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//-----------------------------------------------------------------------------
// User-initiated (not parametric) operations to modify our sketch, by
// changing the requests, like to round a corner or split curves where they
// intersect.
// Copyright 2008-2013 Jonathan Westhues.
//-----------------------------------------------------------------------------
#include "solvespace.h"
//-----------------------------------------------------------------------------
// Replace constraints on oldpt with the same constraints on newpt.
// Useful when splitting, tangent arcing, or removing bezier points.
//-----------------------------------------------------------------------------
void GraphicsWindow::ReplacePointInConstraints(hEntity oldpt, hEntity newpt) {
    for(auto &c : SK.constraint) {
        if(c.ptA == oldpt)
            c.ptA = newpt;
        if(c.ptB == oldpt)
            c.ptB = newpt;
//-----------------------------------------------------------------------------
// Remove constraints on hpt. Useful when removing bezier points.
//-----------------------------------------------------------------------------
void GraphicsWindow::RemoveConstraintsForPointBeingDeleted(hEntity hpt) {
    SK.constraint.ClearTags();
    for(auto &c : SK.constraint) {
        if(c.ptA == hpt || c.ptB == hpt) {
            c.tag = 1;
            (SS.deleted.constraints)++;
            if(c.type != Constraint::Type::POINTS_COINCIDENT &&
               c.type != Constraint::Type::HORIZONTAL &&
               c.type != Constraint::Type::VERTICAL)
                (SS.deleted.nonTrivialConstraints)++;
    SK.constraint.RemoveTagged();
//-----------------------------------------------------------------------------
// Let's say that A is coincident with B, and B is coincident with C. This
// implies that A is coincident with C; but if we delete B, then both
// constraints must be deleted too (since they reference B), and A is no
// longer constrained to C. This routine adds back that constraint.
//-----------------------------------------------------------------------------
void GraphicsWindow::FixConstraintsForRequestBeingDeleted(hRequest hr) {
    Request *r = SK.GetRequest(hr);
    if(r->group != SS.GW.activeGroup) return;
    for(Entity &e : SK.entity) {
        if(!(e.h.isFromRequest())) continue;
        if(e.h.request() != hr) continue;
        if(e.type != Entity::Type::POINT_IN_2D &&
           e.type != Entity::Type::POINT_IN_3D)
            continue;
        // This is a point generated by the request being deleted; so fix
        // the constraints for that.
        FixConstraintsForPointBeingDeleted(e.h);
void GraphicsWindow::FixConstraintsForPointBeingDeleted(hEntity hpt) {
    List<hEntity> ld = {};
    SK.constraint.ClearTags();
    for(Constraint &c : SK.constraint) {
        if(c.type != Constraint::Type::POINTS_COINCIDENT) continue;
        if(c.group != SS.GW.activeGroup) continue;
        if(c.ptA == hpt) {
            ld.Add(&(c.ptB));
            c.tag = 1;
        if(c.ptB == hpt) {
            ld.Add(&(c.ptA));
            c.tag = 1;
    // Remove constraints without waiting for regeneration; this way
    // if another point takes the place of the deleted one (e.g. when
    // removing control points of a bezier) the constraint doesn't
    // spuriously move. Similarly, subsequent calls of this function
    // (if multiple coincident points are getting deleted) will work
    // correctly.
    SK.constraint.RemoveTagged();
    // If more than one point was constrained coincident with hpt, then
    // those two points were implicitly coincident with each other. By
    // deleting hpt (and all constraints that mention it), we will delete
    // that relationship. So put it back here now.
    for(int i = 1; i < ld.n; i++) {
        Constraint::ConstrainCoincident(ld[i-1], ld[i]);
    ld.Clear();
//-----------------------------------------------------------------------------
// A curve by its parametric equation, helper functions for computing tangent
// arcs by a numerical method.
