summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/tkz/tkz-euclide/doc/latex/TKZdoc-euclide-polygons.tex
blob: fe50b39e2cf0d89720822d090c63666653412fd5 (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
\section{Definition of polygons}

\subsection{Defining the points of a square} \label{def_square}
   We have seen the definitions of some triangles. Let us look at the definitions of some quadrilaterals and regular polygons.

 \begin{NewMacroBox}{tkzDefSquare}{\parg{pt1,pt2}}

The square is defined in the forward direction. From two points, two more points are obtained such that the four taken in order form a square. The square is defined in the forward direction.    The results are in \tkzname{tkzFirstPointResult} and \tkzname{tkzSecondPointResult}.\\
We can rename them with \tkzcname{tkzGetPoints}

\medskip
\begin{tabular}{lll}
\toprule
Arguments             & example & explication                         \\ 
\midrule
\TAline{\parg{pt1,pt2}}{\tkzcname{tkzDefSquare}\parg{A,B}}{The square is defined in the direct direction}
\bottomrule
 \end{tabular}
\end{NewMacroBox}

\subsubsection{Using \tkzcname{tkzDefSquare} with two points}

Note the inversion of the first two points and the result.

\begin{tkzexample}[latex=4cm,small]
\begin{tikzpicture}[scale=.5]
  \tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B}
  \tkzDefSquare(A,B)
  \tkzDrawPolygon[color=red](A,B,tkzFirstPointResult,%
               tkzSecondPointResult)
  \tkzDefSquare(B,A)
  \tkzDrawPolygon[color=blue](B,A,tkzFirstPointResult,%
               tkzSecondPointResult) 
\end{tikzpicture} 
\end{tkzexample}

 We may only need one point to draw an isosceles right-angled triangle so we use \tkzcname{tkzGetFirstPoint} or \tkzcname{tkzGetSecondPoint}

\subsubsection{Use of \tkzcname{tkzDefSquare} to obtain an isosceles right-angled triangle}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=1]
  \tkzDefPoint(0,0){A}
  \tkzDefPoint(3,0){B}
  \tkzDefSquare(A,B) \tkzGetFirstPoint{C}
  \tkzDrawPolygon[color=blue,fill=blue!30](A,B,C)
\end{tikzpicture}
\end{tkzexample}

\subsubsection{Pythagorean Theorem and \tkzcname{tkzDefSquare} }
\begin{tkzexample}[latex=8cm,small]
\begin{tikzpicture}[scale=.5]
\tkzInit
\tkzDefPoint(0,0){C}
\tkzDefPoint(4,0){A}
\tkzDefPoint(0,3){B} 
\tkzDefSquare(B,A)\tkzGetPoints{E}{F} 
\tkzDefSquare(A,C)\tkzGetPoints{G}{H} 
\tkzDefSquare(C,B)\tkzGetPoints{I}{J} 
\tkzFillPolygon[fill = red!50 ](A,C,G,H) 
\tkzFillPolygon[fill = blue!50 ](C,B,I,J) 
\tkzFillPolygon[fill = purple!50](B,A,E,F) 
\tkzFillPolygon[fill = orange,opacity=.5](A,B,C) 
\tkzDrawPolygon[line width = 1pt](A,B,C) 
\tkzDrawPolygon[line width = 1pt](A,C,G,H) 
\tkzDrawPolygon[line width = 1pt](C,B,I,J) 
\tkzDrawPolygon[line width = 1pt](B,A,E,F) 
\tkzLabelSegment[](A,C){$a$} 
\tkzLabelSegment[](C,B){$b$} 
\tkzLabelSegment[swap](A,B){$c$} 
\end{tikzpicture}
\end{tkzexample}

\subsection{Definition of parallelogram} 

\subsection{Defining the points of a parallelogram} 
It is a matter of completing three points in order to obtain a parallelogram.
 \begin{NewMacroBox}{tkzDefParallelogram}{\parg{pt1,pt2,pt3}}
From three points, another point is obtained such that the four taken in order form a parallelogram.  The result is in \tkzname{tkzPointResult}. \\
We can rename it with the name \tkzcname{tkzGetPoint}...

