OpenSubdiv/opensubdiv/hbr/catmark.h

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#ifndef HBRCATMARK_H
#define HBRCATMARK_H

/*#define HBR_DEBUG */
#include "../hbr/subdivision.h"

template <class T>
class HbrCatmarkSubdivision : public HbrSubdivision<T> {
public:
    HbrCatmarkSubdivision<T>()
	: HbrSubdivision<T>(), triangleSubdivision(k_Normal) {}

    HbrCatmarkSubdivision<T>(const HbrCatmarkSubdivision<T> &old)
	: HbrSubdivision<T>(), triangleSubdivision(old.triangleSubdivision) {}    

    virtual HbrSubdivision<T>* Clone() const {
        return new HbrCatmarkSubdivision<T>(*this);
    }

    virtual void Refine(HbrMesh<T>* mesh, HbrFace<T>* face);
    virtual HbrFace<T>* RefineFaceAtVertex(HbrMesh<T>* mesh, HbrFace<T>* face, HbrVertex<T>* vertex);    
    virtual void GuaranteeNeighbor(HbrMesh<T>* mesh, HbrHalfedge<T>* edge);
    virtual void GuaranteeNeighbors(HbrMesh<T>* mesh, HbrVertex<T>* vertex);

    virtual bool HasLimit(HbrMesh<T>* mesh, HbrFace<T>* face);
    virtual bool HasLimit(HbrMesh<T>* mesh, HbrHalfedge<T>* edge);
    virtual bool HasLimit(HbrMesh<T>* mesh, HbrVertex<T>* vertex);
    
    virtual HbrVertex<T>* Subdivide(HbrMesh<T>* mesh, HbrFace<T>* face);
    virtual HbrVertex<T>* Subdivide(HbrMesh<T>* mesh, HbrHalfedge<T>* edge);
    virtual HbrVertex<T>* Subdivide(HbrMesh<T>* mesh, HbrVertex<T>* vertex);

    virtual bool VertexIsExtraordinary(HbrMesh<T>* /* mesh */, HbrVertex<T>* vertex) { return vertex->GetValence() != 4; }

    // Triangle subdivision rules, which modifies the rules for
    // triangular faces in order to make them smoother. The "normal"
    // rule is the standard Catmull-Clark rule. The "old" rule
    // modifies only the subdivision rules for a face to vertex
    // refinement. The "new" rule modifies only the subdivision rules
    // for an edge to vertex refinement. These rules are only applied
    // to the top level face, since only top level faces can be
    // triangular; after one level of refinement everything becomes
    // quads.
    enum TriangleSubdivision {
	k_Normal,
	k_Old,
	k_New
    };
    TriangleSubdivision GetTriangleSubdivisionMethod() const { return triangleSubdivision; }
    void SetTriangleSubdivisionMethod(TriangleSubdivision method) { triangleSubdivision = method; }

    virtual int GetFaceChildrenCount(int nvertices) const { return nvertices; }
    
private:

    // Transfers facevarying data from a parent face to a child face
    void transferFVarToChild(HbrMesh<T>* mesh, HbrFace<T>* face, HbrFace<T>* child, int index);

    // Transfers vertex and edge edits from a parent face to a child face
    void transferEditsToChild(HbrFace<T>* face, HbrFace<T>* child, int index);
    
    TriangleSubdivision triangleSubdivision;
};

template <class T>
void
HbrCatmarkSubdivision<T>::transferFVarToChild(HbrMesh<T>* mesh, HbrFace<T>* face, HbrFace<T>* child, int index) {

    typename HbrMesh<T>::InterpolateBoundaryMethod fvarinterp = mesh->GetFVarInterpolateBoundaryMethod();
    const int fvarcount = mesh->GetFVarCount();
    int fvarindex = 0;
    const int nv = face->GetNumVertices();
    bool extraordinary = (nv != 4);
    HbrVertex<T> *v = face->GetVertex(index), *childVertex;
    HbrHalfedge<T>* edge;

