solvespace/entity.cpp

#include "solvespace.h"

char *Entity::DescriptionString(void) {
    if(h.isFromRequest()) {
        Request *r = SS.GetRequest(h.request());
        return r->DescriptionString();
    } else {
        Group *g = SS.GetGroup(h.group());
        return g->DescriptionString();
    }
}

bool Entity::HasVector(void) {
    switch(type) {
        case LINE_SEGMENT:
        case NORMAL_IN_3D:
        case NORMAL_IN_2D:
        case NORMAL_N_COPY:
        case NORMAL_N_ROT:
        case NORMAL_N_ROT_AA:
            return true;

        default:
            return false;
    }
}

ExprVector Entity::VectorGetExprs(void) {
    switch(type) {
        case LINE_SEGMENT:
            return (SS.GetEntity(point[0])->PointGetExprs()).Minus(
                    SS.GetEntity(point[1])->PointGetExprs());

        case NORMAL_IN_3D:
        case NORMAL_IN_2D:
        case NORMAL_N_COPY:
        case NORMAL_N_ROT:
        case NORMAL_N_ROT_AA:
            return NormalExprsN();

        default: oops();
    }
}

Vector Entity::VectorGetNum(void) {
    switch(type) {
        case LINE_SEGMENT:
            return (SS.GetEntity(point[0])->PointGetNum()).Minus(
                    SS.GetEntity(point[1])->PointGetNum());

        case NORMAL_IN_3D:
        case NORMAL_IN_2D:
        case NORMAL_N_COPY:
        case NORMAL_N_ROT:
        case NORMAL_N_ROT_AA:
            return NormalN();

        default: oops();
    }
}

Vector Entity::VectorGetRefPoint(void) {
    switch(type) {
        case LINE_SEGMENT:
            return ((SS.GetEntity(point[0])->PointGetNum()).Plus(
                     SS.GetEntity(point[1])->PointGetNum())).ScaledBy(0.5);

        case NORMAL_IN_3D:
        case NORMAL_IN_2D:
        case NORMAL_N_COPY:
        case NORMAL_N_ROT:
        case NORMAL_N_ROT_AA:
            return SS.GetEntity(point[0])->PointGetNum();

        default: oops();
    }
}

bool Entity::IsCircle(void) {
    return (type == CIRCLE) || (type == ARC_OF_CIRCLE);
}

Expr *Entity::CircleGetRadiusExpr(void) {
    if(type == CIRCLE) {
        return SS.GetEntity(distance)->DistanceGetExpr();
    } else if(type == ARC_OF_CIRCLE) {
        return Constraint::Distance(workplane, point[0], point[1]);
    } else oops();
}

double Entity::CircleGetRadiusNum(void) {
    if(type == CIRCLE) {
        return SS.GetEntity(distance)->DistanceGetNum();
    } else if(type == ARC_OF_CIRCLE) {
        Vector c  = SS.GetEntity(point[0])->PointGetNum();
        Vector pa = SS.GetEntity(point[1])->PointGetNum();
        return (pa.Minus(c)).Magnitude();
    } else oops();
}

void Entity::ArcGetAngles(double *thetaa, double *thetab, double *dtheta) {
    if(type != ARC_OF_CIRCLE) oops();

    Quaternion q = Normal()->NormalGetNum();
    Vector u = q.RotationU(), v = q.RotationV();

    Vector c  = SS.GetEntity(point[0])->PointGetNum();
    Vector pa = SS.GetEntity(point[1])->PointGetNum();
    Vector pb = SS.GetEntity(point[2])->PointGetNum();

    Point2d c2  = c.Project2d(u, v);
    Point2d pa2 = (pa.Project2d(u, v)).Minus(c2);
    Point2d pb2 = (pb.Project2d(u, v)).Minus(c2);

    *thetaa = atan2(pa2.y, pa2.x);
    *thetab = atan2(pb2.y, pb2.x);
    *dtheta = *thetab - *thetaa;
    while(*dtheta < 0) *dtheta += 2*PI;
    while(*dtheta > (2*PI)) *dtheta -= 2*PI;
}

bool Entity::IsWorkplane(void) {
    return (type == WORKPLANE);
}

ExprVector Entity::WorkplaneGetOffsetExprs(void) {
    return SS.GetEntity(point[0])->PointGetExprs();
}

