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solvespace/srf/curve.cpp

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//-----------------------------------------------------------------------------
// Anything involving curves and sets of curves (except for the real math,
// which is in ratpoly.cpp).
//-----------------------------------------------------------------------------
#include "../solvespace.h"
SBezier SBezier::From(Vector4 p0, Vector4 p1) {
SBezier ret;
ZERO(&ret);
ret.deg = 1;
ret.weight[0] = p0.w;
ret.ctrl [0] = p0.PerspectiveProject();
ret.weight[1] = p1.w;
ret.ctrl [1] = p1.PerspectiveProject();
return ret;
}
SBezier SBezier::From(Vector4 p0, Vector4 p1, Vector4 p2) {
SBezier ret;
ZERO(&ret);
ret.deg = 2;
ret.weight[0] = p0.w;
ret.ctrl [0] = p0.PerspectiveProject();
ret.weight[1] = p1.w;
ret.ctrl [1] = p1.PerspectiveProject();
ret.weight[2] = p2.w;
ret.ctrl [2] = p2.PerspectiveProject();
return ret;
}
SBezier SBezier::From(Vector4 p0, Vector4 p1, Vector4 p2, Vector4 p3) {
SBezier ret;
ZERO(&ret);
ret.deg = 3;
ret.weight[0] = p0.w;
ret.ctrl [0] = p0.PerspectiveProject();
ret.weight[1] = p1.w;
ret.ctrl [1] = p1.PerspectiveProject();
ret.weight[2] = p2.w;
ret.ctrl [2] = p2.PerspectiveProject();
ret.weight[3] = p3.w;
ret.ctrl [3] = p3.PerspectiveProject();
return ret;
}
SBezier SBezier::From(Vector p0, Vector p1) {
return SBezier::From(p0.Project4d(),
p1.Project4d());
}
SBezier SBezier::From(Vector p0, Vector p1, Vector p2) {
return SBezier::From(p0.Project4d(),
p1.Project4d(),
p2.Project4d());
}
SBezier SBezier::From(Vector p0, Vector p1, Vector p2, Vector p3) {
return SBezier::From(p0.Project4d(),
p1.Project4d(),
p2.Project4d(),
p3.Project4d());
}
Vector SBezier::Start(void) {
return ctrl[0];
}
Vector SBezier::Finish(void) {
return ctrl[deg];
}
void SBezier::Reverse(void) {
int i;
for(i = 0; i < (deg+1)/2; i++) {
SWAP(Vector, ctrl[i], ctrl[deg-i]);
SWAP(double, weight[i], weight[deg-i]);
}
}
void SBezier::ScaleSelfBy(double s) {
int i;
for(i = 0; i <= deg; i++) {
ctrl[i] = ctrl[i].ScaledBy(s);
}
}
void SBezier::GetBoundingProjd(Vector u, Vector orig,
double *umin, double *umax)
{
int i;
for(i = 0; i <= deg; i++) {
double ut = ((ctrl[i]).Minus(orig)).Dot(u);
if(ut < *umin) *umin = ut;
if(ut > *umax) *umax = ut;
}
}
SBezier SBezier::TransformedBy(Vector t, Quaternion q, bool mirror) {
SBezier ret = *this;
int i;
for(i = 0; i <= deg; i++) {
if(mirror) ret.ctrl[i].z *= -1;
ret.ctrl[i] = (q.Rotate(ret.ctrl[i])).Plus(t);
}
return ret;
}
//-----------------------------------------------------------------------------
// Does this curve lie entirely within the specified plane? It does if all
// the control points lie in that plane.
//-----------------------------------------------------------------------------
bool SBezier::IsInPlane(Vector n, double d) {
int i;
for(i = 0; i <= deg; i++) {
if(fabs((ctrl[i]).Dot(n) - d) > LENGTH_EPS) {
return false;
}
}
return true;
}
//-----------------------------------------------------------------------------
// Is this Bezier exactly the arc of a circle, projected along the specified
// axis? If yes, return that circle's center and radius.
