bool SSurface::LineEntirelyOutsideBbox(Vector a, Vector b, bool segment) {
Vector amax, amin;
GetAxisAlignedBounding(&amax, &amin);
if(!Vector::BoundingBoxIntersectsLine(amax, amin, a, b, segment)) {
// The line segment could fail to intersect the bbox, but lie entirely
// within it and intersect the surface.
if(a.OutsideAndNotOn(amax, amin) && b.OutsideAndNotOn(amax, amin)) {
return true;
}
}
return false;
}
void SSurface::IntersectAgainst(SSurface *b, SShell *agnstA, SShell *agnstB,
SShell *into)
{
Vector amax, amin, bmax, bmin;
GetAxisAlignedBounding(&amax, &amin);
b->GetAxisAlignedBounding(&bmax, &bmin);
if(Vector::BoundingBoxesDisjoint(amax, amin, bmax, bmin)) {
// They cannot possibly intersect, no curves to generate
return;
}
Vector alongt, alongb;
SBezier oft, ofb;
bool isExtdt = this->IsExtrusion(&oft, &alongt),
isExtdb = b->IsExtrusion(&ofb, &alongb);
if(degm == 1 && degn == 1 && b->degm == 1 && b->degn == 1) {
// Line-line intersection; it's a plane or nothing.
Vector na = NormalAt(0, 0).WithMagnitude(1),
nb = b->NormalAt(0, 0).WithMagnitude(1);
double da = na.Dot(PointAt(0, 0)),
db = nb.Dot(b->PointAt(0, 0));
Vector dl = na.Cross(nb);
if(dl.Magnitude() < LENGTH_EPS) return; // parallel planes
dl = dl.WithMagnitude(1);
Vector p = Vector::AtIntersectionOfPlanes(na, da, nb, db);
// Trim it to the region 0 <= {u,v} <= 1 for each plane; not strictly
// necessary, since line will be split and excess edges culled, but
// this improves speed and robustness.
int i;
double tmax = VERY_POSITIVE, tmin = VERY_NEGATIVE;
for(i = 0; i < 2; i++) {
SSurface *s = (i == 0) ? this : b;
Vector tu, tv;
s->TangentsAt(0, 0, &tu, &tv);
double up, vp, ud, vd;
s->ClosestPointTo(p, &up, &vp);
ud = (dl.Dot(tu)) / tu.MagSquared();
vd = (dl.Dot(tv)) / tv.MagSquared();
// so u = up + t*ud
// v = vp + t*vd
if(ud > LENGTH_EPS) {
tmin = max(tmin, -up/ud);
tmax = min(tmax, (1 - up)/ud);
} else if(ud < -LENGTH_EPS) {
tmax = min(tmax, -up/ud);
tmin = max(tmin, (1 - up)/ud);
} else {
if(up < -LENGTH_EPS || up > 1 + LENGTH_EPS) {
// u is constant, and outside [0, 1]
tmax = VERY_NEGATIVE;
}
}
if(vd > LENGTH_EPS) {
tmin = max(tmin, -vp/vd);
tmax = min(tmax, (1 - vp)/vd);
} else if(vd < -LENGTH_EPS) {
tmax = min(tmax, -vp/vd);
tmin = max(tmin, (1 - vp)/vd);
} else {
if(vp < -LENGTH_EPS || vp > 1 + LENGTH_EPS) {
// v is constant, and outside [0, 1]
tmax = VERY_NEGATIVE;
}
}
}
if(tmax > tmin + LENGTH_EPS) {
SBezier bezier = SBezier::From(p.Plus(dl.ScaledBy(tmin)),
p.Plus(dl.ScaledBy(tmax)));
AddExactIntersectionCurve(&bezier, b, agnstA, agnstB, into);
}
} else if((degm == 1 && degn == 1 && isExtdb) ||
(b->degm == 1 && b->degn == 1 && isExtdt))
{
// The intersection between a plane and a surface of extrusion
SSurface *splane, *sext;
if(degm == 1 && degn == 1) {
splane = this;
sext = b;
} else {
splane = b;
sext = this;
}
Vector n = splane->NormalAt(0, 0).WithMagnitude(1), along;
double d = n.Dot(splane->PointAt(0, 0));
SBezier bezier;
(void)sext->IsExtrusion(&bezier, &along);
if(fabs(n.Dot(along)) < LENGTH_EPS) {
// Direction of extrusion is parallel to plane; so intersection
// is zero or more lines. Build a line within the plane, and
// normal to the direction of extrusion, and intersect that line
// against the surface; each intersection point corresponds to
// a line.
