1065 lines
30 KiB
C++
1065 lines
30 KiB
C++
#include "../solvespace.h"
|
|
|
|
// Converge it to better than LENGTH_EPS; we want two points, each
|
|
// independently projected into uv and back, to end up equal with the
|
|
// LENGTH_EPS. Best case that requires LENGTH_EPS/2, but more is better
|
|
// and convergence should be fast by now.
|
|
#define RATPOLY_EPS (LENGTH_EPS/(1e2))
|
|
|
|
static double Bernstein(int k, int deg, double t)
|
|
{
|
|
if(k > deg || k < 0) return 0;
|
|
|
|
switch(deg) {
|
|
case 0:
|
|
return 1;
|
|
break;
|
|
|
|
case 1:
|
|
if(k == 0) {
|
|
return (1 - t);
|
|
} else if(k = 1) {
|
|
return t;
|
|
}
|
|
break;
|
|
|
|
case 2:
|
|
if(k == 0) {
|
|
return (1 - t)*(1 - t);
|
|
} else if(k == 1) {
|
|
return 2*(1 - t)*t;
|
|
} else if(k == 2) {
|
|
return t*t;
|
|
}
|
|
break;
|
|
|
|
case 3:
|
|
if(k == 0) {
|
|
return (1 - t)*(1 - t)*(1 - t);
|
|
} else if(k == 1) {
|
|
return 3*(1 - t)*(1 - t)*t;
|
|
} else if(k == 2) {
|
|
return 3*(1 - t)*t*t;
|
|
} else if(k == 3) {
|
|
return t*t*t;
|
|
}
|
|
break;
|
|
}
|
|
oops();
|
|
}
|
|
|
|
double BernsteinDerivative(int k, int deg, double t)
|
|
{
|
|
switch(deg) {
|
|
case 0:
|
|
return 0;
|
|
break;
|
|
|
|
case 1:
|
|
if(k == 0) {
|
|
return -1;
|
|
} else if(k = 1) {
|
|
return 1;
|
|
}
|
|
break;
|
|
|
|
case 2:
|
|
if(k == 0) {
|
|
return -2 + 2*t;
|
|
} else if(k == 1) {
|
|
return 2 - 4*t;
|
|
} else if(k == 2) {
|
|
return 2*t;
|
|
}
|
|
break;
|
|
|
|
case 3:
|
|
if(k == 0) {
|
|
return -3 + 6*t - 3*t*t;
|
|
} else if(k == 1) {
|
|
return 3 - 12*t + 9*t*t;
|
|
} else if(k == 2) {
|
|
return 6*t - 9*t*t;
|
|
} else if(k == 3) {
|
|
return 3*t*t;
|
|
}
|
|
break;
|
|
}
|
|
oops();
|
|
}
|
|
|
|
SBezier SBezier::From(Vector p0, Vector p1) {
|
|
SBezier ret;
|
|
ZERO(&ret);
|
|
ret.deg = 1;
|
|
ret.weight[0] = ret.weight[1] = 1;
|
|
ret.ctrl[0] = p0;
|
|
ret.ctrl[1] = p1;
|
|
return ret;
|
|
}
|
|
|
|
SBezier SBezier::From(Vector p0, Vector p1, Vector p2) {
|
|
SBezier ret;
|
|
ZERO(&ret);
|
|
ret.deg = 2;
|
|
ret.weight[0] = ret.weight[1] = ret.weight[2] = 1;
|
|
ret.ctrl[0] = p0;
|
|
ret.ctrl[1] = p1;
|
|
ret.ctrl[2] = p2;
|
|
return ret;
|
|
}
|
|
|
|
SBezier SBezier::From(Vector p0, Vector p1, Vector p2, Vector p3) {
|
|
SBezier ret;
|
|
ZERO(&ret);
|
|
ret.deg = 3;
|
|
ret.weight[0] = ret.weight[1] = ret.weight[2] = ret.weight[3] = 1;
|
|
ret.ctrl[0] = p0;
|
|
ret.ctrl[1] = p1;
|
|
ret.ctrl[2] = p2;
|
|
ret.ctrl[3] = p3;
|
|
return ret;
|
|
}
|
|
|
|
Vector SBezier::Start(void) {
|
|
return ctrl[0];
|
|
}
|
|
|
|
Vector SBezier::Finish(void) {
|
|
return ctrl[deg];
|
|
}
|
|
|
|
Vector SBezier::PointAt(double t) {
|
|
Vector pt = Vector::From(0, 0, 0);
|
|
double d = 0;
|
|
|
|
int i;
|
|
for(i = 0; i <= deg; i++) {
|
|
double B = Bernstein(i, deg, t);
|
|
pt = pt.Plus(ctrl[i].ScaledBy(B*weight[i]));
|
|
d += weight[i]*B;
|
|
}
|
|
pt = pt.ScaledBy(1.0/d);
|
|
return pt;
|
|
}
|
|
|
|
void SBezier::MakePwlInto(List<Vector> *l) {
|
|
l->Add(&(ctrl[0]));
|
|
MakePwlWorker(l, 0.0, 1.0);
|
|
}
|
|
void SBezier::MakePwlWorker(List<Vector> *l, double ta, double tb) {
|
|
Vector pa = PointAt(ta);
|
|
Vector pb = PointAt(tb);
|
|
|
|
// Can't test in the middle, or certain cubics would break.
