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
|
\SbSbSSCT{Symétrie par rapport à un point}{Central symmetry}
\psset{unit=.7cm}
\begin{tabular}{|c|c|c|} \hline
%\multicolumn{3}{|c|}{ \BSS{pstSymO}[linecolor=red]\AC{A}\AC{B} }\\ \hline
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(3,1){B} %(3,3){C}
\pstSymO[linecolor=red]{A}{B}
%\psline[linestyle=dotted](B)(B')
%\psline[linestyle=dashed](A)(B)
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(3,1){B} %(3,3){C}
\pstSymO[linecolor=Vert]{A}{B}[D]
%\psline[linestyle=dashed](A)(B)
%\psline[linestyle=dotted](B)(D)
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B}(3,3){C}
\pstSymO[linecolor=red]{A}{B,C}[D,E]
\end{pspicture}
\\ \hline
\BSS{pstSymO}[linecolor=red] \BSI{pstSymO}{pst-eucl} & \BSS{pstSymO}[linecolor=Vert]
&\BSS{pstSymO}[linecolor=red] \\
\AC{A}\AC{B} & \AC{A}\AC{B}[D] & \AC{A}\AC{B,C}[D,E]
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|c|} \hline
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B}(3,3){C}
\pstSymO[CodeFig=true]{A}{B,C}[D,E]
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B}(3,3){C}
\pstSymO[CodeFig=true,CodeFigColor=red]{A}{B,C}[D,E]
\end{pspicture}
\\ \hline
\BS{pstSymO}[\RDD{CodeFig}=true] & \BS{pstSymO}[CodeFig=true,\RDD{CodeFigColor}=red] \\
\AC{A}\AC{B,C}[D,E] \RDI{CodeFig}{pst-eucl} & \AC{A}\AC{B,C}[D,E] \RDI{CodeFigColor}{pst-eucl}
\\ \hline
\dft : CodeFig = false & \dft : CodeFigColor = cyan
\\ \hline
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B}(3,3){C}
\pstSymO[CodeFig=true,CodeFigStyle=dotted,CodeFigColor=red]{A}{B,C}[D,E]
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B}(3,3){C}
\pstSymO[CodeFig=true,CodeFigStyle=solid,CodeFigColor=red]{A}{B,C}[D,E]
\end{pspicture}
\\ \hline
\BS{pstSymO}[CodeFig=true,\RDD{CodeFigStyle}=dotted] & \BS{pstSymO}[CodeFig=true,\RDD{CodeFigStyle}=solid] \\
\AC{A}\AC{B,C}[D,E] \RDI{CodeFigStyle}{pst-eucl} & \AC{A}\AC{B,C}[D,E]
\\ \hline
\dft : CodeFigStyle = dashed &
\\ \hline
\end{tabular}
Autres options possibles : PointSymbol PosAngle PointName PointNameSep PtNameMath
% <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
\SbSbSSCT{Symétrie par rapport à une droite}{Orthogonal symmetry}
\begin{tabular}{|c|c|} \hline
\multicolumn{2}{|c|}{ \BSS{pstOrtSym}[options]\AC{A}\AC{B}\AC{C} \BSI{pstOrtSym}{pst-eucl} }\\ \hline
\begin{pspicture}(-.5,-.5)(5,5.3)
\psaxes[ticksize=5,axesstyle=frame](5,5)
\pstGeonode(1,1){A}(4,1){C}(3,3){B}
\pstOrtSym [linecolor=red]{A}{B}{C}
\psline[linestyle=dashed](B)(A)
\psline[linestyle=dotted](C)(C')
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,5.3)
\psaxes[ticksize=5,axesstyle=frame](5,5)
\pstGeonode(1,1){A}(4,1){C}(3,3){B}
\pstOrtSym [CodeFig=true,CodeFigColor=red]{A}{B}{C} % <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