//-----------------------------------------------------------------------------
bool SBezier::IsCircle(Vector axis, Vector *center, double *r) {
if(deg != 2) return false;
if(ctrl[1].DistanceToLine(ctrl[0], ctrl[2].Minus(ctrl[0])) < LENGTH_EPS) {
// This is almost a line segment. So it's a circle with very large
// radius, which is likely to make code that tries to handle circles
// blow up. So return false.
return false;
}
Vector t0 = (ctrl[0]).Minus(ctrl[1]),
t2 = (ctrl[2]).Minus(ctrl[1]),
r0 = axis.Cross(t0),
r2 = axis.Cross(t2);
*center = Vector::AtIntersectionOfLines(ctrl[0], (ctrl[0]).Plus(r0),
ctrl[2], (ctrl[2]).Plus(r2),
NULL, NULL, NULL);
double rd0 = center->Minus(ctrl[0]).Magnitude(),
rd2 = center->Minus(ctrl[2]).Magnitude();
if(fabs(rd0 - rd2) > LENGTH_EPS) {
return false;
}
*r = rd0;
Vector u = r0.WithMagnitude(1),
v = (axis.Cross(u)).WithMagnitude(1);
Point2d c2 = center->Project2d(u, v),
pa2 = (ctrl[0]).Project2d(u, v).Minus(c2),
pb2 = (ctrl[2]).Project2d(u, v).Minus(c2);
double thetaa = atan2(pa2.y, pa2.x), // in fact always zero due to csys
thetab = atan2(pb2.y, pb2.x),
dtheta = WRAP_NOT_0(thetab - thetaa, 2*PI);
if(dtheta > PI) {
// Not possible with a second order Bezier arc; so we must have
// the points backwards.
dtheta = 2*PI - dtheta;
}
if(fabs(weight[1] - cos(dtheta/2)) > LENGTH_EPS) {
return false;
}
return true;
}
bool SBezier::IsRational(void) {
int i;
for(i = 0; i <= deg; i++) {
if(fabs(weight[i] - 1) > LENGTH_EPS) return true;
}
return false;
}
//-----------------------------------------------------------------------------
// Apply a perspective transformation to a rational Bezier curve, calculating
// the new weights as required.
//-----------------------------------------------------------------------------
SBezier SBezier::InPerspective(Vector u, Vector v, Vector n,
Vector origin, double cameraTan)
{
Quaternion q = Quaternion::From(u, v);
q = q.Inverse();
// we want Q*(p - o) = Q*p - Q*o
SBezier ret = this->TransformedBy(q.Rotate(origin).ScaledBy(-1), q, false);
int i;
for(i = 0; i <= deg; i++) {
Vector4 ct = Vector4::From(ret.weight[i], ret.ctrl[i]);
// so the desired curve, before perspective, is
// (x/w, y/w, z/w)
// and after perspective is
// ((x/w)/(1 - (z/w)*cameraTan, ...
// = (x/(w - z*cameraTan), ...
// so we want to let w' = w - z*cameraTan
ct.w = ct.w - ct.z*cameraTan;
ret.ctrl[i] = ct.PerspectiveProject();
ret.weight[i] = ct.w;
}
return ret;
}
bool SBezier::Equals(SBezier *b) {
// We just test of identical degree and control points, even though two
// curves could still be coincident (even sharing endpoints).
if(deg != b->deg) return false;
int i;
for(i = 0; i <= deg; i++) {
if(!(ctrl[i]).Equals(b->ctrl[i])) return false;
if(fabs(weight[i] - b->weight[i]) > LENGTH_EPS) return false;
}
return true;
}
void SBezierList::Clear(void) {
l.Clear();
}
void SBezierList::ScaleSelfBy(double s) {
SBezier *sb;
for(sb = l.First(); sb; sb = l.NextAfter(sb)) {
sb->ScaleSelfBy(s);
}
}
//-----------------------------------------------------------------------------
// If our list contains multiple identical Beziers (in either forward or
// reverse order), then cull them.
//-----------------------------------------------------------------------------
void SBezierList::CullIdenticalBeziers(void) {
int i, j;
l.ClearTags();
for(i = 0; i < l.n; i++) {
SBezier *bi = &(l.elem[i]), bir;
bir = *bi;
bir.Reverse();
for(j = i + 1; j < l.n; j++) {
SBezier *bj = &(l.elem[j]);
if(bj->Equals(bi) ||
bj->Equals(&bir))
{
bi->tag = 1;
bj->tag = 1;
}
}
}
l.RemoveTagged();
}
//-----------------------------------------------------------------------------
// Find all the points where a list of Bezier curves intersects another list
// of Bezier curves. We do this by intersecting their piecewise linearizations,
// and then refining any intersections that we find to lie exactly on the
// curves. So this will screw up on tangencies and stuff, but otherwise should
// be fine.
