Exemple #1
0
void SBezier::ClosestPointTo(Vector p, double *t, bool converge) {
    int i;
    double minDist = VERY_POSITIVE;
    *t = 0;
    double res = (deg <= 2) ? 7.0 : 20.0;
    for(i = 0; i < (int)res; i++) {
        double tryt = (i/res);
        
        Vector tryp = PointAt(tryt);
        double d = (tryp.Minus(p)).Magnitude();
        if(d < minDist) {
            *t = tryt;
            minDist = d;
        }
    }

    Vector p0;
    for(i = 0; i < (converge ? 15 : 5); i++) {
        p0 = PointAt(*t);
        if(p0.Equals(p, RATPOLY_EPS)) {
            return;
        }

        Vector dp = TangentAt(*t);
        Vector pc = p.ClosestPointOnLine(p0, dp);
        *t += (pc.Minus(p0)).DivPivoting(dp);
    }
    if(converge) {
        dbp("didn't converge (closest point on bezier curve)");
    }
}
Exemple #2
0
SSurface SSurface::FromRevolutionOf(SBezier *sb, Vector pt, Vector axis,
                                    double thetas, double thetaf)
{
    SSurface ret = {};


    ret.degm = sb->deg;
    ret.degn = 2;

    double dtheta = fabs(WRAP_SYMMETRIC(thetaf - thetas, 2*PI));

    // We now wish to revolve the curve about the z axis
    int i;
    for(i = 0; i <= ret.degm; i++) {
        Vector p = sb->ctrl[i];

        Vector ps = p.RotatedAbout(pt, axis, thetas),
               pf = p.RotatedAbout(pt, axis, thetaf);

        Vector ct;
        if(ps.Equals(pf)) {
            // Degenerate case: a control point lies on the axis of revolution,
            // so we get three coincident control points.
            ct = ps;
        } else {
            // Normal case, the control point sweeps out a circle.
            Vector c = ps.ClosestPointOnLine(pt, axis);

            Vector rs = ps.Minus(c),
                   rf = pf.Minus(c);

            Vector ts = axis.Cross(rs),
                   tf = axis.Cross(rf);

            ct = Vector::AtIntersectionOfLines(ps, ps.Plus(ts),
                                               pf, pf.Plus(tf),
                                               NULL, NULL, NULL);
        }

        ret.ctrl[i][0] = ps;
        ret.ctrl[i][1] = ct;
        ret.ctrl[i][2] = pf;

        ret.weight[i][0] = sb->weight[i];
        ret.weight[i][1] = sb->weight[i]*cos(dtheta/2);
        ret.weight[i][2] = sb->weight[i];
    }

    return ret;
}
Exemple #3
0
Vector SSurface::ClosestPointOnThisAndSurface(SSurface *srf2, Vector p) {
    // This is untested.
    int i, j;
    Point2d puv[2];
    SSurface *srf[2] = { this, srf2 };

    for(j = 0; j < 2; j++) {
        (srf[j])->ClosestPointTo(p, &(puv[j]), false);
    }

    for(i = 0; i < 10; i++) {
        Vector tu[2], tv[2], cp[2], n[2];
        double d[2];

        for(j = 0; j < 2; j++) {
            (srf[j])->TangentsAt(puv[j].x, puv[j].y, &(tu[j]), &(tv[j]));

            cp[j] = (srf[j])->PointAt(puv[j]);

            n[j] = ((tu[j]).Cross(tv[j])).WithMagnitude(1);
            d[j] = (n[j]).Dot(cp[j]);
        }

        if((cp[0]).Equals(cp[1], RATPOLY_EPS)) break;

        Vector p0 = Vector::AtIntersectionOfPlanes(n[0], d[0], n[1], d[1]),
               dp = (n[0]).Cross(n[1]);
        
        Vector pc = p.ClosestPointOnLine(p0, dp);

        // Adjust our guess and iterate
        for(j = 0; j < 2; j++) {
            Vector dc = pc.Minus(cp[j]);
            double du = dc.Dot(tu[j]), dv = dc.Dot(tv[j]);
            puv[j].x += du / ((tu[j]).MagSquared());
            puv[j].y += dv / ((tv[j]).MagSquared());
        }
    }
    if(i >= 10) {
        dbp("this and srf, didn't converge, d=%g",
            (puv[0].Minus(puv[1])).Magnitude());
    }

    // If this converged, then the two points are actually equal.
    return ((srf[0])->PointAt(puv[0])).Plus(
           ((srf[1])->PointAt(puv[1]))).ScaledBy(0.5);
}
Exemple #4
0
void SShell::MakeFromRevolutionOf(SBezierLoopSet *sbls, Vector pt, Vector axis, RgbaColor color, Group *group)
{
    SBezierLoop *sbl;

    int i0 = surface.n, i;

