geom.c File Reference

#include "gluos.h"
#include <assert.h>
#include "mesh.h"
#include "geom.h"

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Go to the source code of this file.

Macros
#define	RealInterpolate(a, x, b, y)
#define	Interpolate(a, x, b, y)   RealInterpolate(a,x,b,y)
#define	Swap(a, b)   do { GLUvertex *t = a; a = b; b = t; } while (0)

Functions
int	__gl_vertLeq (GLUvertex *u, GLUvertex *v)
GLdouble	__gl_edgeEval (GLUvertex *u, GLUvertex *v, GLUvertex *w)
GLdouble	__gl_edgeSign (GLUvertex *u, GLUvertex *v, GLUvertex *w)
GLdouble	__gl_transEval (GLUvertex *u, GLUvertex *v, GLUvertex *w)
GLdouble	__gl_transSign (GLUvertex *u, GLUvertex *v, GLUvertex *w)
int	__gl_vertCCW (GLUvertex *u, GLUvertex *v, GLUvertex *w)
void	__gl_edgeIntersect (GLUvertex *o1, GLUvertex *d1, GLUvertex *o2, GLUvertex *d2, GLUvertex *v)

Macro Definition Documentation

Interpolate

#define Interpolate	(		a,
			x,
			b,
			y
	)		RealInterpolate(a,x,b,y)

RealInterpolate

#define RealInterpolate	(		a,
			x,
			b,
			y
	)

Value:

  (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)))))

Swap

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

Function Documentation

__gl_edgeEval()

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;
}

References GLUvertex::s, GLUvertex::t, and VertLeq.

__gl_edgeIntersect()

void __gl_edgeIntersect	(	GLUvertex *	o1,
		GLUvertex *	d1,
		GLUvertex *	o2,
		GLUvertex *	d2,
		GLUvertex *	v
	)

{
  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 );
  }
}

References EdgeEval, EdgeSign, Interpolate, GLUvertex::s, Swap, GLUvertex::t, TransEval, TransLeq, TransSign, and VertLeq.

Referenced by CheckForIntersect().

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__gl_edgeSign()

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;
}

References GLUvertex::s, GLUvertex::t, and VertLeq.

__gl_transEval()

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;
}

References GLUvertex::s, GLUvertex::t, and TransLeq.

__gl_transSign()

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;
}

References GLUvertex::s, GLUvertex::t, and TransLeq.

__gl_vertCCW()

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;
}

References GLUvertex::s, and GLUvertex::t.

__gl_vertLeq()

int __gl_vertLeq	(	GLUvertex *	u,
		GLUvertex *	v
	)

{
  /* Returns TRUE if u is lexicographically <= v. */
 
  return VertLeq( u, v );
}

References VertLeq.

Referenced by InitPriorityQ().

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