\begin{tabular}{lll}
\toprule
arguments &  default & definition  \\ 
\midrule
\TAline{\parg{pt1,pt2,pt3}}{no default}{Three points are necessary}
\bottomrule
\end{tabular}
\end{NewMacroBox}

\subsubsection{Example of a parallelogram definition}

\begin{tkzexample}[latex=7 cm,small]
\begin{tikzpicture}[scale=1]
 \tkzDefPoints{0/0/A,3/0/B,4/2/C} 
 \tkzDefParallelogram(A,B,C) 
 \tkzGetPoint{D}
 \tkzDrawPolygon(A,B,C,D)
 \tkzLabelPoints(A,B) 
 \tkzLabelPoints[above right](C,D)
 \tkzDrawPoints(A,...,D)
\end{tikzpicture}
\end{tkzexample}



\subsubsection{Simple example}
Explanation of the definition of a parallelogram
\begin{tkzexample}[latex=7 cm,small]
\begin{tikzpicture}[scale=1]
  \tkzDefPoints{0/0/A,3/0/B,4/2/C} 
  \tkzDefPointWith[colinear= at C](B,A) 
  \tkzGetPoint{D}
  \tkzDrawPolygon(A,B,C,D)
  \tkzLabelPoints(A,B) 
  \tkzLabelPoints[above right](C,D)
  \tkzDrawPoints(A,...,D)
\end{tikzpicture}
\end{tkzexample}

\subsubsection{Construction of the golden rectangle }

\begin{tkzexample}[latex=8cm,small]
\begin{tikzpicture}[scale=.5]
  \tkzInit[xmax=14,ymax=10]
  \tkzClip[space=1]
  \tkzDefPoint(0,0){A}
  \tkzDefPoint(8,0){B}
  \tkzDefMidPoint(A,B)\tkzGetPoint{I}
  \tkzDefSquare(A,B)\tkzGetPoints{C}{D}
  \tkzDrawSquare(A,B)
  \tkzInterLC(A,B)(I,C)\tkzGetPoints{G}{E}
  \tkzDrawArc[style=dashed,color=gray](I,E)(D)
  \tkzDefPointWith[colinear= at C](E,B)
  \tkzGetPoint{F}
  \tkzDrawPoints(C,D,E,F)
  \tkzLabelPoints(A,B,C,D,E,F)
  \tkzDrawSegments[style=dashed,color=gray]%
(E,F C,F B,E)  
\end{tikzpicture}
\end{tkzexample}




\subsection{Drawing a square} 

 \begin{NewMacroBox}{tkzDrawSquare}{\oarg{local options}\parg{pt1,pt2}}
The macro draws a square but not the vertices. It is possible to color the inside. The order of the points is that of the direct direction of the trigonometric circle.

\medskip
\begin{tabular}{lll}
\toprule
arguments             & example & explication                         \\ 
\midrule
\TAline{\parg{pt1,pt2}}{|\tkzcname{tkzDrawSquare}|\parg{A,B}}{|\tkzcname{tkzGetPoints\{C\}\{D\}}|}
\bottomrule
 \end{tabular}

\medskip 
 \begin{tabular}{lll}
 options             & example & explication                         \\ 
 \midrule
 \TOline{Options TikZ}{|red,line width=1pt|}{}
 \bottomrule
  \end{tabular}
\end{NewMacroBox}