    // Normalize the axis direction so that the direction of revolution
    // ends up parallel to the normal of the sketch, on the side of the
    // axis where the sketch is.
    Vector pto;
    double md = VERY_NEGATIVE;
    for(sbl = sbls->l.First(); sbl; sbl = sbls->l.NextAfter(sbl)) {
        SBezier *sb;
        for(sb = sbl->l.First(); sb; sb = sbl->l.NextAfter(sb)) {
            // Choose the point farthest from the axis; we'll get garbage
            // if we choose a point that lies on the axis, for example.
            // (And our surface will be self-intersecting if the sketch
            // spans the axis, so don't worry about that.)
            Vector p = sb->Start();
            double d = p.DistanceToLine(pt, axis);
            if(d > md) {
                md = d;
                pto = p;
            }
        }
    }
    Vector ptc = pto.ClosestPointOnLine(pt, axis),
           up  = (pto.Minus(ptc)).WithMagnitude(1),
           vp  = (sbls->normal).Cross(up);
    if(vp.Dot(axis) < 0) {
        axis = axis.ScaledBy(-1);
    }

    // Now we actually build and trim the surfaces.
    for(sbl = sbls->l.First(); sbl; sbl = sbls->l.NextAfter(sbl)) {
        int i, j;
        SBezier *sb, *prev;
        List<Revolved> hsl = {};

        for(sb = sbl->l.First(); sb; sb = sbl->l.NextAfter(sb)) {
            Revolved revs;
            for(j = 0; j < 4; j++) {
                if(sb->deg == 1 &&
                        (sb->ctrl[0]).DistanceToLine(pt, axis) < LENGTH_EPS &&
                        (sb->ctrl[1]).DistanceToLine(pt, axis) < LENGTH_EPS)
                {
                    // This is a line on the axis of revolution; it does
                    // not contribute a surface.
                    revs.d[j].v = 0;
                } else {
                    SSurface ss = SSurface::FromRevolutionOf(sb, pt, axis,
                                  (PI/2)*j,
                                  (PI/2)*(j+1));
                    ss.color = color;
                    if(sb->entity != 0) {
                        hEntity he;
                        he.v = sb->entity;
                        hEntity hface = group->Remap(he, Group::REMAP_LINE_TO_FACE);
                        if(SK.entity.FindByIdNoOops(hface) != NULL) {
                            ss.face = hface.v;
                        }
                    }
                    revs.d[j] = surface.AddAndAssignId(&ss);
                }
            }
            hsl.Add(&revs);
        }

        for(i = 0; i < sbl->l.n; i++) {
            Revolved revs  = hsl.elem[i],
                     revsp = hsl.elem[WRAP(i-1, sbl->l.n)];

            sb   = &(sbl->l.elem[i]);
            prev = &(sbl->l.elem[WRAP(i-1, sbl->l.n)]);

            for(j = 0; j < 4; j++) {
                SCurve sc;
                Quaternion qs = Quaternion::From(axis, (PI/2)*j);
                // we want Q*(x - p) + p = Q*x + (p - Q*p)
                Vector ts = pt.Minus(qs.Rotate(pt));

                // If this input curve generate a surface, then trim that
                // surface with the rotated version of the input curve.
                if(revs.d[j].v) {
                    sc = {};
                    sc.isExact = true;
                    sc.exact = sb->TransformedBy(ts, qs, 1.0);
                    (sc.exact).MakePwlInto(&(sc.pts));
                    sc.surfA = revs.d[j];
                    sc.surfB = revs.d[WRAP(j-1, 4)];

                    hSCurve hcb = curve.AddAndAssignId(&sc);

                    STrimBy stb;
                    stb = STrimBy::EntireCurve(this, hcb, true);
                    (surface.FindById(sc.surfA))->trim.Add(&stb);
                    stb = STrimBy::EntireCurve(this, hcb, false);
                    (surface.FindById(sc.surfB))->trim.Add(&stb);
                }

                // And if this input curve and the one after it both generated
                // surfaces, then trim both of those by the appropriate
                // circle.
                if(revs.d[j].v && revsp.d[j].v) {
                    SSurface *ss = surface.FindById(revs.d[j]);

                    sc = {};
                    sc.isExact = true;
                    sc.exact = SBezier::From(ss->ctrl[0][0],
                                             ss->ctrl[0][1],
                                             ss->ctrl[0][2]);
                    sc.exact.weight[1] = ss->weight[0][1];
                    (sc.exact).MakePwlInto(&(sc.pts));
                    sc.surfA = revs.d[j];
                    sc.surfB = revsp.d[j];

                    hSCurve hcc = curve.AddAndAssignId(&sc);

                    STrimBy stb;
                    stb = STrimBy::EntireCurve(this, hcc, false);
                    (surface.FindById(sc.surfA))->trim.Add(&stb);
                    stb = STrimBy::EntireCurve(this, hcc, true);
                    (surface.FindById(sc.surfB))->trim.Add(&stb);
                }
            }
        }

        hsl.Clear();
    }

    for(i = i0; i < surface.n; i++) {
        SSurface *srf = &(surface.elem[i]);

