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1062 lines (915 loc) · 40.9 KB
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//-----------------------------------------------------------------------------
// Given a constraint, generate one or more equations in our symbolic algebra
// system to represent that constraint; also various geometric helper
// functions for that.
//
// Copyright 2008-2013 Jonathan Westhues.
//-----------------------------------------------------------------------------
#include "solvespace.h"
namespace SolveSpace {
const hConstraint ConstraintBase::NO_CONSTRAINT = { 0 };
bool ConstraintBase::HasLabel() const {
switch(type) {
case Type::PT_LINE_DISTANCE:
case Type::PT_PLANE_DISTANCE:
case Type::PT_FACE_DISTANCE:
case Type::PT_PT_DISTANCE:
case Type::PROJ_PT_DISTANCE:
case Type::DIAMETER:
case Type::LENGTH_RATIO:
case Type::ARC_ARC_LEN_RATIO:
case Type::ARC_LINE_LEN_RATIO:
case Type::LENGTH_DIFFERENCE:
case Type::ARC_ARC_DIFFERENCE:
case Type::ARC_LINE_DIFFERENCE:
case Type::ANGLE:
case Type::COMMENT:
return true;
default:
return false;
}
}
bool ConstraintBase::IsProjectible() const {
switch(type) {
case Type::POINTS_COINCIDENT:
case Type::PT_PT_DISTANCE:
case Type::PT_LINE_DISTANCE:
case Type::PT_ON_LINE:
case Type::EQUAL_LENGTH_LINES:
case Type::EQ_LEN_PT_LINE_D:
case Type::EQ_PT_LN_DISTANCES:
case Type::EQUAL_ANGLE:
case Type::LENGTH_RATIO:
case Type::ARC_ARC_LEN_RATIO:
case Type::ARC_LINE_LEN_RATIO:
case Type::LENGTH_DIFFERENCE:
case Type::ARC_ARC_DIFFERENCE:
case Type::ARC_LINE_DIFFERENCE:
case Type::SYMMETRIC:
case Type::SYMMETRIC_HORIZ:
case Type::SYMMETRIC_VERT:
case Type::SYMMETRIC_LINE:
case Type::AT_MIDPOINT:
case Type::HORIZONTAL:
case Type::VERTICAL:
case Type::ANGLE:
case Type::PARALLEL:
case Type::PERPENDICULAR:
case Type::WHERE_DRAGGED:
case Type::COMMENT:
return true;
case Type::PT_PLANE_DISTANCE:
case Type::PT_FACE_DISTANCE:
case Type::PROJ_PT_DISTANCE:
case Type::PT_IN_PLANE:
case Type::PT_ON_FACE:
case Type::EQUAL_LINE_ARC_LEN:
case Type::DIAMETER:
case Type::PT_ON_CIRCLE:
case Type::SAME_ORIENTATION:
case Type::CUBIC_LINE_TANGENT:
case Type::CURVE_CURVE_TANGENT:
case Type::ARC_LINE_TANGENT:
case Type::EQUAL_RADIUS:
return false;
}
ssassert(false, "Impossible");
}
ExprVector ConstraintBase::VectorsParallel3d(ExprVector a, ExprVector b, hParam p) {
return a.Minus(b.ScaledBy(Expr::From(p)));
}
Expr *ConstraintBase::PointLineDistance(hEntity wrkpl, hEntity hpt, hEntity hln)
{
EntityBase *ln = SK.GetEntity(hln);
EntityBase *a = SK.GetEntity(ln->point[0]);
EntityBase *b = SK.GetEntity(ln->point[1]);
EntityBase *p = SK.GetEntity(hpt);
if(wrkpl == EntityBase::FREE_IN_3D) {
ExprVector ep = p->PointGetExprs();
ExprVector ea = a->PointGetExprs();
ExprVector eb = b->PointGetExprs();
ExprVector eab = ea.Minus(eb);
Expr *m = eab.Magnitude();
return ((eab.Cross(ea.Minus(ep))).Magnitude())->Div(m);
} else {
Expr *ua, *va, *ub, *vb;
a->PointGetExprsInWorkplane(wrkpl, &ua, &va);
b->PointGetExprsInWorkplane(wrkpl, &ub, &vb);
Expr *du = ua->Minus(ub);
Expr *dv = va->Minus(vb);
Expr *u, *v;
p->PointGetExprsInWorkplane(wrkpl, &u, &v);
Expr *m = ((du->Square())->Plus(dv->Square()))->Sqrt();
Expr *proj = (dv->Times(ua->Minus(u)))->Minus(
(du->Times(va->Minus(v))));
return proj->Div(m);
}
}
Expr *ConstraintBase::PointPlaneDistance(ExprVector p, hEntity hpl) {
ExprVector n;
Expr *d;
SK.GetEntity(hpl)->WorkplaneGetPlaneExprs(&n, &d);
return (p.Dot(n))->Minus(d);
}
Expr *ConstraintBase::Distance(hEntity wrkpl, hEntity hpa, hEntity hpb) {
EntityBase *pa = SK.GetEntity(hpa);
EntityBase *pb = SK.GetEntity(hpb);
ssassert(pa->IsPoint() && pb->IsPoint(),
"Expected two points to measure projected distance between");
if(wrkpl == EntityBase::FREE_IN_3D) {
// This is true distance
ExprVector ea, eb, eab;
ea = pa->PointGetExprs();
eb = pb->PointGetExprs();
eab = ea.Minus(eb);
return eab.Magnitude();
} else {
// This is projected distance, in the given workplane.
