geom.h File Reference

#include "mesh.h"

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Macros
#define	VertEq(u, v)   ((u)->s == (v)->s && (u)->t == (v)->t)
#define	VertLeq(u, v)
#define	EdgeEval(u, v, w)   __gl_edgeEval(u,v,w)
#define	EdgeSign(u, v, w)   __gl_edgeSign(u,v,w)
#define	TransLeq(u, v)
#define	TransEval(u, v, w)   __gl_transEval(u,v,w)
#define	TransSign(u, v, w)   __gl_transSign(u,v,w)
#define	EdgeGoesLeft(e)   VertLeq( (e)->Dst, (e)->Org )
#define	EdgeGoesRight(e)   VertLeq( (e)->Org, (e)->Dst )
#define	ABS(x)   ((x) < 0 ? -(x) : (x))
#define	VertL1dist(u, v)   (ABS(u->s - v->s) + ABS(u->t - v->t))
#define	VertCCW(u, v, w)   __gl_vertCCW(u,v,w)

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

ABS

#define ABS

(

x

)

((x) < 0 ? -(x) : (x))

Definition at line 69 of file geom.h.

EdgeEval

#define EdgeEval	(		u,
			v,
			w
	)		__gl_edgeEval(u,v,w)

Definition at line 54 of file geom.h.

EdgeGoesLeft

#define EdgeGoesLeft

(

e

)

VertLeq( (e)->Dst, (e)->Org )

Definition at line 65 of file geom.h.

EdgeGoesRight

#define EdgeGoesRight

(

e

)

VertLeq( (e)->Org, (e)->Dst )

Definition at line 66 of file geom.h.

EdgeSign

#define EdgeSign	(		u,
			v,
			w
	)		__gl_edgeSign(u,v,w)

Definition at line 55 of file geom.h.

TransEval

#define TransEval	(		u,
			v,
			w
	)		__gl_transEval(u,v,w)

Definition at line 61 of file geom.h.

TransLeq

#define TransLeq	(		u,
			v
	)

Value:

(((u)->t < (v)->t) || \
                         ((u)->t == (v)->t && (u)->s <= (v)->s))

Definition at line 59 of file geom.h.

TransSign

#define TransSign	(		u,
			v,
			w
	)		__gl_transSign(u,v,w)

Definition at line 62 of file geom.h.

VertCCW

#define VertCCW	(		u,
			v,
			w
	)		__gl_vertCCW(u,v,w)

Definition at line 72 of file geom.h.

VertEq

#define VertEq	(		u,
			v
	)		((u)->s == (v)->s && (u)->t == (v)->t)

Definition at line 49 of file geom.h.

VertL1dist

#define VertL1dist	(		u,
			v
	)		(ABS(u->s - v->s) + ABS(u->t - v->t))

Definition at line 70 of file geom.h.

VertLeq

#define VertLeq	(		u,
			v
	)

Value:

(((u)->s < (v)->s) || \
                         ((u)->s == (v)->s && (u)->t <= (v)->t))

Definition at line 50 of file geom.h.

Function Documentation

__gl_edgeEval()

GLdouble __gl_edgeEval	(	GLUvertex *	u,
		GLUvertex *	v,
		GLUvertex *	w
	)

Definition at line 47 of file geom.c.

{
  /* 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;
}

__gl_edgeIntersect()

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

Definition at line 203 of file geom.c.

{
  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 );
  }
}

Referenced by CheckForIntersect().

__gl_edgeSign()

GLdouble __gl_edgeSign	(	GLUvertex *	u,
		GLUvertex *	v,
		GLUvertex *	w
	)

Definition at line 77 of file geom.c.

{
  /* 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;
}

__gl_transEval()

GLdouble __gl_transEval	(	GLUvertex *	u,
		GLUvertex *	v,
		GLUvertex *	w
	)

Definition at line 102 of file geom.c.

{
  /* 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;
}

__gl_transSign()

GLdouble __gl_transSign	(	GLUvertex *	u,
		GLUvertex *	v,
		GLUvertex *	w
	)

Definition at line 132 of file geom.c.

{
  /* 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;
}

__gl_vertCCW()

int __gl_vertCCW	(	GLUvertex *	u,
		GLUvertex *	v,
		GLUvertex *	w
	)

Definition at line 153 of file geom.c.

{
  /* 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;
}

__gl_vertLeq()

int __gl_vertLeq	(	GLUvertex *	u,
		GLUvertex *	v
	)

Definition at line 40 of file geom.c.

{
  /* Returns TRUE if u is lexicographically <= v. */

  return VertLeq( u, v );
}

Referenced by InitPriorityQ().