Vector Entity::WorkplaneGetOffset(void) {
    return SS.GetEntity(point[0])->PointGetNum();
}

void Entity::WorkplaneGetPlaneExprs(ExprVector *n, Expr **dn) {
    if(type == WORKPLANE) {
        *n = Normal()->NormalExprsN();

        ExprVector p0 = SS.GetEntity(point[0])->PointGetExprs();
        // The plane is n dot (p - p0) = 0, or
        //              n dot p - n dot p0 = 0
        // so dn = n dot p0
        *dn = p0.Dot(*n);
    } else {
        oops();
    }
}

double Entity::DistanceGetNum(void) {
    if(type == DISTANCE) {
        return SS.GetParam(param[0])->val;
    } else if(type == DISTANCE_N_COPY) {
        return numDistance;
    } else oops();
}
Expr *Entity::DistanceGetExpr(void) {
    if(type == DISTANCE) {
        return Expr::From(param[0]);
    } else if(type == DISTANCE_N_COPY) {
        return Expr::From(numDistance);
    } else oops();
}
void Entity::DistanceForceTo(double v) {
    if(type == DISTANCE) {
        (SS.GetParam(param[0]))->val = v;
    } else if(type == DISTANCE_N_COPY) {
        // do nothing, it's locked
    } else oops();
}

Entity *Entity::Normal(void) {
    return SS.GetEntity(normal);
}

bool Entity::IsPoint(void) {
    switch(type) {
        case POINT_IN_3D:
        case POINT_IN_2D:
        case POINT_N_COPY:
        case POINT_N_TRANS:
        case POINT_N_ROT_TRANS:
        case POINT_N_ROT_AA:
            return true;

        default:
            return false;
    }
}

bool Entity::IsNormal(void) {
    switch(type) {
        case NORMAL_IN_3D:
        case NORMAL_IN_2D:
        case NORMAL_N_COPY:
        case NORMAL_N_ROT:
        case NORMAL_N_ROT_AA:
            return true;

        default:           return false;
    }
}

Quaternion Entity::NormalGetNum(void) {
    Quaternion q;
    switch(type) {
        case NORMAL_IN_3D:
            q = Quaternion::From(param[0], param[1], param[2], param[3]);
            break;

        case NORMAL_IN_2D: {
            Entity *wrkpl = SS.GetEntity(workplane);
            Entity *norm = SS.GetEntity(wrkpl->normal);
            q = norm->NormalGetNum();
            break;
        }
        case NORMAL_N_COPY:
            q = numNormal;
            break;

        case NORMAL_N_ROT:
            q = Quaternion::From(param[0], param[1], param[2], param[3]);
            q = q.Times(numNormal);
            break;

        case NORMAL_N_ROT_AA: {
            double theta = timesApplied*SS.GetParam(param[0])->val;
            double s = sin(theta), c = cos(theta);
            q.w = c;
            q.vx = s*SS.GetParam(param[1])->val;
            q.vy = s*SS.GetParam(param[2])->val;
            q.vz = s*SS.GetParam(param[3])->val;
            q = q.Times(numNormal);
            break;
        }

        default: oops();
    }
    return q;
}

void Entity::NormalForceTo(Quaternion q) {
    switch(type) {
        case NORMAL_IN_3D:
            SS.GetParam(param[0])->val = q.w;
            SS.GetParam(param[1])->val = q.vx;
            SS.GetParam(param[2])->val = q.vy;
            SS.GetParam(param[3])->val = q.vz;
            break;

        case NORMAL_IN_2D:
        case NORMAL_N_COPY:
            // There's absolutely nothing to do; these are locked.
            break;
        case NORMAL_N_ROT: {
            Quaternion qp = q.Times(numNormal.Inverse());
            
            SS.GetParam(param[0])->val = qp.w;
            SS.GetParam(param[1])->val = qp.vx;
            SS.GetParam(param[2])->val = qp.vy;
            SS.GetParam(param[3])->val = qp.vz;
            break;
        }

        case NORMAL_N_ROT_AA:
            // Not sure if I'll bother implementing this one
            break;

        default: oops();
    }
}

Vector Entity::NormalU(void) {
    return NormalGetNum().RotationU();
}
Vector Entity::NormalV(void) {
    return NormalGetNum().RotationV();
}
Vector Entity::NormalN(void) {
    return NormalGetNum().RotationN();
}