|
|
double tm1 = (2*ta + tb) / 3;
|
|
double tm2 = (ta + 2*tb) / 3;
|
|
|
|
Vector pm1 = PointAt(tm1);
|
|
Vector pm2 = PointAt(tm2);
|
|
|
|
double d = max(pm1.DistanceToLine(pa, pb.Minus(pa)),
|
|
pm2.DistanceToLine(pa, pb.Minus(pa)));
|
|
|
|
double step = 1.0/SS.maxSegments;
|
|
if((tb - ta) < step || d < SS.ChordTolMm()) {
|
|
// A previous call has already added the beginning of our interval.
|
|
l->Add(&pb);
|
|
} else {
|
|
double tm = (ta + tb) / 2;
|
|
MakePwlWorker(l, ta, tm);
|
|
MakePwlWorker(l, tm, tb);
|
|
}
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
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();
|
|
}
|
|
|
|
|
|
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;
|
|
|
|
Vector *p;
|
|
for(p = a->pts.First(); p; p = a->pts.NextAfter(p)) {
|
|
Vector pp = (q.Rotate(*p)).Plus(t);
|
|
ret.pts.Add(&pp);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
void SCurve::Clear(void) {
|
|
pts.Clear();
|
|
}
|
|
|
|
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];
|
|
stb.start = sc->pts.elem[sc->pts.n - 1];
|
|
stb.backwards = true;
|
|
} else {
|
|
stb.start = sc->pts.elem[0];
|
|
stb.finish = sc->pts.elem[sc->pts.n - 1];
|
|
stb.backwards = false;
|
|
}
|
|
|
|
return stb;
|
|
}
|
|
|
|
SSurface SSurface::FromExtrusionOf(SBezier *sb, Vector t0, Vector t1) {
|
|
SSurface ret;
|
|
ZERO(&ret);
|
|
|
|
ret.degm = sb->deg;
|
|
ret.degn = 1;
|
|
|
|
int i;
|
|
for(i = 0; i <= ret.degm; i++) {
|
|
ret.ctrl[i][0] = (sb->ctrl[i]).Plus(t0);
|
|
ret.weight[i][0] = sb->weight[i];
|
|
|
|
ret.ctrl[i][1] = (sb->ctrl[i]).Plus(t1);
|
|
ret.weight[i][1] = sb->weight[i];
|
|
}
|
|
|
|
return ret;
|
|
}
|
|
|
|
bool SSurface::IsExtrusion(SBezier *of, Vector *alongp) {
|
|
int i;
|
|
|
|
if(degn != 1) return false;
|
|
|
|
Vector along = (ctrl[0][1]).Minus(ctrl[0][0]);
|
|
for(i = 0; i <= degm; i++) {
|
|
if((fabs(weight[i][1] - weight[i][0]) < LENGTH_EPS) &&
|
|
((ctrl[i][1]).Minus(ctrl[i][0])).Equals(along))
|
|
{
|
|
continue;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
// yes, we are a surface of extrusion; copy the original curve and return
|
|
if(of) {
|
|
for(i = 0; i <= degm; i++) {
|
|
of->weight[i] = weight[i][0];
|
|
of->ctrl[i] = ctrl[i][0];
|
|
}
|
|
of->deg = degm;
|
|
*alongp = along;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool SSurface::IsCylinder(Vector *center, Vector *axis, double *r,
