Expr *ExprVector::Magnitude(void) {
Expr *r;
r = x->Square();
r = r->Plus(y->Square());
r = r->Plus(z->Square());
return r->Sqrt();
}
Expr *ExprVector::Dot(ExprVector b) {
Expr *r;
r = x->Times(b.x);
r = r->Plus(y->Times(b.y));
r = r->Plus(z->Times(b.z));
return r;
}
void ConstraintBase::GenerateReal(IdList<Equation,hEquation> *l) const {
Expr *exA = Expr::From(valA);
switch(type) {
case Type::PT_PT_DISTANCE:
AddEq(l, Distance(workplane, ptA, ptB)->Minus(exA), 0);
return;
case Type::PROJ_PT_DISTANCE: {
ExprVector pA = SK.GetEntity(ptA)->PointGetExprs(),
pB = SK.GetEntity(ptB)->PointGetExprs(),
dp = pB.Minus(pA);
ExprVector pp = SK.GetEntity(entityA)->VectorGetExprs();
pp = pp.WithMagnitude(Expr::From(1.0));
AddEq(l, (dp.Dot(pp))->Minus(exA), 0);
return;
}
case Type::PT_LINE_DISTANCE:
AddEq(l,
PointLineDistance(workplane, ptA, entityA)->Minus(exA), 0);
return;
case Type::PT_PLANE_DISTANCE: {
ExprVector pt = SK.GetEntity(ptA)->PointGetExprs();
AddEq(l, (PointPlaneDistance(pt, entityA))->Minus(exA), 0);
return;
}
case Type::PT_FACE_DISTANCE: {
ExprVector pt = SK.GetEntity(ptA)->PointGetExprs();
EntityBase *f = SK.GetEntity(entityA);
ExprVector p0 = f->FaceGetPointExprs();
ExprVector n = f->FaceGetNormalExprs();
AddEq(l, (pt.Minus(p0)).Dot(n)->Minus(exA), 0);
return;
}
case Type::EQUAL_LENGTH_LINES: {
EntityBase *a = SK.GetEntity(entityA);
EntityBase *b = SK.GetEntity(entityB);
AddEq(l, Distance(workplane, a->point[0], a->point[1])->Minus(
Distance(workplane, b->point[0], b->point[1])), 0);
return;
}
// These work on distance squared, since the pt-line distances are
// signed, and we want the absolute value.
case Type::EQ_LEN_PT_LINE_D: {
EntityBase *forLen = SK.GetEntity(entityA);
Expr *d1 = Distance(workplane, forLen->point[0], forLen->point[1]);
Expr *d2 = PointLineDistance(workplane, ptA, entityB);
AddEq(l, (d1->Square())->Minus(d2->Square()), 0);
return;
}
case Type::EQ_PT_LN_DISTANCES: {
Expr *d1 = PointLineDistance(workplane, ptA, entityA);
Expr *d2 = PointLineDistance(workplane, ptB, entityB);
AddEq(l, (d1->Square())->Minus(d2->Square()), 0);
return;
}
case Type::LENGTH_RATIO: {
EntityBase *a = SK.GetEntity(entityA);
EntityBase *b = SK.GetEntity(entityB);
Expr *la = Distance(workplane, a->point[0], a->point[1]);
Expr *lb = Distance(workplane, b->point[0], b->point[1]);
AddEq(l, (la->Div(lb))->Minus(exA), 0);
return;
}
case Type::LENGTH_DIFFERENCE: {
EntityBase *a = SK.GetEntity(entityA);
EntityBase *b = SK.GetEntity(entityB);
Expr *la = Distance(workplane, a->point[0], a->point[1]);
Expr *lb = Distance(workplane, b->point[0], b->point[1]);
AddEq(l, (la->Minus(lb))->Minus(exA), 0);
return;
}
case Type::DIAMETER: {
EntityBase *circle = SK.GetEntity(entityA);
Expr *r = circle->CircleGetRadiusExpr();
AddEq(l, (r->Times(Expr::From(2)))->Minus(exA), 0);
return;
}
case Type::EQUAL_RADIUS: {
EntityBase *c1 = SK.GetEntity(entityA);