//-----------------------------------------------------------------------------
void SBezierList::AllIntersectionsWith(SBezierList *sblb, SPointList *spl) {
SBezier *sba, *sbb;
for(sba = l.First(); sba; sba = l.NextAfter(sba)) {
for(sbb = sblb->l.First(); sbb; sbb = sblb->l.NextAfter(sbb)) {
sbb->AllIntersectionsWith(sba, spl);
}
}
}
void SBezier::AllIntersectionsWith(SBezier *sbb, SPointList *spl) {
SPointList splRaw;
ZERO(&splRaw);
SEdgeList sea, seb;
ZERO(&sea);
ZERO(&seb);
this->MakePwlInto(&sea);
sbb ->MakePwlInto(&seb);
SEdge *se;
for(se = sea.l.First(); se; se = sea.l.NextAfter(se)) {
// This isn't quite correct, since AnyEdgeCrossings doesn't count
// the case where two pairs of line segments intersect at their
// vertices. So this isn't robust, although that case isn't very
// likely.
seb.AnyEdgeCrossings(se->a, se->b, NULL, &splRaw);
}
SPoint *sp;
for(sp = splRaw.l.First(); sp; sp = splRaw.l.NextAfter(sp)) {
Vector p = sp->p;
if(PointOnThisAndCurve(sbb, &p)) {
if(!spl->ContainsPoint(p)) spl->Add(p);
}
}
sea.Clear();
seb.Clear();
splRaw.Clear();
}
SBezierLoop SBezierLoop::FromCurves(SBezierList *sbl,
bool *allClosed, SEdge *errorAt)
{
SBezierLoop loop;
ZERO(&loop);
if(sbl->l.n < 1) return loop;
sbl->l.ClearTags();
SBezier *first = &(sbl->l.elem[0]);
first->tag = 1;
loop.l.Add(first);
Vector start = first->Start();
Vector hanging = first->Finish();
sbl->l.RemoveTagged();
while(sbl->l.n > 0 && !hanging.Equals(start)) {
int i;
bool foundNext = false;
for(i = 0; i < sbl->l.n; i++) {
SBezier *test = &(sbl->l.elem[i]);
if((test->Finish()).Equals(hanging)) {
test->Reverse();
// and let the next test catch it
}
if((test->Start()).Equals(hanging)) {
test->tag = 1;
loop.l.Add(test);
hanging = test->Finish();
sbl->l.RemoveTagged();
foundNext = true;
break;
}
}
if(!foundNext) {
// The loop completed without finding the hanging edge, so
// it's an open loop
errorAt->a = hanging;
errorAt->b = start;
*allClosed = false;
return loop;
}
}
if(hanging.Equals(start)) {
*allClosed = true;
} else {
// We ran out of edges without forming a closed loop.
errorAt->a = hanging;
errorAt->b = start;
*allClosed = false;
}
return loop;
}
void SBezierLoop::Reverse(void) {
l.Reverse();
SBezier *sb;
for(sb = l.First(); sb; sb = l.NextAfter(sb)) {
// If we didn't reverse each curve, then the next curve in list would
// share your start, not your finish.
sb->Reverse();
}
}
void SBezierLoop::GetBoundingProjd(Vector u, Vector orig,
double *umin, double *umax)
{
SBezier *sb;
for(sb = l.First(); sb; sb = l.NextAfter(sb)) {
sb->GetBoundingProjd(u, orig, umin, umax);
}
}
void SBezierLoop::MakePwlInto(SContour *sc) {
List<Vector> lv;
ZERO(&lv);
int i, j;
for(i = 0; i < l.n; i++) {
SBezier *sb = &(l.elem[i]);
sb->MakePwlInto(&lv);
// Each curve's piecewise linearization includes its endpoints,
// which we don't want to duplicate (creating zero-len edges).
for(j = (i == 0 ? 0 : 1); j < lv.n; j++) {
sc->AddPoint(lv.elem[j]);
}
lv.Clear();
}
// Ensure that it's exactly closed, not just within a numerical tolerance.
