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);
}
ON_3dPoint ON_Box::ClosestPointTo( ON_3dPoint point ) const
{
// Do not validate - it is too slow.
double r,s,t;
ClosestPointTo(point,&r,&s,&t);
return PointAt(r,s,t);
}
// returns point on circle that is arc to given point
ON_3dPoint ON_Arc::ClosestPointTo(
const ON_3dPoint& pt
) const
{
double t = m_angle[0];
ClosestPointTo( pt, &t );
return PointAt(t);
}
ON_3dPoint ON_Polyline::ClosestPointTo( const ON_3dPoint& point ) const
{
double t;
ON_BOOL32 rc = ClosestPointTo( point, &t );
if ( !rc )
t = 0.0;
return PointAt(t);
}
// returns point on cylinder that is closest to given point
ON_3dPoint ON_Cylinder::ClosestPointTo(
ON_3dPoint point
) const
{
double s, t;
ClosestPointTo( point, &s, &t );
return PointAt( s, t );
}
//-----------------------------------------------------------------------------
// Find all points where the indicated finite (if segment) or infinite (if not
// segment) line intersects our surface. Report them in uv space in the list.
// We first do a bounding box check; if the line doesn't intersect, then we're
// done. If it does, then we check how small our surface is. If it's big,
// then we subdivide into quarters and recurse. If it's small, then we refine
// by Newton's method and record the point.
//-----------------------------------------------------------------------------
void SSurface::AllPointsIntersectingUntrimmed(Vector a, Vector b,
int *cnt, int *level,
List<Inter> *l, bool segment,
SSurface *sorig)
{
// Test if the line intersects our axis-aligned bounding box; if no, then
// no possibility of an intersection
if(LineEntirelyOutsideBbox(a, b, segment)) return;
if(*cnt > 2000) {
dbp("!!! too many subdivisions (level=%d)!", *level);
dbp("degm = %d degn = %d", degm, degn);
return;
}
(*cnt)++;
// If we might intersect, and the surface is small, then switch to Newton
// iterations.
if(DepartureFromCoplanar() < 0.2*SS.ChordTolMm()) {
Vector p = (ctrl[0 ][0 ]).Plus(
ctrl[0 ][degn]).Plus(
ctrl[degm][0 ]).Plus(
ctrl[degm][degn]).ScaledBy(0.25);
Inter inter;
sorig->ClosestPointTo(p, &(inter.p.x), &(inter.p.y), false);
if(sorig->PointIntersectingLine(a, b, &(inter.p.x), &(inter.p.y))) {
Vector p = sorig->PointAt(inter.p.x, inter.p.y);
// Debug check, verify that the point lies in both surfaces
// (which it ought to, since the surfaces should be coincident)
double u, v;
ClosestPointTo(p, &u, &v);
l->Add(&inter);
} else {
// Might not converge if line is almost tangent to surface...
}
return;
}
// But the surface is big, so split it, alternating by u and v
SSurface surf0, surf1;
SplitInHalf((*level & 1) == 0, &surf0, &surf1);
int nextLevel = (*level) + 1;
(*level) = nextLevel;
surf0.AllPointsIntersectingUntrimmed(a, b, cnt, level, l, segment, sorig);
(*level) = nextLevel;
surf1.AllPointsIntersectingUntrimmed(a, b, cnt, level, l, segment, sorig);
}
double ON_Line::MinimumDistanceTo( const ON_3dPoint& P ) const
{
double d, t;
if (ClosestPointTo(P,&t))
{
if ( t < 0.0 ) t = 0.0; else if (t > 1.0) t = 1.0;
d = PointAt(t).DistanceTo(P);
}
else
{
// degenerate line
d = from.DistanceTo(P);
t = to.DistanceTo(P);
if ( t < d )
d = t;
}
return d;
}
//-----------------------------------------------------------------------------
// Generate the piecewise linear approximation of the trim stb, which applies
// to the curve sc.
