bool SSurface::PointIntersectingLine(Vector p0, Vector p1, double *u, double *v)
{
int i;
for(i = 0; i < 15; i++) {
Vector pi, p, tu, tv;
p = PointAt(*u, *v);
TangentsAt(*u, *v, &tu, &tv);
Vector n = (tu.Cross(tv)).WithMagnitude(1);
double d = p.Dot(n);
bool parallel;
pi = Vector::AtIntersectionOfPlaneAndLine(n, d, p0, p1, ¶llel);
if(parallel) break;
// Check for convergence
if(pi.Equals(p, RATPOLY_EPS)) return true;
// 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());
}
// dbp("didn't converge (surface intersecting line)");
return false;
}
bool SSurface::ClosestPointNewton(Vector p, double *u, double *v, bool converge)
{
// Initial guess is in u, v; refine by Newton iteration.
Vector p0 = Vector::From(0, 0, 0);
for(int i = 0; i < (converge ? 25 : 5); i++) {
p0 = PointAt(*u, *v);
if(converge) {
if(p0.Equals(p, RATPOLY_EPS)) {
return true;
}
}
Vector tu, tv;
TangentsAt(*u, *v, &tu, &tv);
// 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());
}
if(converge) {
dbp("didn't converge");
dbp("have %.3f %.3f %.3f", CO(p0));
dbp("want %.3f %.3f %.3f", CO(p));
dbp("distance = %g", (p.Minus(p0)).Magnitude());
}
return false;
}
void SSurface::EdgeNormalsWithinSurface(Point2d auv, Point2d buv,
Vector *pt,
Vector *enin, Vector *enout,
Vector *surfn,
uint32_t auxA,
SShell *shell, SShell *sha, SShell *shb)
{
// the midpoint of the edge
Point2d muv = (auv.Plus(buv)).ScaledBy(0.5);
*pt = PointAt(muv);
// If this edge just approximates a curve, then refine our midpoint so
// so that it actually lies on that curve too. Otherwise stuff like
// point-on-face tests will fail, since the point won't actually lie
// on the other face.
hSCurve hc = { auxA };
SCurve *sc = shell->curve.FindById(hc);
if(sc->isExact && sc->exact.deg != 1) {
double t;
sc->exact.ClosestPointTo(*pt, &t, false);
*pt = sc->exact.PointAt(t);
ClosestPointTo(*pt, &muv);
} else if(!sc->isExact) {
SSurface *trimmedA = sc->GetSurfaceA(sha, shb),
*trimmedB = sc->GetSurfaceB(sha, shb);
*pt = trimmedA->ClosestPointOnThisAndSurface(trimmedB, *pt);
ClosestPointTo(*pt, &muv);
}
*surfn = NormalAt(muv.x, muv.y);
// Compute the edge's inner normal in xyz space.
Vector ab = (PointAt(auv)).Minus(PointAt(buv)),
enxyz = (ab.Cross(*surfn)).WithMagnitude(SS.ChordTolMm());
// And based on that, compute the edge's inner normal in uv space. This
// vector is perpendicular to the edge in xyz, but not necessarily in uv.
Vector tu, tv;
TangentsAt(muv.x, muv.y, &tu, &tv);
Point2d enuv;
enuv.x = enxyz.Dot(tu) / tu.MagSquared();
enuv.y = enxyz.Dot(tv) / tv.MagSquared();
// Compute the inner and outer normals of this edge (within the srf),
// in xyz space. These are not necessarily antiparallel, if the
// surface is curved.
Vector pin = PointAt(muv.Minus(enuv)),
pout = PointAt(muv.Plus(enuv));
*enin = pin.Minus(*pt),
*enout = pout.Minus(*pt);
}
Vector SSurface::NormalAt(double u, double v) {
Vector tu, tv;
TangentsAt(u, v, &tu, &tv);
return tu.Cross(tv);
}
