ReactOS  0.4.14-dev-384-g5b37caa
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.
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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>
186 extern int RandomInterpolate;
187 
189 {
190 printf("*********************%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 }
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
double GLdouble
Definition: gl.h:163
GLubyte GLubyte GLubyte GLubyte w
Definition: glext.h:6102
void __gl_edgeIntersect(GLUvertex *o1, GLUvertex *d1, GLUvertex *o2, GLUvertex *d2, GLUvertex *v)
Definition: geom.c:203
GLdouble __gl_edgeEval(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:47
#define TransLeq(u, v)
Definition: geom.h:59
#define TransSign(u, v, w)
Definition: geom.h:62
#define assert(x)
Definition: debug.h:53
GLint GLint GLint GLint GLint x
Definition: gl.h:1548
#define EdgeEval(u, v, w)
Definition: geom.h:54
#define a
Definition: ke_i.h:78
#define Interpolate(a, x, b, y)
Definition: geom.c:179
GLdouble t
Definition: mesh.h:122
GLboolean GLboolean GLboolean b
Definition: glext.h:6204
int __gl_vertCCW(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:153
#define RealInterpolate(a, x, b, y)
Definition: geom.c:172
#define TransEval(u, v, w)
Definition: geom.h:61
#define Swap(a, b)
Definition: geom.c:201
GLdouble s
Definition: mesh.h:122
#define EdgeSign(u, v, w)
Definition: geom.h:55
GLdouble __gl_transEval(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:102
const GLdouble * v
Definition: gl.h:2040
int __gl_vertLeq(GLUvertex *u, GLUvertex *v)
Definition: geom.c:40
#define VertLeq(u, v)
Definition: geom.h:50
GLint GLint GLint GLint GLint GLint y
Definition: gl.h:1548
GLboolean GLboolean GLboolean GLboolean a
Definition: glext.h:6204
GLdouble __gl_edgeSign(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:77
GLdouble __gl_transSign(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:132
#define printf
Definition: config.h:203