kstars/libtess/geom.c

/*
** Author: Eric Veach, July 1994.
**
*/

#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)        \
    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);
    }
}