Expr *au, *av, *bu, *bv;
pa->PointGetExprsInWorkplane(wrkpl, &au, &av);
pb->PointGetExprsInWorkplane(wrkpl, &bu, &bv);
Expr *du = au->Minus(bu);
Expr *dv = av->Minus(bv);
return ((du->Square())->Plus(dv->Square()))->Sqrt();
}
}
//-----------------------------------------------------------------------------
// Return the cosine of the angle between two vectors. If a workplane is
// specified, then it's the cosine of their projections into that workplane.
//-----------------------------------------------------------------------------
Expr *ConstraintBase::DirectionCosine(hEntity wrkpl,
ExprVector ae, ExprVector be)
{
if(wrkpl == EntityBase::FREE_IN_3D) {
Expr *mags = (ae.Magnitude())->Times(be.Magnitude());
return (ae.Dot(be))->Div(mags);
} else {
EntityBase *w = SK.GetEntity(wrkpl);
ExprVector u = w->Normal()->NormalExprsU();
ExprVector v = w->Normal()->NormalExprsV();
Expr *ua = u.Dot(ae);
Expr *va = v.Dot(ae);
Expr *ub = u.Dot(be);
Expr *vb = v.Dot(be);
Expr *maga = (ua->Square()->Plus(va->Square()))->Sqrt();
Expr *magb = (ub->Square()->Plus(vb->Square()))->Sqrt();
Expr *dot = (ua->Times(ub))->Plus(va->Times(vb));
return dot->Div(maga->Times(magb));
}
}
ExprVector ConstraintBase::PointInThreeSpace(hEntity workplane,
Expr *u, Expr *v)
{
EntityBase *w = SK.GetEntity(workplane);
ExprVector ub = w->Normal()->NormalExprsU();
ExprVector vb = w->Normal()->NormalExprsV();
ExprVector ob = w->WorkplaneGetOffsetExprs();
return (ub.ScaledBy(u)).Plus(vb.ScaledBy(v)).Plus(ob);
}
void ConstraintBase::ModifyToSatisfy() {
if(type == Type::ANGLE) {
Vector a = SK.GetEntity(entityA)->VectorGetNum();
Vector b = SK.GetEntity(entityB)->VectorGetNum();
if(other) a = a.ScaledBy(-1);
if(workplane != EntityBase::FREE_IN_3D) {
a = a.ProjectVectorInto(workplane);
b = b.ProjectVectorInto(workplane);
}
double c = (a.Dot(b))/(a.Magnitude() * b.Magnitude());
valA = acos(c)*180/PI;
} else if(type == Type::PT_ON_LINE) {
EntityBase *eln = SK.GetEntity(entityA);
EntityBase *ea = SK.GetEntity(eln->point[0]);
EntityBase *eb = SK.GetEntity(eln->point[1]);
EntityBase *ep = SK.GetEntity(ptA);
ExprVector exp = ep->PointGetExprsInWorkplane(workplane);
ExprVector exa = ea->PointGetExprsInWorkplane(workplane);
ExprVector exb = eb->PointGetExprsInWorkplane(workplane);
ExprVector exba = exb.Minus(exa);
SK.GetParam(valP)->val = exba.Dot(exp.Minus(exa))->Eval() / exba.Dot(exba)->Eval();
} else {
// We'll fix these ones up by looking at their symbolic equation;
// that means no extra work.