//-----------------------------------------------------------------------------
void GraphicsWindow::ParametricCurve::MakeFromEntity(hEntity he, bool reverse) {
    *this = {};
    Entity *e = SK.GetEntity(he);
    if(e->type == Entity::Type::LINE_SEGMENT) {
        isLine = true;
        p0 = e->EndpointStart(),
        p1 = e->EndpointFinish();
        if(reverse) {
            swap(p0, p1);
    } else if(e->type == Entity::Type::ARC_OF_CIRCLE) {
        isLine = false;
        p0 = SK.GetEntity(e->point[0])->PointGetNum();
        Vector pe = SK.GetEntity(e->point[1])->PointGetNum();
        r = (pe.Minus(p0)).Magnitude();
        e->ArcGetAngles(&theta0, &theta1, &dtheta);
        if(reverse) {
            swap(theta0, theta1);
            dtheta = -dtheta;
        EntityBase *wrkpln = SK.GetEntity(e->workplane)->Normal();
        u = wrkpln->NormalU();
        v = wrkpln->NormalV();
    } else ssassert(false, "Unexpected entity type");
double GraphicsWindow::ParametricCurve::LengthForAuto() {
    if(isLine) {
        // Allow a third of the line to disappear with auto radius
        return (p1.Minus(p0)).Magnitude() / 3;
    } else {
        // But only a twentieth of the arc; shorter means fewer numerical
        // problems since the curve is more linear over shorter sections.
        return (fabs(dtheta)*r)/20;
Vector GraphicsWindow::ParametricCurve::PointAt(double t) {
    if(isLine) {
        return p0.Plus((p1.Minus(p0)).ScaledBy(t));
    } else {
        double theta = theta0 + dtheta*t;
        return p0.Plus(u.ScaledBy(r*cos(theta)).Plus(v.ScaledBy(r*sin(theta))));
Vector GraphicsWindow::ParametricCurve::TangentAt(double t) {
    if(isLine) {
        return p1.Minus(p0);
    } else {
        double theta = theta0 + dtheta*t;
        Vector t =  u.ScaledBy(-r*sin(theta)).Plus(v.ScaledBy(r*cos(theta)));
        t = t.ScaledBy(dtheta);
        return t;
/** Changes or copies the given entity and connects it to the arc.
 * \param t Where on this parametric curve does it connect to the arc.
 * \param reuseOrig Should the original entity be modified
 * \param orig The original entity.
 * \param arc The arc that will be connected to.
 * \param arcFinish Whether to connect to the end point of the arc.
 * \param pointf When changing the original entity, whether the end point should be modified.
void GraphicsWindow::ParametricCurve::CreateRequestTrimmedTo(double t,
    bool reuseOrig, hEntity orig, hEntity arc, bool arcFinish, bool pointf)
    hRequest hr;
    Entity *e;
    if(isLine) {
        if (reuseOrig) {
            e = SK.GetEntity(orig);
            int i = pointf ? 1 : 0;
            SK.GetEntity(e->point[i])->PointForceTo(PointAt(t));
            ConstrainPointIfCoincident(e->point[i]);
        } else {
            hr = SS.GW.AddRequest(Request::Type::LINE_SEGMENT, /*rememberForUndo=*/false),
            e = SK.GetEntity(hr.entity(0));
            SK.GetEntity(e->point[0])->PointForceTo(PointAt(t));
            SK.GetEntity(e->point[1])->PointForceTo(PointAt(1));
            ConstrainPointIfCoincident(e->point[0]);
            ConstrainPointIfCoincident(e->point[1]);
            Constraint::Constrain(Constraint::Type::PT_ON_LINE,
                hr.entity(1), Entity::NO_ENTITY, orig);
        Constraint::Constrain(Constraint::Type::ARC_LINE_TANGENT,
            Entity::NO_ENTITY, Entity::NO_ENTITY,
            arc, e->h, /*other=*/arcFinish, /*other2=*/false);
    } else {
        if (reuseOrig) {
            e = SK.GetEntity(orig);
            int i = pointf ? 2 : 1;
            SK.GetEntity(e->point[i])->PointForceTo(PointAt(t));
            ConstrainPointIfCoincident(e->point[i]);
        } else {
            hr = SS.GW.AddRequest(Request::Type::ARC_OF_CIRCLE, /*rememberForUndo=*/false),
            e = SK.GetEntity(hr.entity(0));
            SK.GetEntity(e->point[0])->PointForceTo(p0);
            if(dtheta > 0) {
                SK.GetEntity(e->point[1])->PointForceTo(PointAt(t));
                SK.GetEntity(e->point[2])->PointForceTo(PointAt(1));
            } else {
                SK.GetEntity(e->point[2])->PointForceTo(PointAt(t));
                SK.GetEntity(e->point[1])->PointForceTo(PointAt(1));
            ConstrainPointIfCoincident(e->point[0]);
            ConstrainPointIfCoincident(e->point[1]);
            ConstrainPointIfCoincident(e->point[2]);
        // The tangency constraint alone is enough to fully constrain it,
        // so there's no need for more.
