static double TransSign(ContourVertex u, ContourVertex v, ContourVertex 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.
*/
double gapL, gapR;
if (!u.TransLeq(v) || !v.TransLeq(w))
{
throw new Exception();
}
gapL = v.y - u.y;
gapR = w.y - v.y;
if (gapL + gapR > 0)
{
return (v.x - w.x) * gapL + (v.x - u.x) * gapR;
}
/* vertical line */
return 0;
}
static void EdgeIntersect(ContourVertex o1, ContourVertex d1,
ContourVertex o2, ContourVertex d2,
ref ContourVertex 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.
*/
{
double 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 (!o1.VertLeq(d1)) { Swap(ref o1, ref d1); }
if (!o2.VertLeq(d2)) { Swap(ref o2, ref d2); }
if (!o1.VertLeq(o2)) { Swap(ref o1, ref o2); Swap(ref d1, ref d2); }
if (!o2.VertLeq(d1))
{
/* Technically, no intersection -- do our best */
v.x = (o2.x + d1.x) / 2;
}
else if (d1.VertLeq(d2))
{
/* Interpolate between o2 and d1 */
z1 = ContourVertex.EdgeEval(o1, o2, d1);
z2 = ContourVertex.EdgeEval(o2, d1, d2);
if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; }
v.x = Interpolate(z1, o2.x, z2, d1.x);
}
else
{
/* Interpolate between o2 and d2 */
z1 = ContourVertex.EdgeSign(o1, o2, d1);
z2 = -ContourVertex.EdgeSign(o1, d2, d1);
if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; }
v.x = Interpolate(z1, o2.x, z2, d2.x);
}
/* Now repeat the process for t */
if (!o1.TransLeq(d1)) { Swap(ref o1, ref d1); }
if (!o2.TransLeq(d2)) { Swap(ref o2, ref d2); }
if (!o1.TransLeq(o2)) { Swap(ref o1, ref o2); Swap(ref d1, ref d2); }
if (!o2.TransLeq(d1))
{
/* Technically, no intersection -- do our best */
v.y = (o2.y + d1.y) / 2;
}
else if (d1.TransLeq(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.y = Interpolate(z1, o2.y, z2, d1.y);
}
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.y = Interpolate(z1, o2.y, z2, d2.y);
}
}
static double TransEval(ContourVertex u, ContourVertex v, ContourVertex 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).
*/
double gapL, gapR;
if (!u.TransLeq(v) || !v.TransLeq(w))
{
throw new Exception();
}
gapL = v.y - u.y;
gapR = w.y - v.y;
if (gapL + gapR > 0)
{
if (gapL < gapR)
{
return (v.x - u.x) + (u.x - w.x) * (gapL / (gapL + gapR));
}
else
{
return (v.x - w.x) + (w.x - u.x) * (gapR / (gapL + gapR));
}
}
/* vertical line */
return 0;
}