EntityBase *c2 = SK.GetEntity(entityB);
AddEq(l, (c1->CircleGetRadiusExpr())->Minus(
c2->CircleGetRadiusExpr()), 0);
return;
}
case Type::EQUAL_LINE_ARC_LEN: {
EntityBase *line = SK.GetEntity(entityA),
*arc = SK.GetEntity(entityB);
// Get the line length
ExprVector l0 = SK.GetEntity(line->point[0])->PointGetExprs(),
l1 = SK.GetEntity(line->point[1])->PointGetExprs();
Expr *ll = (l1.Minus(l0)).Magnitude();
// And get the arc radius, and the cosine of its angle
EntityBase *ao = SK.GetEntity(arc->point[0]),
*as = SK.GetEntity(arc->point[1]),
*af = SK.GetEntity(arc->point[2]);
ExprVector aos = (as->PointGetExprs()).Minus(ao->PointGetExprs()),
aof = (af->PointGetExprs()).Minus(ao->PointGetExprs());
Expr *r = aof.Magnitude();
ExprVector n = arc->Normal()->NormalExprsN();
ExprVector u = aos.WithMagnitude(Expr::From(1.0));
ExprVector v = n.Cross(u);
// so in our new csys, we start at (1, 0, 0)
Expr *costheta = aof.Dot(u)->Div(r);
Expr *sintheta = aof.Dot(v)->Div(r);
double thetas, thetaf, dtheta;
arc->ArcGetAngles(&thetas, &thetaf, &dtheta);
Expr *theta;
if(dtheta < 3*PI/4) {
theta = costheta->ACos();
} else if(dtheta < 5*PI/4) {
// As the angle crosses pi, cos theta is not invertible;
// so use the sine to stop blowing up
theta = Expr::From(PI)->Minus(sintheta->ASin());
} else {
theta = (Expr::From(2*PI))->Minus(costheta->ACos());
}
// And write the equation; r*theta = L
AddEq(l, (r->Times(theta))->Minus(ll), 0);
return;
}
case Type::POINTS_COINCIDENT: {
EntityBase *a = SK.GetEntity(ptA);
EntityBase *b = SK.GetEntity(ptB);
if(workplane.v == EntityBase::FREE_IN_3D.v) {
ExprVector pa = a->PointGetExprs();
ExprVector pb = b->PointGetExprs();
AddEq(l, pa.x->Minus(pb.x), 0);
AddEq(l, pa.y->Minus(pb.y), 1);
AddEq(l, pa.z->Minus(pb.z), 2);
} else {
Expr *au, *av;
Expr *bu, *bv;
a->PointGetExprsInWorkplane(workplane, &au, &av);
b->PointGetExprsInWorkplane(workplane, &bu, &bv);
AddEq(l, au->Minus(bu), 0);
AddEq(l, av->Minus(bv), 1);
}
return;
}
case Type::PT_IN_PLANE:
// This one works the same, whether projected or not.
AddEq(l, PointPlaneDistance(
SK.GetEntity(ptA)->PointGetExprs(), entityA), 0);
return;
case Type::PT_ON_FACE: {
// a plane, n dot (p - p0) = 0
ExprVector p = SK.GetEntity(ptA)->PointGetExprs();
EntityBase *f = SK.GetEntity(entityA);
ExprVector p0 = f->FaceGetPointExprs();
ExprVector n = f->FaceGetNormalExprs();
AddEq(l, (p.Minus(p0)).Dot(n), 0);
return;
}
case Type::PT_ON_LINE:
if(workplane.v == EntityBase::FREE_IN_3D.v) {
EntityBase *ln = SK.GetEntity(entityA);
EntityBase *a = SK.GetEntity(ln->point[0]);
EntityBase *b = SK.GetEntity(ln->point[1]);
EntityBase *p = SK.GetEntity(ptA);
ExprVector ep = p->PointGetExprs();
ExprVector ea = a->PointGetExprs();
ExprVector eb = b->PointGetExprs();
ExprVector eab = ea.Minus(eb);
// Construct a vector from the point to either endpoint of
// the line segment, and choose the longer of these.