ExprVector Entity::NormalExprsU(void) {
    return NormalGetExprs().RotationU();
}
ExprVector Entity::NormalExprsV(void) {
    return NormalGetExprs().RotationV();
}
ExprVector Entity::NormalExprsN(void) {
    return NormalGetExprs().RotationN();
}

ExprQuaternion Entity::NormalGetExprs(void) {
    ExprQuaternion q;
    switch(type) {
        case NORMAL_IN_3D:
            q = ExprQuaternion::From(param[0], param[1], param[2], param[3]);
            break;

        case NORMAL_IN_2D: {
            Entity *wrkpl = SS.GetEntity(workplane);
            Entity *norm = SS.GetEntity(wrkpl->normal);
            q = norm->NormalGetExprs();
            break;
        }
        case NORMAL_N_COPY:
            q = ExprQuaternion::From(numNormal);
            break;

        case NORMAL_N_ROT: {
            ExprQuaternion orig = ExprQuaternion::From(numNormal);
            q = ExprQuaternion::From(param[0], param[1], param[2], param[3]);

            q = q.Times(orig);
            break;
        }

        case NORMAL_N_ROT_AA: {
            ExprQuaternion orig = ExprQuaternion::From(numNormal);

            Expr *theta = Expr::From(timesApplied)->Times(
                          Expr::From(param[0]));
            Expr *c = theta->Cos(), *s = theta->Sin();
            q.w = c;
            q.vx = s->Times(Expr::From(param[1]));
            q.vy = s->Times(Expr::From(param[2]));
            q.vz = s->Times(Expr::From(param[3]));

            q = q.Times(orig);
            break;
        }

        default: oops();
    }
    return q;
}

bool Entity::PointIsFromReferences(void) {
    return h.request().IsFromReferences();
}

void Entity::PointForceTo(Vector p) {
    switch(type) {
        case POINT_IN_3D:
            SS.GetParam(param[0])->val = p.x;
            SS.GetParam(param[1])->val = p.y;
            SS.GetParam(param[2])->val = p.z;
            break;

        case POINT_IN_2D: {
            Entity *c = SS.GetEntity(workplane);
            p = p.Minus(c->WorkplaneGetOffset());
            SS.GetParam(param[0])->val = p.Dot(c->Normal()->NormalU());
            SS.GetParam(param[1])->val = p.Dot(c->Normal()->NormalV());
            break;
        }

        case POINT_N_TRANS: {
            if(timesApplied == 0) break;
            Vector trans = (p.Minus(numPoint)).ScaledBy(1.0/timesApplied);
            SS.GetParam(param[0])->val = trans.x;
            SS.GetParam(param[1])->val = trans.y;
            SS.GetParam(param[2])->val = trans.z;
            break;
        }

        case POINT_N_ROT_TRANS: {
            // Force only the translation; leave the rotation unchanged. But
            // remember that we're working with respect to the rotated
            // point.
            Vector trans = p.Minus(PointGetQuaternion().Rotate(numPoint));
            SS.GetParam(param[0])->val = trans.x;
            SS.GetParam(param[1])->val = trans.y;
            SS.GetParam(param[2])->val = trans.z;
            break;
        }

        case POINT_N_ROT_AA: {
            // Force only the angle; the axis and center of rotation stay
            Vector offset = Vector::From(param[0], param[1], param[2]);
            Vector normal = Vector::From(param[4], param[5], param[6]);
            Vector u = normal.Normal(0), v = normal.Normal(1);
            Vector po = p.Minus(offset), numo = numPoint.Minus(offset);
            double thetap = atan2(v.Dot(po), u.Dot(po));
            double thetan = atan2(v.Dot(numo), u.Dot(numo));
            double thetaf = (thetap - thetan);
            double thetai = (SS.GetParam(param[3])->val)*timesApplied*2;
            double dtheta = thetaf - thetai;
            // Take the smallest possible change in the actual step angle,
            // in order to avoid jumps when you cross from +pi to -pi
            while(dtheta < -PI) dtheta += 2*PI;
            while(dtheta > PI) dtheta -= 2*PI;
            SS.GetParam(param[3])->val = (thetai + dtheta)/(timesApplied*2);
            break;
        }

        case POINT_N_COPY:
            // Nothing to do; it's a static copy
            break;

        default: oops();
    }
}

Vector Entity::PointGetNum(void) {
    Vector p;
    switch(type) {
        case POINT_IN_3D:
            p = Vector::From(param[0], param[1], param[2]);
            break;

