dlls/glu32/geom.c - wine - Git at Google

 /*
  * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
  * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
  *
  * Permission is hereby granted, free of charge, to any person obtaining a
  * copy of this software and associated documentation files (the "Software"),
  * to deal in the Software without restriction, including without limitation
  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
  * and/or sell copies of the Software, and to permit persons to whom the
  * Software is furnished to do so, subject to the following conditions:
  *
  * The above copyright notice including the dates of first publication and
  * either this permission notice or a reference to
  * http://oss.sgi.com/projects/FreeB/
  * shall be included in all copies or substantial portions of the Software.
  *
  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
  * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
  * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
  * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  * SOFTWARE.
  *
  * Except as contained in this notice, the name of Silicon Graphics, Inc.
  * shall not be used in advertising or otherwise to promote the sale, use or
  * other dealings in this Software without prior written authorization from
  * Silicon Graphics, Inc.
  */
 /*
 ** Author: Eric Veach, July 1994.
 **
 */

 #include <stdarg.h>
 #include <assert.h>

 #include "windef.h"
 #include "winbase.h"

 #include "tess.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 Interpolate(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)))))

 #define Swap(a,b)	do { GLUvertex *t = a; a = b; b = t; } while (0)

 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 );
   }
 }
	/*
	* SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
	* Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
	*
	* Permission is hereby granted, free of charge, to any person obtaining a
	* copy of this software and associated documentation files (the "Software"),
	* to deal in the Software without restriction, including without limitation
	* the rights to use, copy, modify, merge, publish, distribute, sublicense,
	* and/or sell copies of the Software, and to permit persons to whom the
	* Software is furnished to do so, subject to the following conditions:
	*
	* The above copyright notice including the dates of first publication and
	* either this permission notice or a reference to
	* http://oss.sgi.com/projects/FreeB/
	* shall be included in all copies or substantial portions of the Software.
	*
	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
	* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
	* SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
	* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
	* OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
	* SOFTWARE.
	*
	* Except as contained in this notice, the name of Silicon Graphics, Inc.
	* shall not be used in advertising or otherwise to promote the sale, use or
	* other dealings in this Software without prior written authorization from
	* Silicon Graphics, Inc.
	*/
	/*
	** Author: Eric Veach, July 1994.
	**
	*/

	#include <stdarg.h>
	#include <assert.h>

	#include "windef.h"
	#include "winbase.h"

	#include "tess.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 (bx+ay)/(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 Interpolate(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)))))

	#define Swap(a,b) do { GLUvertex *t = a; a = b; b = t; } while (0)

	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 );
	}
	}