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3<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
4  <head>
5    <title>square2quadrilateral.pro (SAXO Documentation Assistant)</title>
6  </head>
7
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9
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50<font size=-1><i>SAXO Documentation Assistant</i>: <a href="./../home.html">Overview</a></font></td>
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55
56
57    <h1><font size="-2">Interpolation/</font></h1>
58    <h2>square2quadrilateral.pro</h2>
59
60    <dl>
61    </dl>
62
63   
64 warm (or map) a unit square onto an arbitrary quadrilateral
65 according to the 4-point correspondences:
66       (0,0) -> (x0,y0)
67       (1,0) -> (x1,y1)
68       (1,1) -> (x2,y2)
69       (0,1) -> (x3,y3)
70 The mapping is done using perspective transformation which preserve
71 lines in all orientations and permit quadrilateral to quadrilateral
72 mappings. see ref. bellow.
73
74
75   
76
77     
78      <a name="#_square2quadrilateral"></a>
79
80      <h2>square2quadrilateral  <font size="-1" color="#006633"> 
81 Picture, Grid
82</font></h2>
83
84      <p><font face="Courier"><i>result = </i>square2quadrilateral(<i><a href="#_square2quadrilateral_keyword_x0in">x0in</a>, <a href="#_square2quadrilateral_keyword_y0in">y0in</a>, <a href="#_square2quadrilateral_keyword_x1in">x1in</a>, <a href="#_square2quadrilateral_keyword_y1in">y1in</a>, <a href="#_square2quadrilateral_keyword_x2in">x2in</a>, <a href="#_square2quadrilateral_keyword_y2in">y2in</a>, <a href="#_square2quadrilateral_keyword_x3in">x3in</a>, <a href="#_square2quadrilateral_keyword_y3in">y3in</a>[, <a href="#_square2quadrilateral_keyword_xxin">xxin</a>][, <a href="#_square2quadrilateral_keyword_yyin">yyin</a>]</i>)</font></p>
85
86   
87
88
89    <h3>Return value</h3>
90 (2,n) array: the new coordinates (xout, yout) of the (xin,yin)
91 point(s) after mapping.
92 If xin is a scalar, then n is equal to the number of elements of
93 x0. If xin is an array , then n is equal to the number of
94 elements of xin.
95 If xin and yin are omited, square2quadrilateral returns the
96 matrix A which is used for the inverse transformation.
97
98
99   
100    <h3>Parameters</h3>
101   
102
103    <a name="#_square2quadrilateral_keyword_x0in"></a>
104    <h4>x0in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
105      <font size="-1" color="#006633">in</font>
106     
107     
108      <font size="-1" color="#006633">required</font>
109     
110     
111     
112     
113    </h4>
114
115   
116   
117
118    <a name="#_square2quadrilateral_keyword_y0in"></a>
119    <h4>y0in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
120      <font size="-1" color="#006633">in</font>
121     
122     
123      <font size="-1" color="#006633">required</font>
124     
125     
126     
127     
128    </h4>
129
130   
131   
132
133    <a name="#_square2quadrilateral_keyword_x1in"></a>
134    <h4>x1in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
135      <font size="-1" color="#006633">in</font>
136     
137     
138      <font size="-1" color="#006633">required</font>
139     
140     
141     
142     
143    </h4>
144
145   
146   
147
148    <a name="#_square2quadrilateral_keyword_y1in"></a>
149    <h4>y1in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
150      <font size="-1" color="#006633">in</font>
151     
152     
153      <font size="-1" color="#006633">required</font>
154     
155     
156     
157     
158    </h4>
159
160   
161   
162
163    <a name="#_square2quadrilateral_keyword_x2in"></a>
164    <h4>x2in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
165      <font size="-1" color="#006633">in</font>
166     
167     
168      <font size="-1" color="#006633">required</font>
169     
170     
171     
172     
173    </h4>
174
175   
176   
177
178    <a name="#_square2quadrilateral_keyword_y2in"></a>
179    <h4>y2in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
180      <font size="-1" color="#006633">in</font>
181     
182     
183      <font size="-1" color="#006633">required</font>
184     
185     
186     
187     
188    </h4>
189
190   
191   
192
193    <a name="#_square2quadrilateral_keyword_x3in"></a>
194    <h4>x3in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
195      <font size="-1" color="#006633">in</font>
196     
197     
198      <font size="-1" color="#006633">required</font>
199     
200     
201     
202     
203    </h4>
204
205   
206   
207
208    <a name="#_square2quadrilateral_keyword_y3in"></a>
209    <h4>y3in&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
210      <font size="-1" color="#006633">in</font>
211     
212     
213      <font size="-1" color="#006633">required</font>
214     
215     
216     
217     
218    </h4>
219
220   
221 the coordinates of the quadrilateral (see above for correspondence with the
222 unit square).
223 Can be scalar or array.
224 (x0,y0), (x1,y1), (x2,y2) and (x3,y3) are given in the anticlockwise order.
225
226
227   
228
229    <a name="#_square2quadrilateral_keyword_xxin"></a>
230    <h4>xxin&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
231      <font size="-1" color="#006633">in</font>
232     
233      <font size="-1" color="#006633">optional</font>
234     
235     
236     
237     
238     
239    </h4>
240
241   
242   
243
244    <a name="#_square2quadrilateral_keyword_yyin"></a>
245    <h4>yyin&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
246      <font size="-1" color="#006633">in</font>
247     
248      <font size="-1" color="#006633">optional</font>
249     
250     
251     
252     
253     
254    </h4>
255
256   
257 the coordinates of the point(s) for which we want to do the mapping.
258
259   
260   
261
262   
263
264    <h3>Examples</h3>
265
266 IDL> splot,[0,5],[0,3],/nodata,xstyle=1,ystyle=1
267 IDL> tracegrille, findgen(11)*.1, findgen(11)*.1,color=indgen(12)*20
268 IDL> xin = (findgen(11)*.1)#replicate(1, 11)
269 IDL> yin = replicate(1, 11)#(findgen(11)*.1)
270 IDL> out = square2quadrilateral(2,1,3,0,5,1,2,3, xin, yin)
271 IDL> tracegrille, reform(out[0,*],11,11), reform(out[1,*],11,11),color=indgen(12)*20
272
273    <h3>Version history</h3>
274   
275    <h4>Version</h4> $Id: square2quadrilateral.pro 157 2006-08-21 09:01:50Z navarro $
276
277    <h4>History</h4>
278      Sebastien Masson (smasson@lodyc.jussieu.fr)
279      August 2003
280      Based on "Digital Image Warping" by G. Wolberg
281      IEEE Computer Society Press, Los Alamitos, California
282      Chapter 3, see p 52-56
283
284
285   
286
287    <h3>Known issues</h3>
288   
289   
290   
291    <h4>Restrictions</h4>
292 I think degenerated quadrilateral (e.g. flat of twisted) is not work.
293 This has to be tested.
294
295
296   
297   
298   
299   
300   
301   
302   
303
304    <font size="-3"><p>&nbsp;</p></font>
305    <hr size="1" color="#CCCCCC"/>
306     
307
308   
309
310    <p><font color="gray" size="-3">&nbsp;&nbsp;Produced by IDLdoc 2.0 on Tue Aug 29 14:49:21 2006.</font></p>
311
312  </body>
313</html>
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