SCurve SCurve::MakeCopySplitAgainst(SShell *agnstA, SShell *agnstB,
SSurface *srfA, SSurface *srfB)
{
SCurve ret;
ret = *this;
ret.pts = {};
SCurvePt *p = pts.First();
if(!p) oops();
SCurvePt prev = *p;
ret.pts.Add(p);
p = pts.NextAfter(p);
for(; p; p = pts.NextAfter(p)) {
List<SInter> il = {};
// Find all the intersections with the two passed shells
if(agnstA)
agnstA->AllPointsIntersecting(prev.p, p->p, &il, true, false, true);
if(agnstB)
agnstB->AllPointsIntersecting(prev.p, p->p, &il, true, false, true);
if(il.n > 0) {
// The intersections were generated by intersecting the pwl
// edge against a surface; so they must be refined to lie
// exactly on the original curve.
il.ClearTags();
SInter *pi;
for(pi = il.First(); pi; pi = il.NextAfter(pi)) {
if(pi->srf == srfA || pi->srf == srfB) {
// The edge certainly intersects the surfaces that it
// trims (at its endpoints), but those ones don't count.
// They are culled later, but no sense calculating them
// and they will cause numerical problems (since two
// of the three surfaces they're refined to lie on will
// be identical, so the matrix will be singular).
pi->tag = 1;
continue;
}
Point2d puv;
(pi->srf)->ClosestPointTo(pi->p, &puv, false);
// Split the edge if the intersection lies within the surface's
// trim curves, or within the chord tol of the trim curve; want
// some slop if points are close to edge and pwl is too coarse,
// and it doesn't hurt to split unnecessarily.
Point2d dummy = { 0, 0 };
int c = (pi->srf->bsp) ? pi->srf->bsp->ClassifyPoint(puv, dummy, pi->srf) : SBspUv::OUTSIDE;
if(c == SBspUv::OUTSIDE) {
double d = VERY_POSITIVE;
if(pi->srf->bsp) d = pi->srf->bsp->MinimumDistanceToEdge(puv, pi->srf);
if(d > SS.ChordTolMm()) {
pi->tag = 1;
continue;
}
}
// We're keeping the intersection, so actually refine it.
(pi->srf)->PointOnSurfaces(srfA, srfB, &(puv.x), &(puv.y));
pi->p = (pi->srf)->PointAt(puv);
}
il.RemoveTagged();
// And now sort them in order along the line. Note that we must
// do that after refining, in case the refining would make two
// points switch places.
LineStart = prev.p;
LineDirection = (p->p).Minus(prev.p);
qsort(il.elem, il.n, sizeof(il.elem[0]), ByTAlongLine);
// And now uses the intersections to generate our split pwl edge(s)
Vector prev = Vector::From(VERY_POSITIVE, 0, 0);
for(pi = il.First(); pi; pi = il.NextAfter(pi)) {
// On-edge intersection will generate same split point for
// both surfaces, so don't create zero-length edge.
if(!prev.Equals(pi->p)) {
SCurvePt scpt;
scpt.tag = 0;
scpt.p = pi->p;
scpt.vertex = true;
ret.pts.Add(&scpt);
}
prev = pi->p;
}
}
il.Clear();
ret.pts.Add(p);
prev = *p;
}
return ret;
}
//-----------------------------------------------------------------------------
// Find all points where a line through a and b intersects our surface, and
// add them to the list. If seg is true then report only intersections that
// lie within the finite line segment (not including the endpoints); otherwise
// we work along the infinite line. And we report either just intersections
// inside the trim curve, or any intersection with u, v in [0, 1]. And we
// either disregard or report tangent points.
//-----------------------------------------------------------------------------
void SSurface::AllPointsIntersecting(Vector a, Vector b,
List<SInter> *l,
bool seg, bool trimmed, bool inclTangent)
{
if(LineEntirelyOutsideBbox(a, b, seg)) return;
Vector ba = b.Minus(a);
double bam = ba.Magnitude();
List<Inter> inters;
ZERO(&inters);
// All the intersections between the line and the surface; either special
// cases that we can quickly solve in closed form, or general numerical.
Vector center, axis, start, finish;
double radius;
if(degm == 1 && degn == 1) {
// Against a plane, easy.
