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Nurbs (#473)

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* Limit u,v range between 0 and 1 in Newton. Fixes issue #471
* Change the math for projecting a point onto a plane to work better with non-orthogonal U,V derivatives in several places. Fixes #472.
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phkahler 2020-03-27 15:40:58 -04:00 committed by GitHub
parent 83b0402c84
commit f7b6f6930e
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GPG Key ID: 4AEE18F83AFDEB23
1 changed files with 46 additions and 16 deletions
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62
src/srf/ratpoly.cpp
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@ -439,9 +439,14 @@ void SSurface::ClosestPointTo(Vector p, double *u, double *v, bool mustConverge)
bu = (ctrl[1][0]).Minus(orig),
bv = (ctrl[0][1]).Minus(orig);
if((ctrl[1][1]).Equals(orig.Plus(bu).Plus(bv))) {
Vector n = bu.Cross(bv);
Vector ty = n.Cross(bu).ScaledBy(1.0/bu.MagSquared());
Vector tx = bv.Cross(n).ScaledBy(1.0/bv.MagSquared());
Vector dp = p.Minus(orig);
*u = dp.Dot(bu) / bu.MagSquared();
*v = dp.Dot(bv) / bv.MagSquared();
*u = dp.Dot(bu) / tx.MagSquared();
*v = dp.Dot(bv) / ty.MagSquared();
return;
}
}
@ -501,16 +506,28 @@ bool SSurface::ClosestPointNewton(Vector p, double *u, double *v, bool mustConve
}
}
Vector tu, tv;
Vector tu, tv, tx, ty;
TangentsAt(*u, *v, &tu, &tv);
Vector n = tu.Cross(tv);
// since tu and tv may not be orthogonal, use y in place of v.
// |y| = |v|sin(theta) where theta is the angle between tu and tv.
ty = n.Cross(tu).ScaledBy(1.0/tu.MagSquared());
tx = tv.Cross(n).ScaledBy(1.0/tv.MagSquared());
// Project the point into a plane through p0, with basis tu, tv; a
// second-order thing would converge faster but needs second
// derivatives.
Vector dp = p.Minus(p0);
double du = dp.Dot(tu), dv = dp.Dot(tv);
*u += du / (tu.MagSquared());
*v += dv / (tv.MagSquared());
double du = dp.Dot(tx),
dv = dp.Dot(ty);
*u += du / (tx.MagSquared());
*v += dv / (ty.MagSquared());
if (*u < 0.0) *u = 0.0;
else if (*u > 1.0) *u = 1.0;
if (*v < 0.0) *v = 0.0;
else if (*v > 1.0) *v = 1.0;
}
if(mustConverge) {
@ -540,13 +557,17 @@ bool SSurface::PointIntersectingLine(Vector p0, Vector p1, double *u, double *v)
// Check for convergence
if(pi.Equals(p, RATPOLY_EPS)) return true;
n = tu.Cross(tv);
Vector ty = n.Cross(tu).ScaledBy(1.0/tu.MagSquared());
Vector tx = tv.Cross(n).ScaledBy(1.0/tv.MagSquared());
// Adjust our guess and iterate
Vector dp = pi.Minus(p);
double du = dp.Dot(tu), dv = dp.Dot(tv);
*u += du / (tu.MagSquared());
*v += dv / (tv.MagSquared());
double du = dp.Dot(tx), dv = dp.Dot(ty);
*u += du / tx.MagSquared();
*v += dv / ty.MagSquared();
}
// dbp("didn't converge (surface intersecting line)");
dbp("didn't converge (surface intersecting line)");
return false;
}
@ -582,10 +603,14 @@ Vector SSurface::ClosestPointOnThisAndSurface(SSurface *srf2, Vector p) {
// Adjust our guess and iterate
for(j = 0; j < 2; j++) {
Vector n = tu[j].Cross(tv[j]);
Vector ty = n.Cross(tu[j]).ScaledBy(1.0/tu[j].MagSquared());
Vector tx = tv[j].Cross(n).ScaledBy(1.0/tv[j].MagSquared());
Vector dc = pc.Minus(cp[j]);
double du = dc.Dot(tu[j]), dv = dc.Dot(tv[j]);
puv[j].x += du / ((tu[j]).MagSquared());
puv[j].y += dv / ((tv[j]).MagSquared());
double du = dc.Dot(tx), dv = dc.Dot(ty);
puv[j].x += du / tx.MagSquared();
puv[j].y += dv / ty.MagSquared();
}
}
if(i >= 10) {
@ -637,10 +662,15 @@ void SSurface::PointOnSurfaces(SSurface *s1, SSurface *s2, double *up, double *v
if(parallel) break;
for(j = 0; j < 3; j++) {
Vector n = tu[j].Cross(tv[j]);
Vector ty = n.Cross(tu[j]).ScaledBy(1.0/tu[j].MagSquared());
Vector tx = tv[j].Cross(n).ScaledBy(1.0/tv[j].MagSquared());
Vector dp = pi.Minus(p[j]);
double du = dp.Dot(tu[j]), dv = dp.Dot(tv[j]);
u[j] += du / (tu[j]).MagSquared();
v[j] += dv / (tv[j]).MagSquared();
double du = dp.Dot(tx), dv = dp.Dot(ty);
u[j] += du / tx.MagSquared();
v[j] += dv / ty.MagSquared();
}
}
dbp("didn't converge (three surfaces intersecting)");