        case POINT_IN_2D: {
            Entity *c = SS.GetEntity(workplane);
            Vector u = c->Normal()->NormalU();
            Vector v = c->Normal()->NormalV();
            p =        u.ScaledBy(SS.GetParam(param[0])->val);
            p = p.Plus(v.ScaledBy(SS.GetParam(param[1])->val));
            p = p.Plus(c->WorkplaneGetOffset());
            break;
        }

        case POINT_N_TRANS: {
            Vector trans = Vector::From(param[0], param[1], param[2]);
            p = numPoint.Plus(trans.ScaledBy(timesApplied));
            break;
        }

        case POINT_N_ROT_TRANS: {
            Vector offset = Vector::From(param[0], param[1], param[2]);
            Quaternion q = PointGetQuaternion();
            p = q.Rotate(numPoint);
            p = p.Plus(offset);
            break;
        }

        case POINT_N_ROT_AA: {
            Vector offset = Vector::From(param[0], param[1], param[2]);
            Quaternion q = PointGetQuaternion();
            p = numPoint.Minus(offset);
            p = q.Rotate(p);
            p = p.Plus(offset);
            break;
        }

        case POINT_N_COPY:
            p = numPoint;
            break;

        default: oops();
    }
    return p;
}

ExprVector Entity::PointGetExprs(void) {
    ExprVector r;
    switch(type) {
        case POINT_IN_3D:
            r = ExprVector::From(param[0], param[1], param[2]);
            break;

        case POINT_IN_2D: {
            Entity *c = SS.GetEntity(workplane);
            ExprVector u = c->Normal()->NormalExprsU();
            ExprVector v = c->Normal()->NormalExprsV();
            r = c->WorkplaneGetOffsetExprs();
            r = r.Plus(u.ScaledBy(Expr::From(param[0])));
            r = r.Plus(v.ScaledBy(Expr::From(param[1])));
            break;
        }
        case POINT_N_TRANS: {
            ExprVector orig = ExprVector::From(numPoint);
            ExprVector trans = ExprVector::From(param[0], param[1], param[2]);
            r = orig.Plus(trans.ScaledBy(Expr::From(timesApplied)));
            break;
        }
        case POINT_N_ROT_TRANS: {
            ExprVector orig = ExprVector::From(numPoint);
            ExprVector trans = ExprVector::From(param[0], param[1], param[2]);
            ExprQuaternion q =
                ExprQuaternion::From(param[3], param[4], param[5], param[6]);
            orig = q.Rotate(orig);
            r = orig.Plus(trans);
            break;
        }
        case POINT_N_ROT_AA: {
            ExprVector orig = ExprVector::From(numPoint);
            ExprVector trans = ExprVector::From(param[0], param[1], param[2]);
            Expr *theta = Expr::From(timesApplied)->Times(
                          Expr::From(param[3]));
            Expr *c = theta->Cos(), *s = theta->Sin();
            ExprQuaternion q = { 
                c,
                s->Times(Expr::From(param[4])),
                s->Times(Expr::From(param[5])),
                s->Times(Expr::From(param[6])) };
            orig = orig.Minus(trans);
            orig = q.Rotate(orig);
            r = orig.Plus(trans);
            break;
        }
        case POINT_N_COPY:
            r = ExprVector::From(numPoint);
            break;

        default: oops();
    }
    return r;
}

void Entity::PointGetExprsInWorkplane(hEntity wrkpl, Expr **u, Expr **v) {
    if(type == POINT_IN_2D && workplane.v == wrkpl.v) {
        // They want our coordinates in the form that we've written them,
        // very nice.
        *u = Expr::From(param[0]);
        *v = Expr::From(param[1]);
    } else {
        // Get the offset and basis vectors for this weird exotic csys.
        Entity *w = SS.GetEntity(wrkpl);
        ExprVector wp = w->WorkplaneGetOffsetExprs();
        ExprVector wu = w->Normal()->NormalExprsU();
        ExprVector wv = w->Normal()->NormalExprsV();

        // Get our coordinates in three-space, and project them into that
        // coordinate system.
        ExprVector ev = PointGetExprs();
        ev = ev.Minus(wp);
        *u = ev.Dot(wu);
        *v = ev.Dot(wv);
    }
}

void Entity::PointForceQuaternionTo(Quaternion q) {
    if(type != POINT_N_ROT_TRANS) oops();

