public static T EdgeEval(ContourVertex <T> u, ContourVertex <T> v, ContourVertex <T> 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).
*/
T gapL, gapR;
if (!((u.VertLeq(u) && v.VertLeq(v))))
{
throw new Exception();
}
gapL = v.x.Subtract(u.x);
gapR = w.x.Subtract(v.x);
if (gapL.Add(gapR).GreaterThan(0))
{
if (gapL.LessThan(gapR))
{
return(v.y.Subtract(u.y).Add(
u.y.Subtract(w.y).Multiply(
gapL.Divide(gapL.Add(gapR)))));
}
else
{
return(v.y.Subtract(w.y).Add(w.y.Subtract(u.y).Multiply(gapR.Divide(gapL.Add(gapR)))));
}
}
// vertical line
return(M.Zero <T>());
}
static public T EdgeSign(ContourVertex <T> u, ContourVertex <T> v, ContourVertex <T> w)
{
/* Returns a number whose sign matches EdgeEval(u,w) but which
* is cheaper to evaluate. Returns > 0, == 0 , or < 0
* as v is above, on, or below the edge uw.
*/
T gapL, gapR;
if (!u.VertLeq(v) || !v.VertLeq(w))
{
throw new System.Exception();
}
gapL = v.x.Subtract(u.x);
gapR = w.x.Subtract(v.x);
if (gapL.Add(gapR).GreaterThan(0))
{
return(v.y.Subtract(w.y).Multiply(gapL).Add(v.y.Subtract(u.y).Multiply(gapR)));
}
/* vertical line */
return(M.Zero <T>());
}