sc->l.elem[sc->l.n - 1] = sc->l.elem[0];
}
bool SBezierLoop::IsClosed(void) {
if(l.n < 1) return false;
Vector s = l.elem[0].Start(),
f = l.elem[l.n-1].Finish();
return s.Equals(f);
}
SBezierLoopSet SBezierLoopSet::From(SBezierList *sbl, SPolygon *poly,
bool *allClosed, SEdge *errorAt)
{
int i;
SBezierLoopSet ret;
ZERO(&ret);
while(sbl->l.n > 0) {
bool thisClosed;
SBezierLoop loop;
loop = SBezierLoop::FromCurves(sbl, &thisClosed, errorAt);
if(!thisClosed) {
ret.Clear();
*allClosed = false;
return ret;
}
ret.l.Add(&loop);
poly->AddEmptyContour();
loop.MakePwlInto(&(poly->l.elem[poly->l.n-1]));
}
poly->normal = poly->ComputeNormal();
ret.normal = poly->normal;
if(poly->l.n > 0) {
ret.point = poly->AnyPoint();
} else {
ret.point = Vector::From(0, 0, 0);
}
poly->FixContourDirections();
for(i = 0; i < poly->l.n; i++) {
if(poly->l.elem[i].tag) {
// We had to reverse this contour in order to fix the poly
// contour directions; so need to do the same with the curves.
ret.l.elem[i].Reverse();
}
}
*allClosed = true;
return ret;
}
void SBezierLoopSet::GetBoundingProjd(Vector u, Vector orig,
double *umin, double *umax)
{
SBezierLoop *sbl;
for(sbl = l.First(); sbl; sbl = l.NextAfter(sbl)) {
sbl->GetBoundingProjd(u, orig, umin, umax);
}
}
void SBezierLoopSet::Clear(void) {
int i;
for(i = 0; i < l.n; i++) {
(l.elem[i]).Clear();
}
l.Clear();
}
//-----------------------------------------------------------------------------
// An export helper function. We start with a list of Bezier curves, and
// assemble them into loops. We find the outer loops, and find the outer loops'
// inner loops, and group them accordingly.
//-----------------------------------------------------------------------------
void SBezierLoopSetSet::FindOuterFacesFrom(SBezierList *sbl, SSurface *srfuv) {
int i, j;
bool allClosed;
SEdge errorAt;
SPolygon sp;
ZERO(&sp);
// Assemble the Bezier trim curves into closed loops; we also get the
// piecewise linearization of the curves (in the SPolygon sp), as a
// calculation aid for the loop direction.
SBezierLoopSet sbls = SBezierLoopSet::From(sbl, &sp, &allClosed, &errorAt);
// Convert the xyz piecewise linear to uv piecewise linear.
SContour *contour;
for(contour = sp.l.First(); contour; contour = sp.l.NextAfter(contour)) {
SPoint *pt;
for(pt = contour->l.First(); pt; pt = contour->l.NextAfter(pt)) {
double u, v;
srfuv->ClosestPointTo(pt->p, &u, &v);
pt->p = Vector::From(u, v, 0);
}
}
sp.normal = Vector::From(0, 0, 1);
static const int OUTER_LOOP = 10;
static const int INNER_LOOP = 20;
static const int USED_LOOP = 30;
// Fix the contour directions; SBezierLoopSet::From() works only for
// planes, since it uses the polygon xyz space.
sp.FixContourDirections();
for(i = 0; i < sp.l.n; i++) {
SContour *contour = &(sp.l.elem[i]);
SBezierLoop *bl = &(sbls.l.elem[i]);
if(contour->tag) {
// This contour got reversed in the polygon to make the directions
// consistent, so the same must be necessary for the Bezier loop.
bl->Reverse();
}
if(contour->IsClockwiseProjdToNormal(sp.normal)) {
bl->tag = INNER_LOOP;
} else {
bl->tag = OUTER_LOOP;
}
}
bool loopsRemaining = true;
while(loopsRemaining) {
loopsRemaining = false;
for(i = 0; i < sbls.l.n; i++) {
SBezierLoop *loop = &(sbls.l.elem[i]);
if(loop->tag != OUTER_LOOP) continue;
// Check if this contour contains any outer loops; if it does, then
// we should do those "inner outer loops" first; otherwise we
// will steal their holes, since their holes also lie inside this
// contour.
for(j = 0; j < sbls.l.n; j++) {
SBezierLoop *outer = &(sbls.l.elem[j]);
if(i == j) continue;
if(outer->tag != OUTER_LOOP) continue;
Vector p = sp.l.elem[j].AnyEdgeMidpoint();
if(sp.l.elem[i].ContainsPointProjdToNormal(sp.normal, p)) {
break;
}
}
if(j < sbls.l.n) {
// It does, can't do this one yet.