        Constraint::Constrain(Constraint::Type::CURVE_CURVE_TANGENT,
            Entity::NO_ENTITY, Entity::NO_ENTITY,
            arc, e->h, /*other=*/arcFinish, /*other2=*/(dtheta < 0));
//-----------------------------------------------------------------------------
// If a point in the same group as hpt, and numerically coincident with hpt,
// happens to exist, then constrain that point coincident to hpt.
//-----------------------------------------------------------------------------
void GraphicsWindow::ParametricCurve::ConstrainPointIfCoincident(hEntity hpt) {
    Entity *pt;
    pt = SK.GetEntity(hpt);
    Vector ev, ptv;
    ptv = pt->PointGetNum();
    for(Entity &e : SK.entity) {
        if(e.h == pt->h) continue;
        if(!e.IsPoint()) continue;
        if(e.group != pt->group) continue;
        if(e.workplane != pt->workplane) continue;
        ev = e.PointGetNum();
        if(!ev.Equals(ptv)) continue;
        Constraint::ConstrainCoincident(hpt, e.h);
        break;
//-----------------------------------------------------------------------------
// A single point must be selected when this function is called. We find two
// non-construction line segments that join at this point, and create a
// tangent arc joining them.
//-----------------------------------------------------------------------------
void GraphicsWindow::MakeTangentArc() {
    if(!LockedInWorkplane()) {
        Error(_("Must be sketching in workplane to create tangent arc."));
        return;
    // The point corresponding to the vertex to be rounded.
    Vector pshared = SK.GetEntity(gs.point[0])->PointGetNum();
    ClearSelection();
    // First, find two requests (that are not construction, and that are
    // in our group and workplane) that generate entities that have an
    // endpoint at our vertex to be rounded.
    int i, c = 0;
    Entity *ent[2];
    Request *req[2];
    hRequest hreq[2];
    hEntity hent[2];
    bool pointf[2];
    for(auto &r : SK.request) {
        if(r.group != activeGroup)
            continue;
        if(r.workplane != ActiveWorkplane())
            continue;
        if(r.construction)
            continue;
        if(r.type != Request::Type::LINE_SEGMENT && r.type != Request::Type::ARC_OF_CIRCLE) {
            continue;
        Entity *e = SK.GetEntity(r.h.entity(0));
        Vector ps = e->EndpointStart(),
               pf = e->EndpointFinish();
        if(ps.Equals(pshared) || pf.Equals(pshared)) {
            if(c < 2) {
                // We record the entity and request and their handles,
                // and whether the vertex to be rounded is the start or
                // finish of this entity.
                ent[c] = e;
                hent[c] = e->h;
                req[c] = &r;
                hreq[c] = r.h;
                pointf[c] = (pf.Equals(pshared));
            c++;
    if(c != 2) {
        Error(_("To create a tangent arc, select a point where two "
                "non-construction lines or circles in this group and "
                "workplane join."));
        return;
    Entity *wrkpl = SK.GetEntity(ActiveWorkplane());
    Vector wn = wrkpl->Normal()->NormalN();
    // Based on these two entities, we make the objects that we'll use to
    // numerically find the tangent arc.