        // Revolution of a line; this is potentially a plane, which we can
        // rewrite to have degree (1, 1).
        if(srf->degm == 1 && srf->degn == 2) {
            // close start, far start, far finish
            Vector cs, fs, ff;
            double d0, d1;
            d0 = (srf->ctrl[0][0]).DistanceToLine(pt, axis);
            d1 = (srf->ctrl[1][0]).DistanceToLine(pt, axis);

            if(d0 > d1) {
                cs = srf->ctrl[1][0];
                fs = srf->ctrl[0][0];
                ff = srf->ctrl[0][2];
            } else {
                cs = srf->ctrl[0][0];
                fs = srf->ctrl[1][0];
                ff = srf->ctrl[1][2];
            }

            // origin close, origin far
            Vector oc = cs.ClosestPointOnLine(pt, axis),
                   of = fs.ClosestPointOnLine(pt, axis);

            if(oc.Equals(of)) {
                // This is a plane, not a (non-degenerate) cone.
                Vector oldn = srf->NormalAt(0.5, 0.5);

                Vector u = fs.Minus(of), v;

                v = (axis.Cross(u)).WithMagnitude(1);

                double vm = (ff.Minus(of)).Dot(v);
                v = v.ScaledBy(vm);

                srf->degm = 1;
                srf->degn = 1;
                srf->ctrl[0][0] = of;
                srf->ctrl[0][1] = of.Plus(u);
                srf->ctrl[1][0] = of.Plus(v);
                srf->ctrl[1][1] = of.Plus(u).Plus(v);
                srf->weight[0][0] = 1;
                srf->weight[0][1] = 1;
                srf->weight[1][0] = 1;
                srf->weight[1][1] = 1;

                if(oldn.Dot(srf->NormalAt(0.5, 0.5)) < 0) {
                    swap(srf->ctrl[0][0], srf->ctrl[1][0]);
                    swap(srf->ctrl[0][1], srf->ctrl[1][1]);
                }
                continue;
            }

            if(fabs(d0 - d1) < LENGTH_EPS) {
                // This is a cylinder; so transpose it so that we'll recognize
                // it as a surface of extrusion.
                SSurface sn = *srf;

                // Transposing u and v flips the normal, so reverse u to
                // flip it again and put it back where we started.
                sn.degm = 2;
                sn.degn = 1;
                int dm, dn;
                for(dm = 0; dm <= 1; dm++) {
                    for(dn = 0; dn <= 2; dn++) {
                        sn.ctrl  [dn][dm] = srf->ctrl  [1-dm][dn];
                        sn.weight[dn][dm] = srf->weight[1-dm][dn];
                    }
                }

                *srf = sn;
                continue;
            }
        }

    }

}
void Constraint::DrawOrGetDistance(Vector *labelPos) {
    if(!SS.GW.showConstraints) return;
    Group *g = SK.GetGroup(group);
    // If the group is hidden, then the constraints are hidden and not
    // able to be selected.
    if(!(g->visible)) return;
    // And likewise if the group is not the active group; except for comments
    // with an assigned style.
    if(g->h.v != SS.GW.activeGroup.v && !(type == COMMENT && disp.style.v)) {
        return;
    }
    if(disp.style.v) {
        Style *s = Style::Get(disp.style);
        if(!s->visible) return;
    }

    // Unit vectors that describe our current view of the scene. One pixel
    // long, not one actual unit.
    Vector gr = SS.GW.projRight.ScaledBy(1/SS.GW.scale);
    Vector gu = SS.GW.projUp.ScaledBy(1/SS.GW.scale);
    Vector gn = (gr.Cross(gu)).WithMagnitude(1/SS.GW.scale);

    switch(type) {
        case PT_PT_DISTANCE: {
            Vector ap = SK.GetEntity(ptA)->PointGetNum();
            Vector bp = SK.GetEntity(ptB)->PointGetNum();

            if(workplane.v != Entity::FREE_IN_3D.v) {
                DoProjectedPoint(&ap);
                DoProjectedPoint(&bp);
            }

            Vector ref = ((ap.Plus(bp)).ScaledBy(0.5)).Plus(disp.offset);

            DoLineWithArrows(ref, ap, bp, false);
            DoLabel(ref, labelPos, gr, gu);
            break;
        }

        case PROJ_PT_DISTANCE: {
            Vector ap = SK.GetEntity(ptA)->PointGetNum(),
                   bp = SK.GetEntity(ptB)->PointGetNum(),
                   dp = (bp.Minus(ap)),
                   pp = SK.GetEntity(entityA)->VectorGetNum();

            Vector ref = ((ap.Plus(bp)).ScaledBy(0.5)).Plus(disp.offset);

            pp = pp.WithMagnitude(1);
            double d = dp.Dot(pp);
            Vector bpp = ap.Plus(pp.ScaledBy(d));
            StippledLine(ap, bpp);
            StippledLine(bp, bpp);

            DoLineWithArrows(ref, ap, bpp, false);
            DoLabel(ref, labelPos, gr, gu);
            break;
        }

        case PT_FACE_DISTANCE:
        case PT_PLANE_DISTANCE: {
            Vector pt = SK.GetEntity(ptA)->PointGetNum();
            Entity *enta = SK.GetEntity(entityA);
            Vector n, p;
            if(type == PT_PLANE_DISTANCE) {
                n = enta->Normal()->NormalN();
                p = enta->WorkplaneGetOffset();
            } else {
                n = enta->FaceGetNormalNum();
                p = enta->FaceGetPointNum();
            }

            double d = (p.Minus(pt)).Dot(n);
            Vector closest = pt.Plus(n.WithMagnitude(d));