ExprVector eap = ea.Minus(ep);
ExprVector ebp = eb.Minus(ep);
ExprVector elp =
(ebp.Magnitude()->Eval() > eap.Magnitude()->Eval()) ?
ebp : eap;
if(p->group.v == group.v) {
AddEq(l, VectorsParallel(0, eab, elp), 0);
AddEq(l, VectorsParallel(1, eab, elp), 1);
} else {
AddEq(l, VectorsParallel(0, elp, eab), 0);
AddEq(l, VectorsParallel(1, elp, eab), 1);
}
} else {
AddEq(l, PointLineDistance(workplane, ptA, entityA), 0);
}
return;
case Type::PT_ON_CIRCLE: {
// This actually constrains the point to lie on the cylinder.
EntityBase *circle = SK.GetEntity(entityA);
ExprVector center = SK.GetEntity(circle->point[0])->PointGetExprs();
ExprVector pt = SK.GetEntity(ptA)->PointGetExprs();
EntityBase *normal = SK.GetEntity(circle->normal);
ExprVector u = normal->NormalExprsU(),
v = normal->NormalExprsV();
Expr *du = (center.Minus(pt)).Dot(u),
*dv = (center.Minus(pt)).Dot(v);
Expr *r = circle->CircleGetRadiusExpr();
AddEq(l,
((du->Square())->Plus(dv->Square()))->Minus(r->Square()), 0);
return;
}
case Type::AT_MIDPOINT:
if(workplane.v == EntityBase::FREE_IN_3D.v) {
EntityBase *ln = SK.GetEntity(entityA);
ExprVector a = SK.GetEntity(ln->point[0])->PointGetExprs();
ExprVector b = SK.GetEntity(ln->point[1])->PointGetExprs();
ExprVector m = (a.Plus(b)).ScaledBy(Expr::From(0.5));
if(ptA.v) {
ExprVector p = SK.GetEntity(ptA)->PointGetExprs();
AddEq(l, (m.x)->Minus(p.x), 0);
AddEq(l, (m.y)->Minus(p.y), 1);
AddEq(l, (m.z)->Minus(p.z), 2);
} else {
AddEq(l, PointPlaneDistance(m, entityB), 0);
}
} else {
EntityBase *ln = SK.GetEntity(entityA);
EntityBase *a = SK.GetEntity(ln->point[0]);
EntityBase *b = SK.GetEntity(ln->point[1]);
Expr *au, *av, *bu, *bv;
a->PointGetExprsInWorkplane(workplane, &au, &av);
b->PointGetExprsInWorkplane(workplane, &bu, &bv);
Expr *mu = Expr::From(0.5)->Times(au->Plus(bu));
Expr *mv = Expr::From(0.5)->Times(av->Plus(bv));
if(ptA.v) {
EntityBase *p = SK.GetEntity(ptA);
Expr *pu, *pv;
p->PointGetExprsInWorkplane(workplane, &pu, &pv);
AddEq(l, pu->Minus(mu), 0);
AddEq(l, pv->Minus(mv), 1);
} else {
ExprVector m = PointInThreeSpace(workplane, mu, mv);
AddEq(l, PointPlaneDistance(m, entityB), 0);
}
}
return;
case Type::SYMMETRIC:
if(workplane.v == EntityBase::FREE_IN_3D.v) {
EntityBase *plane = SK.GetEntity(entityA);
EntityBase *ea = SK.GetEntity(ptA);
EntityBase *eb = SK.GetEntity(ptB);
ExprVector a = ea->PointGetExprs();
ExprVector b = eb->PointGetExprs();
// The midpoint of the line connecting the symmetric points
// lies on the plane of the symmetry.
