/* ** License Applicability. Except to the extent portions of this file are ** made subject to an alternative license as permitted in the SGI Free ** Software License B, Version 1.1 (the "License"), the contents of this ** file are subject only to the provisions of the License. You may not use ** this file except in compliance with the License. You may obtain a copy ** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600 ** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at: ** ** http://oss.sgi.com/projects/FreeB ** ** Note that, as provided in the License, the Software is distributed on an ** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS ** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND ** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A ** PARTICULAR PURPOSE, AND NON-INFRINGEMENT. ** ** Original Code. The Original Code is: OpenGL Sample Implementation, ** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics, ** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc. ** Copyright in any portions created by third parties is as indicated ** elsewhere herein. All Rights Reserved. ** ** Additional Notice Provisions: The application programming interfaces ** established by SGI in conjunction with the Original Code are The ** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released ** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version ** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X ** Window System(R) (Version 1.3), released October 19, 1998. This software ** was created using the OpenGL(R) version 1.2.1 Sample Implementation ** published by SGI, but has not been independently verified as being ** compliant with the OpenGL(R) version 1.2.1 Specification. ** */ /* ** Author: Eric Veach, July 1994. ** ** $Date: 2001/03/17 00:25:41 $ $Revision: 1.1 $ ** $Header: /cvs/mesa/Mesa/src/glu/sgi/libtess/geom.c,v 1.1 2001/03/17 00:25:41 brianp Exp $ */ #include "gluos.h" #include <assert.h> #include "mesh.h" #include "geom.h" int __gl_vertLeq( GLUvertex *u, GLUvertex *v ) { /* Returns TRUE if u is lexicographically <= v. */ return VertLeq( u, v ); } GLdouble __gl_edgeEval( GLUvertex *u, GLUvertex *v, GLUvertex *w ) { /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w), * evaluates the t-coord of the edge uw at the s-coord of the vertex v. * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v. * If uw is vertical (and thus passes thru v), the result is zero. * * The calculation is extremely accurate and stable, even when v * is very close to u or w. In particular if we set v->t = 0 and * let r be the negated result (this evaluates (uw)(v->s)), then * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t). */ GLdouble gapL, gapR; assert( VertLeq( u, v ) && VertLeq( v, w )); gapL = v->s - u->s; gapR = w->s - v->s; if( gapL + gapR > 0 ) { if( gapL < gapR ) { return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR)); } else { return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR)); } } /* vertical line */ return 0; } GLdouble __gl_edgeSign( GLUvertex *u, GLUvertex *v, GLUvertex *w ) { /* Returns a number whose sign matches EdgeEval(u,v,w) but which * is cheaper to evaluate. Returns > 0, == 0 , or < 0 * as v is above, on, or below the edge uw. */ GLdouble gapL, gapR; assert( VertLeq( u, v ) && VertLeq( v, w )); gapL = v->s - u->s; gapR = w->s - v->s; if( gapL + gapR > 0 ) { return (v->t - w->t) * gapL + (v->t - u->t) * gapR; } /* vertical line */ return 0; } /*********************************************************************** * Define versions of EdgeSign, EdgeEval with s and t transposed. */ GLdouble __gl_transEval( GLUvertex *u, GLUvertex *v, GLUvertex *w ) { /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w), * evaluates the t-coord of the edge uw at the s-coord of the vertex v. * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v. * If uw is vertical (and thus passes thru v), the result is zero. * * The calculation is extremely accurate and stable, even when v * is very close to u or w. In particular if we set v->s = 0 and * let r be the negated result (this evaluates (uw)(v->t)), then * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s). */ GLdouble gapL, gapR; assert( TransLeq( u, v ) && TransLeq( v, w )); gapL = v->t - u->t; gapR = w->t - v->t; if( gapL + gapR > 0 ) { if( gapL < gapR ) { return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR)); } else { return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR)); } } /* vertical line */ return 0; } GLdouble __gl_transSign( GLUvertex *u, GLUvertex *v, GLUvertex *w ) { /* Returns a number whose sign matches TransEval(u,v,w) but which * is cheaper to evaluate. Returns > 0, == 0 , or < 0 * as v is above, on, or below the edge uw. */ GLdouble gapL, gapR; assert( TransLeq( u, v ) && TransLeq( v, w )); gapL = v->t - u->t; gapR = w->t - v->t; if( gapL + gapR > 0 ) { return (v->s - w->s) * gapL + (v->s - u->s) * gapR; } /* vertical line */ return 0; } int __gl_vertCCW( GLUvertex *u, GLUvertex *v, GLUvertex *w ) { /* For almost-degenerate situations, the results are not reliable. * Unless the floating-point arithmetic can be performed without * rounding errors, *any* implementation will give incorrect results * on some degenerate inputs, so the client must have some way to * handle this situation. */ return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0; } /* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b), * or (x+y)/2 if a==b==0. It requires that a,b >= 0, and enforces * this in the rare case that one argument is slightly negative. * The implementation is extremely stable numerically. * In particular it guarantees that the result r satisfies * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate * even when a and b differ greatly in magnitude. */ #define RealInterpolate(a,x,b,y) \ (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b, \ ((a <= b) ? ((b == 0) ? ((x+y) / 2) \ : (x + (y-x) * (a/(a+b)))) \ : (y + (x-y) * (b/(a+b))))) #ifndef FOR_TRITE_TEST_PROGRAM #define Interpolate(a,x,b,y) RealInterpolate(a,x,b,y) #else /* Claim: the ONLY property the sweep algorithm relies on is that * MIN(x,y) <= r <= MAX(x,y). This is a nasty way to test that. */ #include <stdlib.h> extern int RandomInterpolate; GLdouble Interpolate( GLdouble a, GLdouble x, GLdouble b, GLdouble y) { printf("*********************%d\n",RandomInterpolate); if( RandomInterpolate ) { a = 1.2 * drand48() - 0.1; a = (a < 0) ? 0 : ((a > 1) ? 1 : a); b = 1.0 - a; } return RealInterpolate(a,x,b,y); } #endif #define Swap(a,b) if (1) { GLUvertex *t = a; a = b; b = t; } else void __gl_edgeIntersect( GLUvertex *o1, GLUvertex *d1, GLUvertex *o2, GLUvertex *d2, GLUvertex *v ) /* Given edges (o1,d1) and (o2,d2), compute their point of intersection. * The computed point is guaranteed to lie in the intersection of the * bounding rectangles defined by each edge. */ { GLdouble z1, z2; /* This is certainly not the most efficient way to find the intersection * of two line segments, but it is very numerically stable. * * Strategy: find the two middle vertices in the VertLeq ordering, * and interpolate the intersection s-value from these. Then repeat * using the TransLeq ordering to find the intersection t-value. */ if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); } if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); } if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); } if( ! VertLeq( o2, d1 )) { /* Technically, no intersection -- do our best */ v->s = (o2->s + d1->s) / 2; } else if( VertLeq( d1, d2 )) { /* Interpolate between o2 and d1 */ z1 = EdgeEval( o1, o2, d1 ); z2 = EdgeEval( o2, d1, d2 ); if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; } v->s = Interpolate( z1, o2->s, z2, d1->s ); } else { /* Interpolate between o2 and d2 */ z1 = EdgeSign( o1, o2, d1 ); z2 = -EdgeSign( o1, d2, d1 ); if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; } v->s = Interpolate( z1, o2->s, z2, d2->s ); } /* Now repeat the process for t */ if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); } if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); } if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); } if( ! TransLeq( o2, d1 )) { /* Technically, no intersection -- do our best */ v->t = (o2->t + d1->t) / 2; } else if( TransLeq( d1, d2 )) { /* Interpolate between o2 and d1 */ z1 = TransEval( o1, o2, d1 ); z2 = TransEval( o2, d1, d2 ); if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; } v->t = Interpolate( z1, o2->t, z2, d1->t ); } else { /* Interpolate between o2 and d2 */ z1 = TransSign( o1, o2, d1 ); z2 = -TransSign( o1, d2, d1 ); if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; } v->t = Interpolate( z1, o2->t, z2, d2->t ); } }