            Vector ref = ((closest.Plus(pt)).ScaledBy(0.5)).Plus(disp.offset);

            if(!pt.Equals(closest)) {
                DoLineWithArrows(ref, pt, closest, true);
            }

            DoLabel(ref, labelPos, gr, gu);
            break;
        }

        case PT_LINE_DISTANCE: {
            Vector pt = SK.GetEntity(ptA)->PointGetNum();
            Entity *line = SK.GetEntity(entityA);
            Vector lA = SK.GetEntity(line->point[0])->PointGetNum();
            Vector lB = SK.GetEntity(line->point[1])->PointGetNum();
            Vector dl = lB.Minus(lA);

            if(workplane.v != Entity::FREE_IN_3D.v) {
                lA = lA.ProjectInto(workplane);
                lB = lB.ProjectInto(workplane);
                DoProjectedPoint(&pt);
            }

            // Find the closest point on the line
            Vector closest = pt.ClosestPointOnLine(lA, dl);

            Vector ref = ((closest.Plus(pt)).ScaledBy(0.5)).Plus(disp.offset);
            DoLabel(ref, labelPos, gr, gu);

            if(!pt.Equals(closest)) {
                DoLineWithArrows(ref, pt, closest, true);
            }

            if(workplane.v != Entity::FREE_IN_3D.v) {
                // Draw the projection marker from the closest point on the
                // projected line to the projected point on the real line.
                Vector lAB = (lA.Minus(lB));
                double t = (lA.Minus(closest)).DivPivoting(lAB);

                Vector lA = SK.GetEntity(line->point[0])->PointGetNum();
                Vector lB = SK.GetEntity(line->point[1])->PointGetNum();

                Vector c2 = (lA.ScaledBy(1-t)).Plus(lB.ScaledBy(t));
                DoProjectedPoint(&c2);
            }
            break;
        }

        case DIAMETER: {
            Entity *circle = SK.GetEntity(entityA);
            Vector center = SK.GetEntity(circle->point[0])->PointGetNum();
            Quaternion q = SK.GetEntity(circle->normal)->NormalGetNum();
            Vector n = q.RotationN().WithMagnitude(1);
            double r = circle->CircleGetRadiusNum();

            Vector ref = center.Plus(disp.offset);
            // Force the label into the same plane as the circle.
            ref = ref.Minus(n.ScaledBy(n.Dot(ref) - n.Dot(center)));

            Vector mark = ref.Minus(center);
            mark = mark.WithMagnitude(mark.Magnitude()-r);
            DoLineTrimmedAgainstBox(ref, ref, ref.Minus(mark));

            Vector topLeft;
            DoLabel(ref, &topLeft, gr, gu);
            if(labelPos) *labelPos = topLeft;

            // Show this as diameter or radius?
            if(!other) {
                // Draw the diameter symbol
                Vector dc = topLeft;
                dc = dc.Plus(gu.WithMagnitude(5/SS.GW.scale));
                dc = dc.Plus(gr.WithMagnitude(9/SS.GW.scale));
                double dr = 5/SS.GW.scale;
                double theta, dtheta = (2*PI)/12;
                for(theta = 0; theta < 2*PI-0.01; theta += dtheta) {
                    LineDrawOrGetDistance(
                        dc.Plus(gu.WithMagnitude(cos(theta)*dr)).Plus(
                                gr.WithMagnitude(sin(theta)*dr)),
                        dc.Plus(gu.WithMagnitude(cos(theta+dtheta)*dr)).Plus(
                                gr.WithMagnitude(sin(theta+dtheta)*dr)));
                }
                theta = 25*(PI/180);
                dr *= 1.7;
                dtheta = PI;
                LineDrawOrGetDistance(
                    dc.Plus(gu.WithMagnitude(cos(theta)*dr)).Plus(
                            gr.WithMagnitude(sin(theta)*dr)),
                    dc.Plus(gu.WithMagnitude(cos(theta+dtheta)*dr)).Plus(
                            gr.WithMagnitude(sin(theta+dtheta)*dr)));
            }
            break;
        }

        case POINTS_COINCIDENT: {
            if(!dogd.drawing) {
                for(int i = 0; i < 2; i++) {
                    Vector p = SK.GetEntity(i == 0 ? ptA : ptB)-> PointGetNum();
                    Point2d pp = SS.GW.ProjectPoint(p);
                    // The point is selected within a radius of 7, from the
                    // same center; so if the point is visible, then this
                    // constraint cannot be selected. But that's okay.
                    dogd.dmin = min(dogd.dmin, pp.DistanceTo(dogd.mp) - 3);
                    dogd.refp = p;
                }
                break;
            }

