Gabriele Cosmo
242 lines
7.7 KiB
Plaintext
242 lines
7.7 KiB
Plaintext
// see license file for original license.
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#ifndef tools_glutess_geom
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#define tools_glutess_geom
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#include "mesh"
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#define VertEq(u,v) ((u)->s == (v)->s && (u)->t == (v)->t)
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#define VertLeq(u,v) (((u)->s < (v)->s) || ((u)->s == (v)->s && (u)->t <= (v)->t))
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#define EdgeEval(u,v,w) __gl_edgeEval(u,v,w)
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#define EdgeSign(u,v,w) __gl_edgeSign(u,v,w)
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/* Versions of VertLeq, EdgeSign, EdgeEval with s and t transposed. */
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#define TransLeq(u,v) (((u)->t < (v)->t) || \
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((u)->t == (v)->t && (u)->s <= (v)->s))
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#define TransEval(u,v,w) __gl_transEval(u,v,w)
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#define TransSign(u,v,w) __gl_transSign(u,v,w)
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#define EdgeGoesLeft(e) VertLeq( (e)->Dst, (e)->Org )
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#define EdgeGoesRight(e) VertLeq( (e)->Org, (e)->Dst )
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#define VertL1dist(u,v) (GLU_ABS(u->s - v->s) + GLU_ABS(u->t - v->t))
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#define VertCCW(u,v,w) __gl_vertCCW(u,v,w)
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////////////////////////////////////////////////////////
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/// inlined C code : ///////////////////////////////////
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////////////////////////////////////////////////////////
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inline int __gl_vertLeq( GLUvertex *u, GLUvertex *v )
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{
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/* Returns TOOLS_GLU_TRUE if u is lexicographically <= v. */
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return VertLeq( u, v );
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}
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inline GLUdouble __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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GLUdouble 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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inline GLUdouble __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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GLUdouble gapL, gapR;
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/*
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#define VertLeq(u,v) (((u)->s < (v)->s) || \
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((u)->s == (v)->s && (u)->t <= (v)->t))
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*/
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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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inline GLUdouble __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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GLUdouble 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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inline GLUdouble __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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GLUdouble 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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inline 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 Interpolate(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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//#define Swap(a,b) if (1) { GLUvertex *t = a; a = b; b = t; } else
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#define Swap(a,b) do { GLUvertex *t = a; a = b; b = t; } while(false)
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inline 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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GLUdouble 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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#endif
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