    SS.GetParam(param[3])->val = q.w;
    SS.GetParam(param[4])->val = q.vx;
    SS.GetParam(param[5])->val = q.vy;
    SS.GetParam(param[6])->val = q.vz;
}

Quaternion Entity::PointGetQuaternion(void) {
    Quaternion q;

    if(type == POINT_N_ROT_AA) {
        double theta = timesApplied*SS.GetParam(param[3])->val;
        double s = sin(theta), c = cos(theta);
        q.w = c;
        q.vx = s*SS.GetParam(param[4])->val;
        q.vy = s*SS.GetParam(param[5])->val;
        q.vz = s*SS.GetParam(param[6])->val;
    } else if(type == POINT_N_ROT_TRANS) {
        q = Quaternion::From(param[3], param[4], param[5], param[6]);
    } else oops();

    return q;
}

bool Entity::IsFace(void) {
    switch(type) {
        case FACE_NORMAL_PT:
        case FACE_XPROD:
        case FACE_N_ROT_TRANS:
            return true;
        default:
            return false;
    }
}

ExprVector Entity::FaceGetNormalExprs(void) {
    ExprVector r;
    if(type == FACE_NORMAL_PT) {
        r = ExprVector::From(numNormal.vx, numNormal.vy, numNormal.vz);
    } else if(type == FACE_XPROD) {
        ExprVector vc = ExprVector::From(param[0], param[1], param[2]);
        ExprVector vn = ExprVector::From(numVector);
        r = vc.Cross(vn);
    } else if(type == FACE_N_ROT_TRANS) {
        // The numerical normal vector gets the rotation
        r = ExprVector::From(numNormal.vx, numNormal.vy, numNormal.vz);
        ExprQuaternion q =
            ExprQuaternion::From(param[3], param[4], param[5], param[6]);
        r = q.Rotate(r);
    } else oops();
    return r;
}

Vector Entity::FaceGetNormalNum(void) {
    Vector r;
    if(type == FACE_NORMAL_PT) {
        r = Vector::From(numNormal.vx, numNormal.vy, numNormal.vz);
    } else if(type == FACE_XPROD) {
        Vector vc = Vector::From(param[0], param[1], param[2]);
        r = vc.Cross(numVector);
    } else if(type == FACE_N_ROT_TRANS) {
        // The numerical normal vector gets the rotation
        r = Vector::From(numNormal.vx, numNormal.vy, numNormal.vz);
        Quaternion q = Quaternion::From(param[3], param[4], param[5], param[6]);
        r = q.Rotate(r);
    } else oops();
    return r;
}

ExprVector Entity::FaceGetPointExprs(void) {
    ExprVector r;
    if(type == FACE_NORMAL_PT) {
        r = SS.GetEntity(point[0])->PointGetExprs();
    } else if(type == FACE_XPROD) {
        r = ExprVector::From(numPoint);
    } else if(type == FACE_N_ROT_TRANS) {
        // The numerical point gets the rotation and translation.
        ExprVector trans = ExprVector::From(param[0], param[1], param[2]);
        ExprQuaternion q =
            ExprQuaternion::From(param[3], param[4], param[5], param[6]);
        r = ExprVector::From(numPoint);
        r = q.Rotate(r);
        r = r.Plus(trans);
    } else oops();
    return r;
}

void Entity::LineDrawOrGetDistance(Vector a, Vector b) {
    if(dogd.drawing) {
        // glPolygonOffset works only on polys, not lines, so do it myself
        Vector adj = SS.GW.projRight.Cross(SS.GW.projUp);
        adj = adj.ScaledBy(5/SS.GW.scale);
        glBegin(GL_LINES);
            glxVertex3v(a.Plus(adj));
            glxVertex3v(b.Plus(adj));
        glEnd();
    } else {
        Point2d ap = SS.GW.ProjectPoint(a);
        Point2d bp = SS.GW.ProjectPoint(b);

        double d = dogd.mp.DistanceToLine(ap, bp.Minus(ap), true);
        dogd.dmin = min(dogd.dmin, d);
    }
    dogd.refp = (a.Plus(b)).ScaledBy(0.5);
}

void Entity::LineDrawOrGetDistanceOrEdge(Vector a, Vector b) {
    LineDrawOrGetDistance(a, b);
    if(dogd.edges && !construction) {
        dogd.edges->AddEdge(a, b);
    }
}

void Entity::Draw(int order) {
    dogd.drawing = true;
    dogd.edges = NULL;
    DrawOrGetDistance(order);
}

void Entity::GenerateEdges(SEdgeList *el) {
    dogd.drawing = false;
    dogd.edges = el;
    DrawOrGetDistance(-1);
    dogd.edges = NULL;
}

double Entity::GetDistance(Point2d mp) {
    dogd.drawing = false;
    dogd.edges = NULL;
    dogd.mp = mp;
    dogd.dmin = 1e12;