Vector pm, alu, p0, dp;
// a point halfway along the extrusion
pm = ((sext->ctrl[0][0]).Plus(sext->ctrl[0][1])).ScaledBy(0.5);
alu = along.WithMagnitude(1);
dp = (n.Cross(along)).WithMagnitude(1);
// n, alu, and dp form an orthogonal csys; set n component to
// place it on the plane, alu component to lie halfway along
// extrusion, and dp component doesn't matter so zero
p0 = n.ScaledBy(d).Plus(alu.ScaledBy(pm.Dot(alu)));
List<SInter> inters = {};
sext->AllPointsIntersecting(p0, p0.Plus(dp), &inters,
/*asSegment=*/false, /*trimmed=*/false, /*inclTangent=*/true);
SInter *si;
for(si = inters.First(); si; si = inters.NextAfter(si)) {
Vector al = along.ScaledBy(0.5);
SBezier bezier;
bezier = SBezier::From((si->p).Minus(al), (si->p).Plus(al));
AddExactIntersectionCurve(&bezier, b, agnstA, agnstB, into);
}
inters.Clear();
} else {
// Direction of extrusion is not parallel to plane; so
// intersection is projection of extruded curve into our plane.
int i;
for(i = 0; i <= bezier.deg; i++) {
Vector p0 = bezier.ctrl[i],
p1 = p0.Plus(along);
bezier.ctrl[i] =
Vector::AtIntersectionOfPlaneAndLine(n, d, p0, p1, NULL);
}
AddExactIntersectionCurve(&bezier, b, agnstA, agnstB, into);
}
} else if(isExtdt && isExtdb &&
sqrt(fabs(alongt.Dot(alongb))) >
sqrt(alongt.Magnitude() * alongb.Magnitude()) - LENGTH_EPS)
{
// Two surfaces of extrusion along the same axis. So they might
// intersect along some number of lines parallel to the axis.
Vector axis = alongt.WithMagnitude(1);
List<SInter> inters = {};
List<Vector> lv = {};
double a_axis0 = ( ctrl[0][0]).Dot(axis),
a_axis1 = ( ctrl[0][1]).Dot(axis),
b_axis0 = (b->ctrl[0][0]).Dot(axis),
b_axis1 = (b->ctrl[0][1]).Dot(axis);
if(a_axis0 > a_axis1) swap(a_axis0, a_axis1);
if(b_axis0 > b_axis1) swap(b_axis0, b_axis1);
double ab_axis0 = max(a_axis0, b_axis0),
ab_axis1 = min(a_axis1, b_axis1);
if(fabs(ab_axis0 - ab_axis1) < LENGTH_EPS) {
// The line would be zero-length
return;
}
Vector axis0 = axis.ScaledBy(ab_axis0),
axis1 = axis.ScaledBy(ab_axis1),
axisc = (axis0.Plus(axis1)).ScaledBy(0.5);
oft.MakePwlInto(&lv);
int i;
for(i = 0; i < lv.n - 1; i++) {
Vector pa = lv.elem[i], pb = lv.elem[i+1];
pa = pa.Minus(axis.ScaledBy(pa.Dot(axis)));
pb = pb.Minus(axis.ScaledBy(pb.Dot(axis)));
pa = pa.Plus(axisc);
pb = pb.Plus(axisc);
b->AllPointsIntersecting(pa, pb, &inters,
/*asSegment=*/true,/*trimmed=*/false, /*inclTangent=*/false);
}
SInter *si;
for(si = inters.First(); si; si = inters.NextAfter(si)) {
Vector p = (si->p).Minus(axis.ScaledBy((si->p).Dot(axis)));
double ub, vb;
b->ClosestPointTo(p, &ub, &vb, /*mustConverge=*/true);
SSurface plane;
plane = SSurface::FromPlane(p, axis.Normal(0), axis.Normal(1));
b->PointOnSurfaces(this, &plane, &ub, &vb);
p = b->PointAt(ub, vb);
SBezier bezier;
bezier = SBezier::From(p.Plus(axis0), p.Plus(axis1));
AddExactIntersectionCurve(&bezier, b, agnstA, agnstB, into);
}
inters.Clear();
lv.Clear();
} else {
// Try intersecting the surfaces numerically, by a marching algorithm.
// First, we find all the intersections between a surface and the
// boundary of the other surface.
