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3<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
4  <head>
5    <title>quadrilateral2square.pro (SAXO Documentation Assistant)</title>
6  </head>
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55
56
57    <h1><font size="-2">Interpolation/</font></h1>
58    <h2>quadrilateral2square.pro</h2>
59
60    <dl>
61    </dl>
62
63   
64 warm (or map) an arbitrary quadrilateral onto a unit square
65 according to the 4-point correspondences:
66       (x0,y0) -> (0,0)
67       (x1,y1) -> (1,0)
68       (x2,y2) -> (1,1)
69       (x3,y3) -> (0,1)
70 This is the inverse function of <a href="..//Interpolation/square2quadrilateral.html">square2quadrilateral</a>.
71
72 The mapping is done using perspective transformation which preserve
73 lines in all orientations and permit quadrilateral to quadrilateral
74 mappings. see ref. bellow.
75
76
77   
78
79     
80      <a name="#_quadrilateral2square"></a>
81
82      <h2>quadrilateral2square  <font size="-1" color="#006633">
83 Picture, Grid
84</font></h2>
85
86      <p><font face="Courier"><i>result = </i>quadrilateral2square(<i><a href="#_quadrilateral2square_keyword_x0in">x0in</a>, <a href="#_quadrilateral2square_keyword_y0in">y0in</a>, <a href="#_quadrilateral2square_keyword_x1in">x1in</a>, <a href="#_quadrilateral2square_keyword_y1in">y1in</a>, <a href="#_quadrilateral2square_keyword_x2in">x2in</a>, <a href="#_quadrilateral2square_keyword_y2in">y2in</a>, <a href="#_quadrilateral2square_keyword_x3in">x3in</a>, <a href="#_quadrilateral2square_keyword_y3in">y3in</a>, <a href="#_quadrilateral2square_keyword_xxin">xxin</a>, <a href="#_quadrilateral2square_keyword_yyin">yyin</a></i>, <a href="#_quadrilateral2square_keyword_PERF">PERF</a>=<i>salar 0 or 1</i>, <a href="#_quadrilateral2square_keyword_DOUBLE">DOUBLE</a>=<i>salar 0 or 1</i>)</font></p>
87
88   
89
90
91    <h3>Return value</h3>
92 (2,n) array: the new coordinates (xout,yout) of the (xin,yin) point(s) after
93 mapping.
94 If xin is a scalar, then n is equal to the number of elements of x0.
95 If xin is an array, then n is equal to the number of elements of xin.
96
97
98   
99    <h3>Parameters</h3>
100   
101
102    <a name="#_quadrilateral2square_keyword_x0in"></a>
103    <h4>x0in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
104      <font size="-1" color="#006633">in</font>
105     
106     
107      <font size="-1" color="#006633">required</font>
108     
109     
110     
111     
112    </h4>
113
114   
115   
116
117    <a name="#_quadrilateral2square_keyword_y0in"></a>
118    <h4>y0in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
119      <font size="-1" color="#006633">in</font>
120     
121     
122      <font size="-1" color="#006633">required</font>
123     
124     
125     
126     
127    </h4>
128
129   
130   
131
132    <a name="#_quadrilateral2square_keyword_x1in"></a>
133    <h4>x1in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
134      <font size="-1" color="#006633">in</font>
135     
136     
137      <font size="-1" color="#006633">required</font>
138     
139     
140     
141     
142    </h4>
143
144   
145   
146
147    <a name="#_quadrilateral2square_keyword_y1in"></a>
148    <h4>y1in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
149      <font size="-1" color="#006633">in</font>
150     
151     
152      <font size="-1" color="#006633">required</font>
153     
154     
155     
156     
157    </h4>
158
159   
160   
161
162    <a name="#_quadrilateral2square_keyword_x2in"></a>
163    <h4>x2in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
164      <font size="-1" color="#006633">in</font>
165     
166     
167      <font size="-1" color="#006633">required</font>
168     
169     
170     
171     
172    </h4>
173
174   
175   
176
177    <a name="#_quadrilateral2square_keyword_y2in"></a>
178    <h4>y2in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
179      <font size="-1" color="#006633">in</font>
180     
181     
182      <font size="-1" color="#006633">required</font>
183     
184     
185     
186     
187    </h4>
188
189   
190   
191
192    <a name="#_quadrilateral2square_keyword_x3in"></a>
193    <h4>x3in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
194      <font size="-1" color="#006633">in</font>
195     
196     
197      <font size="-1" color="#006633">required</font>
198     
199     
200     
201     
202    </h4>
203
204   
205   
206
207    <a name="#_quadrilateral2square_keyword_y3in"></a>
208    <h4>y3in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
209      <font size="-1" color="#006633">in</font>
210     
211     
212      <font size="-1" color="#006633">required</font>
213     
214     
215     
216     
217    </h4>
218
219   
220 the coordinates of the quadrilateral
221 (see above for correspondence with the unit square). Can be
222 scalar or array. (x0,y0), (x1,y1), (x2,y2) and (x3,y3) are
223 given in the anticlockwise order.