    DrawOrGetDistance(-1);
    
    return dogd.dmin;
}

Vector Entity::GetReferencePos(void) {
    dogd.drawing = false;
    dogd.edges = NULL;

    dogd.refp = SS.GW.offset.ScaledBy(-1);
    DrawOrGetDistance(-1);

    return dogd.refp;
}

void Entity::DrawOrGetDistance(int order) {  
    Group *g = SS.GetGroup(group);
    // If an entity is invisible, then it doesn't get shown, and it doesn't
    // contribute a distance for the selection, but it still generates edges.
    if(!(g->visible) && !dogd.edges) return;

    glLineWidth(1.5);

    if(group.v != SS.GW.activeGroup.v) {
        glxColor3d(0.5, 0.3, 0.0);
    } else if(construction) {
        glxColor3d(0.1, 0.7, 0.1);
    } else {
        glxColor3d(1, 1, 1);
    }

    switch(type) {
        case POINT_N_COPY:
        case POINT_N_TRANS:
        case POINT_N_ROT_TRANS:
        case POINT_N_ROT_AA:
        case POINT_IN_3D:
        case POINT_IN_2D: {
            if(order >= 0 && order != 2) break;
            if(!SS.GW.showPoints) break;

            if(h.isFromRequest()) {
                Entity *isfor = SS.GetEntity(h.request().entity(0));
                if(!SS.GW.showWorkplanes && isfor->type == Entity::WORKPLANE) {
                    break;
                }
            }

            Vector v = PointGetNum();

            if(dogd.drawing) {
                double s = 3.5;
                Vector r = SS.GW.projRight.ScaledBy(s/SS.GW.scale);
                Vector d = SS.GW.projUp.ScaledBy(s/SS.GW.scale);

                glxColor3d(0, 0.8, 0);
                glPolygonOffset(-10, -10);
                glBegin(GL_QUADS);
                    glxVertex3v(v.Plus (r).Plus (d));
                    glxVertex3v(v.Plus (r).Minus(d));
                    glxVertex3v(v.Minus(r).Minus(d));
                    glxVertex3v(v.Minus(r).Plus (d));
                glEnd();
                glPolygonOffset(0, 0);
            } else {
                Point2d pp = SS.GW.ProjectPoint(v);
                // Make a free point slightly easier to select, so that with
                // coincident points, we select the free one.
                dogd.dmin = pp.DistanceTo(dogd.mp) - 4;
            }
            break;
        }

        case NORMAL_N_COPY:
        case NORMAL_N_ROT:
        case NORMAL_N_ROT_AA:
        case NORMAL_IN_3D:
        case NORMAL_IN_2D: {
            if(order >= 0 && order != 2) break;

            int i;
            for(i = 0; i < 2; i++) {
                hRequest hr = h.request();
                double f = (i == 0 ? 0.4 : 1);
                if(hr.v == Request::HREQUEST_REFERENCE_XY.v) {
                    glxColor3d(0, 0, f);
                } else if(hr.v == Request::HREQUEST_REFERENCE_YZ.v) {
                    glxColor3d(f, 0, 0);
                } else if(hr.v == Request::HREQUEST_REFERENCE_ZX.v) {
                    glxColor3d(0, f, 0);
                } else {
                    glxColor3d(0, 0.4, 0.4);
                    if(i > 0) break;
                    if(!SS.GW.showNormals) break;
                }

                Quaternion q = NormalGetNum();
                Vector tail;
                if(i == 0) {
                    tail = SS.GetEntity(point[0])->PointGetNum();
                    glLineWidth(1);
                } else {
                    // Draw an extra copy of the x, y, and z axes, that's
                    // always in the corner of the view and at the front.
                    // So those are always available, perhaps useful.
                    double s = SS.GW.scale;
                    double h = 60 - SS.GW.height/2;
                    double w = 60 - SS.GW.width/2;
                    Vector gn = SS.GW.projRight.Cross(SS.GW.projUp);
                    tail = SS.GW.projRight.ScaledBy(w/s).Plus(
                           SS.GW.projUp.   ScaledBy(h/s)).Plus(
                           gn.ScaledBy(-4*w/s)).Minus(SS.GW.offset);
                    glLineWidth(2);
                }

