shape using
for example <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">shape=circle</span></span></span> or just <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">circle</span></span></span>. If we include the package <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">pgflibraryshapes</span></span></span> we also get
<span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">ellipse</span></span></span>:
<!--l. 1372--><p class="noindent"><div class="obeylines-v"></div><!--tex4ht:inline--><div class="tabular">
<table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-61-" ><colgroup id="TBL-61-1g"><col 
id="TBL-61-1"><col 
id="TBL-61-2"></colgroup><tr  
 valign="baseline" id="TBL-61-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-61-1-1"  
class="td11">  &nbsp;<object data="pgfmanual-58.svg" width="81.28409pt" height="94.87352pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object>&nbsp;  </td><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-61-1-2"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\path</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;node[ellipse,fill=examplefill,draw]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(h1)</span><span 
class="cmtt-8">&nbsp;{hello</span><span 
class="cmtt-8">&nbsp;world}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(0.5,2)</span><span 
class="cmtt-8">&nbsp;node[circle,shade,ball</span><span 
class="cmtt-8">&nbsp;color=examplefill]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;(h2)</span><span 
class="cmtt-8">&nbsp;{hello</span><span 
class="cmtt-8">&nbsp;world};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;[-&gt;,shorten</span><span 
class="cmtt-8">&nbsp;&gt;=2pt]</span><span 
class="cmtt-8">&nbsp;(h1.north)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(h2.south);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 1382--><p class="indent">   As the above example shows, we can add the a name to a node by putting it in parentheses between <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">node</span></span></span> and
the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">{</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">text</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">}</span></span></span> (you can also use the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">name=</span></span></span> option). This will make Ti<span 
class="cmti-10">k</span>Z&nbsp;remember your node and all its anchors. You
can then refer to these anchors when specifying coordinates. The syntax is <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">(</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">node name</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">.</span></span></span><span 
class="cmsy-10">&lt;</span><span 
class="cmti-10">anchor</span><span 
class="cmsy-10">&gt;</span><span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">)</span></span></span>. Currently, and
also in the near future, <span 
class="cmti-10">this will not work across pictures since Ti</span>k<span 
class="cmti-10">Z</span><span 
class="cmti-10">&nbsp;looses track of the positions when it returns</span>
<span 
class="cmti-10">control to </span><span class="TEX"><span 
class="cmti-10">T</span><span 
class="E"><span 
class="cmti-10">E</span></span><span 
class="cmti-10">X</span></span><span 
class="cmti-10">. </span>Magic hackery is possible for certain drivers, but a portable implementation seems impossible (just
think of a possible <span 
class="cmcsc-10"><small 
class="small-caps">S</small><small 
class="small-caps">V</small><small 
class="small-caps">G</small> </span>driver).
<!--l. 1393--><p class="indent">   The option <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">shorten</span><span 
class="cmtt-10">&nbsp;&gt;</span></span></span> causes lines to be shortened by 2pt at the end. Similarly, <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">shorten</span><span 
class="cmtt-10">&nbsp;&lt;</span></span></span> can be used to
shorten (or even lengthen) lines at the beginning. This is possible even if no arrow is drawn.
<!--l. 1397--><p class="indent">   It is not always necessary to specify the anchor. If you do not give an anchor, Ti<span 
class="cmti-10">k</span>Z&nbsp;will try to determine a
reasonable border anchor by itself (if Ti<span 
class="cmti-10">k</span>Z&nbsp;fails to find anything useful, it will use the center instead). Here is a
typical example:
<!--l. 1402--><p class="noindent"><div class="obeylines-v"></div><object data="pgfmanual-59.svg" width="199.56918pt" height="85.75821pt" type="image/svg+xml"><p>SVG-Viewer needed.</p></object><!--tex4ht:inline--><div class="tabular"><table class="tabular" 
cellspacing="0" cellpadding="0"  
frame="void" id="TBL-62-" ><colgroup id="TBL-62-1g"><col 
id="TBL-62-1"></colgroup><tr  
 valign="baseline" id="TBL-62-1-"><td  align="left" style="white-space:nowrap; text-align:left;" id="TBL-62-1-1"  
class="td11">  <table class="minipage"><tr><td><div class="obeylines-v">
<br><span 
class="cmtt-8">\begin{tikzpicture}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\begin{scope}[shape=circle,minimum</span><span 
class="cmtt-8">&nbsp;size=1cm,fill=examplefill]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\tikzstyle{every</span><span 
class="cmtt-8">&nbsp;node}=[draw,fill]</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;(q_A)</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(0,0)</span><span 
class="cmtt-8">&nbsp;{$q_A$};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;(q_E)</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(6,0)</span><span 
class="cmtt-8">&nbsp;{$q_E$};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;(q_1)</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(2,0)</span><span 
class="cmtt-8">&nbsp;{$q_1$};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\node</span><span 
class="cmtt-8">&nbsp;(q_2)</span><span 
class="cmtt-8">&nbsp;at</span><span 
class="cmtt-8">&nbsp;(4,2)</span><span 
class="cmtt-8">&nbsp;{$q_2$};</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\end{scope}</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw</span><span 
class="cmtt-8">&nbsp;(q_A)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(q_1)</span><span 
class="cmtt-8">&nbsp;--</span><span 
class="cmtt-8">&nbsp;(q_2)</span><span 
class="cmtt-8">&nbsp;-|</span><span 
class="cmtt-8">&nbsp;(q_E);</span>
<br><span 
class="cmtt-8">&nbsp;</span><span 
class="cmtt-8">&nbsp;\draw[-&gt;,shorten</span><span 
class="cmtt-8">&nbsp;&gt;=2pt]</span><span 
class="cmtt-8">&nbsp;(q_A)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;controls</span><span 
class="cmtt-8">&nbsp;+(75:1.4cm)</span><span 
class="cmtt-8">&nbsp;and</span><span 
class="cmtt-8">&nbsp;+(105:1.4cm)</span><span 
class="cmtt-8">&nbsp;..</span><span 
class="cmtt-8">&nbsp;node[above]</span><span 
class="cmtt-8">&nbsp;{$x$}</span><span 
class="cmtt-8">&nbsp;(q_A);</span>
<br><span 
class="cmtt-8">\end{tikzpicture}</span></div>                                                                                             </td></tr></table> </td>
</tr></table></div>
<!--l. 1416--><p class="indent">   In the example, we used the <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\node</span></span></span> command, which is an abbreviation for <span class="obeylines-h"><span class="verb"><span 
class="cmtt-10">\path</span><span 
class="cmtt-10">&nbsp;node</span></span></span>.
                                                                                         
                                                                                         
                                                                                         
                                                                                         
                                                                                         
                                                                                         
   <div class="crosslinks"><p class="noindent">[<a 
href="pgfmanualse4.html" >next</a>] [<a 
href="pgfmanualse2.html" >prev</a>] [<a 
href="pgfmanualse2.html#tailpgfmanualse2.html" >prev-tail</a>] [<a 
href="pgfmanualse3.html" >front</a>] [<a 
href="pgfmanual.html#pgfmanualse3.html" >up</a>] </p></div>
<!--l. 10--><p class="indent">   <a 
 id="tailpgfmanualse3.html"></a>   
</body></html>