    ParametricCurve pc[2];
    pc[0].MakeFromEntity(ent[0]->h, pointf[0]);
    pc[1].MakeFromEntity(ent[1]->h, pointf[1]);
    // And thereafter we mustn't touch the entity or req ptrs,
    // because the new requests/entities we add might force a
    // realloc.
    memset(ent, 0, sizeof(ent));
    memset(req, 0, sizeof(req));
    Vector pinter;
    double r = 0.0, vv = 0.0;
    // We now do Newton iterations to find the tangent arc, and its positions
    // t back along the two curves, starting from shared point of the curves
    // at t = 0. Lots of iterations helps convergence, and this is still
    // ~10 ms for everything.
    int iters = 1000;
    double t[2] = { 0, 0 }, tp[2];
    for(i = 0; i < iters + 20; i++) {
        Vector p0 = pc[0].PointAt(t[0]),
               p1 = pc[1].PointAt(t[1]),
               t0 = pc[0].TangentAt(t[0]),
               t1 = pc[1].TangentAt(t[1]);
        pinter = Vector::AtIntersectionOfLines(p0, p0.Plus(t0),
                                               NULL, NULL, NULL);
        // The sign of vv determines whether shortest distance is
        // clockwise or anti-clockwise.
        Vector v = (wn.Cross(t0)).WithMagnitude(1);
        vv = t1.Dot(v);
        double dot = (t0.WithMagnitude(1)).Dot(t1.WithMagnitude(1));
        double theta = acos(dot);
        if(SS.tangentArcManual) {
            r = SS.tangentArcRadius;
        } else {
            r = 200/scale;
            // Set the radius so that no more than one third of the
            // line segment disappears.
            r = min(r, pc[0].LengthForAuto()*tan(theta/2));
            r = min(r, pc[1].LengthForAuto()*tan(theta/2));;
        // We are source-stepping the radius, to improve convergence. So
        // ramp that for most of the iterations, and then do a few at
        // the end with that constant for polishing.
        if(i < iters) {
            r *= 0.1 + 0.9*i/((double)iters);
        // The distance from the intersection of the lines to the endpoint
        // of the arc, along each line.
        double el = r/tan(theta/2);
        // Compute the endpoints of the arc, for each curve
        Vector pa0 = pinter.Plus(t0.WithMagnitude(el)),
               pa1 = pinter.Plus(t1.WithMagnitude(el));
        tp[0] = t[0];
        tp[1] = t[1];
        // And convert those points to parameter values along the curve.
        t[0] += (pa0.Minus(p0)).DivProjected(t0);
        t[1] += (pa1.Minus(p1)).DivProjected(t1);
    // Stupid check for convergence, and for an out of range result (as
    // we would get, for example, if the line is too short to fit the
    // rounding arc).
    if(fabs(tp[0] - t[0]) > 1e-3 || fabs(tp[1] - t[1]) > 1e-3 ||
        t[0] < 0.01 || t[1] < 0.01 ||
        t[0] > 0.99 || t[1] > 0.99 ||
        IsReasonable(t[0]) || IsReasonable(t[1]))
        Error(_("Couldn't round this corner. Try a smaller radius, or try "
                "creating the desired geometry by hand with tangency "
                "constraints."));
        return;
    // Compute the location of the center of the arc
    Vector center = pc[0].PointAt(t[0]),
           v0inter = pinter.Minus(center);
    int a, b;
    if(vv < 0) {
        a = 1; b = 2;
        center = center.Minus(v0inter.Cross(wn).WithMagnitude(r));
    } else {
        a = 2; b = 1;
        center = center.Plus(v0inter.Cross(wn).WithMagnitude(r));
    SS.UndoRemember();
    if (SS.tangentArcModify) {
        // Delete the coincident constraint for the removed point.
        SK.constraint.ClearTags();
        for(i = 0; i < SK.constraint.n; i++) {
            Constraint *cs = &(SK.constraint[i]);
            if(cs->group != activeGroup) continue;
            if(cs->workplane != ActiveWorkplane()) continue;
            if(cs->type != Constraint::Type::POINTS_COINCIDENT) continue;
            if (SK.GetEntity(cs->ptA)->PointGetNum().Equals(pshared)) {
            cs->tag = 1;
        SK.constraint.RemoveTagged();
    } else {
        // Make the original entities construction, or delete them
        // entirely, according to user preference.
