ReactOS 0.4.15-dev-8339-g4028de8
geom.c
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1/*
2 * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
3 * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
4 *
5 * Permission is hereby granted, free of charge, to any person obtaining a
6 * copy of this software and associated documentation files (the "Software"),
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9 * and/or sell copies of the Software, and to permit persons to whom the
10 * Software is furnished to do so, subject to the following conditions:
11 *
12 * The above copyright notice including the dates of first publication and
13 * either this permission notice or a reference to
14 * http://oss.sgi.com/projects/FreeB/
15 * shall be included in all copies or substantial portions of the Software.
16 *
17 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
18 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
19 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
20 * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
21 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
22 * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
23 * SOFTWARE.
24 *
25 * Except as contained in this notice, the name of Silicon Graphics, Inc.
26 * shall not be used in advertising or otherwise to promote the sale, use or
27 * other dealings in this Software without prior written authorization from
28 * Silicon Graphics, Inc.
29 */
30/*
31** Author: Eric Veach, July 1994.
32**
33*/
34
35#include "gluos.h"
36#include <assert.h>
37//#include "mesh.h"
38#include "geom.h"
39
41{
42 /* Returns TRUE if u is lexicographically <= v. */
43
44 return VertLeq( u, v );
45}
46
48{
49 /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
50 * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
51 * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
52 * If uw is vertical (and thus passes thru v), the result is zero.
53 *
54 * The calculation is extremely accurate and stable, even when v
55 * is very close to u or w. In particular if we set v->t = 0 and
56 * let r be the negated result (this evaluates (uw)(v->s)), then
57 * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
58 */
59 GLdouble gapL, gapR;
60
61 assert( VertLeq( u, v ) && VertLeq( v, w ));
62
63 gapL = v->s - u->s;
64 gapR = w->s - v->s;
65
66 if( gapL + gapR > 0 ) {
67 if( gapL < gapR ) {
68 return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
69 } else {
70 return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
71 }
72 }
73 /* vertical line */
74 return 0;
75}
76
78{
79 /* Returns a number whose sign matches EdgeEval(u,v,w) but which
80 * is cheaper to evaluate. Returns > 0, == 0 , or < 0
81 * as v is above, on, or below the edge uw.
82 */
83 GLdouble gapL, gapR;
84
85 assert( VertLeq( u, v ) && VertLeq( v, w ));
86
87 gapL = v->s - u->s;
88 gapR = w->s - v->s;
89
90 if( gapL + gapR > 0 ) {
91 return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
92 }
93 /* vertical line */
94 return 0;
95}
96
97
98/***********************************************************************
99 * Define versions of EdgeSign, EdgeEval with s and t transposed.
100 */
101
103{
104 /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
105 * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
106 * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v.
107 * If uw is vertical (and thus passes thru v), the result is zero.
108 *
109 * The calculation is extremely accurate and stable, even when v
110 * is very close to u or w. In particular if we set v->s = 0 and
111 * let r be the negated result (this evaluates (uw)(v->t)), then
112 * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
113 */
114 GLdouble gapL, gapR;
115
116 assert( TransLeq( u, v ) && TransLeq( v, w ));
117
118 gapL = v->t - u->t;
119 gapR = w->t - v->t;
120
121 if( gapL + gapR > 0 ) {
122 if( gapL < gapR ) {
123 return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
124 } else {
125 return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
126 }
127 }
128 /* vertical line */
129 return 0;
130}
131
133{
134 /* Returns a number whose sign matches TransEval(u,v,w) but which
135 * is cheaper to evaluate. Returns > 0, == 0 , or < 0
136 * as v is above, on, or below the edge uw.
137 */
138 GLdouble gapL, gapR;
139
140 assert( TransLeq( u, v ) && TransLeq( v, w ));
141
142 gapL = v->t - u->t;
143 gapR = w->t - v->t;
144
145 if( gapL + gapR > 0 ) {
146 return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
147 }
148 /* vertical line */
149 return 0;
150}
151
152
154{
155 /* For almost-degenerate situations, the results are not reliable.
156 * Unless the floating-point arithmetic can be performed without
157 * rounding errors, *any* implementation will give incorrect results
158 * on some degenerate inputs, so the client must have some way to
159 * handle this situation.
160 */
161 return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0;
162}
163
164/* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
165 * or (x+y)/2 if a==b==0. It requires that a,b >= 0, and enforces
166 * this in the rare case that one argument is slightly negative.
167 * The implementation is extremely stable numerically.
168 * In particular it guarantees that the result r satisfies
169 * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
170 * even when a and b differ greatly in magnitude.
171 */
172#define RealInterpolate(a,x,b,y) \
173 (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b, \
174 ((a <= b) ? ((b == 0) ? ((x+y) / 2) \
175 : (x + (y-x) * (a/(a+b)))) \
176 : (y + (x-y) * (b/(a+b)))))
177
178#ifndef FOR_TRITE_TEST_PROGRAM
179#define Interpolate(a,x,b,y) RealInterpolate(a,x,b,y)
180#else
181
182/* Claim: the ONLY property the sweep algorithm relies on is that
183 * MIN(x,y) <= r <= MAX(x,y). This is a nasty way to test that.
184 */
185#include <stdlib.h>
186extern int RandomInterpolate;
187
189{
190printf("*********************%d\n",RandomInterpolate);
191 if( RandomInterpolate ) {
192 a = 1.2 * drand48() - 0.1;
193 a = (a < 0) ? 0 : ((a > 1) ? 1 : a);
194 b = 1.0 - a;
195 }
196 return RealInterpolate(a,x,b,y);
197}
198
199#endif
200
201#define Swap(a,b) do { GLUvertex *t = a; a = b; b = t; } while (0)
202
204 GLUvertex *o2, GLUvertex *d2,
205 GLUvertex *v )
206/* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
207 * The computed point is guaranteed to lie in the intersection of the
208 * bounding rectangles defined by each edge.