continue;
}
SBezierLoopSet outerAndInners;
ZERO(&outerAndInners);
loopsRemaining = true;
loop->tag = USED_LOOP;
outerAndInners.l.Add(loop);
for(j = 0; j < sbls.l.n; j++) {
SBezierLoop *inner = &(sbls.l.elem[j]);
if(inner->tag != INNER_LOOP) continue;
Vector p = sp.l.elem[j].AnyEdgeMidpoint();
if(sp.l.elem[i].ContainsPointProjdToNormal(sp.normal, p)) {
outerAndInners.l.Add(inner);
inner->tag = USED_LOOP;
}
}
l.Add(&outerAndInners);
}
}
sp.Clear();
// Don't free sbls; we've shallow-copied all of its members to ourself.
}
void SBezierLoopSetSet::Clear(void) {
l.Clear();
}
SCurve SCurve::FromTransformationOf(SCurve *a, Vector t, Quaternion q,
bool mirror)
{
SCurve ret;
ZERO(&ret);
ret.h = a->h;
ret.isExact = a->isExact;
ret.exact = (a->exact).TransformedBy(t, q, mirror);
ret.surfA = a->surfA;
ret.surfB = a->surfB;
SCurvePt *p;
for(p = a->pts.First(); p; p = a->pts.NextAfter(p)) {
SCurvePt pp = *p;
if(mirror) pp.p.z *= -1;
pp.p = (q.Rotate(pp.p)).Plus(t);
ret.pts.Add(&pp);
}
return ret;
}
void SCurve::Clear(void) {
pts.Clear();
}
SSurface *SCurve::GetSurfaceA(SShell *a, SShell *b) {
if(source == FROM_A) {
return a->surface.FindById(surfA);
} else if(source == FROM_B) {
return b->surface.FindById(surfA);
} else if(source == FROM_INTERSECTION) {
return a->surface.FindById(surfA);
} else oops();
}
SSurface *SCurve::GetSurfaceB(SShell *a, SShell *b) {
if(source == FROM_A) {
return a->surface.FindById(surfB);
} else if(source == FROM_B) {
return b->surface.FindById(surfB);
} else if(source == FROM_INTERSECTION) {
return b->surface.FindById(surfB);
} else oops();
}
//-----------------------------------------------------------------------------
// When we split line segments wherever they intersect a surface, we introduce
// extra pwl points. This may create very short edges that could be removed
// without violating the chord tolerance. Those are ugly, and also break
// stuff in the Booleans. So remove them.
//-----------------------------------------------------------------------------
void SCurve::RemoveShortSegments(SSurface *srfA, SSurface *srfB) {
if(pts.n < 2) return;
pts.ClearTags();
Vector prev = pts.elem[0].p;
int i, a;
for(i = 1; i < pts.n - 1; i++) {
SCurvePt *sct = &(pts.elem[i]),
*scn = &(pts.elem[i+1]);
if(sct->vertex) {
prev = sct->p;
continue;
}
bool mustKeep = false;
// We must check against both surfaces; the piecewise linear edge
// may have a different chord tolerance in the two surfaces. (For
// example, a circle in the surface of a cylinder is just a straight
// line, so it always has perfect chord tol, but that circle in
// a plane is a circle so it doesn't).
for(a = 0; a < 2; a++) {
SSurface *srf = (a == 0) ? srfA : srfB;
Vector puv, nuv;
srf->ClosestPointTo(prev, &(puv.x), &(puv.y));
srf->ClosestPointTo(scn->p, &(nuv.x), &(nuv.y));
if(srf->ChordToleranceForEdge(nuv, puv) > SS.ChordTolMm()) {
mustKeep = true;
}
}
if(mustKeep) {
prev = sct->p;
} else {
sct->tag = 1;
// and prev is unchanged, since there's no longer any point
// in between
}
}
pts.RemoveTagged();
}
STrimBy STrimBy::EntireCurve(SShell *shell, hSCurve hsc, bool backwards) {
STrimBy stb;
ZERO(&stb);
stb.curve = hsc;
SCurve *sc = shell->curve.FindById(hsc);
if(backwards) {
stb.finish = sc->pts.elem[0].p;
stb.start = sc->pts.elem[sc->pts.n - 1].p;
stb.backwards = true;
} else {
stb.start = sc->pts.elem[0].p;
stb.finish = sc->pts.elem[sc->pts.n - 1].p;
stb.backwards = false;
}
return stb;
}
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