|
|
Vector *start, Vector *finish)
|
|
{
|
|
SBezier sb;
|
|
if(!IsExtrusion(&sb, axis)) return false;
|
|
if(sb.deg != 2) return false;
|
|
|
|
Vector t0 = (sb.ctrl[0]).Minus(sb.ctrl[1]),
|
|
t2 = (sb.ctrl[2]).Minus(sb.ctrl[1]),
|
|
r0 = axis->Cross(t0),
|
|
r2 = axis->Cross(t2);
|
|
|
|
*center = Vector::AtIntersectionOfLines(sb.ctrl[0], (sb.ctrl[0]).Plus(r0),
|
|
sb.ctrl[2], (sb.ctrl[2]).Plus(r2),
|
|
NULL, NULL, NULL);
|
|
|
|
double rd0 = center->Minus(sb.ctrl[0]).Magnitude(),
|
|
rd2 = center->Minus(sb.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 = (sb.ctrl[0]).Project2d(u, v).Minus(c2),
|
|
pb2 = (sb.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(sb.weight[1] - cos(dtheta/2)) > LENGTH_EPS) {
|
|
return false;
|
|
}
|
|
|
|
*start = sb.ctrl[0];
|
|
*finish = sb.ctrl[2];
|
|
|
|
return true;
|
|
}
|
|
|
|
SSurface SSurface::FromPlane(Vector pt, Vector u, Vector v) {
|
|
SSurface ret;
|
|
ZERO(&ret);
|
|
|
|
ret.degm = 1;
|
|
ret.degn = 1;
|
|
|
|
ret.weight[0][0] = ret.weight[0][1] = 1;
|
|
ret.weight[1][0] = ret.weight[1][1] = 1;
|
|
|
|
ret.ctrl[0][0] = pt;
|
|
ret.ctrl[0][1] = pt.Plus(u);
|
|
ret.ctrl[1][0] = pt.Plus(v);
|
|
ret.ctrl[1][1] = pt.Plus(v).Plus(u);
|
|
|
|
return ret;
|
|
}
|
|
|
|
SSurface SSurface::FromTransformationOf(SSurface *a, Vector t, Quaternion q,
|
|
bool includingTrims)
|
|
{
|
|
SSurface ret;
|
|
ZERO(&ret);
|
|
|
|
ret.h = a->h;
|
|
ret.color = a->color;
|
|
ret.face = a->face;
|
|
|
|
ret.degm = a->degm;
|
|
ret.degn = a->degn;
|
|
int i, j;
|
|
for(i = 0; i <= 3; i++) {
|
|
for(j = 0; j <= 3; j++) {
|
|
ret.ctrl[i][j] = (q.Rotate(a->ctrl[i][j])).Plus(t);
|
|
ret.weight[i][j] = a->weight[i][j];
|
|
}
|
|
}
|
|
|
|
if(includingTrims) {
|
|
STrimBy *stb;
|
|
for(stb = a->trim.First(); stb; stb = a->trim.NextAfter(stb)) {
|
|
STrimBy n = *stb;
|
|
n.start = (q.Rotate(n.start)) .Plus(t);
|
|
n.finish = (q.Rotate(n.finish)).Plus(t);
|
|
ret.trim.Add(&n);
|
|
}
|
|
}
|
|
|
|
return ret;
|
|
}
|
|
|
|
Vector SSurface::PointAt(double u, double v) {
|
|
Vector num = Vector::From(0, 0, 0);
|
|
double den = 0;
|
|
|
|
int i, j;
|
|
for(i = 0; i <= degm; i++) {
|
|
for(j = 0; j <= degn; j++) {
|
|
double Bi = Bernstein(i, degm, u),
|
|
Bj = Bernstein(j, degn, v);
|
|
|
|
num = num.Plus(ctrl[i][j].ScaledBy(Bi*Bj*weight[i][j]));
|
|