224
225   
226
227    <a name="#_quadrilateral2square_keyword_xxin"></a>
228    <h4>xxin&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
229      <font size="-1" color="#006633">in</font>
230     
231     
232      <font size="-1" color="#006633">required</font>
233     
234     
235     
236     
237    </h4>
238
239   
240 the coordinates of the point(s) for which we want to do the mapping.
241 Can be scalar or array.
242
243   
244
245    <a name="#_quadrilateral2square_keyword_yyin"></a>
246    <h4>yyin&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
247      <font size="-1" color="#006633">in</font>
248     
249     
250      <font size="-1" color="#006633">required</font>
251     
252     
253     
254     
255    </h4>
256
257   
258 the coordinates of the point(s) for which we want to do the mapping.
259 Can be scalar or array.
260
261   
262   
263
264   
265    <h3>Keywords</h3>
266
267   
268    <a name="#_quadrilateral2square_keyword_PERF"></a>
269    <h4>PERF&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
270     
271     
272     
273     
274     
275      <font size="-1" color="#006633">type:</font> <font size="-1" color="#006633"><i>salar 0 or 1</i></font>
276      <font size="-1" color="#006633">default:</font> <font size="-1" color="#006633"><i>0</i></font>
277     
278    </h4>
279
280   
281 activate to print the elapsed time spent within quadrilateral2square
282
283   
284    <a name="#_quadrilateral2square_keyword_DOUBLE"></a>
285    <h4>DOUBLE&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
286     
287     
288     
289     
290     
291      <font size="-1" color="#006633">type:</font> <font size="-1" color="#006633"><i>salar 0 or 1</i></font>
292      <font size="-1" color="#006633">default:</font> <font size="-1" color="#006633"><i>0</i></font>
293     
294    </h4>
295
296   
297 activate to perform double precision computation
298
299   
300   
301
302    <h3>Examples</h3><pre>
303
304 IDL> splot,[0,5],[0,3],/nodata,xstyle=1,ystyle=1
305 IDL> tracegrille, findgen(11)*.1, findgen(11)*.1,color=indgen(12)*20
306 IDL> xin = (findgen(11)*.1)#replicate(1, 11)
307 IDL> yin = replicate(1, 11)#(findgen(11)*.1)
308 IDL> out = square2quadrilateral(2,1,3,0,5,1,2,3, xin, yin)
309 IDL> tracegrille, reform(out[0,*],11,11), reform(out[1,*],11,11),color=indgen(12)*20
310
311 IDL> inorg=quadrilateral2square(2,1,3,0,5,1,2,3,out[0,*],out[1,*])
312 IDL> tracegrille, reform(inorg[0,*],11,11), reform(inorg[1,*],11,11),color=indgen(12)*20
313
314    </pre><h3>Version history</h3>
315   
316    <h4>Version</h4>
317 $Id: quadrilateral2square.pro 327 2007-12-13 16:22:35Z pinsard $
318
319    <h4>History</h4>
320      Sebastien Masson (smasson@lodyc.jussieu.fr)
321      August 2003
322      Based on "Digital Image Warping" by G. Wolberg
323      IEEE Computer Society Press, Los Alamitos, California
324      Chapter 3, see p 52-56
325
326
327   
328
329    <h3>Known issues</h3>
330   
331   
332   
333    <h4>Restrictions</h4>
334 I think degenerated quadrilateral (e.g. flat of twisted) is not work.
335 This has to be tested.
336
337
338   
339   
340   
341   
342   
343   
344   
345
346    <font size="-3"><p>&nbsp;</p></font>
347    <hr size="1" color="#CCCCCC"/>
348     
349
350   
351
352    <p><font color="gray" size="-3">&nbsp;&nbsp;Produced by IDLdoc 2.0.</font></p>
353
354  </body>
355</html>
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