//-----------------------------------------------------------------------------
void SSurface::MakeTrimEdgesInto(SEdgeList *sel, int flags,
SCurve *sc, STrimBy *stb)
{
Vector prev = Vector::From(0, 0, 0);
bool inCurve = false, empty = true;
double u = 0, v = 0;
int i, first, last, increment;
if(stb->backwards) {
first = sc->pts.n - 1;
last = 0;
increment = -1;
} else {
first = 0;
last = sc->pts.n - 1;
increment = 1;
}
for(i = first; i != (last + increment); i += increment) {
Vector tpt, *pt = &(sc->pts.elem[i].p);
if(flags & AS_UV) {
ClosestPointTo(*pt, &u, &v);
tpt = Vector::From(u, v, 0);
} else {
tpt = *pt;
}
if(inCurve) {
sel->AddEdge(prev, tpt, sc->h.v, stb->backwards);
empty = false;
}
prev = tpt; // either uv or xyz, depending on flags
if(pt->Equals(stb->start)) inCurve = true;
if(pt->Equals(stb->finish)) inCurve = false;
}
if(inCurve) dbp("trim was unterminated");
if(empty) dbp("trim was empty");
}
double ON_Line::MinimumDistanceTo( const ON_Line& L ) const
{
ON_3dPoint A, B;
double a, b, t, x, d;
bool bCheckA, bCheckB;
bool bGoodX = ON_Intersect(*this,L,&a,&b);
bCheckA = true;
if ( a < 0.0) a = 0.0; else if (a > 1.0) a = 1.0; else bCheckA=!bGoodX;
bCheckB = true;
if ( b < 0.0) b = 0.0; else if (b > 1.0) b = 1.0; else bCheckB=!bGoodX;
A = PointAt(a);
B = L.PointAt(b);
d = A.DistanceTo(B);
if ( bCheckA )
{
L.ClosestPointTo(A,&t);
if (t<0.0) t = 0.0; else if (t > 1.0) t = 1.0;
x = L.PointAt(t).DistanceTo(A);
if ( x < d )
d = x;
}
if ( bCheckB )
{
ClosestPointTo(B,&t);
if (t<0.0) t = 0.0; else if (t > 1.0) t = 1.0;
x = PointAt(t).DistanceTo(B);
if (x < d )
d = x;
}
return d;
}
void SSurface::ClosestPointTo(Vector p, Point2d *puv, bool converge) {
ClosestPointTo(p, &(puv->x), &(puv->y), converge);
}
bool ON_Polyline::ClosestPointTo( const ON_3dPoint& point, double *t ) const
{
return ClosestPointTo( point, t, 0, SegmentCount() );
}
void SSurface::AddExactIntersectionCurve(SBezier *sb, SSurface *srfB,
SShell *agnstA, SShell *agnstB, SShell *into)
{
SCurve sc = {};
// Important to keep the order of (surfA, surfB) consistent; when we later
// rewrite the identifiers, we rewrite surfA from A and surfB from B.
sc.surfA = h;
sc.surfB = srfB->h;
sc.exact = *sb;
sc.isExact = true;
// Now we have to piecewise linearize the curve. If there's already an
// identical curve in the shell, then follow that pwl exactly, otherwise
// calculate from scratch.
SCurve split, *existing = NULL, *se;
SBezier sbrev = *sb;
sbrev.Reverse();
bool backwards = false;
for(se = into->curve.First(); se; se = into->curve.NextAfter(se)) {
if(se->isExact) {
if(sb->Equals(&(se->exact))) {
existing = se;
break;
}
if(sbrev.Equals(&(se->exact))) {
existing = se;
backwards = true;
break;
}
}
}
if(existing) {
SCurvePt *v;
for(v = existing->pts.First(); v; v = existing->pts.NextAfter(v)) {
sc.pts.Add(v);
}
if(backwards) sc.pts.Reverse();
split = sc;
sc = {};
} else {
sb->MakePwlInto(&(sc.pts));
// and split the line where it intersects our existing surfaces
split = sc.MakeCopySplitAgainst(agnstA, agnstB, this, srfB);
sc.Clear();
}
// Test if the curve lies entirely outside one of the
SCurvePt *scpt;
bool withinA = false, withinB = false;
for(scpt = split.pts.First(); scpt; scpt = split.pts.NextAfter(scpt)) {
double tol = 0.01;
Point2d puv;
ClosestPointTo(scpt->p, &puv);
if(puv.x > -tol && puv.x < 1 + tol &&
puv.y > -tol && puv.y < 1 + tol)
{
withinA = true;
}
srfB->ClosestPointTo(scpt->p, &puv);
if(puv.x > -tol && puv.x < 1 + tol &&
puv.y > -tol && puv.y < 1 + tol)
{
withinB = true;
}
// Break out early, no sense wasting time if we already have the answer.