den += weight[i][j]*Bi*Bj;
|
|
}
|
|
}
|
|
num = num.ScaledBy(1.0/den);
|
|
return num;
|
|
}
|
|
|
|
void SSurface::TangentsAt(double u, double v, Vector *tu, Vector *tv) {
|
|
Vector num = Vector::From(0, 0, 0),
|
|
num_u = Vector::From(0, 0, 0),
|
|
num_v = Vector::From(0, 0, 0);
|
|
double den = 0,
|
|
den_u = 0,
|
|
den_v = 0;
|
|
|
|
int i, j;
|
|
for(i = 0; i <= degm; i++) {
|
|
for(j = 0; j <= degn; j++) {
|
|
double Bi = Bernstein(i, degm, u),
|
|
Bj = Bernstein(j, degn, v),
|
|
Bip = BernsteinDerivative(i, degm, u),
|
|
Bjp = BernsteinDerivative(j, degn, v);
|
|
|
|
num = num.Plus(ctrl[i][j].ScaledBy(Bi*Bj*weight[i][j]));
|
|
den += weight[i][j]*Bi*Bj;
|
|
|
|
num_u = num_u.Plus(ctrl[i][j].ScaledBy(Bip*Bj*weight[i][j]));
|
|
den_u += weight[i][j]*Bip*Bj;
|
|
|
|
num_v = num_v.Plus(ctrl[i][j].ScaledBy(Bi*Bjp*weight[i][j]));
|
|
den_v += weight[i][j]*Bi*Bjp;
|
|
}
|
|
}
|
|
// Quotient rule; f(t) = n(t)/d(t), so f' = (n'*d - n*d')/(d^2)
|
|
*tu = ((num_u.ScaledBy(den)).Minus(num.ScaledBy(den_u)));
|
|
*tu = tu->ScaledBy(1.0/(den*den));
|
|
|
|
*tv = ((num_v.ScaledBy(den)).Minus(num.ScaledBy(den_v)));
|
|
*tv = tv->ScaledBy(1.0/(den*den));
|
|
}
|
|
|
|
Vector SSurface::NormalAt(double u, double v) {
|
|
Vector tu, tv;
|
|
TangentsAt(u, v, &tu, &tv);
|
|
return tu.Cross(tv);
|
|
}
|
|
|
|
void SSurface::ClosestPointTo(Vector p, double *u, double *v, bool converge) {
|
|
int i, j;
|
|
|
|
if(degm == 1 && degn == 1) {
|
|
*u = *v = 0; // a plane, perfect no matter what the initial guess
|
|
} else {
|
|
double minDist = VERY_POSITIVE;
|
|
double res = (max(degm, degn) == 2) ? 7.0 : 20.0;
|
|
for(i = 0; i < (int)res; i++) {
|
|
for(j = 0; j <= (int)res; j++) {
|
|
double tryu = (i/res), tryv = (j/res);
|
|
|
|
Vector tryp = PointAt(tryu, tryv);
|
|
double d = (tryp.Minus(p)).Magnitude();
|
|
if(d < minDist) {
|
|
*u = tryu;
|
|
*v = tryv;
|
|
minDist = d;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Initial guess is in u, v
|
|
Vector p0;
|
|
for(i = 0; i < (converge ? 15 : 3); i++) {
|
|
p0 = PointAt(*u, *v);
|
|
if(converge) {
|
|
if(p0.Equals(p, RATPOLY_EPS)) {
|
|
return;
|
|
}
|
|
}
|
|
|
|
Vector tu, tv;
|
|
TangentsAt(*u, *v, &tu, &tv);
|
|
|
|
// Project the point into a plane through p0, with basis tu, tv; a
|
|
// second-order thing would converge faster but needs second
|
|
// derivatives.