SPointList spl = {};
int a;
for(a = 0; a < 2; a++) {
SShell *shA = (a == 0) ? agnstA : agnstB;
SSurface *srfA = (a == 0) ? this : b,
*srfB = (a == 0) ? b : this;
SEdgeList el = {};
srfA->MakeEdgesInto(shA, &el, MakeAs::XYZ, NULL);
SEdge *se;
for(se = el.l.First(); se; se = el.l.NextAfter(se)) {
List<SInter> lsi = {};
srfB->AllPointsIntersecting(se->a, se->b, &lsi,
/*asSegment=*/true, /*trimmed=*/true, /*inclTangent=*/false);
if(lsi.n == 0) continue;
// Find the other surface that this curve trims.
hSCurve hsc = { (uint32_t)se->auxA };
SCurve *sc = shA->curve.FindById(hsc);
hSSurface hother = (sc->surfA.v == srfA->h.v) ?
sc->surfB : sc->surfA;
SSurface *other = shA->surface.FindById(hother);
SInter *si;
for(si = lsi.First(); si; si = lsi.NextAfter(si)) {
Vector p = si->p;
double u, v;
srfB->ClosestPointTo(p, &u, &v);
srfB->PointOnSurfaces(srfA, other, &u, &v);
p = srfB->PointAt(u, v);
if(!spl.ContainsPoint(p)) {
SPoint sp;
sp.p = p;
// We also need the edge normal, so that we know in
// which direction to march.
srfA->ClosestPointTo(p, &u, &v);
Vector n = srfA->NormalAt(u, v);
sp.auxv = n.Cross((se->b).Minus(se->a));
sp.auxv = (sp.auxv).WithMagnitude(1);
spl.l.Add(&sp);
}
}
lsi.Clear();
}
el.Clear();
}
while(spl.l.n >= 2) {
SCurve sc = {};
sc.surfA = h;
sc.surfB = b->h;
sc.isExact = false;
sc.source = SCurve::Source::INTERSECTION;
Vector start = spl.l.elem[0].p,
startv = spl.l.elem[0].auxv;
spl.l.ClearTags();
spl.l.elem[0].tag = 1;
spl.l.RemoveTagged();
// Our chord tolerance is whatever the user specified
double maxtol = SS.ChordTolMm();
int maxsteps = max(300, SS.GetMaxSegments()*3);
// The curve starts at our starting point.
SCurvePt padd = {};
padd.vertex = true;
padd.p = start;
sc.pts.Add(&padd);
Point2d pa, pb;
Vector np, npc = Vector::From(0, 0, 0);
bool fwd = false;
// Better to start with a too-small step, so that we don't miss
// features of the curve entirely.
double tol, step = maxtol;
for(a = 0; a < maxsteps; a++) {
ClosestPointTo(start, &pa);
b->ClosestPointTo(start, &pb);
Vector na = NormalAt(pa).WithMagnitude(1),
nb = b->NormalAt(pb).WithMagnitude(1);
if(a == 0) {
Vector dp = nb.Cross(na);
if(dp.Dot(startv) < 0) {
// We want to march in the more inward direction.
fwd = true;
} else {
fwd = false;
}
}
int i;
for(i = 0; i < 20; i++) {
Vector dp = nb.Cross(na);
if(!fwd) dp = dp.ScaledBy(-1);
dp = dp.WithMagnitude(step);
np = start.Plus(dp);
npc = ClosestPointOnThisAndSurface(b, np);
tol = (npc.Minus(np)).Magnitude();
if(tol > maxtol*0.8) {
step *= 0.90;
} else {
step /= 0.90;
}
if((tol < maxtol) && (tol > maxtol/2)) {
// If we meet the chord tolerance test, and we're
// not too fine, then we break out.
break;
}
}
SPoint *sp;
for(sp = spl.l.First(); sp; sp = spl.l.NextAfter(sp)) {
if((sp->p).OnLineSegment(start, npc, 2*SS.ChordTolMm())) {
sp->tag = 1;
a = maxsteps;
npc = sp->p;
}
}
padd.p = npc;
padd.vertex = (a == maxsteps);
sc.pts.Add(&padd);
start = npc;
}
spl.l.RemoveTagged();
// And now we split and insert the curve
SCurve split = sc.MakeCopySplitAgainst(agnstA, agnstB, this, b);
sc.Clear();
into->curve.AddAndAssignId(&split);
}
spl.Clear();
}
}