            if(dogd.drawing) {
                // Let's adjust the color of this constraint to have the same
                // rough luma as the point color, so that the constraint does not
                // stand out in an ugly way.
                RgbaColor cd = Style::Color(Style::DATUM),
                         cc = Style::Color(Style::CONSTRAINT);
                // convert from 8-bit color to a vector
                Vector vd = Vector::From(cd.redF(), cd.greenF(), cd.blueF()),
                       vc = Vector::From(cc.redF(), cc.greenF(), cc.blueF());
                // and scale the constraint color to have the same magnitude as
                // the datum color, maybe a bit dimmer
                vc = vc.WithMagnitude(vd.Magnitude()*0.9);
                // and set the color to that.
                ssglColorRGB(RGBf(vc.x, vc.y, vc.z));

                for(int a = 0; a < 2; a++) {
                    Vector r = SS.GW.projRight.ScaledBy((a+1)/SS.GW.scale);
                    Vector d = SS.GW.projUp.ScaledBy((2-a)/SS.GW.scale);
                    for(int i = 0; i < 2; i++) {
                        Vector p = SK.GetEntity(i == 0 ? ptA : ptB)-> PointGetNum();
                        glBegin(GL_QUADS);
                            ssglVertex3v(p.Plus (r).Plus (d));
                            ssglVertex3v(p.Plus (r).Minus(d));
                            ssglVertex3v(p.Minus(r).Minus(d));
                            ssglVertex3v(p.Minus(r).Plus (d));
                        glEnd();
                    }

                }
            }
            break;
        }

        case PT_ON_CIRCLE:
        case PT_ON_LINE:
        case PT_ON_FACE:
        case PT_IN_PLANE: {
            double s = 8/SS.GW.scale;
            Vector p = SK.GetEntity(ptA)->PointGetNum();
            Vector r, d;
            if(type == PT_ON_FACE) {
                Vector n = SK.GetEntity(entityA)->FaceGetNormalNum();
                r = n.Normal(0);
                d = n.Normal(1);
            } else if(type == PT_IN_PLANE) {
                EntityBase *n = SK.GetEntity(entityA)->Normal();
                r = n->NormalU();
                d = n->NormalV();
            } else {
                r = gr;
                d = gu;
                s *= (6.0/8); // draw these a little smaller
            }
            r = r.WithMagnitude(s); d = d.WithMagnitude(s);
            LineDrawOrGetDistance(p.Plus (r).Plus (d), p.Plus (r).Minus(d));
            LineDrawOrGetDistance(p.Plus (r).Minus(d), p.Minus(r).Minus(d));
            LineDrawOrGetDistance(p.Minus(r).Minus(d), p.Minus(r).Plus (d));
            LineDrawOrGetDistance(p.Minus(r).Plus (d), p.Plus (r).Plus (d));
            break;
        }

        case WHERE_DRAGGED: {
            Vector p = SK.GetEntity(ptA)->PointGetNum(),
                   u = p.Plus(gu.WithMagnitude(8/SS.GW.scale)).Plus(
                              gr.WithMagnitude(8/SS.GW.scale)),
                   uu = u.Minus(gu.WithMagnitude(5/SS.GW.scale)),
                   ur = u.Minus(gr.WithMagnitude(5/SS.GW.scale));
            // Draw four little crop marks, uniformly spaced (by ninety
            // degree rotations) around the point.
            int i;
            for(i = 0; i < 4; i++) {
                LineDrawOrGetDistance(u, uu);
                LineDrawOrGetDistance(u, ur);
                u = u.RotatedAbout(p, gn, PI/2);
                ur = ur.RotatedAbout(p, gn, PI/2);
                uu = uu.RotatedAbout(p, gn, PI/2);
            }
            break;
        }

        case SAME_ORIENTATION: {
            for(int i = 0; i < 2; i++) {
                Entity *e = SK.GetEntity(i == 0 ? entityA : entityB);
                Quaternion q = e->NormalGetNum();
                Vector n = q.RotationN().WithMagnitude(25/SS.GW.scale);
                Vector u = q.RotationU().WithMagnitude(6/SS.GW.scale);
                Vector p = SK.GetEntity(e->point[0])->PointGetNum();
                p = p.Plus(n.WithMagnitude(10/SS.GW.scale));

                LineDrawOrGetDistance(p.Plus(u), p.Minus(u).Plus(n));
                LineDrawOrGetDistance(p.Minus(u), p.Plus(u).Plus(n));
            }
            break;
        }

        case EQUAL_ANGLE: {
            Vector ref;
            Entity *a = SK.GetEntity(entityA);
            Entity *b = SK.GetEntity(entityB);
            Entity *c = SK.GetEntity(entityC);
            Entity *d = SK.GetEntity(entityD);

            Vector a0 = a->VectorGetRefPoint();
            Vector b0 = b->VectorGetRefPoint();
            Vector c0 = c->VectorGetRefPoint();
            Vector d0 = d->VectorGetRefPoint();
            Vector da = a->VectorGetNum();
            Vector db = b->VectorGetNum();
            Vector dc = c->VectorGetNum();
            Vector dd = d->VectorGetNum();

            if(other) da = da.ScaledBy(-1);

