2 * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
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14 * http://oss.sgi.com/projects/FreeB/
15 * shall be included in all copies or substantial portions of the Software.
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18 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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22 * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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28 * Silicon Graphics, Inc.
31 ** Author: Eric Veach, July 1994.
40 int __gl_vertLeq( GLUvertex
*u
, GLUvertex
*v
)
42 /* Returns TRUE if u is lexicographically <= v. */
44 return VertLeq( u
, v
);
47 GLdouble
__gl_edgeEval( GLUvertex
*u
, GLUvertex
*v
, GLUvertex
*w
)
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.
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).
61 assert( VertLeq( u
, v
) && VertLeq( v
, w
));
66 if( gapL
+ gapR
> 0 ) {
68 return (v
->t
- u
->t
) + (u
->t
- w
->t
) * (gapL
/ (gapL
+ gapR
));
70 return (v
->t
- w
->t
) + (w
->t
- u
->t
) * (gapR
/ (gapL
+ gapR
));
77 GLdouble
__gl_edgeSign( GLUvertex
*u
, GLUvertex
*v
, GLUvertex
*w
)
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.
85 assert( VertLeq( u
, v
) && VertLeq( v
, w
));
90 if( gapL
+ gapR
> 0 ) {
91 return (v
->t
- w
->t
) * gapL
+ (v
->t
- u
->t
) * gapR
;
98 /***********************************************************************
99 * Define versions of EdgeSign, EdgeEval with s and t transposed.
102 GLdouble
__gl_transEval( GLUvertex
*u
, GLUvertex
*v
, GLUvertex
*w
)
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.
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).
116 assert( TransLeq( u
, v
) && TransLeq( v
, w
));
121 if( gapL
+ gapR
> 0 ) {
123 return (v
->s
- u
->s
) + (u
->s
- w
->s
) * (gapL
/ (gapL
+ gapR
));
125 return (v
->s
- w
->s
) + (w
->s
- u
->s
) * (gapR
/ (gapL
+ gapR
));
132 GLdouble
__gl_transSign( GLUvertex
*u
, GLUvertex
*v
, GLUvertex
*w
)
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.
140 assert( TransLeq( u
, v
) && TransLeq( v
, w
));
145 if( gapL
+ gapR
> 0 ) {
146 return (v
->s
- w
->s
) * gapL
+ (v
->s
- u
->s
) * gapR
;
153 int __gl_vertCCW( GLUvertex
*u
, GLUvertex
*v
, GLUvertex
*w
)
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.
161 return (u
->s
*(v
->t
- w
->t
) + v
->s
*(w
->t
- u
->t
) + w
->s
*(u
->t
- v
->t
)) >= 0;
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.
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)))))
178 #ifndef FOR_TRITE_TEST_PROGRAM
179 #define Interpolate(a,x,b,y) RealInterpolate(a,x,b,y)
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.
186 extern int RandomInterpolate
;
188 GLdouble
Interpolate( GLdouble a
, GLdouble x
, GLdouble b
, GLdouble y
)
190 printf("*********************%d\n",RandomInterpolate
);
191 if( RandomInterpolate
) {
192 a
= 1.2 * drand48() - 0.1;
193 a
= (a
< 0) ? 0 : ((a
> 1) ? 1 : a
);
196 return RealInterpolate(a
,x
,b
,y
);
201 #define Swap(a,b) do { GLUvertex *t = a; a = b; b = t; } while (0)
203 void __gl_edgeIntersect( GLUvertex
*o1
, GLUvertex
*d1
,
204 GLUvertex
*o2
, GLUvertex
*d2
,
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.
213 /* This is certainly not the most efficient way to find the intersection
214 * of two line segments, but it is very numerically stable.
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.
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
); }
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
);
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
);
242 /* Now repeat the process for t */
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
); }
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
);
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
);