                Vector v = (q.RotationN()).WithMagnitude(50/SS.GW.scale);
                Vector tip = tail.Plus(v);
                LineDrawOrGetDistance(tail, tip);

                v = v.WithMagnitude(12/SS.GW.scale);
                Vector axis = q.RotationV();
                LineDrawOrGetDistance(tip,tip.Minus(v.RotatedAbout(axis, 0.6)));
                LineDrawOrGetDistance(tip,tip.Minus(v.RotatedAbout(axis,-0.6)));
            }
            glLineWidth(1);
            break;
        }

        case DISTANCE:
        case DISTANCE_N_COPY:
            // These are used only as data structures, nothing to display.
            break;

        case WORKPLANE: {
            if(order >= 0 && order != 0) break;
            if(!SS.GW.showWorkplanes) break;

            if((!h.isFromRequest()) && (h.group().v != SS.GW.activeGroup.v)) {
                // Workplanes that are automatically created by an in-wrkpl
                // drawing group appear only when that group is active.
                break;
            }

            Vector p;
            p = SS.GetEntity(point[0])->PointGetNum();

            Vector u = Normal()->NormalU();
            Vector v = Normal()->NormalV();

            double s = (min(SS.GW.width, SS.GW.height))*0.45/SS.GW.scale;

            Vector us = u.ScaledBy(s);
            Vector vs = v.ScaledBy(s);

            Vector pp = p.Plus (us).Plus (vs);
            Vector pm = p.Plus (us).Minus(vs);
            Vector mm = p.Minus(us).Minus(vs), mm2 = mm;
            Vector mp = p.Minus(us).Plus (vs);

            glLineWidth(1);
            glxColor3d(0, 0.3, 0.3);
            glEnable(GL_LINE_STIPPLE);
            glLineStipple(3, 0x1111);
            if(!h.isFromRequest()) {
                mm = mm.Plus(v.ScaledBy(60/SS.GW.scale));
                mm2 = mm2.Plus(u.ScaledBy(60/SS.GW.scale));
                LineDrawOrGetDistance(mm2, mm);
            }
            LineDrawOrGetDistance(pp, pm);
            LineDrawOrGetDistance(pm, mm2);
            LineDrawOrGetDistance(mm, mp);
            LineDrawOrGetDistance(mp, pp);
            glDisable(GL_LINE_STIPPLE);

            char *str = DescriptionString()+5;
            if(dogd.drawing) {
                glPushMatrix();
                    glxTranslatev(mm2);
                    glxOntoWorkplane(u, v);
                    glxWriteText(str);
                glPopMatrix();
            } else {
                Vector pos = mm2.Plus(u.ScaledBy(glxStrWidth(str)/2)).Plus(
                                      v.ScaledBy(glxStrHeight()/2));
                Point2d pp = SS.GW.ProjectPoint(pos);
                dogd.dmin = min(dogd.dmin, pp.DistanceTo(dogd.mp) - 10);
                // If a line lies in a plane, then select the line, not
                // the plane.
                dogd.dmin += 3;
            }
            break;
        }

        case LINE_SEGMENT: {
            if(order >= 0 && order != 1) break;
            Vector a = SS.GetEntity(point[0])->PointGetNum();
            Vector b = SS.GetEntity(point[1])->PointGetNum();
            LineDrawOrGetDistanceOrEdge(a, b);
            break;
        }

        case CUBIC: {
            if(order >= 0 && order != 1) break;
            Vector p0 = SS.GetEntity(point[0])->PointGetNum();
            Vector p1 = SS.GetEntity(point[1])->PointGetNum();
            Vector p2 = SS.GetEntity(point[2])->PointGetNum();
            Vector p3 = SS.GetEntity(point[3])->PointGetNum();
            int i, n = 20;
            Vector prev = p0;
            for(i = 1; i <= n; i++) {
                double t = ((double)i)/n;
                Vector p =
                    (p0.ScaledBy((1 - t)*(1 - t)*(1 - t))).Plus(
                    (p1.ScaledBy(3*t*(1 - t)*(1 - t))).Plus(
                    (p2.ScaledBy(3*t*t*(1 - t))).Plus(
                    (p3.ScaledBy(t*t*t)))));
                LineDrawOrGetDistanceOrEdge(prev, p);
                prev = p;
            }
            break;
        }