ExprVector m = (a.Plus(b)).ScaledBy(Expr::From(0.5));
AddEq(l, PointPlaneDistance(m, plane->h), 0);
// And projected into the plane of symmetry, the points are
// coincident.
Expr *au, *av, *bu, *bv;
ea->PointGetExprsInWorkplane(plane->h, &au, &av);
eb->PointGetExprsInWorkplane(plane->h, &bu, &bv);
AddEq(l, au->Minus(bu), 1);
AddEq(l, av->Minus(bv), 2);
} else {
EntityBase *plane = SK.GetEntity(entityA);
EntityBase *a = SK.GetEntity(ptA);
EntityBase *b = SK.GetEntity(ptB);
Expr *au, *av, *bu, *bv;
a->PointGetExprsInWorkplane(workplane, &au, &av);
b->PointGetExprsInWorkplane(workplane, &bu, &bv);
Expr *mu = Expr::From(0.5)->Times(au->Plus(bu));
Expr *mv = Expr::From(0.5)->Times(av->Plus(bv));
ExprVector m = PointInThreeSpace(workplane, mu, mv);
AddEq(l, PointPlaneDistance(m, plane->h), 0);
// Construct a vector within the workplane that is normal
// to the symmetry pane's normal (i.e., that lies in the
// plane of symmetry). The line connecting the points is
// perpendicular to that constructed vector.
EntityBase *w = SK.GetEntity(workplane);
ExprVector u = w->Normal()->NormalExprsU();
ExprVector v = w->Normal()->NormalExprsV();
ExprVector pa = a->PointGetExprs();
ExprVector pb = b->PointGetExprs();
ExprVector n;
Expr *d;
plane->WorkplaneGetPlaneExprs(&n, &d);
AddEq(l, (n.Cross(u.Cross(v))).Dot(pa.Minus(pb)), 1);
}
return;
case Type::SYMMETRIC_HORIZ:
case Type::SYMMETRIC_VERT: {
EntityBase *a = SK.GetEntity(ptA);
EntityBase *b = SK.GetEntity(ptB);
Expr *au, *av, *bu, *bv;
a->PointGetExprsInWorkplane(workplane, &au, &av);
b->PointGetExprsInWorkplane(workplane, &bu, &bv);
if(type == Type::SYMMETRIC_HORIZ) {
AddEq(l, av->Minus(bv), 0);
AddEq(l, au->Plus(bu), 1);
} else {
AddEq(l, au->Minus(bu), 0);
AddEq(l, av->Plus(bv), 1);
}
return;
}
case Type::SYMMETRIC_LINE: {
EntityBase *pa = SK.GetEntity(ptA);
EntityBase *pb = SK.GetEntity(ptB);
Expr *pau, *pav, *pbu, *pbv;
pa->PointGetExprsInWorkplane(workplane, &pau, &pav);
pb->PointGetExprsInWorkplane(workplane, &pbu, &pbv);
EntityBase *ln = SK.GetEntity(entityA);
EntityBase *la = SK.GetEntity(ln->point[0]);
EntityBase *lb = SK.GetEntity(ln->point[1]);
Expr *lau, *lav, *lbu, *lbv;
la->PointGetExprsInWorkplane(workplane, &lau, &lav);
lb->PointGetExprsInWorkplane(workplane, &lbu, &lbv);
Expr *dpu = pbu->Minus(pau), *dpv = pbv->Minus(pav);
Expr *dlu = lbu->Minus(lau), *dlv = lbv->Minus(lav);
// The line through the points is perpendicular to the line
// of symmetry.