Vector n = NormalAt(0, 0).WithMagnitude(1);
double d = n.Dot(PointAt(0, 0));
// Trim to line segment now if requested, don't generate points that
// would just get discarded later.
if(!seg ||
(n.Dot(a) > d + LENGTH_EPS && n.Dot(b) < d - LENGTH_EPS) ||
(n.Dot(b) > d + LENGTH_EPS && n.Dot(a) < d - LENGTH_EPS))
{
Vector p = Vector::AtIntersectionOfPlaneAndLine(n, d, a, b, NULL);
Inter inter;
ClosestPointTo(p, &(inter.p.x), &(inter.p.y));
inters.Add(&inter);
}
} else if(IsCylinder(&axis, ¢er, &radius, &start, &finish)) {
// This one can be solved in closed form too.
Vector ab = b.Minus(a);
if(axis.Cross(ab).Magnitude() < LENGTH_EPS) {
// edge is parallel to axis of cylinder, no intersection points
return;
}
// A coordinate system centered at the center of the circle, with
// the edge under test horizontal
Vector u, v, n = axis.WithMagnitude(1);
u = (ab.Minus(n.ScaledBy(ab.Dot(n)))).WithMagnitude(1);
v = n.Cross(u);
Point2d ap = (a.Minus(center)).DotInToCsys(u, v, n).ProjectXy(),
bp = (b.Minus(center)).DotInToCsys(u, v, n).ProjectXy(),
sp = (start. Minus(center)).DotInToCsys(u, v, n).ProjectXy(),
fp = (finish.Minus(center)).DotInToCsys(u, v, n).ProjectXy();
double thetas = atan2(sp.y, sp.x), thetaf = atan2(fp.y, fp.x);
Point2d ip[2];
int ip_n = 0;
if(fabs(fabs(ap.y) - radius) < LENGTH_EPS) {
// tangent
if(inclTangent) {
ip[0] = Point2d::From(0, ap.y);
ip_n = 1;
}
} else if(fabs(ap.y) < radius) {
// two intersections
double xint = sqrt(radius*radius - ap.y*ap.y);
ip[0] = Point2d::From(-xint, ap.y);
ip[1] = Point2d::From( xint, ap.y);
ip_n = 2;
}
int i;
for(i = 0; i < ip_n; i++) {
double t = (ip[i].Minus(ap)).DivPivoting(bp.Minus(ap));
// This is a point on the circle; but is it on the arc?
Point2d pp = ap.Plus((bp.Minus(ap)).ScaledBy(t));
double theta = atan2(pp.y, pp.x);
double dp = WRAP_SYMMETRIC(theta - thetas, 2*PI),
df = WRAP_SYMMETRIC(thetaf - thetas, 2*PI);
double tol = LENGTH_EPS/radius;
if((df > 0 && ((dp < -tol) || (dp > df + tol))) ||
(df < 0 && ((dp > tol) || (dp < df - tol))))
{
continue;
}
Vector p = a.Plus((b.Minus(a)).ScaledBy(t));
Inter inter;
ClosestPointTo(p, &(inter.p.x), &(inter.p.y));
inters.Add(&inter);
}
} else {
// General numerical solution by subdivision, fallback
int cnt = 0, level = 0;
AllPointsIntersectingUntrimmed(a, b, &cnt, &level, &inters, seg, this);
}
// Remove duplicate intersection points
inters.ClearTags();
int i, j;
for(i = 0; i < inters.n; i++) {
for(j = i + 1; j < inters.n; j++) {
if(inters.elem[i].p.Equals(inters.elem[j].p)) {
inters.elem[j].tag = 1;
}
}
}
inters.RemoveTagged();
for(i = 0; i < inters.n; i++) {
Point2d puv = inters.elem[i].p;
// Make sure the point lies within the finite line segment
Vector pxyz = PointAt(puv.x, puv.y);
double t = (pxyz.Minus(a)).DivPivoting(ba);
if(seg && (t > 1 - LENGTH_EPS/bam || t < LENGTH_EPS/bam)) {
continue;
}
// And that it lies inside our trim region
Point2d dummy = { 0, 0 };
int c = bsp->ClassifyPoint(puv, dummy, this);
if(trimmed && c == SBspUv::OUTSIDE) {
continue;
}
// It does, so generate the intersection
SInter si;
si.p = pxyz;
si.surfNormal = NormalAt(puv.x, puv.y);
si.pinter = puv;
si.srf = this;
si.onEdge = (c != SBspUv::INSIDE);
l->Add(&si);
}
inters.Clear();
}