    // We do the face subdivision rule first, because we may reuse the
    // result (stored in fv2) for the other subdivisions.
    float weight =  1.0f / nv;
    // For the face center vertex, the facevarying data can be cleared
    // and averaged en masse, since the subdivision rules don't change
    // for any of the data - we use the smooth rule for all of it.
    // And since we know that the fvardata for this particular vertex
    // is smooth and therefore shareable amongst all incident faces,
    // we don't have to allocate extra storage for it. We also don't
    // have to compute it if some other face got to it first (as
    // indicated by the IsInitialized() flag).
    HbrFVarData<T>& fv2 = child->GetFVarData(extraordinary ? 2 : (index+2)%4);
    if (!fv2.IsInitialized()) {
        const int totalfvarwidth = mesh->GetTotalFVarWidth();
        fv2.ClearAll(totalfvarwidth);
        for (int j = 0; j < nv; ++j) {
            fv2.AddWithWeightAll(face->GetFVarData(j), totalfvarwidth, weight);
        }
    }
    assert(fv2.IsInitialized());

    v->GuaranteeNeighbors();

    // Make sure that that each of the vertices of the child face have
    // the appropriate facevarying storage as needed. If there are
    // discontinuities in any facevarying datum, the vertex must
    // allocate a new block of facevarying storage specific to the
    // child face.
    bool fv0IsSmooth, fv1IsSmooth, fv3IsSmooth;
    
    childVertex = child->GetVertex(extraordinary ? 0 : (index+0)%4);
    fv0IsSmooth = v->IsFVarAllSmooth();
    if (!fv0IsSmooth) {
        childVertex->NewFVarData(child);
    }
    HbrFVarData<T>& fv0 = childVertex->GetFVarData(child);
    
    edge = face->GetEdge(index);
    GuaranteeNeighbor(mesh, edge);
    assert(edge->GetOrgVertex() == v);
    childVertex = child->GetVertex(extraordinary ? 1 : (index+1)%4);
    fv1IsSmooth = !edge->IsFVarInfiniteSharpAnywhere();
    if (!fv1IsSmooth) {
        childVertex->NewFVarData(child);
    }
    HbrFVarData<T>& fv1 = childVertex->GetFVarData(child);

    edge = edge->GetPrev();
    GuaranteeNeighbor(mesh, edge);    
    assert(edge == face->GetEdge((index + nv - 1) % nv));
    assert(edge->GetDestVertex() == v);
    childVertex = child->GetVertex(extraordinary ? 3 : (index+3)%4);
    fv3IsSmooth = !edge->IsFVarInfiniteSharpAnywhere();
    if (!fv3IsSmooth) {
        childVertex->NewFVarData(child);
    }
    HbrFVarData<T>& fv3 = childVertex->GetFVarData(child);
    fvarindex = 0;
    for (int fvaritem = 0; fvaritem < fvarcount; ++fvaritem) {
        // Vertex subdivision rule. Analyze whether the vertex is on the
        // boundary and whether it's an infinitely sharp corner. We
        // determine the last by checking the propagate corners flag on
        // the mesh; if it's off, we check the two edges of this face
        // incident to that vertex and determining whether they are
        // facevarying boundary edges - this is analogous to what goes on
        // for the interpolateboundary tag (which when set to
        // EDGEANDCORNER marks vertices with a valence of two as being
        // sharp corners). If propagate corners is on, we check *all*
        // faces to see if two edges side by side are facevarying boundary
        // edges. The facevarying boundary check ignores geometric
        // sharpness, otherwise we may swim at geometric creases which
        // aren't actually discontinuous.
        bool infcorner = false;
        const int fvarwidth = mesh->GetFVarWidths()[fvaritem];
        const unsigned char fvarmask = v->GetFVarMask(fvaritem);
        if (fvarinterp == HbrMesh<T>::k_InterpolateBoundaryEdgeAndCorner) {
            if (fvarmask >= HbrVertex<T>::k_Corner) {
                infcorner = true;
            } else if (mesh->GetFVarPropagateCorners()) {
                if (v->IsFVarCorner(fvaritem)) {
                    infcorner = true;
                }
            } else {
                if (face->GetEdge(index)->GetFVarSharpness(fvaritem, true) && face->GetEdge(index)->GetPrev()->GetFVarSharpness(fvaritem, true)) {
                    infcorner = true;
                }
            }
        }