|
|
Vector dp = p.Minus(p0);
|
|
double du = dp.Dot(tu), dv = dp.Dot(tv);
|
|
*u += du / (tu.MagSquared());
|
|
*v += dv / (tv.MagSquared());
|
|
}
|
|
|
|
if(converge) {
|
|
dbp("didn't converge");
|
|
dbp("have %.3f %.3f %.3f", CO(p0));
|
|
dbp("want %.3f %.3f %.3f", CO(p));
|
|
dbp("distance = %g", (p.Minus(p0)).Magnitude());
|
|
}
|
|
|
|
if(isnan(*u) || isnan(*v)) {
|
|
*u = *v = 0;
|
|
}
|
|
}
|
|
|
|
bool SSurface::PointIntersectingLine(Vector p0, Vector p1, double *u, double *v)
|
|
{
|
|
int i;
|
|
for(i = 0; i < 15; i++) {
|
|
Vector pi, p, tu, tv;
|
|
p = PointAt(*u, *v);
|
|
TangentsAt(*u, *v, &tu, &tv);
|
|
|
|
Vector n = (tu.Cross(tv)).WithMagnitude(1);
|
|
double d = p.Dot(n);
|
|
|
|
bool parallel;
|
|
pi = Vector::AtIntersectionOfPlaneAndLine(n, d, p0, p1, ¶llel);
|
|
if(parallel) break;
|
|
|
|
// Check for convergence
|
|
if(pi.Equals(p, RATPOLY_EPS)) return true;
|
|
|
|
// Adjust our guess and iterate
|
|
Vector dp = pi.Minus(p);
|
|
double du = dp.Dot(tu), dv = dp.Dot(tv);
|
|
*u += du / (tu.MagSquared());
|
|
*v += dv / (tv.MagSquared());
|
|
}
|
|
// dbp("didn't converge (surface intersecting line)");
|
|
return false;
|
|
}
|
|
|
|
void SSurface::PointOnSurfaces(SSurface *s1, SSurface *s2,
|
|
double *up, double *vp)
|
|
{
|
|
double u[3] = { *up, 0, 0 }, v[3] = { *vp, 0, 0 };
|
|
SSurface *srf[3] = { this, s1, s2 };
|
|
|
|
// Get initial guesses for (u, v) in the other surfaces
|
|
Vector p = PointAt(*u, *v);
|
|
(srf[1])->ClosestPointTo(p, &(u[1]), &(v[1]), false);
|
|
(srf[2])->ClosestPointTo(p, &(u[2]), &(v[2]), false);
|
|
|
|
int i, j;
|
|
for(i = 0; i < 15; i++) {
|
|
// Approximate each surface by a plane
|
|
Vector p[3], tu[3], tv[3], n[3];
|
|
double d[3];
|
|
for(j = 0; j < 3; j++) {
|
|
p[j] = (srf[j])->PointAt(u[j], v[j]);
|
|
(srf[j])->TangentsAt(u[j], v[j], &(tu[j]), &(tv[j]));
|
|
n[j] = ((tu[j]).Cross(tv[j])).WithMagnitude(1);
|
|
d[j] = (n[j]).Dot(p[j]);
|
|
}
|
|
|
|
// If a = b and b = c, then does a = c? No, it doesn't.
|
|
if((p[0]).Equals(p[1], RATPOLY_EPS) &&
|
|
(p[1]).Equals(p[2], RATPOLY_EPS) &&
|
|
(p[2]).Equals(p[0], RATPOLY_EPS))
|
|
{
|
|
*up = u[0];
|
|
*vp = v[0];
|
|
return;
|
|
}
|
|
|
|
bool parallel;
|
|
Vector pi = Vector::AtIntersectionOfPlanes(n[0], d[0],
|
|
n[1], d[1],
|
|
n[2], d[2], ¶llel);
|
|
if(parallel) break;
|
|
|
|
for(j = 0; j < 3; j++) {
|
|
Vector dp = pi.Minus(p[j]);
|
|
double du = dp.Dot(tu[j]), dv = dp.Dot(tv[j]);
|
|
u[j] += du / (tu[j]).MagSquared();
|
|
v[j] += dv / (tv[j]).MagSquared();
|
|
}
|
|
}
|
|
dbp("didn't converge (three surfaces intersecting)");
|
|
}
|
|
|
|
void SSurface::GetAxisAlignedBounding(Vector *ptMax, Vector *ptMin) {
|
|
*ptMax = Vector::From(VERY_NEGATIVE, VERY_NEGATIVE, VERY_NEGATIVE);
|
|
*ptMin = Vector::From(VERY_POSITIVE, VERY_POSITIVE, VERY_POSITIVE);
|
|
|
|
int i, j;
|
|
for(i = 0; i <= degm; i++) {
|
|
for(j = 0; j <= degn; j++) {
|
|
(ctrl[i][j]).MakeMaxMin(ptMax, ptMin);
|
|
}
|
|
}
|
|
}
|
|
|
|
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::MakeEdgesInto(SShell *shell, SEdgeList *sel, bool asUv,
|
|
SShell *useCurvesFrom) {
|
|
STrimBy *stb;
|
|
for(stb = trim.First(); stb; stb = trim.NextAfter(stb)) {
|
|
SCurve *sc = shell->curve.FindById(stb->curve);
|
|
|
|
// We have the option to use the curves from another shell; this
|
|
// is relevant when generating the coincident edges while doing the
|
|
// Booleans, since the curves from the output shell will be split
|
|
// against any intersecting surfaces (and the originals aren't).