            DoArcForAngle(a0, da, b0, db,
                da.WithMagnitude(40/SS.GW.scale), &ref);
            DoArcForAngle(c0, dc, d0, dd,
                dc.WithMagnitude(40/SS.GW.scale), &ref);

            break;
        }

        case ANGLE: {
            Entity *a = SK.GetEntity(entityA);
            Entity *b = SK.GetEntity(entityB);

            Vector a0 = a->VectorGetRefPoint();
            Vector b0 = b->VectorGetRefPoint();
            Vector da = a->VectorGetNum();
            Vector db = b->VectorGetNum();
            if(other) da = da.ScaledBy(-1);

            Vector ref;
            DoArcForAngle(a0, da, b0, db, disp.offset, &ref);
            DoLabel(ref, labelPos, gr, gu);
            break;
        }

        case PERPENDICULAR: {
            Vector u = Vector::From(0, 0, 0), v = Vector::From(0, 0, 0);
            Vector rn, ru;
            if(workplane.v == Entity::FREE_IN_3D.v) {
                rn = gn;
                ru = gu;
            } else {
                EntityBase *normal = SK.GetEntity(workplane)->Normal();
                rn = normal->NormalN();
                ru = normal->NormalV(); // ru meaning r_up, not u/v
            }

            for(int i = 0; i < 2; i++) {
                Entity *e = SK.GetEntity(i == 0 ? entityA : entityB);

                if(i == 0) {
                    // Calculate orientation of perpendicular sign only
                    // once, so that it's the same both times it's drawn
                    u = e->VectorGetNum();
                    u = u.WithMagnitude(16/SS.GW.scale);
                    v = (rn.Cross(u)).WithMagnitude(16/SS.GW.scale);
                    // a bit of bias to stop it from flickering between the
                    // two possibilities
                    if(fabs(u.Dot(ru)) < fabs(v.Dot(ru)) + LENGTH_EPS) {
                        SWAP(Vector, u, v);
                    }
                    if(u.Dot(ru) < 0) u = u.ScaledBy(-1);
                }

                Vector p = e->VectorGetRefPoint();
                Vector s = p.Plus(u).Plus(v);
                LineDrawOrGetDistance(s, s.Plus(v));

                Vector m = s.Plus(v.ScaledBy(0.5));
                LineDrawOrGetDistance(m, m.Plus(u));
            }
            break;
        }

        case CURVE_CURVE_TANGENT:
        case CUBIC_LINE_TANGENT:
        case ARC_LINE_TANGENT: {
            Vector textAt, u, v;

            if(type == ARC_LINE_TANGENT) {
                Entity *arc = SK.GetEntity(entityA);
                Entity *norm = SK.GetEntity(arc->normal);
                Vector c = SK.GetEntity(arc->point[0])->PointGetNum();
                Vector p =
                    SK.GetEntity(arc->point[other ? 2 : 1])->PointGetNum();
                Vector r = p.Minus(c);
                textAt = p.Plus(r.WithMagnitude(14/SS.GW.scale));
                u = norm->NormalU();
                v = norm->NormalV();
            } else if(type == CUBIC_LINE_TANGENT) {
                Vector n;
                if(workplane.v == Entity::FREE_IN_3D.v) {
                    u = gr;
                    v = gu;
                    n = gn;
                } else {
                    EntityBase *wn = SK.GetEntity(workplane)->Normal();
                    u = wn->NormalU();
                    v = wn->NormalV();
                    n = wn->NormalN();
                }

                Entity *cubic = SK.GetEntity(entityA);
                Vector p = other ? cubic->CubicGetFinishNum() :
                                   cubic->CubicGetStartNum();
                Vector dir = SK.GetEntity(entityB)->VectorGetNum();
                Vector out = n.Cross(dir);
                textAt = p.Plus(out.WithMagnitude(14/SS.GW.scale));
            } else {
                Vector n, dir;
                EntityBase *wn = SK.GetEntity(workplane)->Normal();
                u = wn->NormalU();
                v = wn->NormalV();
                n = wn->NormalN();
                EntityBase *eA = SK.GetEntity(entityA);
                // Big pain; we have to get a vector tangent to the curve
                // at the shared point, which could be from either a cubic
                // or an arc.
                if(other) {
                    textAt = eA->EndpointFinish();
                    if(eA->type == Entity::CUBIC) {
                        dir = eA->CubicGetFinishTangentNum();
                    } else {
                        dir = SK.GetEntity(eA->point[0])->PointGetNum().Minus(
                              SK.GetEntity(eA->point[2])->PointGetNum());
                        dir = n.Cross(dir);
                    }
                } else {
                    textAt = eA->EndpointStart();
                    if(eA->type == Entity::CUBIC) {
                        dir = eA->CubicGetStartTangentNum();
                    } else {
                        dir = SK.GetEntity(eA->point[0])->PointGetNum().Minus(
                              SK.GetEntity(eA->point[1])->PointGetNum());
                        dir = n.Cross(dir);
                    }
                }
                dir = n.Cross(dir);
                textAt = textAt.Plus(dir.WithMagnitude(14/SS.GW.scale));
            }

            if(dogd.drawing) {
                ssglWriteTextRefCenter("T", DEFAULT_TEXT_HEIGHT,
                    textAt, u, v, LineCallback, this);
            } else {
                dogd.refp = textAt;
                Point2d ref = SS.GW.ProjectPoint(dogd.refp);
                dogd.dmin = min(dogd.dmin, ref.DistanceTo(dogd.mp)-10);
            }
            break;
        }

        case PARALLEL: {
            for(int i = 0; i < 2; i++) {
                Entity *e = SK.GetEntity(i == 0 ? entityA : entityB);
                Vector n = e->VectorGetNum();
                n = n.WithMagnitude(25/SS.GW.scale);
                Vector u = (gn.Cross(n)).WithMagnitude(4/SS.GW.scale);
                Vector p = e->VectorGetRefPoint();