IdList<Equation,hEquation> l = {};
// Generate the equations even if this is a reference dimension
GenerateEquations(&l, /*forReference=*/true);
ssassert(l.n == 1, "Expected constraint to generate a single equation");
// These equations are written in the form f(...) - d = 0, where
// d is the value of the valA.
valA += (l[0].e)->Eval();
l.Clear();
}
}
void ConstraintBase::AddEq(IdList<Equation,hEquation> *l, Expr *expr, int index) const
{
Equation eq;
eq.e = expr;
eq.h = h.equation(index);
l->Add(&eq);
}
void ConstraintBase::AddEq(IdList<Equation,hEquation> *l, const ExprVector &v,
int baseIndex) const {
AddEq(l, v.x, baseIndex);
AddEq(l, v.y, baseIndex + 1);
if(workplane == EntityBase::FREE_IN_3D) {
AddEq(l, v.z, baseIndex + 2);
}
}
void ConstraintBase::Generate(ParamList *l) {
switch(type) {
case Type::PARALLEL:
case Type::CUBIC_LINE_TANGENT:
// Add new parameter only when we operate in 3d space
if(workplane != EntityBase::FREE_IN_3D) break;
// fallthrough
case Type::SAME_ORIENTATION:
case Type::PT_ON_LINE: {
Param p = {};
valP = h.param(0);
p.h = valP;
l->Add(&p);
break;
}
default:
break;
}
}
void ConstraintBase::GenerateEquations(IdList<Equation,hEquation> *l,
bool forReference) const {
if(reference && !forReference) return;
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::ARC_ARC_LEN_RATIO: {
EntityBase *arc1 = SK.GetEntity(entityA),
*arc2 = SK.GetEntity(entityB);
// And get the arc1 radius, and the cosine of its angle
EntityBase *ao1 = SK.GetEntity(arc1->point[0]),
*as1 = SK.GetEntity(arc1->point[1]),
*af1 = SK.GetEntity(arc1->point[2]);
ExprVector aos1 = (as1->PointGetExprs()).Minus(ao1->PointGetExprs()),
aof1 = (af1->PointGetExprs()).Minus(ao1->PointGetExprs());
Expr *r1 = aof1.Magnitude();
ExprVector n1 = arc1->Normal()->NormalExprsN();
ExprVector u1 = aos1.WithMagnitude(Expr::From(1.0));
ExprVector v1 = n1.Cross(u1);
// so in our new csys, we start at (1, 0, 0)
Expr *costheta1 = aof1.Dot(u1)->Div(r1);
Expr *sintheta1 = aof1.Dot(v1)->Div(r1);
double thetas1, thetaf1, dtheta1;
arc1->ArcGetAngles(&thetas1, &thetaf1, &dtheta1);
Expr *theta1;
if(dtheta1 < 3*PI/4) {
theta1 = costheta1->ACos();
} else if(dtheta1 < 5*PI/4) {
// As the angle crosses pi, cos theta1 is not invertible;
// so use the sine to stop blowing up
theta1 = Expr::From(PI)->Minus(sintheta1->ASin());
} else {
theta1 = (Expr::From(2*PI))->Minus(costheta1->ACos());
}
// And get the arc2 radius, and the cosine of its angle
EntityBase *ao2 = SK.GetEntity(arc2->point[0]),
*as2 = SK.GetEntity(arc2->point[1]),
*af2 = SK.GetEntity(arc2->point[2]);
ExprVector aos2 = (as2->PointGetExprs()).Minus(ao2->PointGetExprs()),
aof2 = (af2->PointGetExprs()).Minus(ao2->PointGetExprs());
Expr *r2 = aof2.Magnitude();
ExprVector n2 = arc2->Normal()->NormalExprsN();
ExprVector u2 = aos2.WithMagnitude(Expr::From(1.0));
ExprVector v2 = n2.Cross(u2);
// so in our new csys, we start at (1, 0, 0)
Expr *costheta2 = aof2.Dot(u2)->Div(r2);
Expr *sintheta2 = aof2.Dot(v2)->Div(r2);
double thetas2, thetaf2, dtheta2;
arc2->ArcGetAngles(&thetas2, &thetaf2, &dtheta2);
Expr *theta2;
if(dtheta2 < 3*PI/4) {
theta2 = costheta2->ACos();
} else if(dtheta2 < 5*PI/4) {
// As the angle crosses pi, cos theta2 is not invertible;
// so use the sine to stop blowing up
theta2 = Expr::From(PI)->Minus(sintheta2->ASin());
} else {
theta2 = (Expr::From(2*PI))->Minus(costheta2->ACos());
}