AddEq(l, (dlu->Times(dpu))->Plus(dlv->Times(dpv)), 0);
// And the signed distances of the points to the line are
// equal in magnitude and opposite in sign, so sum to zero
Expr *dista = (dlv->Times(lau->Minus(pau)))->Minus(
(dlu->Times(lav->Minus(pav))));
Expr *distb = (dlv->Times(lau->Minus(pbu)))->Minus(
(dlu->Times(lav->Minus(pbv))));
AddEq(l, dista->Plus(distb), 1);
return;
}
case Type::HORIZONTAL:
case Type::VERTICAL: {
hEntity ha, hb;
if(entityA.v) {
EntityBase *e = SK.GetEntity(entityA);
ha = e->point[0];
hb = e->point[1];
} else {
ha = ptA;
hb = ptB;
}
EntityBase *a = SK.GetEntity(ha);
EntityBase *b = SK.GetEntity(hb);
Expr *au, *av, *bu, *bv;
a->PointGetExprsInWorkplane(workplane, &au, &av);
b->PointGetExprsInWorkplane(workplane, &bu, &bv);
AddEq(l, (type == Type::HORIZONTAL) ? av->Minus(bv) : au->Minus(bu), 0);
return;
}
case Type::SAME_ORIENTATION: {
EntityBase *a = SK.GetEntity(entityA);
EntityBase *b = SK.GetEntity(entityB);
if(b->group.v != group.v) {
swap(a, b);
}
ExprVector au = a->NormalExprsU(),
an = a->NormalExprsN();
ExprVector bu = b->NormalExprsU(),
bv = b->NormalExprsV(),
bn = b->NormalExprsN();
AddEq(l, VectorsParallel(0, an, bn), 0);
AddEq(l, VectorsParallel(1, an, bn), 1);
Expr *d1 = au.Dot(bv);
Expr *d2 = au.Dot(bu);
// Allow either orientation for the coordinate system, depending
// on how it was drawn.
if(fabs(d1->Eval()) < fabs(d2->Eval())) {
AddEq(l, d1, 2);
} else {
AddEq(l, d2, 2);
}
return;
}
case Type::PERPENDICULAR:
case Type::ANGLE: {
EntityBase *a = SK.GetEntity(entityA);
EntityBase *b = SK.GetEntity(entityB);
ExprVector ae = a->VectorGetExprs();
ExprVector be = b->VectorGetExprs();
if(other) ae = ae.ScaledBy(Expr::From(-1));
Expr *c = DirectionCosine(workplane, ae, be);
if(type == Type::ANGLE) {
// The direction cosine is equal to the cosine of the
// specified angle
Expr *rads = exA->Times(Expr::From(PI/180)),
*rc = rads->Cos();
double arc = fabs(rc->Eval());
// avoid false detection of inconsistent systems by gaining
// up as the difference in dot products gets small at small
// angles; doubles still have plenty of precision, only
// problem is that rank test
Expr *mult = Expr::From(arc > 0.99 ? 0.01/(1.00001 - arc) : 1);
AddEq(l, (c->Minus(rc))->Times(mult), 0);
} else {
// The dot product (and therefore the direction cosine)
// is equal to zero, perpendicular.