#define CIRCLE_SIDES(r) (7 + (int)(sqrt(r*SS.GW.scale)))
        case ARC_OF_CIRCLE: {
            if(order >= 0 && order != 1) break;
            Vector c  = SS.GetEntity(point[0])->PointGetNum();
            Vector pa = SS.GetEntity(point[1])->PointGetNum();
            Vector pb = SS.GetEntity(point[2])->PointGetNum();
            Quaternion q = SS.GetEntity(normal)->NormalGetNum();
            Vector u = q.RotationU(), v = q.RotationV();

            double ra = (pa.Minus(c)).Magnitude();
            double rb = (pb.Minus(c)).Magnitude();

            double thetaa, thetab, dtheta;
            ArcGetAngles(&thetaa, &thetab, &dtheta);

            int i, n = 3 + (int)(CIRCLE_SIDES(ra)*dtheta/(2*PI));
            Vector prev = pa;
            for(i = 1; i <= n; i++) {
                double theta = thetaa + (dtheta*i)/n;
                double r = ra + ((rb - ra)*i)/n;
                Vector d = u.ScaledBy(cos(theta)).Plus(v.ScaledBy(sin(theta)));
                Vector p = c.Plus(d.ScaledBy(r));
                LineDrawOrGetDistanceOrEdge(prev, p);
                prev = p;
            }
            break;
        }

        case CIRCLE: {
            if(order >= 0 && order != 1) break;

            Quaternion q = SS.GetEntity(normal)->NormalGetNum();
            double r = SS.GetEntity(distance)->DistanceGetNum();
            Vector center = SS.GetEntity(point[0])->PointGetNum();
            Vector u = q.RotationU(), v = q.RotationV();

            int i, c = CIRCLE_SIDES(r); 
            Vector prev = u.ScaledBy(r).Plus(center);
            for(i = 1; i <= c; i++) {
                double phi = (2*PI*i)/c;
                Vector p = (u.ScaledBy(r*cos(phi))).Plus(
                            v.ScaledBy(r*sin(phi)));
                p = p.Plus(center);
                LineDrawOrGetDistanceOrEdge(prev, p);
                prev = p;
            }
            break;
        }

        case FACE_NORMAL_PT:
        case FACE_XPROD:
        case FACE_N_ROT_TRANS:
            // Do nothing; these are drawn with the triangle mesh
            break;

        default:
            oops();
    }

    glLineWidth(1);
}

void Entity::AddEq(IdList<Equation,hEquation> *l, Expr *expr, int index) {
    Equation eq;
    eq.e = expr;
    eq.h = h.equation(index);
    l->Add(&eq);
}

void Entity::GenerateEquations(IdList<Equation,hEquation> *l) {
    switch(type) {
        case NORMAL_IN_3D: {
            ExprQuaternion q = NormalGetExprs();
            AddEq(l, (q.Magnitude())->Minus(Expr::From(1)), 0);
            break;
        }
        case ARC_OF_CIRCLE: {
            // If this is a copied entity, with its point already fixed
            // with respect to each other, then we don't want to generate
            // the distance constraint!
            if(SS.GetEntity(point[0])->type == POINT_IN_2D) {
                Expr *ra = Constraint::Distance(workplane, point[0], point[1]);
                Expr *rb = Constraint::Distance(workplane, point[0], point[2]);
                AddEq(l, ra->Minus(rb), 0);
            }
            break;
        }
        default:;
            // Most entities do not generate equations.
    }
}

void Entity::CalculateNumerical(void) {
    if(IsPoint()) actPoint = PointGetNum();
    if(IsNormal()) actNormal = NormalGetNum();
    if(type == DISTANCE || type == DISTANCE_N_COPY) {
        actDistance = DistanceGetNum();
    }
    if(IsFace()) {
        ExprVector p = FaceGetPointExprs();
        ExprVector n = FaceGetNormalExprs();
        numPoint  = Vector::From(       p.x->Eval(), p.y->Eval(), p.z->Eval());
        numNormal = Quaternion::From(0, n.x->Eval(), n.y->Eval(), n.z->Eval());
    }
}