|
|
if(useCurvesFrom) {
|
|
sc = useCurvesFrom->curve.FindById(sc->newH);
|
|
}
|
|
|
|
Vector prev, prevuv, ptuv;
|
|
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 *pt = &(sc->pts.elem[i]);
|
|
if(asUv) {
|
|
ClosestPointTo(*pt, &u, &v);
|
|
ptuv = Vector::From(u, v, 0);
|
|
if(inCurve) {
|
|
sel->AddEdge(prevuv, ptuv, sc->h.v, stb->backwards);
|
|
empty = false;
|
|
}
|
|
prevuv = ptuv;
|
|
} else {
|
|
if(inCurve) {
|
|
sel->AddEdge(prev, *pt, sc->h.v, stb->backwards);
|
|
empty = false;
|
|
}
|
|
prev = *pt;
|
|
}
|
|
|
|
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");
|
|
}
|
|
}
|
|
|
|
void SSurface::TriangulateInto(SShell *shell, SMesh *sm) {
|
|
SEdgeList el;
|
|
ZERO(&el);
|
|
|
|
MakeEdgesInto(shell, &el, true);
|
|
|
|
SPolygon poly;
|
|
ZERO(&poly);
|
|
if(el.AssemblePolygon(&poly, NULL, true)) {
|
|
int i, start = sm->l.n;
|
|
// Curved surfaces are triangulated in such a way as to minimize
|
|
// deviation between edges and surface; but doesn't matter for planes.
|
|
poly.UvTriangulateInto(sm, (degm == 1 && degn == 1) ? NULL : this);
|
|
|
|
STriMeta meta = { face, color };
|
|
for(i = start; i < sm->l.n; i++) {
|
|
STriangle *st = &(sm->l.elem[i]);
|
|
st->meta = meta;
|
|
st->an = NormalAt(st->a.x, st->a.y);
|
|
st->bn = NormalAt(st->b.x, st->b.y);
|
|
st->cn = NormalAt(st->c.x, st->c.y);
|
|
st->a = PointAt(st->a.x, st->a.y);
|
|
st->b = PointAt(st->b.x, st->b.y);
|
|
st->c = PointAt(st->c.x, st->c.y);
|
|
// Works out that my chosen contour direction is inconsistent with
|
|
// the triangle direction, sigh.
|
|
st->FlipNormal();
|
|
}
|
|
} else {
|
|
dbp("failed to assemble polygon to trim nurbs surface in uv space");
|
|
}
|
|
|
|
el.Clear();
|
|
poly.Clear();
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Reverse the parametrisation of one of our dimensions, which flips the
|
|
// normal. We therefore must reverse all our trim curves too. The uv
|
|
// coordinates change, but trim curves are stored as xyz so nothing happens
|
|
//-----------------------------------------------------------------------------
|
|
void SSurface::Reverse(void) {
|
|
int i, j;
|
|
for(i = 0; i < (degm+1)/2; i++) {
|
|
for(j = 0; j <= degn; j++) {
|
|
SWAP(Vector, ctrl[i][j], ctrl[degm-i][j]);
|
|
SWAP(double, weight[i][j], weight[degm-i][j]);
|
|
}
|
|
}
|
|
|
|
STrimBy *stb;
|
|
for(stb = trim.First(); stb; stb = trim.NextAfter(stb)) {
|
|
stb->backwards = !stb->backwards;
|
|
SWAP(Vector, stb->start, stb->finish);
|
|
}
|
|
}
|
|
|
|
void SSurface::Clear(void) {
|
|
trim.Clear();
|
|
}
|
|
|
|
void SShell::MakeFromExtrusionOf(SBezierLoopSet *sbls, Vector t0, Vector t1,
|
|
int color)
|
|
{
|
|
ZERO(this);
|
|
|
|
// Make the extrusion direction consistent with respect to the normal
|
|
// of the sketch we're extruding.