                LineDrawOrGetDistance(p.Plus(u), p.Plus(u).Plus(n));
                LineDrawOrGetDistance(p.Minus(u), p.Minus(u).Plus(n));
            }
            break;
        }

        case EQUAL_RADIUS: {
            for(int i = 0; i < 2; i++) {
                DoEqualRadiusTicks(i == 0 ? entityA : entityB);
            }
            break;
        }

        case EQUAL_LINE_ARC_LEN: {
            Entity *line = SK.GetEntity(entityA);
            DoEqualLenTicks(
                SK.GetEntity(line->point[0])->PointGetNum(),
                SK.GetEntity(line->point[1])->PointGetNum(),
                gn);

            DoEqualRadiusTicks(entityB);
            break;
        }

        case LENGTH_RATIO:
        case EQUAL_LENGTH_LINES: {
            Vector a, b = Vector::From(0, 0, 0);
            for(int i = 0; i < 2; i++) {
                Entity *e = SK.GetEntity(i == 0 ? entityA : entityB);
                a = SK.GetEntity(e->point[0])->PointGetNum();
                b = SK.GetEntity(e->point[1])->PointGetNum();

                if(workplane.v != Entity::FREE_IN_3D.v) {
                    DoProjectedPoint(&a);
                    DoProjectedPoint(&b);
                }

                DoEqualLenTicks(a, b, gn);
            }
            if(type == LENGTH_RATIO) {
                Vector ref = ((a.Plus(b)).ScaledBy(0.5)).Plus(disp.offset);
                DoLabel(ref, labelPos, gr, gu);
            }
            break;
        }

        case EQ_LEN_PT_LINE_D: {
            Entity *forLen = SK.GetEntity(entityA);
            Vector a = SK.GetEntity(forLen->point[0])->PointGetNum(),
                   b = SK.GetEntity(forLen->point[1])->PointGetNum();
            if(workplane.v != Entity::FREE_IN_3D.v) {
                DoProjectedPoint(&a);
                DoProjectedPoint(&b);
            }
            DoEqualLenTicks(a, b, gn);

            Entity *ln = SK.GetEntity(entityB);
            Vector la = SK.GetEntity(ln->point[0])->PointGetNum(),
                   lb = SK.GetEntity(ln->point[1])->PointGetNum();
            Vector pt = SK.GetEntity(ptA)->PointGetNum();
            if(workplane.v != Entity::FREE_IN_3D.v) {
                DoProjectedPoint(&pt);
                la = la.ProjectInto(workplane);
                lb = lb.ProjectInto(workplane);
            }

            Vector closest = pt.ClosestPointOnLine(la, lb.Minus(la));
            LineDrawOrGetDistance(pt, closest);
            DoEqualLenTicks(pt, closest, gn);
            break;
        }

        case EQ_PT_LN_DISTANCES: {
            for(int i = 0; i < 2; i++) {
                Entity *ln = SK.GetEntity(i == 0 ? entityA : entityB);
                Vector la = SK.GetEntity(ln->point[0])->PointGetNum(),
                       lb = SK.GetEntity(ln->point[1])->PointGetNum();
                Entity *pte = SK.GetEntity(i == 0 ? ptA : ptB);
                Vector pt = pte->PointGetNum();

                if(workplane.v != Entity::FREE_IN_3D.v) {
                    DoProjectedPoint(&pt);
                    la = la.ProjectInto(workplane);
                    lb = lb.ProjectInto(workplane);
                }

                Vector closest = pt.ClosestPointOnLine(la, lb.Minus(la));

                LineDrawOrGetDistance(pt, closest);
                DoEqualLenTicks(pt, closest, gn);
            }
            break;
        }

        {
        case SYMMETRIC:
            Vector n;
            n = SK.GetEntity(entityA)->Normal()->NormalN(); goto s;
        case SYMMETRIC_HORIZ:
            n = SK.GetEntity(workplane)->Normal()->NormalU(); goto s;
        case SYMMETRIC_VERT:
            n = SK.GetEntity(workplane)->Normal()->NormalV(); goto s;
        case SYMMETRIC_LINE: {
            Entity *ln = SK.GetEntity(entityA);
            Vector la = SK.GetEntity(ln->point[0])->PointGetNum(),
                   lb = SK.GetEntity(ln->point[1])->PointGetNum();
            la = la.ProjectInto(workplane);
            lb = lb.ProjectInto(workplane);
            n = lb.Minus(la);
            Vector nw = SK.GetEntity(workplane)->Normal()->NormalN();
            n = n.RotatedAbout(nw, PI/2);
            goto s;
        }
s:
            Vector a = SK.GetEntity(ptA)->PointGetNum();
            Vector b = SK.GetEntity(ptB)->PointGetNum();