\psline[linestyle=dashed](B)(A)
\end{pspicture}
\\ \hline
[linecolor=red] & [CodeFig=true,\RDD{CodeFigColor}=red] \RDI{CodeFigColor}{pst-eucl} \\ \hline
& {\blue \dft : CodeFigColor=cyan } \\ \hline
\end{tabular}
%%--------------------------------------------------
\subsubsection{Rotation}
\begin{tabular}{|c|c|c|} \hline
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B} %(1,3){C}
\pstRotation[linecolor=red,CodeFig=true]{A}{B}
%\pstRotation[linecolor=Vert]{A}{C}[D]
\psline[linestyle=dotted](A)(B')
\psline(A)(B)
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(1,3){A}(2,1){B} %(1,3){C}
\pstRotation[linecolor=red,RotAngle=45,CodeFig=true]{A}{B}[D]
\psline(B)(A)
\psline[linestyle=dotted](A)(D)
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B}(1,3){C}
\pstRotation[linecolor=red,RotAngle=45,CodeFig=true]{A}{B,C}[D,E]
\psline (B)(A) (C) %(D)
%\psline[linestyle=dashed](C)(A) %(E)
\psline[linestyle=dotted](A)(D)
\psline[linestyle=dotted](A)(E)
\end{pspicture}
\\ \hline
\BSS{pstRotation}[linecolor=red] & \textbf{\BS{pstRotation}}[\RDD{RotAngle}=45] & \textbf{\BS{pstRotation}}[\RDD{RotAngle}=45] \RDI{RotAngle}{pst-eucl} \\
\AC{A}\AC{B} \BSI{pstRotation}{pst-eucl} & \AC{A}\AC{C}[D] \RDI{RotAngle}{pst-eucl}& \AC{A}\AC{B,C}[D,E] \\\hline
& \multicolumn{2}{|c|} {\blue \dft : RotAngle=60 }\\
\hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|c|} \hline
\multicolumn{2}{|c|} {\BS{pstRotation}[CodeFig=true,CodeFigColor=red,\RDD{TransformLabel}=\BS{alpha}]\AC{A}\AC{B} \RDI{TransformLabel}{pst-eucl} }
\\ \hline
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B}
\pstRotation[CodeFig=true,CodeFigColor=red,TransformLabel=\alpha]{A}{B} %<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
\psline[linestyle=dashed](B)(A)
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(2,2){A}(4,1){B}
\pstRotation[CodeFig=true,CodeFigColor=red,TransformLabel=\frac{\pi}{3}]{A}{B}[C]
\psline[linestyle=dashed](B)(A)
\end{pspicture}
\\ \hline
\RDD{TransformLabel}=\BS{alpha} \RDI{TransformLabel}{pst-eucl} & \RDD{TransformLabel}=\BS{frac}\AC{\BS{pi}}\AC{3} \RDI{TransformLabel}{pst-eucl} \\ \hline
\end{tabular}
\bigskip
%%
%%%>>>>>>>>>>>>>>>>>>> \BS{pstAngleAOB} incompatible avec pst-3dplot <<<<<<<<<<<<<<<<<<<<<<<
%%
\begin{tabular}{|c|c|c|} \hline
\multicolumn{3}{|c|} {\BS{pstRotation}[CodeFig=true,RotAngle=\RDD{pstAngleAOB}\AC{C}\AC{A}\AC{B}] \AC{A}\AC{B} \AC{D} \RDI{pstAngleAOB}{pst-eucl} }
\\ \hline
\parbox{4cm}{
\begin{pspicture}(-.5,-.5)(5,5.3)
\psaxes[xticksize=5,yticksize=5,axesstyle=frame](5,5)
\pstGeonode(3,3){A}(1,1){B} (1,3){C}
\pstRotation[linecolor=red,RotAngle=\pstAngleAOB{C}{A}{B},CodeFig=true]{A}{B}[D]
\psline(B)(A)