// And write the equation; (r1*theta1) / ( r2*theta2) = some ratio
AddEq(l, (r1->Times(theta1))->Div(r2->Times(theta2))->Minus(exA), 0);
return;
}
case Type::ARC_LINE_LEN_RATIO: {
EntityBase *line = SK.GetEntity(entityA),
*arc1 = SK.GetEntity(entityB);
Expr *ll = Distance(workplane, line->point[0], line->point[1]);
// And get the arc1 radius, and the cosine of its angle
EntityBase *ao1 = SK.GetEntity(arc1->point[0]),
*as1 = SK.GetEntity(arc1->point[1]),
*af1 = SK.GetEntity(arc1->point[2]);
ExprVector aos1 = (as1->PointGetExprs()).Minus(ao1->PointGetExprs()),
aof1 = (af1->PointGetExprs()).Minus(ao1->PointGetExprs());
Expr *r1 = aof1.Magnitude();
ExprVector n1 = arc1->Normal()->NormalExprsN();
ExprVector u1 = aos1.WithMagnitude(Expr::From(1.0));
ExprVector v1 = n1.Cross(u1);
// so in our new csys, we start at (1, 0, 0)
Expr *costheta1 = aof1.Dot(u1)->Div(r1);
Expr *sintheta1 = aof1.Dot(v1)->Div(r1);
double thetas1, thetaf1, dtheta1;
arc1->ArcGetAngles(&thetas1, &thetaf1, &dtheta1);
Expr *theta1;
if(dtheta1 < 3*PI/4) {
theta1 = costheta1->ACos();
} else if(dtheta1 < 5*PI/4) {
// As the angle crosses pi, cos theta1 is not invertible;
// so use the sine to stop blowing up
theta1 = Expr::From(PI)->Minus(sintheta1->ASin());
} else {
theta1 = (Expr::From(2*PI))->Minus(costheta1->ACos());
}
// And write the equation; (r1*theta1) / ( length) = some ratio
AddEq(l, (r1->Times(theta1))->Div(ll)->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::ARC_ARC_DIFFERENCE: {
EntityBase *arc1 = SK.GetEntity(entityA),
*arc2 = SK.GetEntity(entityB);
// And get the arc1 radius, and the cosine of its angle
EntityBase *ao1 = SK.GetEntity(arc1->point[0]),
*as1 = SK.GetEntity(arc1->point[1]),
*af1 = SK.GetEntity(arc1->point[2]);
ExprVector aos1 = (as1->PointGetExprs()).Minus(ao1->PointGetExprs()),
aof1 = (af1->PointGetExprs()).Minus(ao1->PointGetExprs());
Expr *r1 = aof1.Magnitude();
ExprVector n1 = arc1->Normal()->NormalExprsN();
ExprVector u1 = aos1.WithMagnitude(Expr::From(1.0));
ExprVector v1 = n1.Cross(u1);
// so in our new csys, we start at (1, 0, 0)
Expr *costheta1 = aof1.Dot(u1)->Div(r1);
Expr *sintheta1 = aof1.Dot(v1)->Div(r1);
double thetas1, thetaf1, dtheta1;
arc1->ArcGetAngles(&thetas1, &thetaf1, &dtheta1);
Expr *theta1;
if(dtheta1 < 3*PI/4) {
theta1 = costheta1->ACos();
} else if(dtheta1 < 5*PI/4) {
// As the angle crosses pi, cos theta1 is not invertible;
// so use the sine to stop blowing up
theta1 = Expr::From(PI)->Minus(sintheta1->ASin());
} else {
theta1 = (Expr::From(2*PI))->Minus(costheta1->ACos());
}
// And get the arc2 radius, and the cosine of its angle
EntityBase *ao2 = SK.GetEntity(arc2->point[0]),
*as2 = SK.GetEntity(arc2->point[1]),
*af2 = SK.GetEntity(arc2->point[2]);
ExprVector aos2 = (as2->PointGetExprs()).Minus(ao2->PointGetExprs()),
aof2 = (af2->PointGetExprs()).Minus(ao2->PointGetExprs());
Expr *r2 = aof2.Magnitude();
ExprVector n2 = arc2->Normal()->NormalExprsN();
ExprVector u2 = aos2.WithMagnitude(Expr::From(1.0));
ExprVector v2 = n2.Cross(u2);
// so in our new csys, we start at (1, 0, 0)
Expr *costheta2 = aof2.Dot(u2)->Div(r2);
Expr *sintheta2 = aof2.Dot(v2)->Div(r2);
double thetas2, thetaf2, dtheta2;
arc2->ArcGetAngles(&thetas2, &thetaf2, &dtheta2);
Expr *theta2;
if(dtheta2 < 3*PI/4) {
theta2 = costheta2->ACos();
} else if(dtheta2 < 5*PI/4) {
// As the angle crosses pi, cos theta2 is not invertible;