            for(int i = 0; i < 2; i++) {
                Vector tail = (i == 0) ? a : b;
                Vector d = (i == 0) ? b : a;
                d = d.Minus(tail);
                // Project the direction in which the arrow is drawn normal
                // to the symmetry plane; for projected symmetry constraints,
                // they might not be in the same direction, even when the
                // constraint is fully solved.
                d = n.ScaledBy(d.Dot(n));
                d = d.WithMagnitude(20/SS.GW.scale);
                Vector tip = tail.Plus(d);

                LineDrawOrGetDistance(tail, tip);
                d = d.WithMagnitude(9/SS.GW.scale);
                LineDrawOrGetDistance(tip, tip.Minus(d.RotatedAbout(gn,  0.6)));
                LineDrawOrGetDistance(tip, tip.Minus(d.RotatedAbout(gn, -0.6)));
            }
            break;
        }

        case AT_MIDPOINT:
        case HORIZONTAL:
        case VERTICAL:
            if(entityA.v) {
                Vector r, u, n;
                if(workplane.v == Entity::FREE_IN_3D.v) {
                    r = gr; u = gu; n = gn;
                } else {
                    r = SK.GetEntity(workplane)->Normal()->NormalU();
                    u = SK.GetEntity(workplane)->Normal()->NormalV();
                    n = r.Cross(u);
                }
                // For "at midpoint", this branch is always taken.
                Entity *e = SK.GetEntity(entityA);
                Vector a = SK.GetEntity(e->point[0])->PointGetNum();
                Vector b = SK.GetEntity(e->point[1])->PointGetNum();
                Vector m = (a.ScaledBy(0.5)).Plus(b.ScaledBy(0.5));
                Vector offset = (a.Minus(b)).Cross(n);
                offset = offset.WithMagnitude(13/SS.GW.scale);
                // Draw midpoint constraint on other side of line, so that
                // a line can be midpoint and horizontal at same time.
                if(type == AT_MIDPOINT) offset = offset.ScaledBy(-1);

                if(dogd.drawing) {
                    const char *s = (type == HORIZONTAL)  ? "H" : (
                                    (type == VERTICAL)    ? "V" : (
                                    (type == AT_MIDPOINT) ? "M" : NULL));

                    ssglWriteTextRefCenter(s, DEFAULT_TEXT_HEIGHT,
                        m.Plus(offset), r, u, LineCallback, this);
                } else {
                    dogd.refp = m.Plus(offset);
                    Point2d ref = SS.GW.ProjectPoint(dogd.refp);
                    dogd.dmin = min(dogd.dmin, ref.DistanceTo(dogd.mp)-10);
                }
            } else {
                Vector a = SK.GetEntity(ptA)->PointGetNum();
                Vector b = SK.GetEntity(ptB)->PointGetNum();

                Entity *w = SK.GetEntity(workplane);
                Vector cu = w->Normal()->NormalU();
                Vector cv = w->Normal()->NormalV();
                Vector cn = w->Normal()->NormalN();

                int i;
                for(i = 0; i < 2; i++) {
                    Vector o = (i == 0) ? a : b;
                    Vector oo = (i == 0) ? a.Minus(b) : b.Minus(a);
                    Vector d = (type == HORIZONTAL) ? cu : cv;
                    if(oo.Dot(d) < 0) d = d.ScaledBy(-1);

                    Vector dp = cn.Cross(d);
                    d = d.WithMagnitude(14/SS.GW.scale);
                    Vector c = o.Minus(d);
                    LineDrawOrGetDistance(o, c);
                    d = d.WithMagnitude(3/SS.GW.scale);
                    dp = dp.WithMagnitude(2/SS.GW.scale);
                    if(dogd.drawing) {
                        glBegin(GL_QUADS);
                            ssglVertex3v((c.Plus(d)).Plus(dp));
                            ssglVertex3v((c.Minus(d)).Plus(dp));
                            ssglVertex3v((c.Minus(d)).Minus(dp));
                            ssglVertex3v((c.Plus(d)).Minus(dp));
                        glEnd();
                    } else {
                        Point2d ref = SS.GW.ProjectPoint(c);
                        dogd.dmin = min(dogd.dmin, ref.DistanceTo(dogd.mp)-6);
                    }
                }
            }
            break;

        case COMMENT: {
            if(dogd.drawing && disp.style.v) {
                ssglLineWidth(Style::Width(disp.style));
                ssglColorRGB(Style::Color(disp.style));
            }
            Vector u, v;
            if(workplane.v == Entity::FREE_IN_3D.v) {
                u = gr;
                v = gu;
            } else {
                EntityBase *norm = SK.GetEntity(workplane)->Normal();
                u = norm->NormalU();
                v = norm->NormalV();
            }
            DoLabel(disp.offset, labelPos, u, v);
            break;
        }

        default: oops();
    }
}