        // Infinitely sharp vertex rule. Applied if the vertex is:
        // - undergoing no facevarying boundary interpolation;
        // - at a geometric crease, in either boundary interpolation case; or
        // - is an infinitely sharp facevarying vertex, in the EDGEANDCORNER case; or
        // - has a mask equal or greater than one, in the "always
        //   sharp" interpolate boundary case
        if (fvarinterp == HbrMesh<T>::k_InterpolateBoundaryNone ||
            (fvarinterp == HbrMesh<T>::k_InterpolateBoundaryAlwaysSharp &&
             fvarmask >= 1) ||
            v->GetSharpness() > HbrVertex<T>::k_Smooth ||
            infcorner) {
            fv0.SetWithWeight(face->GetFVarData(index), fvarindex, fvarwidth, 1.0f);
        }
        // Dart rule: unlike geometric creases, because there's two
        // discontinuous values for the one incident edge, we use the
        // boundary rule and not the smooth rule
        else if (fvarmask == 1) {
            assert(!v->OnBoundary());

            // Use 0.75 of the current vert
            fv0.SetWithWeight(face->GetFVarData(index), fvarindex, fvarwidth, 0.75f);

            // 0.125 of "two adjacent edge vertices", which in actuality
            // are the facevarying values of the same vertex but on each
            // side of the single incident facevarying sharp edge
            HbrHalfedge<T>* start = v->GetIncidentEdge(), *nextedge;
            edge = start;
            while (edge) {
                if (edge->GetFVarSharpness(fvaritem)) {
                    break;
                }
                nextedge = v->GetNextEdge(edge);
                if (nextedge == start) {
                    assert(0); // we should have found it by now
                    break;
                } else if (!nextedge) {
                    // should never get into this case - if the vertex is
                    // on a boundary, it can never be a facevarying dart
                    // vertex
                    assert(0);
                    edge = edge->GetPrev();
                    break;
                } else {
                    edge = nextedge;
                }
            }
            HbrVertex<T>* w = edge->GetDestVertex();
            HbrFace<T>* bestface = edge->GetLeftFace();
            int j;
            for (j = 0; j < bestface->GetNumVertices(); ++j) {
                if (bestface->GetVertex(j) == w) break;
            }
            assert(j != bestface->GetNumVertices());
            fv0.AddWithWeight(bestface->GetFVarData(j), fvarindex, fvarwidth, 0.125f);
            bestface = edge->GetRightFace();
            for (j = 0; j < bestface->GetNumVertices(); ++j) {
                if (bestface->GetVertex(j) == w) break;
            }
            assert(j != bestface->GetNumVertices());
            fv0.AddWithWeight(bestface->GetFVarData(j), fvarindex, fvarwidth, 0.125f);
        }
        // Boundary vertex rule
        else if (fvarmask != 0) {

            // Use 0.75 of the current vert
            fv0.SetWithWeight(face->GetFVarData(index), fvarindex, fvarwidth, 0.75f);

            // Compute 0.125 of two adjacent edge vertices. However the
            // two adjacent edge vertices we use must be part of the
            // facevarying "boundary". To find the first edge we cycle
            // counterclockwise around the current vertex v and look for
            // the first boundary edge