        SK.GetRequest(hreq[0])->construction = true;
        SK.GetRequest(hreq[1])->construction = true;
    // Create and position the new tangent arc.
    hRequest harc = AddRequest(Request::Type::ARC_OF_CIRCLE, /*rememberForUndo=*/false);
    Entity *earc = SK.GetEntity(harc.entity(0));
    hEntity hearc = earc->h;
    SK.GetEntity(earc->point[0])->PointForceTo(center);
    SK.GetEntity(earc->point[a])->PointForceTo(pc[0].PointAt(t[0]));
    SK.GetEntity(earc->point[b])->PointForceTo(pc[1].PointAt(t[1]));
    earc = NULL;
    // Modify or duplicate the original entities and connect them to the tangent arc.
    pc[0].CreateRequestTrimmedTo(t[0], SS.tangentArcModify,
                hent[0], hearc, /*arcFinish=*/(b == 1), pointf[0]);
    pc[1].CreateRequestTrimmedTo(t[1], SS.tangentArcModify,
                hent[1], hearc, /*arcFinish=*/(a == 1), pointf[1]);
hEntity GraphicsWindow::SplitLine(hEntity he, Vector pinter) {
    // Save the original endpoints, since we're about to delete this entity.
    Entity *e01 = SK.GetEntity(he);
    hEntity hep0 = e01->point[0], hep1 = e01->point[1];
    Vector p0 = SK.GetEntity(hep0)->PointGetNum(),
           p1 = SK.GetEntity(hep1)->PointGetNum();
    // Add the two line segments this one gets split into.
    hRequest r0i = AddRequest(Request::Type::LINE_SEGMENT, /*rememberForUndo=*/false),
             ri1 = AddRequest(Request::Type::LINE_SEGMENT, /*rememberForUndo=*/false);
    // Don't get entities till after adding, realloc issues
    Entity *e0i = SK.GetEntity(r0i.entity(0)),
           *ei1 = SK.GetEntity(ri1.entity(0));
    SK.GetEntity(e0i->point[0])->PointForceTo(p0);
    SK.GetEntity(e0i->point[1])->PointForceTo(pinter);
    SK.GetEntity(ei1->point[0])->PointForceTo(pinter);
    SK.GetEntity(ei1->point[1])->PointForceTo(p1);
    ReplacePointInConstraints(hep0, e0i->point[0]);
    ReplacePointInConstraints(hep1, ei1->point[1]);
    Constraint::ConstrainCoincident(e0i->point[1], ei1->point[0]);
    return e0i->point[1];
hEntity GraphicsWindow::SplitCircle(hEntity he, Vector pinter) {
    Entity *circle = SK.GetEntity(he);
    if(circle->type == Entity::Type::CIRCLE) {
        // Start with an unbroken circle, split it into a 360 degree arc.
        Vector center = SK.GetEntity(circle->point[0])->PointGetNum();
        circle = NULL; // shortly invalid!
        hRequest hr = AddRequest(Request::Type::ARC_OF_CIRCLE, /*rememberForUndo=*/false);
        Entity *arc = SK.GetEntity(hr.entity(0));
        SK.GetEntity(arc->point[0])->PointForceTo(center);
        SK.GetEntity(arc->point[1])->PointForceTo(pinter);
        SK.GetEntity(arc->point[2])->PointForceTo(pinter);
        Constraint::ConstrainCoincident(arc->point[1], arc->point[2]);
        return arc->point[1];
    } else {
        // Start with an arc, break it in to two arcs
        hEntity hc = circle->point[0],
                hs = circle->point[1],
                hf = circle->point[2];
        Vector center = SK.GetEntity(hc)->PointGetNum(),
               start  = SK.GetEntity(hs)->PointGetNum(),
               finish = SK.GetEntity(hf)->PointGetNum();
        circle = NULL; // shortly invalid!
        hRequest hr0 = AddRequest(Request::Type::ARC_OF_CIRCLE, /*rememberForUndo=*/false),
                 hr1 = AddRequest(Request::Type::ARC_OF_CIRCLE, /*rememberForUndo=*/false);
        Entity *arc0 = SK.GetEntity(hr0.entity(0)),
               *arc1 = SK.GetEntity(hr1.entity(0));
        SK.GetEntity(arc0->point[0])->PointForceTo(center);
        SK.GetEntity(arc0->point[1])->PointForceTo(start);
        SK.GetEntity(arc0->point[2])->PointForceTo(pinter);
        SK.GetEntity(arc1->point[0])->PointForceTo(center);
        SK.GetEntity(arc1->point[1])->PointForceTo(pinter);
        SK.GetEntity(arc1->point[2])->PointForceTo(finish);
        ReplacePointInConstraints(hs, arc0->point[1]);
        ReplacePointInConstraints(hf, arc1->point[2]);
        Constraint::ConstrainCoincident(arc0->point[2], arc1->point[1]);
        return arc0->point[2];
hEntity GraphicsWindow::SplitCubic(hEntity he, Vector pinter) {
    // Save the original endpoints, since we're about to delete this entity.