\subsubsection{The idea is to inscribe two squares in a semi-circle.}

\begin{tkzexample}[latex=6 cm,small]
\begin{tikzpicture}[scale=.75] 
   \tkzInit[ymax=8,xmax=8]
 \tkzClip[space=.25]    \tkzDefPoint(0,0){A}
 \tkzDefPoint(8,0){B}  \tkzDefPoint(4,0){I}
 \tkzDefSquare(A,B)    \tkzGetPoints{C}{D}
 \tkzInterLC(I,C)(I,B) \tkzGetPoints{E'}{E}
 \tkzInterLC(I,D)(I,B) \tkzGetPoints{F'}{F} 
 \tkzDefPointsBy[projection=onto A--B](E,F){H,G}
 \tkzDefPointsBy[symmetry   = center H](I){J}
 \tkzDefSquare(H,J)    \tkzGetPoints{K}{L}
 \tkzDrawSector[fill=yellow](I,B)(A)
 \tkzFillPolygon[color=red!40](H,E,F,G)
 \tkzFillPolygon[color=blue!40](H,J,K,L)
 \tkzDrawPolySeg[color=red](H,E,F,G) 
 \tkzDrawPolySeg[color=red](J,K,L)
 \tkzDrawPoints(E,G,H,F,J,K,L)
\end{tikzpicture}
\end{tkzexample}

\subsection{The golden rectangle} 
 \begin{NewMacroBox}{tkzDefGoldRectangle}{\parg{point,point}}
The macro determines a rectangle whose size ratio is the number $\Phi$. The created points are in \tkzname{tkzFirstPointResult} and \tkzname{tkzSecondPointResult}. They can be obtained with the macro \tkzcname{tkzGetPoints}. The following macro is used to draw the rectangle.

\begin{tabular}{lll}
\toprule
arguments             & example & explication                         \\
\midrule
\TAline{\parg{pt1,pt2}}{\parg{A,B}}{Si C et D sont créés alors $AB/BC=\Phi$}
 \end{tabular}
\end{NewMacroBox}

 \begin{NewMacroBox}{tkzDrawGoldRectangle}{\oarg{local options}\parg{point,point}}
\begin{tabular}{lll}
arguments             & example & explication                         \\
\midrule
\TAline{\parg{pt1,pt2}}{\parg{A,B}}{Draws the golden rectangle based on the segment $[AB]$}
 \end{tabular}

\medskip 
 \begin{tabular}{lll}
 options             & example & explication                         \\ 
 \midrule
 \TOline{Options TikZ}{|red,line width=1pt|}{}
 \bottomrule
  \end{tabular} 
 
\end{NewMacroBox}

% 
\subsubsection{Golden Rectangles}
 
\begin{tkzexample}[latex=6 cm,small]
\begin{tikzpicture}[scale=.6]
 \tkzDefPoint(0,0){A}      \tkzDefPoint(8,0){B}
 \tkzDefGoldRectangle(A,B) \tkzGetPoints{C}{D}
 \tkzDefGoldRectangle(B,C) \tkzGetPoints{E}{F}
 \tkzDrawPolygon[color=red,fill=red!20](A,B,C,D)
 \tkzDrawPolygon[color=blue,fill=blue!20](B,C,E,F)
\end{tikzpicture}
\end{tkzexample}

\subsection{Drawing a polygon} 

 \begin{NewMacroBox}{tkzDrawPolygon}{\oarg{local options}\parg{liste de points}}
Just give a list of points and the macro plots the polygon using the \TIKZ\ options present.

\begin{tabular}{lll}
\toprule
arguments             & example & explication                         \\
\midrule
\TAline{\parg{pt1,pt2,pt3,...}}{|\BS tkzDrawPolygon[gray,dashed](A,B,C)|}{Drawing a triangle}
 \end{tabular}

\medskip
\begin{tabular}{lll}
\toprule
options             & default & example                         \\
\midrule
\TOline{Options TikZ}{...}{|\BS tkzDrawPolygon[red,line width=2pt](A,B,C)|}
 \end{tabular} 
\end{NewMacroBox}

\subsubsection{Draw a polygon 1}

\begin{tkzexample}[latex=7cm, small]  
\begin{tikzpicture} [rotate=18,scale=1.5]
 \tkzDefPoint(0,0){A}
 \tkzDefPoint(2.25,0.2){B}
 \tkzDefPoint(2.5,2.75){C}
 \tkzDefPoint(-0.75,2){D}
 \tkzDrawPolygon[fill=black!50!blue!20!](A,B,C,D)
 \tkzDrawSegments[style=dashed](A,C B,D) 
\end{tikzpicture}\end{tkzexample}

 
\subsection{Clip a polygon} 
 \begin{NewMacroBox}{tkzClipPolygon}{\oarg{local options}\parg{points list}}
This macro makes it possible to contain the different plots in the designated polygon.

