| Geant4 Cross Reference |
1 // see license file for original license.
2
3 #ifndef tools_glutess_geom
4 #define tools_glutess_geom
5
6 #include "mesh"
7
8 #define VertEq(u,v) ((u)->s == (v)->s && (u)->t == (v)->t)
9 #define VertLeq(u,v) (((u)->s < (v)->s) || ((u)->s == (v)->s && (u)->t <= (v)->t))
10
11 #define EdgeEval(u,v,w) __gl_edgeEval(u,v,w)
12 #define EdgeSign(u,v,w) __gl_edgeSign(u,v,w)
13
14 /* Versions of VertLeq, EdgeSign, EdgeEval with s and t transposed. */
15
16 #define TransLeq(u,v) (((u)->t < (v)->t) || \
17 ((u)->t == (v)->t && (u)->s <= (v)->s))
18 #define TransEval(u,v,w) __gl_transEval(u,v,w)
19 #define TransSign(u,v,w) __gl_transSign(u,v,w)
20
21
22 #define EdgeGoesLeft(e) VertLeq( (e)->Dst, (e)->Org )
23 #define EdgeGoesRight(e) VertLeq( (e)->Org, (e)->Dst )
24
25 #define VertL1dist(u,v) (GLU_ABS(u->s - v->s) + GLU_ABS(u->t - v->t))
26
27 #define VertCCW(u,v,w) __gl_vertCCW(u,v,w)
28
29 ////////////////////////////////////////////////////////
30 /// inlined C code : ///////////////////////////////////
31 ////////////////////////////////////////////////////////
32
33 inline int __gl_vertLeq( GLUvertex *u, GLUvertex *v )
34 {
35 /* Returns TOOLS_GLU_TRUE if u is lexicographically <= v. */
36
37 return VertLeq( u, v );
38 }
39
40 inline GLUdouble __gl_edgeEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
41 {
42 /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
43 * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
44 * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
45 * If uw is vertical (and thus passes thru v), the result is zero.
46 *
47 * The calculation is extremely accurate and stable, even when v
48 * is very close to u or w. In particular if we set v->t = 0 and
49 * let r be the negated result (this evaluates (uw)(v->s)), then
50 * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
51 */
52 GLUdouble gapL, gapR;
53
54 assert( VertLeq( u, v ) && VertLeq( v, w ));
55
56 gapL = v->s - u->s;
57 gapR = w->s - v->s;
58
59 if( gapL + gapR > 0 ) {
60 if( gapL < gapR ) {
61 return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
62 } else {
63 return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
64 }
65 }
66 /* vertical line */
67 return 0;
68 }
69
70 inline GLUdouble __gl_edgeSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
71 {
72 /* Returns a number whose sign matches EdgeEval(u,v,w) but which
73 * is cheaper to evaluate. Returns > 0, == 0 , or < 0
74 * as v is above, on, or below the edge uw.
75 */
76 GLUdouble gapL, gapR;
77
78 /*
79 #define VertLeq(u,v) (((u)->s < (v)->s) || \
80 ((u)->s == (v)->s && (u)->t <= (v)->t))
81 */
82 assert( VertLeq( u, v ) && VertLeq( v, w ));
83
84 gapL = v->s - u->s;
85 gapR = w->s - v->s;
86
87 if( gapL + gapR > 0 ) {
88 return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
89 }
90 /* vertical line */
91 return 0;
92 }
93
94
95 /***********************************************************************
96 * Define versions of EdgeSign, EdgeEval with s and t transposed.
97 */
98
99 inline GLUdouble __gl_transEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
100 {
101 /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
102 * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
103 * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v.
104 * If uw is vertical (and thus passes thru v), the result is zero.
105 *
106 * The calculation is extremely accurate and stable, even when v
107 * is very close to u or w. In particular if we set v->s = 0 and
108 * let r be the negated result (this evaluates (uw)(v->t)), then
109 * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
110 */
111 GLUdouble gapL, gapR;
112
113 assert( TransLeq( u, v ) && TransLeq( v, w ));
114
115 gapL = v->t - u->t;
116 gapR = w->t - v->t;
117
118 if( gapL + gapR > 0 ) {
119 if( gapL < gapR ) {
120 return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
121 } else {
122 return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
123 }
124 }
125 /* vertical line */
126 return 0;
127 }
128
129 inline GLUdouble __gl_transSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
130 {
131 /* Returns a number whose sign matches TransEval(u,v,w) but which
132 * is cheaper to evaluate. Returns > 0, == 0 , or < 0
133 * as v is above, on, or below the edge uw.