    Entity *e01 = SK.GetEntity(he);
    SBezierList sbl = {};
    e01->GenerateBezierCurves(&sbl);
    hEntity hep0 = e01->point[0],
            hep1 = e01->point[3+e01->extraPoints],
            hep0n = Entity::NO_ENTITY, // the new start point
            hep1n = Entity::NO_ENTITY, // the new finish point
            hepin = Entity::NO_ENTITY; // the intersection point
    // The curve may consist of multiple cubic segments. So find which one
    // contains the intersection point.
    double t;
    int i, j;
    for(i = 0; i < sbl.l.n; i++) {
        SBezier *sb = &(sbl.l[i]);
        ssassert(sb->deg == 3, "Expected a cubic bezier");
        sb->ClosestPointTo(pinter, &t, /*mustConverge=*/false);
        if(pinter.Equals(sb->PointAt(t))) {
            // Split that segment at the intersection.
            SBezier b0i, bi1, b01 = *sb;
            b01.SplitAt(t, &b0i, &bi1);
            // Add the two cubic segments this one gets split into.
            hRequest r0i = AddRequest(Request::Type::CUBIC, /*rememberForUndo=*/false),
                     ri1 = AddRequest(Request::Type::CUBIC, /*rememberForUndo=*/false);
            // Don't get entities till after adding, realloc issues
            Entity *e0i = SK.GetEntity(r0i.entity(0)),
                   *ei1 = SK.GetEntity(ri1.entity(0));
            for(j = 0; j <= 3; j++) {
                SK.GetEntity(e0i->point[j])->PointForceTo(b0i.ctrl[j]);
            for(j = 0; j <= 3; j++) {
                SK.GetEntity(ei1->point[j])->PointForceTo(bi1.ctrl[j]);
            Constraint::ConstrainCoincident(e0i->point[3], ei1->point[0]);
            if(i == 0) hep0n = e0i->point[0];
            hep1n = ei1->point[3];
            hepin = e0i->point[3];
        } else {
            hRequest r = AddRequest(Request::Type::CUBIC, /*rememberForUndo=*/false);
            Entity *e = SK.GetEntity(r.entity(0));
            for(j = 0; j <= 3; j++) {
                SK.GetEntity(e->point[j])->PointForceTo(sb->ctrl[j]);
            if(i == 0) hep0n = e->point[0];
            hep1n = e->point[3];
    sbl.Clear();
    ReplacePointInConstraints(hep0, hep0n);
    ReplacePointInConstraints(hep1, hep1n);
    return hepin;
hEntity GraphicsWindow::SplitEntity(hEntity he, Vector pinter) {
    Entity *e = SK.GetEntity(he);
    Entity::Type entityType = e->type;
    hEntity ret;
    if(e->IsCircle()) {
        ret = SplitCircle(he, pinter);
    } else if(e->type == Entity::Type::LINE_SEGMENT) {
        ret = SplitLine(he, pinter);
    } else if(e->type == Entity::Type::CUBIC || e->type == Entity::Type::CUBIC_PERIODIC) {
        ret = SplitCubic(he, pinter);
    } else {
        Error(_("Couldn't split this entity; lines, circles, or cubics only."));
        return Entity::NO_ENTITY;
    // Finally, delete the request that generated the original entity.