209 */
210{
211 GLdouble z1, z2;
212
213 /* This is certainly not the most efficient way to find the intersection
214 * of two line segments, but it is very numerically stable.
215 *
216 * Strategy: find the two middle vertices in the VertLeq ordering,
217 * and interpolate the intersection s-value from these. Then repeat
218 * using the TransLeq ordering to find the intersection t-value.
219 */
220
221 if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); }
222 if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); }
223 if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
224
225 if( ! VertLeq( o2, d1 )) {
226 /* Technically, no intersection -- do our best */
227 v->s = (o2->s + d1->s) / 2;
228 } else if( VertLeq( d1, d2 )) {
229 /* Interpolate between o2 and d1 */
230 z1 = EdgeEval( o1, o2, d1 );
231 z2 = EdgeEval( o2, d1, d2 );
232 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
233 v->s = Interpolate( z1, o2->s, z2, d1->s );
234 } else {
235 /* Interpolate between o2 and d2 */
236 z1 = EdgeSign( o1, o2, d1 );
237 z2 = -EdgeSign( o1, d2, d1 );
238 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
239 v->s = Interpolate( z1, o2->s, z2, d2->s );
240 }
241
242 /* Now repeat the process for t */
243
244 if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); }
245 if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); }
246 if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
247
248 if( ! TransLeq( o2, d1 )) {
249 /* Technically, no intersection -- do our best */
250 v->t = (o2->t + d1->t) / 2;
251 } else if( TransLeq( d1, d2 )) {
252 /* Interpolate between o2 and d1 */
253 z1 = TransEval( o1, o2, d1 );
254 z2 = TransEval( o2, d1, d2 );
255 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
256 v->t = Interpolate( z1, o2->t, z2, d1->t );
257 } else {
258 /* Interpolate between o2 and d2 */
259 z1 = TransSign( o1, o2, d1 );
260 z2 = -TransSign( o1, d2, d1 );
261 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
262 v->t = Interpolate( z1, o2->t, z2, d2->t );
263 }
264}
#define assert(x)
Definition: debug.h:53
#define printf
Definition: freeldr.h:97
int __gl_vertCCW(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:153
GLdouble __gl_edgeSign(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:77
GLdouble __gl_transEval(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:102
#define RealInterpolate(a, x, b, y)
Definition: geom.c:172
GLdouble __gl_edgeEval(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:47
void __gl_edgeIntersect(GLUvertex *o1, GLUvertex *d1, GLUvertex *o2, GLUvertex *d2, GLUvertex *v)
Definition: geom.c:203
#define Interpolate(a, x, b, y)
Definition: geom.c:179
int __gl_vertLeq(GLUvertex *u, GLUvertex *v)
Definition: geom.c:40
GLdouble __gl_transSign(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:132
#define Swap(a, b)
Definition: geom.c:201
#define VertLeq(u, v)
Definition: geom.h:50
#define TransEval(u, v, w)
Definition: geom.h:61
#define TransLeq(u, v)
Definition: geom.h:59
#define EdgeSign(u, v, w)
Definition: geom.h:55
#define TransSign(u, v, w)
Definition: geom.h:62
#define EdgeEval(u, v, w)
Definition: geom.h:54
GLint GLint GLint GLint GLint x
Definition: gl.h:1548
const GLdouble * v
Definition: gl.h:2040
double GLdouble
Definition: gl.h:163
GLint GLint GLint GLint GLint GLint y
Definition: gl.h:1548
GLboolean GLboolean GLboolean b
Definition: glext.h:6204
GLboolean GLboolean GLboolean GLboolean a
Definition: glext.h:6204
GLubyte GLubyte GLubyte GLubyte w
Definition: glext.h:6102
GLsizei GLenum const GLvoid GLsizei GLenum GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLint GLint GLint GLshort GLshort GLshort GLubyte GLubyte GLubyte GLuint GLuint GLuint GLushort GLushort GLushort GLbyte GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLfloat GLint GLint GLint GLint GLshort GLshort GLshort GLshort GLubyte GLubyte GLubyte GLubyte GLuint GLuint GLuint GLuint GLushort GLushort GLushort GLushort GLboolean const GLdouble const GLfloat const GLint const GLshort const GLbyte const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLdouble const GLfloat const GLfloat const GLint const GLint const GLshort const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort GLenum GLenum GLenum GLfloat GLenum GLint GLenum GLenum GLenum GLfloat GLenum GLenum GLint GLenum GLfloat GLenum GLint GLint GLushort GLenum GLenum GLfloat GLenum GLenum GLint GLfloat const GLubyte GLenum GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLint GLint GLsizei GLsizei GLint GLenum GLenum const GLvoid GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLenum const GLdouble GLenum GLenum const GLfloat GLenum GLenum const GLint GLsizei GLuint GLfloat GLuint GLbitfield GLfloat GLint GLuint GLboolean GLenum GLfloat GLenum GLbitfield GLenum GLfloat GLfloat GLint GLint const GLfloat GLenum GLfloat GLfloat GLint GLint GLfloat GLfloat GLint GLint const GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat const GLdouble * u
Definition: glfuncs.h:240
#define a
Definition: ke_i.h:78
GLdouble t
Definition: mesh.h:122
GLdouble s
Definition: mesh.h:122