if(withinA && withinB) break;
}
if(!(withinA && withinB)) {
// Intersection curve lies entirely outside one of the surfaces, so
// it's fake.
split.Clear();
return;
}
#if 0
if(sb->deg == 2) {
dbp(" ");
SCurvePt *prev = NULL, *v;
dbp("split.pts.n = %d", split.pts.n);
for(v = split.pts.First(); v; v = split.pts.NextAfter(v)) {
if(prev) {
Vector e = (prev->p).Minus(v->p).WithMagnitude(0);
SS.nakedEdges.AddEdge((prev->p).Plus(e), (v->p).Minus(e));
}
prev = v;
}
}
#endif // 0
ssassert(!(sb->Start()).Equals(sb->Finish()),
"Unexpected zero-length edge");
split.source = SCurve::Source::INTERSECTION;
into->curve.AddAndAssignId(&split);
}
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();
}
}
//-----------------------------------------------------------------------------
// 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();
}
bool ON_Line::IsFartherThan( double d, const ON_Line& L ) const
{
ON_3dPoint A, B;
double a, b, t, x;
bool bCheckA, bCheckB;
a = from.x; if (to.x < a) {b=a; a = to.x;} else b = to.x;
if ( b+d < L.from.x && b+d < L.to.x )
return true;
if ( a-d > L.from.x && a-d > L.to.x )
return true;
a = from.y; if (to.y < a) {b=a; a = to.y;} else b = to.y;
if ( b+d < L.from.y && b+d < L.to.y )
return true;
if ( a-d > L.from.y && a-d > L.to.y )
return true;
a = from.z; if (to.z < a) {b=a; a = to.z;} else b = to.z;
if ( b+d < L.from.z && b+d < L.to.z )
return true;
if ( a-d > L.from.z && a-d > L.to.z )
return true;
if ( !ON_Intersect(*this,L,&a,&b) )
{
// lines are parallel or anti parallel
if ( Direction()*L.Direction() >= 0.0 )
{
// lines are parallel
a = 0.0;
L.ClosestPointTo(from,&b);
// If ( b >= 0.0), then this->from and L(b) are a pair of closest points.
if ( b < 0.0 )
{
// Othersise L.from and this(a) are a pair of closest points.
b = 0.0;
ClosestPointTo(L.from,&a);
}
}
else
{
// lines are anti parallel
a = 1.0;
L.ClosestPointTo(to,&b);
// If ( b >= 0.0), then this->to and L(b) are a pair of closest points.
if ( b < 0.0 )
{
// Othersise L.to and this(a) are a pair of closest points.
b = 0.0;
ClosestPointTo(L.from,&a);
}
}
}
A = PointAt(a);
B = L.PointAt(b);
x = A.DistanceTo(B);
if (x > d)
return true;
bCheckA = true;
if ( a < 0.0) a = 0.0; else if (a > 1.0) a = 1.0; else bCheckA=false;
if (bCheckA )
{
A = PointAt(a);
L.ClosestPointTo(A,&t);
if (t<0.0) t = 0.0; else if (t > 1.0) t = 1.0;
x = L.PointAt(t).DistanceTo(A);
}
bCheckB = true;
if ( b < 0.0) b = 0.0; else if (b > 1.0) b = 1.0; else bCheckB=false;
if ( bCheckB )
{
B = L.PointAt(b);
ClosestPointTo(B,&t);
if (t<0.0) t = 0.0; else if (t > 1.0) t = 1.0;
t = PointAt(t).DistanceTo(B);
if ( bCheckA )
{
if ( t<x ) x = t;
}
else
{
x = t;
}
}
return (x > d);
}
ON_3dPoint ON_Ellipse::ClosestPointTo( const ON_3dPoint& point ) const
{
double t;
ClosestPointTo( point, &t );
return PointAt( t );
}
ON_3dPoint ON_Plane::ClosestPointTo( ON_3dPoint p ) const
{
double s, t;
ClosestPointTo( p, &s, &t );
return PointAt( s, t );
}
double ON_Line::DistanceTo( ON_3dPoint test_point ) const
{
return test_point.DistanceTo(ClosestPointTo(test_point));
}