    Request::Type reqType = EntReqTable::GetRequestForEntity(entityType);
    SK.request.ClearTags();
    for(auto &r : SK.request) {
        if(r.group != activeGroup)
            continue;
        if(r.type != reqType)
            continue;
        // If the user wants to keep the old entities around, they can just
        // mark them construction first.
        if(he == r.h.entity(0) && !r.construction) {
            r.tag = 1;
            break;
    DeleteTaggedRequests();
    return ret;
void GraphicsWindow::SplitLinesOrCurves() {
    if(!LockedInWorkplane()) {
        Error(_("Must be sketching in workplane to split."));
        return;
    GroupSelection();
    int n = gs.lineSegments + gs.circlesOrArcs + gs.cubics + gs.periodicCubics;
    if(!((n == 2 && gs.points == 0) || (n == 1 && gs.points == 1))) {
        Error(_("Select two entities that intersect each other "
                "(e.g. two lines/circles/arcs or a line/circle/arc and a point)."));
        return;
    bool splitAtPoint = (gs.points == 1);
    hEntity ha = gs.entity[0],
            hb = splitAtPoint ? gs.point[0] : gs.entity[1];
    Entity *ea = SK.GetEntity(ha),
           *eb = SK.GetEntity(hb);
    SPointList inters = {};
    SBezierList sbla = {},
                sblb = {};
    Vector pi = Vector::From(0, 0, 0);
    SK.constraint.ClearTags();
    // First, decide the point where we're going to make the split.
    bool foundInters = false;
    if(splitAtPoint) {
        // One of the entities is a point, and this point must be on the other entity.
        // Verify that a corresponding point-coincident constraint exists for the point/entity.
        Vector p0, p1;
        if(ea->type == Entity::Type::LINE_SEGMENT) {
            p0 = ea->EndpointStart();
            p1 = ea->EndpointFinish();
        for(Constraint &c : SK.constraint) {
            if(c.ptA.request() == hb.request() &&
               c.entityA.request() == ha.request()) {
                pi = SK.GetEntity(c.ptA)->PointGetNum();
                if(ea->type == Entity::Type::LINE_SEGMENT && !pi.OnLineSegment(p0, p1)) {
                    // The point isn't between line endpoints, so there isn't an actual
                    // intersection.
                    continue;
                c.tag = 1;
                foundInters = true;
                break;
    } else {
        // Compute the possibly-rational Bezier curves for each of these non-point entities...
        ea->GenerateBezierCurves(&sbla);
        eb->GenerateBezierCurves(&sblb);
        // ... and then compute the points where they intersect, based on those curves.
        sbla.AllIntersectionsWith(&sblb, &inters);
        // If there's multiple points, then take the one closest to the mouse pointer.
        if(!inters.l.IsEmpty()) {
            double dmin = VERY_POSITIVE;
            SPoint *sp;
            for(sp = inters.l.First(); sp; sp = inters.l.NextAfter(sp)) {
                double d = ProjectPoint(sp->p).DistanceTo(currentMousePosition);
                if(d < dmin) {
                    dmin = d;
                    pi = sp->p;
        foundInters = true;
    // Then, actually split the entities.
    if(foundInters) {
        SS.UndoRemember();
        // Remove any constraints we're going to replace.
        SK.constraint.RemoveTagged();
        hEntity hia = SplitEntity(ha, pi),
                hib = {};
        // SplitEntity adds the coincident constraints to join the split halves
        // of each original entity; and then we add the constraint to join
        // the two entities together at the split point.
        if(splitAtPoint) {
            // Remove datum point, as it has now been superseded by the split point.
            SK.request.ClearTags();
            for(Request &r : SK.request) {
                if(r.h == hb.request()) {
                    if(r.type == Request::Type::DATUM_POINT) {
                        // Delete datum point.
                        r.tag = 1;
                        FixConstraintsForRequestBeingDeleted(r.h);
                    } else {
                        // Add constraint if not datum point, but endpoint of line/arc etc.
                        Constraint::ConstrainCoincident(hia, hb);
                    break;
            SK.request.RemoveTagged();
        } else {
            // Split second non-point entity and add constraint.
            hib = SplitEntity(hb, pi);
            if(hia.v && hib.v) {
                Constraint::ConstrainCoincident(hia, hib);
    } else {
        Error(_("Can't split; no intersection found."));
        return;
    // All done, clean up and regenerate.
    inters.Clear();
    sbla.Clear();
    sblb.Clear();
    ClearSelection();
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