|
|
if((t0.Minus(t1)).Dot(sbls->normal) < 0) {
|
|
SWAP(Vector, t0, t1);
|
|
}
|
|
|
|
// Define a coordinate system to contain the original sketch, and get
|
|
// a bounding box in that csys
|
|
Vector n = sbls->normal.ScaledBy(-1);
|
|
Vector u = n.Normal(0), v = n.Normal(1);
|
|
Vector orig = sbls->point;
|
|
double umax = 1e-10, umin = 1e10;
|
|
sbls->GetBoundingProjd(u, orig, &umin, &umax);
|
|
double vmax = 1e-10, vmin = 1e10;
|
|
sbls->GetBoundingProjd(v, orig, &vmin, &vmax);
|
|
// and now fix things up so that all u and v lie between 0 and 1
|
|
orig = orig.Plus(u.ScaledBy(umin));
|
|
orig = orig.Plus(v.ScaledBy(vmin));
|
|
u = u.ScaledBy(umax - umin);
|
|
v = v.ScaledBy(vmax - vmin);
|
|
|
|
// So we can now generate the top and bottom surfaces of the extrusion,
|
|
// planes within a translated (and maybe mirrored) version of that csys.
|
|
SSurface s0, s1;
|
|
s0 = SSurface::FromPlane(orig.Plus(t0), u, v);
|
|
s0.color = color;
|
|
s1 = SSurface::FromPlane(orig.Plus(t1).Plus(u), u.ScaledBy(-1), v);
|
|
s1.color = color;
|
|
hSSurface hs0 = surface.AddAndAssignId(&s0),
|
|
hs1 = surface.AddAndAssignId(&s1);
|
|
|
|
// Now go through the input curves. For each one, generate its surface
|
|
// of extrusion, its two translated trim curves, and one trim line. We
|
|
// go through by loops so that we can assign the lines correctly.
|
|
SBezierLoop *sbl;
|
|
for(sbl = sbls->l.First(); sbl; sbl = sbls->l.NextAfter(sbl)) {
|
|
SBezier *sb;
|
|
|
|
typedef struct {
|
|
hSCurve hc;
|
|
hSSurface hs;
|
|
} TrimLine;
|
|
List<TrimLine> trimLines;
|
|
ZERO(&trimLines);
|
|
|
|
for(sb = sbl->l.First(); sb; sb = sbl->l.NextAfter(sb)) {
|
|
// Generate the surface of extrusion of this curve, and add
|
|
// it to the list
|
|
SSurface ss = SSurface::FromExtrusionOf(sb, t0, t1);
|
|
ss.color = color;
|
|
hSSurface hsext = surface.AddAndAssignId(&ss);
|
|
|
|
// Translate the curve by t0 and t1 to produce two trim curves
|
|
SCurve sc;
|
|
ZERO(&sc);
|
|
sc.isExact = true;
|
|
sc.exact = sb->TransformedBy(t0, Quaternion::IDENTITY);
|
|
(sc.exact).MakePwlInto(&(sc.pts));
|
|
sc.surfA = hs0;
|
|
sc.surfB = hsext;
|
|
hSCurve hc0 = curve.AddAndAssignId(&sc);
|
|
|
|
ZERO(&sc);
|
|
sc.isExact = true;
|
|
sc.exact = sb->TransformedBy(t1, Quaternion::IDENTITY);
|
|
(sc.exact).MakePwlInto(&(sc.pts));
|
|
sc.surfA = hs1;
|
|
sc.surfB = hsext;
|
|
hSCurve hc1 = curve.AddAndAssignId(&sc);
|
|
|
|
STrimBy stb0, stb1;
|
|
// The translated curves trim the flat top and bottom surfaces.