AddEq(l, c, 0);
}
return;
}
case Type::EQUAL_ANGLE: {
EntityBase *a = SK.GetEntity(entityA);
EntityBase *b = SK.GetEntity(entityB);
EntityBase *c = SK.GetEntity(entityC);
EntityBase *d = SK.GetEntity(entityD);
ExprVector ae = a->VectorGetExprs();
ExprVector be = b->VectorGetExprs();
ExprVector ce = c->VectorGetExprs();
ExprVector de = d->VectorGetExprs();
if(other) ae = ae.ScaledBy(Expr::From(-1));
Expr *cab = DirectionCosine(workplane, ae, be);
Expr *ccd = DirectionCosine(workplane, ce, de);
AddEq(l, cab->Minus(ccd), 0);
return;
}
case Type::ARC_LINE_TANGENT: {
EntityBase *arc = SK.GetEntity(entityA);
EntityBase *line = SK.GetEntity(entityB);
ExprVector ac = SK.GetEntity(arc->point[0])->PointGetExprs();
ExprVector ap =
SK.GetEntity(arc->point[other ? 2 : 1])->PointGetExprs();
ExprVector ld = line->VectorGetExprs();
// The line is perpendicular to the radius
AddEq(l, ld.Dot(ac.Minus(ap)), 0);
return;
}
case Type::CUBIC_LINE_TANGENT: {
EntityBase *cubic = SK.GetEntity(entityA);
EntityBase *line = SK.GetEntity(entityB);
ExprVector a;
if(other) {
a = cubic->CubicGetFinishTangentExprs();
} else {
a = cubic->CubicGetStartTangentExprs();
}
ExprVector b = line->VectorGetExprs();
if(workplane.v == EntityBase::FREE_IN_3D.v) {
AddEq(l, VectorsParallel(0, a, b), 0);
AddEq(l, VectorsParallel(1, a, b), 1);
} else {
EntityBase *w = SK.GetEntity(workplane);
ExprVector wn = w->Normal()->NormalExprsN();
AddEq(l, (a.Cross(b)).Dot(wn), 0);
}
return;
}
case Type::CURVE_CURVE_TANGENT: {
bool parallel = true;
int i;
ExprVector dir[2];
for(i = 0; i < 2; i++) {
EntityBase *e = SK.GetEntity((i == 0) ? entityA : entityB);
bool oth = (i == 0) ? other : other2;
if(e->type == Entity::Type::ARC_OF_CIRCLE) {
ExprVector center, endpoint;
center = SK.GetEntity(e->point[0])->PointGetExprs();
endpoint =
SK.GetEntity(e->point[oth ? 2 : 1])->PointGetExprs();
dir[i] = endpoint.Minus(center);
// We're using the vector from the center of the arc to
// an endpoint; so that's normal to the tangent, not
// parallel.
parallel = !parallel;
} else if(e->type == Entity::Type::CUBIC) {
if(oth) {
dir[i] = e->CubicGetFinishTangentExprs();
} else {
dir[i] = e->CubicGetStartTangentExprs();
}
} else {
ssassert(false, "Unexpected entity types for CURVE_CURVE_TANGENT");
}
}
if(parallel) {
EntityBase *w = SK.GetEntity(workplane);
ExprVector wn = w->Normal()->NormalExprsN();
AddEq(l, ((dir[0]).Cross(dir[1])).Dot(wn), 0);
} else {
AddEq(l, (dir[0]).Dot(dir[1]), 0);
}
return;
}
case Type::PARALLEL: {
EntityBase *ea = SK.GetEntity(entityA), *eb = SK.GetEntity(entityB);
if(eb->group.v != group.v) {
swap(ea, eb);
}
ExprVector a = ea->VectorGetExprs();
ExprVector b = eb->VectorGetExprs();
if(workplane.v == EntityBase::FREE_IN_3D.v) {
AddEq(l, VectorsParallel(0, a, b), 0);
AddEq(l, VectorsParallel(1, a, b), 1);
} else {
EntityBase *w = SK.GetEntity(workplane);
ExprVector wn = w->Normal()->NormalExprsN();
AddEq(l, (a.Cross(b)).Dot(wn), 0);
}
return;
}
case Type::WHERE_DRAGGED: {
EntityBase *ep = SK.GetEntity(ptA);
if(workplane.v == EntityBase::FREE_IN_3D.v) {
ExprVector ev = ep->PointGetExprs();
Vector v = ep->PointGetNum();
AddEq(l, ev.x->Minus(Expr::From(v.x)), 0);
AddEq(l, ev.y->Minus(Expr::From(v.y)), 1);
AddEq(l, ev.z->Minus(Expr::From(v.z)), 2);
} else {
Expr *u, *v;
ep->PointGetExprsInWorkplane(workplane, &u, &v);
AddEq(l, u->Minus(Expr::From(u->Eval())), 0);
AddEq(l, v->Minus(Expr::From(v->Eval())), 1);
}
return;
}
case Type::COMMENT:
return;
}
ssassert(false, "Unexpected constraint ID");
}