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-/*
-** 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.
-**
-** $Date$ $Revision$
-** $Header$
-*/
-
-#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 );
- }
-}
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