// so use the sine to stop blowing up
theta2 = Expr::From(PI)->Minus(sintheta2->ASin());
} else {
theta2 = (Expr::From(2*PI))->Minus(costheta2->ACos());
}
// And write the equation; (r1*theta1) - ( r2*theta2) = some difference
AddEq(l, (r1->Times(theta1))->Minus(r2->Times(theta2))->Minus(exA), 0);
return;
}
case Type::ARC_LINE_DIFFERENCE: {
EntityBase *line = SK.GetEntity(entityA),
*arc1 = SK.GetEntity(entityB);
Expr *ll = Distance(workplane, line->point[0], line->point[1]);
// And get the arc1 radius, and the cosine of its angle
EntityBase *ao1 = SK.GetEntity(arc1->point[0]),
*as1 = SK.GetEntity(arc1->point[1]),
*af1 = SK.GetEntity(arc1->point[2]);
ExprVector aos1 = (as1->PointGetExprs()).Minus(ao1->PointGetExprs()),
aof1 = (af1->PointGetExprs()).Minus(ao1->PointGetExprs());
Expr *r1 = aof1.Magnitude();
ExprVector n1 = arc1->Normal()->NormalExprsN();
ExprVector u1 = aos1.WithMagnitude(Expr::From(1.0));
ExprVector v1 = n1.Cross(u1);
// so in our new csys, we start at (1, 0, 0)
Expr *costheta1 = aof1.Dot(u1)->Div(r1);
Expr *sintheta1 = aof1.Dot(v1)->Div(r1);
double thetas1, thetaf1, dtheta1;
arc1->ArcGetAngles(&thetas1, &thetaf1, &dtheta1);
Expr *theta1;
if(dtheta1 < 3*PI/4) {
theta1 = costheta1->ACos();
} else if(dtheta1 < 5*PI/4) {
// As the angle crosses pi, cos theta1 is not invertible;
// so use the sine to stop blowing up
theta1 = Expr::From(PI)->Minus(sintheta1->ASin());
} else {
theta1 = (Expr::From(2*PI))->Minus(costheta1->ACos());
}
// And write the equation; (r1*theta1) - ( length) = some difference
AddEq(l, (r1->Times(theta1))->Minus(ll)->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 == EntityBase::FREE_IN_3D) {
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: {
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->PointGetExprsInWorkplane(workplane);
ExprVector ea = a->PointGetExprsInWorkplane(workplane);
ExprVector eb = b->PointGetExprsInWorkplane(workplane);
ExprVector ptOnLine = ea.Plus(eb.Minus(ea).ScaledBy(Expr::From(valP)));
ExprVector eq = ptOnLine.Minus(ep);
AddEq(l, eq);
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())->Sqrt()->Minus(r), 0);
return;
}
case Type::AT_MIDPOINT:
if(workplane == EntityBase::FREE_IN_3D) {
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 == EntityBase::FREE_IN_3D) {
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: {
ssassert(workplane != Entity::FREE_IN_3D,
"Unexpected horizontal/vertical symmetric constraint in 3d");
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: {
ssassert(workplane != Entity::FREE_IN_3D,
"Unexpected horizontal/vertical constraint in 3d");
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);
ExprVector au = a->NormalExprsU(),
an = a->NormalExprsN();
ExprVector bu = b->NormalExprsU(),
bv = b->NormalExprsV(),
bn = b->NormalExprsN();
ExprVector eq = VectorsParallel3d(an, bn, valP);
AddEq(l, eq.x, 0);
AddEq(l, eq.y, 1);
AddEq(l, eq.z, 2);
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, 3);
} else {
AddEq(l, d2, 3);
}
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 == EntityBase::FREE_IN_3D) {
ExprVector eq = VectorsParallel3d(a, b, valP);
AddEq(l, eq);
} 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) { // BRANCH_ALWAYS_TAKEN
if(oth) {
dir[i] = e->CubicGetFinishTangentExprs();
} else {
dir[i] = e->CubicGetStartTangentExprs();
}
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