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272 lines
9.0 KiB
C
272 lines
9.0 KiB
C
/*
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** License Applicability. Except to the extent portions of this file are
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** made subject to an alternative license as permitted in the SGI Free
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** Software License B, Version 1.1 (the "License"), the contents of this
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** file are subject only to the provisions of the License. You may not use
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** this file except in compliance with the License. You may obtain a copy
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** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
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** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
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**
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** http://oss.sgi.com/projects/FreeB
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**
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** Note that, as provided in the License, the Software is distributed on an
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** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
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** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
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** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
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** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
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**
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** Original Code. The Original Code is: OpenGL Sample Implementation,
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** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
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** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
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** Copyright in any portions created by third parties is as indicated
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** elsewhere herein. All Rights Reserved.
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**
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** Additional Notice Provisions: The application programming interfaces
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** established by SGI in conjunction with the Original Code are The
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** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
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** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
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** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
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** Window System(R) (Version 1.3), released October 19, 1998. This software
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** was created using the OpenGL(R) version 1.2.1 Sample Implementation
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** published by SGI, but has not been independently verified as being
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** compliant with the OpenGL(R) version 1.2.1 Specification.
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**
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*/
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/*
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** Author: Eric Veach, July 1994.
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**
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** $Date$ $Revision$
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** $Header: //depot/main/gfx/lib/glu/libtess/geom.c#5 $
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*/
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#include "gluos.h"
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#include <assert.h>
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#include "mesh.h"
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#include "geom.h"
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int __gl_vertLeq( GLUvertex *u, GLUvertex *v )
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{
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/* Returns TRUE if u is lexicographically <= v. */
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return VertLeq( u, v );
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}
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GLdouble __gl_edgeEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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{
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/* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
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* evaluates the t-coord of the edge uw at the s-coord of the vertex v.
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* Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
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* If uw is vertical (and thus passes thru v), the result is zero.
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*
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* The calculation is extremely accurate and stable, even when v
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* is very close to u or w. In particular if we set v->t = 0 and
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* let r be the negated result (this evaluates (uw)(v->s)), then
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* r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
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*/
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GLdouble gapL, gapR;
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assert( VertLeq( u, v ) && VertLeq( v, w ));
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gapL = v->s - u->s;
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gapR = w->s - v->s;
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if( gapL + gapR > 0 ) {
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if( gapL < gapR ) {
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return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
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} else {
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return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
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}
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}
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/* vertical line */
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return 0;
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}
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GLdouble __gl_edgeSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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{
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/* Returns a number whose sign matches EdgeEval(u,v,w) but which
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* is cheaper to evaluate. Returns > 0, == 0 , or < 0
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* as v is above, on, or below the edge uw.
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*/
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GLdouble gapL, gapR;
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assert( VertLeq( u, v ) && VertLeq( v, w ));
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gapL = v->s - u->s;
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gapR = w->s - v->s;
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if( gapL + gapR > 0 ) {
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return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
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}
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/* vertical line */
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return 0;
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}
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/***********************************************************************
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* Define versions of EdgeSign, EdgeEval with s and t transposed.
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*/
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GLdouble __gl_transEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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{
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/* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
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* evaluates the t-coord of the edge uw at the s-coord of the vertex v.
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* Returns v->s - (uw)(v->t), ie. the signed distance from uw to v.
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* If uw is vertical (and thus passes thru v), the result is zero.
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*
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* The calculation is extremely accurate and stable, even when v
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* is very close to u or w. In particular if we set v->s = 0 and
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* let r be the negated result (this evaluates (uw)(v->t)), then
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* r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
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*/
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GLdouble gapL, gapR;
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assert( TransLeq( u, v ) && TransLeq( v, w ));
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gapL = v->t - u->t;
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gapR = w->t - v->t;
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if( gapL + gapR > 0 ) {
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if( gapL < gapR ) {
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return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
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} else {
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return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
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}
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}
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/* vertical line */
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return 0;
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}
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GLdouble __gl_transSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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{
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/* Returns a number whose sign matches TransEval(u,v,w) but which
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* is cheaper to evaluate. Returns > 0, == 0 , or < 0
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* as v is above, on, or below the edge uw.
