534 lines
16 KiB
C++
534 lines
16 KiB
C++
//-----------------------------------------------------------------------------
|
|
// 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::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) {
|
|
SBezier ret = *this;
|
|
int i;
|
|
for(i = 0; i <= deg; i++) {
|
|
ret.ctrl[i] = (q.Rotate(ret.ctrl[i])).Plus(t);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// 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;
|
|
|
|
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);
|
|
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();
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// 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];
|
|
}
|
|
|
|
|
|
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();
|
|
}
|
|
|
|
SCurve SCurve::FromTransformationOf(SCurve *a, Vector t, Quaternion q) {
|
|
SCurve ret;
|
|
ZERO(&ret);
|
|
|
|
ret.h = a->h;
|
|
ret.isExact = a->isExact;
|
|
ret.exact = (a->exact).TransformedBy(t, q);
|
|
ret.surfA = a->surfA;
|
|
ret.surfB = a->surfB;
|
|
|
|
SCurvePt *p;
|
|
for(p = a->pts.First(); p; p = a->pts.NextAfter(p)) {
|
|
SCurvePt pp = *p;
|
|
pp.p = (q.Rotate(p->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;
|
|
}
|
|
|