\medskip
\begin{tabular}{lll}
\toprule
options             & example & explication                         \\ 
\midrule
\TAline{\parg{pt1,pt2}}{\parg{A,B}}{}
%\bottomrule
 \end{tabular}
\end{NewMacroBox}
\subsubsection{Simple Example} 
\begin{tkzexample}[latex=7 cm,small]
\begin{tikzpicture}[scale=1.25]
 \tkzInit[xmin=0,xmax=4,ymin=0,ymax=3] 
 \tkzClip[space=.5] 
 \tkzDefPoint(0,0){A} \tkzDefPoint(4,0){B}
 \tkzDefPoint(1,3){C} \tkzDrawPolygon(A,B,C)
 \tkzDefPoint(0,2){D}  \tkzDefPoint(2,0){E}
 \tkzDrawPoints(D,E) \tkzLabelPoints(D,E) 
 \tkzClipPolygon(A,B,C)
 \tkzDrawLine[color=red](D,E)
\end{tikzpicture}
\end{tkzexample}

\subsubsection{Example Sangaku in a square} 
\begin{tkzexample}[latex=7cm, small]  
\begin{tikzpicture}[scale=.75]
 \tkzDefPoint(0,0){A} \tkzDefPoint(8,0){B}
 \tkzDefSquare(A,B) \tkzGetPoints{C}{D}
 \tkzDrawPolygon(B,C,D,A)
 \tkzClipPolygon(B,C,D,A)
 \tkzDefPoint(4,8){F}
 \tkzDefTriangle[equilateral](C,D) 
 \tkzGetPoint{I}
 \tkzDrawPoint(I)
 \tkzDefPointBy[projection=onto B--C](I) 
 \tkzGetPoint{J}
 \tkzInterLL(D,B)(I,J)  \tkzGetPoint{K}
 \tkzDefPointBy[symmetry=center K](B) 
 \tkzGetPoint{M}
 \tkzDrawCircle(M,I)
 \tkzCalcLength(M,I)   \tkzGetLength{dMI}
 \tkzFillPolygon[color = orange](A,B,C,D)
 \tkzFillCircle[R,color = yellow](M,\dMI pt)
 \tkzFillCircle[R,color = blue!50!black](F,4 cm)%
\end{tikzpicture}
\end{tkzexample}
 
\subsection{Color a polygon} 
 \begin{NewMacroBox}{tkzFillPolygon}{\oarg{local options}\parg{points list}}
You can color by drawing the polygon, but in this case you color the inside of the polygon without drawing it.

\medskip
\begin{tabular}{lll}
\toprule
options             & example & explication                         \\ 
\midrule
\TAline{\parg{pt1,pt2,\dots}}{\parg{A,B,\dots}}{}
%\bottomrule
 \end{tabular}
\end{NewMacroBox} 

\subsubsection{Color a polygon} 
\begin{tkzexample}[latex=7cm, small]  
\begin{tikzpicture}[scale=0.7]
\tkzInit[xmin=-3,xmax=6,ymin=-1,ymax=6]
\tkzDrawX[noticks]
\tkzDrawY[noticks]    
\tkzDefPoint(0,0){O}  \tkzDefPoint(4,2){A}
\tkzDefPoint(-2,6){B}
\tkzPointShowCoord[xlabel=$x$,ylabel=$y$](A)
\tkzPointShowCoord[xlabel=$x'$,ylabel=$y'$,%
                   ystyle={right=2pt}](B) 
\tkzDrawSegments[->](O,A O,B)
\tkzLabelSegment[above=3pt](O,A){$\vec{u}$}
\tkzLabelSegment[above=3pt](O,B){$\vec{v}$}
\tkzMarkAngle[fill= yellow,size=1.8cm,%
              opacity=.5](A,O,B)
\tkzFillPolygon[red!30,opacity=0.25](A,B,O)
\tkzLabelAngle[pos = 1.5](A,O,B){$\alpha$} 
\end{tikzpicture}
\end{tkzexample}
\endinput