%\rput (2,-1){\framebox{Rotation = \makebox[1cm][l]{\psPrintValue[decimals=2]{\pstAngleAOB{C}{A}{B}}}}}
%\rput (2,-1){Rotation = \psPrintValue[decimals=2] {\pstAngleAOB{C}{A}{B}}}
\psline[linestyle=dotted](A)(D)
\end{pspicture} \\
Rotation = \psPrintValue[decimals=2]{\pstAngleAOB{C}{A}{B}}}
&
\parbox{4cm}{
\begin{pspicture}(-.5,-.5)(5,5.3)
\psaxes[xticksize=5,yticksize=5,axesstyle=frame](5,5)
\pstGeonode(1,2){A}(4,1){B}(3,3){C}
\pstRotation[linecolor=red,RotAngle=\pstAngleAOB{C}{B}{A},CodeFig=true]{A}{B,C}[D,E]
%\rput* (2,-1){\framebox{Rotation = \makebox[1cm][l]{\psPrintValue[decimals=2]{\pstAngleAOB{C}{B}{A}}}}}
%\rput (2,-1){Rotation = \psPrintValue[decimals=2] {\pstAngleAOB{C}{B}{A}}}
\psline (B)(A) (C) %(D)
\psline[linestyle=dashed](C)(A) %(E)
\psline[linestyle=dotted](A)(D)
\psline[linestyle=dotted](A)(E)
\end{pspicture}\\
Rotation = \psPrintValue[decimals=2]{\pstAngleAOB{C}{B}{A}}}
&
\parbox{4cm}{
\begin{pspicture}(-.5,-.5)(5,5.3)
\psaxes[xticksize=5,yticksize=5,axesstyle=frame](5,5)
\pstGeonode(2,2){A}(4,1){B}(3,3){C}
\pstRotation[linecolor=red,AngleCoef=3,RotAngle=\pstAngleAOB{C}{B}{A},CodeFig=true]{A}{B,C}[D,E]
%\psline (B)(A) (C) %(D)
%\rput (2,-1){\framebox{Rotation = \makebox[1cm][l]{\psPrintValue[decimals=2] { \pstAngleAOB{C}{B}{A} 3 mul}}}}
%\psline[linestyle=dashed](C)(A) %(E)
%\psline[linestyle=dotted](A)(D)
%\psline[linestyle=dotted](A)(E)
\end{pspicture}\\
Rotation = \psPrintValue[decimals=2] { \pstAngleAOB{C}{B}{A} 3 mul}}
\\ \hline
\end{tabular}
%<<<<<<<<
%\bigskip
%%
%%%\begin{pspicture}(-.5,-.5)(5,4.3)
%%%\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
%%%\pstGeonode(3,2){A}(3,3){B}(1,2){C}
%%%\pstRotation[RotAngle=45, CodeFig=true]{A}{D}[E]
%%%%\pstRotation[RotAngle=\pstAngleAOB{C}{A}{B}, CodeFig=true]{A}{D}[E]
%%%%\pstRotation[ RotAngle=\pstAngleAOB{B}{A}{C} ,CodeFigColor=red, CodeFig=true]{A}{B}[C]
%%%%\pstRotation[CodeFig=true,CodeFigColor=red,TransformLabel=\alpha]{A}{B}
%%%%\pstRotation[linecolor=Vert,RotAngle=\pstAngleAOB{B}{A}{C}]{A}{C}[D]
%%%
%%%\end{pspicture}
%%
%%%\begin{tabular}{|c|c|} \hline
%%%\begin{pspicture}(-.5,-.5)(5,4.3)
%%%\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
%%%\pstGeonode(3,2){A}(3,3){B}(1,3){C}
%%%\pstRotation[RotAngle=\pstAngleAOB{B}{A}{C}]{A}{D}[E] %<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
%%%\pstRotation[AngleCoef=.5, RotAngle=\pstAngleAOB{B}{A}{C},CodeFigColor=red, CodeFig=true]{A}{B}[C]
%%%\pstRotation[CodeFig=true,CodeFigColor=red,TransformLabel=\alpha]{A}{B}
%%%\pstRotation[linecolor=Vert,RotAngle=\pstAngleAOB{B}{A}{C}]{A}{C}[D]
%%%
%%%\end{pspicture}
%%%&
%%%\begin{pspicture}(-.5,-.5)(4,4.3)
%%%\psaxes[ticksize=4,axesstyle=frame](4,4)
%%%\pstGeonode(3,2){A}(3,3){B} %(1,3){C}
%%%\pstRotation[CodeFig=true,CodeFigColor=red,TransformLabel=\alpha]{A}{B}