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*/
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GLdouble gapL, gapR;
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assert( TransLeq( u, v ) && TransLeq( v, w ));
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gapL = v->t - u->t;
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gapR = w->t - v->t;
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if( gapL + gapR > 0 ) {
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return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
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}
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/* vertical line */
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return 0;
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}
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int __gl_vertCCW( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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{
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/* For almost-degenerate situations, the results are not reliable.
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* Unless the floating-point arithmetic can be performed without
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* rounding errors, *any* implementation will give incorrect results
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* on some degenerate inputs, so the client must have some way to
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* handle this situation.
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*/
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return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0;
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}
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/* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
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* or (x+y)/2 if a==b==0. It requires that a,b >= 0, and enforces
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* this in the rare case that one argument is slightly negative.
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* The implementation is extremely stable numerically.
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* In particular it guarantees that the result r satisfies
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* MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
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* even when a and b differ greatly in magnitude.
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*/
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#define RealInterpolate(a,x,b,y) \
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(a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b, \
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((a <= b) ? ((b == 0) ? ((x+y) / 2) \
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: (x + (y-x) * (a/(a+b)))) \
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: (y + (x-y) * (b/(a+b)))))
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#ifndef FOR_TRITE_TEST_PROGRAM
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#define Interpolate(a,x,b,y) RealInterpolate(a,x,b,y)
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#else
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/* Claim: the ONLY property the sweep algorithm relies on is that
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* MIN(x,y) <= r <= MAX(x,y). This is a nasty way to test that.
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*/
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#include <stdlib.h>
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extern int RandomInterpolate;
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GLdouble Interpolate( GLdouble a, GLdouble x, GLdouble b, GLdouble y)
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{
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printf("*********************%d\n",RandomInterpolate);
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if( RandomInterpolate ) {
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a = 1.2 * drand48() - 0.1;
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a = (a < 0) ? 0 : ((a > 1) ? 1 : a);
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b = 1.0 - a;
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}
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return RealInterpolate(a,x,b,y);
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}
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#endif
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#define Swap(a,b) do { GLUvertex *t = a; a = b; b = t; } while(0)
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void __gl_edgeIntersect( GLUvertex *o1, GLUvertex *d1,
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GLUvertex *o2, GLUvertex *d2,
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GLUvertex *v )
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/* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
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* The computed point is guaranteed to lie in the intersection of the
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* bounding rectangles defined by each edge.
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*/
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{
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GLdouble z1, z2;
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/* This is certainly not the most efficient way to find the intersection
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* of two line segments, but it is very numerically stable.
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*
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* Strategy: find the two middle vertices in the VertLeq ordering,
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* and interpolate the intersection s-value from these. Then repeat
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* using the TransLeq ordering to find the intersection t-value.
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*/
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if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); }
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if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); }
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if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
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if( ! VertLeq( o2, d1 )) {
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/* Technically, no intersection -- do our best */
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v->s = (o2->s + d1->s) / 2;
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} else if( VertLeq( d1, d2 )) {
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/* Interpolate between o2 and d1 */
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z1 = EdgeEval( o1, o2, d1 );
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z2 = EdgeEval( o2, d1, d2 );
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if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
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v->s = Interpolate( z1, o2->s, z2, d1->s );
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} else {
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/* Interpolate between o2 and d2 */
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z1 = EdgeSign( o1, o2, d1 );
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z2 = -EdgeSign( o1, d2, d1 );
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if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
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v->s = Interpolate( z1, o2->s, z2, d2->s );
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}
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/* Now repeat the process for t */
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if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); }
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if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); }
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if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
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if( ! TransLeq( o2, d1 )) {
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/* Technically, no intersection -- do our best */
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v->t = (o2->t + d1->t) / 2;
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} else if( TransLeq( d1, d2 )) {
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/* Interpolate between o2 and d1 */
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z1 = TransEval( o1, o2, d1 );
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z2 = TransEval( o2, d1, d2 );
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if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
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v->t = Interpolate( z1, o2->t, z2, d1->t );
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} else {
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/* Interpolate between o2 and d2 */
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z1 = TransSign( o1, o2, d1 );
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z2 = -TransSign( o1, d2, d1 );
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if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
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v->t = Interpolate( z1, o2->t, z2, d2->t );
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}
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}
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