|
|
stb0 = STrimBy::EntireCurve(this, hc0, false);
|
|
stb1 = STrimBy::EntireCurve(this, hc1, true);
|
|
(surface.FindById(hs0))->trim.Add(&stb0);
|
|
(surface.FindById(hs1))->trim.Add(&stb1);
|
|
|
|
// The translated curves also trim the surface of extrusion.
|
|
stb0 = STrimBy::EntireCurve(this, hc0, true);
|
|
stb1 = STrimBy::EntireCurve(this, hc1, false);
|
|
(surface.FindById(hsext))->trim.Add(&stb0);
|
|
(surface.FindById(hsext))->trim.Add(&stb1);
|
|
|
|
// And form the trim line
|
|
Vector pt = sb->Finish();
|
|
ZERO(&sc);
|
|
sc.isExact = true;
|
|
sc.exact = SBezier::From(pt.Plus(t0), pt.Plus(t1));
|
|
(sc.exact).MakePwlInto(&(sc.pts));
|
|
hSCurve hl = curve.AddAndAssignId(&sc);
|
|
// save this for later
|
|
TrimLine tl;
|
|
tl.hc = hl;
|
|
tl.hs = hsext;
|
|
trimLines.Add(&tl);
|
|
}
|
|
|
|
int i;
|
|
for(i = 0; i < trimLines.n; i++) {
|
|
TrimLine *tl = &(trimLines.elem[i]);
|
|
SSurface *ss = surface.FindById(tl->hs);
|
|
|
|
TrimLine *tlp = &(trimLines.elem[WRAP(i-1, trimLines.n)]);
|
|
|
|
STrimBy stb;
|
|
stb = STrimBy::EntireCurve(this, tl->hc, true);
|
|
ss->trim.Add(&stb);
|
|
stb = STrimBy::EntireCurve(this, tlp->hc, false);
|
|
ss->trim.Add(&stb);
|
|
|
|
(curve.FindById(tl->hc))->surfA = ss->h;
|
|
(curve.FindById(tlp->hc))->surfB = ss->h;
|
|
}
|
|
trimLines.Clear();
|
|
}
|
|
}
|
|
|
|
void SShell::MakeFromCopyOf(SShell *a) {
|
|
MakeFromTransformationOf(a, Vector::From(0, 0, 0), Quaternion::IDENTITY);
|
|
}
|
|
|
|
void SShell::MakeFromTransformationOf(SShell *a, Vector t, Quaternion q) {
|
|
SSurface *s;
|
|
for(s = a->surface.First(); s; s = a->surface.NextAfter(s)) {
|
|
SSurface n;
|
|
n = SSurface::FromTransformationOf(s, t, q, true);
|
|
surface.Add(&n); // keeping the old ID
|
|
}
|
|
|
|
SCurve *c;
|
|
for(c = a->curve.First(); c; c = a->curve.NextAfter(c)) {
|
|
SCurve n;
|
|
n = SCurve::FromTransformationOf(c, t, q);
|
|
curve.Add(&n); // keeping the old ID
|
|
}
|
|
}
|
|
|
|
void SShell::MakeEdgesInto(SEdgeList *sel) {
|
|
SSurface *s;
|
|
for(s = surface.First(); s; s = surface.NextAfter(s)) {
|
|
s->MakeEdgesInto(this, sel, false);
|
|
}
|
|
}
|
|
|
|
void SShell::TriangulateInto(SMesh *sm) {
|
|
SSurface *s;
|
|
for(s = surface.First(); s; s = surface.NextAfter(s)) {
|
|
s->TriangulateInto(this, sm);
|
|
}
|
|
}
|
|
|
|
void SShell::Clear(void) {
|
|
SSurface *s;
|
|
for(s = surface.First(); s; s = surface.NextAfter(s)) {
|
|
s->Clear();
|
|
}
|
|
surface.Clear();
|
|
|
|
SCurve *c;
|
|
for(c = curve.First(); c; c = curve.NextAfter(c)) {
|
|
c->Clear();
|
|
}
|
|
curve.Clear();
|
|
}
|
|
|