%%%\pstRotation[RotAngle=\pstAngleAOB{B}{A}{C},CodeFig=true,CodeFigColor=red,TransformLabel=\widehat{BAC}]{A}{C}[D]
%%%\psline[linestyle=dashed](B)(A)(B')
%%%\psline[linestyle=dashed](C)(A)(D)
%%%\end{pspicture}
%%%\\ \hline
%%%RotAngle=\textbf{\BS{}pstAngleAOB}\AC{B}\AC{A}\AC{C} & {\red TransformLabel}=\BS{widehat}\AC{BAC}
%%%\\ \hline
%%%\end{tabular}
%%
%%
%%%------------------------------------------------------
\subsubsection{Translation}
\begin{tabular}{|c|c|c|} \hline
\BSS{pstTranslation}[options]\AC{B}\AC{A}\AC{C} \BSI{pstTranslation}{pst-eucl} &
\multicolumn{2}{|c|}{ \BSS{pstTranslation}[options]\AC{A}\AC{B}\AC{C} \BSI{pstTranslation}{pst-eucl} }\\ \hline
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(1,2){A}(3,1){B}(3,2){C}
\pstTranslation[linecolor=red]{B}{A}{C}
\psline[linestyle=dashed](B)(A)
\psline[linestyle=dashed](C)(C')
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(1,2){A}(3,1){B}(3,2){C}
\pstTranslation[linecolor=red,DistCoef=.5]{A}{B}{C}
\psline[linestyle=dashed](B)(A)
\psline[linestyle=dashed](C)(C')
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(6,4.3)
\psaxes[xticksize=4,yticksize=6,axesstyle=frame](6,4)
\pstGeonode(1,2){A}(3,1){B}(3,2){C}
\pstTranslation[CodeFig=true]{A}{B}{C}
\psline[linestyle=dashed](B)(A)
%\psline[linestyle=dashed](C)(C')
\end{pspicture}
\\ \hline
& [\RDD{DistCoef}=0.5] \RDI{DistCoef}{pst-eucl} & [\RDD{CodeFig}=true] \RDI{CodeFig}{pst-eucl}
\\ \hline
\end{tabular}
%
%%--------------------------------------------------------------------------
\SbSbSSCT{Homothétie}{Homothetie}
\begin{tabular}{|c|c|c|} \hline
\multicolumn{2}{|c|}{ \BSS{pstHomO}\AC{A}\AC{B,C}[D,E] \BSI{pstHomO}{pst-eucl} }\\ \hline
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(0,2){A}(4,1){B}(4,3){C}
\pstLineAB[nodesepB=-1,linestyle=dashed]{A}{B}
\pstLineAB[nodesepB=-1,linestyle=dashed]{A}{C}
\pstHomO[linecolor=red]{A}{B,C}[D,E]
\end{pspicture}
&
\begin{pspicture}(-.5,-.5)(5,4.3)
\psaxes[xticksize=4,yticksize=5,axesstyle=frame](5,4)
\pstGeonode(0,2){A}(4,1){B}(4,3){C}
\pstLineAB[nodesepB=-1,linestyle=dashed]{A}{B}
\pstLineAB[nodesepB=-1,linestyle=dashed]{A}{C}
\pstHomO[linecolor=red,HomCoef=.75]{A}{B,C}[D,E]
\end{pspicture}
\\ \hline
&
[\RDD{HomCoef}=.75] \RDI{HomCoef}{pst-eucl}
\\ \hline
\end{tabular}
%%-------------------------------------------------------------
\SbSbSSCT{Projection orthogonale}{Orthogonal projection}
\begin{tabular}{|c|} \hline
\begin{pspicture}(-.5,-.5)(5,5.3)
\psaxes[ticksize=5,axesstyle=frame](5,5)
\pstTriangle(1,3){A}(3,1){B}(4,4){C}
\pstProjection[CodeFig=true, CodeFigColor=red]{A}{B}{C}[D]
\end{pspicture}
\\ \hline
\BSS{pstProjection}[CodeFig=true,CodeFigColor=red]\AC{A}\AC{B}\AC{C}[D] \BSI{pstProjection}{pst-eucl}
\\ \hline
\end{tabular}
|