134 */
135 GLUdouble gapL, gapR;
136
137 assert( TransLeq( u, v ) && TransLeq( v, w ));
138
139 gapL = v->t - u->t;
140 gapR = w->t - v->t;
141
142 if( gapL + gapR > 0 ) {
143 return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
144 }
145 /* vertical line */
146 return 0;
147 }
148
149
150 inline int __gl_vertCCW( GLUvertex *u, GLUvertex *v, GLUvertex *w )
151 {
152 /* For almost-degenerate situations, the results are not reliable.
153 * Unless the floating-point arithmetic can be performed without
154 * rounding errors, *any* implementation will give incorrect results
155 * on some degenerate inputs, so the client must have some way to
156 * handle this situation.
157 */
158 return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0;
159 }
160
161 /* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
162 * or (x+y)/2 if a==b==0. It requires that a,b >= 0, and enforces
163 * this in the rare case that one argument is slightly negative.
164 * The implementation is extremely stable numerically.
165 * In particular it guarantees that the result r satisfies
166 * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
167 * even when a and b differ greatly in magnitude.
168 */
169 #define Interpolate(a,x,b,y) \
170 (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b, \
171 ((a <= b) ? ((b == 0) ? ((x+y) / 2) \
172 : (x + (y-x) * (a/(a+b)))) \
173 : (y + (x-y) * (b/(a+b)))))
174
175 //#define Swap(a,b) if (1) { GLUvertex *t = a; a = b; b = t; } else
176 #define Swap(a,b) do { GLUvertex *t = a; a = b; b = t; } while(false)
177
178 inline void __gl_edgeIntersect( GLUvertex *o1, GLUvertex *d1,
179 GLUvertex *o2, GLUvertex *d2,
180 GLUvertex *v )
181 /* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
182 * The computed point is guaranteed to lie in the intersection of the
183 * bounding rectangles defined by each edge.
184 */
185 {
186 GLUdouble z1, z2;
187
188 /* This is certainly not the most efficient way to find the intersection
189 * of two line segments, but it is very numerically stable.
190 *
191 * Strategy: find the two middle vertices in the VertLeq ordering,
192 * and interpolate the intersection s-value from these. Then repeat
193 * using the TransLeq ordering to find the intersection t-value.
194 */
195
196 if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); }
197 if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); }
198 if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
199
200 if( ! VertLeq( o2, d1 )) {
201 /* Technically, no intersection -- do our best */
202 v->s = (o2->s + d1->s) / 2;
203 } else if( VertLeq( d1, d2 )) {
204 /* Interpolate between o2 and d1 */
205 z1 = EdgeEval( o1, o2, d1 );
206 z2 = EdgeEval( o2, d1, d2 );
207 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
208 v->s = Interpolate( z1, o2->s, z2, d1->s );
209 } else {
210 /* Interpolate between o2 and d2 */
211 z1 = EdgeSign( o1, o2, d1 );
212 z2 = -EdgeSign( o1, d2, d1 );
213 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
214 v->s = Interpolate( z1, o2->s, z2, d2->s );
215 }
216
217 /* Now repeat the process for t */
218
219 if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); }
220 if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); }
221 if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
222
223 if( ! TransLeq( o2, d1 )) {
224 /* Technically, no intersection -- do our best */
225 v->t = (o2->t + d1->t) / 2;
226 } else if( TransLeq( d1, d2 )) {
227 /* Interpolate between o2 and d1 */
228 z1 = TransEval( o1, o2, d1 );
229 z2 = TransEval( o2, d1, d2 );
230 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
231 v->t = Interpolate( z1, o2->t, z2, d1->t );
232 } else {
233 /* Interpolate between o2 and d2 */
234 z1 = TransSign( o1, o2, d1 );
235 z2 = -TransSign( o1, d2, d1 );
236 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
237 v->t = Interpolate( z1, o2->t, z2, d2->t );
238 }
239 }
240
241 #endif