            HbrFace<T>* bestface = face;
            HbrHalfedge<T>* bestedge = face->GetEdge(index)->GetPrev();
            HbrHalfedge<T>* starte = bestedge->GetOpposite();
            HbrVertex<T>* w = 0;
            if (!starte) {
                w = face->GetEdge(index)->GetPrev()->GetOrgVertex();
            } else {
                HbrHalfedge<T>* e = starte, *next;
                assert(starte->GetOrgVertex() == v);
                do {
                    if (e->GetFVarSharpness(fvaritem) || !e->GetLeftFace()) {
                        bestface = e->GetRightFace();
                        bestedge = e;
                        break;
                    }
                    next = v->GetNextEdge(e);
                    if (!next) {
                        bestface = e->GetLeftFace();
                        w = e->GetPrev()->GetOrgVertex();
                        break;
                    }
                    e = next;
                } while (e && e != starte);
            }
            if (!w) w = bestedge->GetDestVertex();
            int j;
            for (j = 0; j < bestface->GetNumVertices(); ++j) {
                if (bestface->GetVertex(j) == w) break;
            }
            assert(j != bestface->GetNumVertices());
            fv0.AddWithWeight(bestface->GetFVarData(j), fvarindex, fvarwidth, 0.125f);

            // Look for the other edge by cycling clockwise around v
            bestface = face;
            bestedge = face->GetEdge(index);
            starte = bestedge;
            w = 0;
            if (HbrHalfedge<T>* e = starte) {
                assert(starte->GetOrgVertex() == v);	
                do {
                    if (e->GetFVarSharpness(fvaritem) || !e->GetRightFace()) {
                        bestface = e->GetLeftFace();
                        bestedge = e;
                        break;
                    }
                    assert(e->GetOpposite());
                    e = v->GetPreviousEdge(e);
                } while (e && e != starte);
            }
            if (!w) w = bestedge->GetDestVertex();
            for (j = 0; j < bestface->GetNumVertices(); ++j) {
                if (bestface->GetVertex(j) == w) break;
            }
            assert(j != bestface->GetNumVertices());
            fv0.AddWithWeight(bestface->GetFVarData(j), fvarindex, fvarwidth, 0.125f);
	
        }
        // Smooth rule. Here, we can take a shortcut if we know that
        // the vertex is smooth and some other vertex has completely
        // computed the facevarying values
        else if (!fv0IsSmooth || !fv0.IsInitialized()) {
            int valence = v->GetValence();
            float invvalencesquared = 1.0f / (valence * valence);

            // Use n-2/n of the current vertex value
            fv0.SetWithWeight(face->GetFVarData(index), fvarindex, fvarwidth, invvalencesquared * valence * (valence - 2));

            // Add 1/n^2 of surrounding edge vertices and surrounding face
            // averages. We loop over all surrounding faces..
            HbrHalfedge<T>* start = v->GetIncidentEdge(), *edge;
            edge = start;
            while (edge) {
                HbrFace<T>* g = edge->GetLeftFace();
                weight = invvalencesquared / g->GetNumVertices();
                // .. and compute the average of each face. At the same
                // time, we look for the edge on that face whose origin is
                // the same as v, and add a contribution from its
                // destination vertex value; this takes care of the
                // surrounding edge vertex addition.
                for (int j = 0; j < g->GetNumVertices(); ++j) {
                    fv0.AddWithWeight(g->GetFVarData(j), fvarindex, fvarwidth, weight);
                    if (g->GetEdge(j)->GetOrgVertex() == v) {
                        fv0.AddWithWeight(g->GetFVarData((j + 1) % g->GetNumVertices()), fvarindex, fvarwidth, invvalencesquared);
                    }
                }
                edge = v->GetNextEdge(edge);
                if (edge == start) break;
            }
        }

        // Edge subdivision rule
        edge = face->GetEdge(index);

        if (fvarinterp == HbrMesh<T>::k_InterpolateBoundaryNone ||
            edge->GetFVarSharpness(fvaritem) || edge->IsBoundary()) {

            // Sharp edge rule
            fv1.SetWithWeight(face->GetFVarData(index), fvarindex, fvarwidth, 0.5f);
            fv1.AddWithWeight(face->GetFVarData((index + 1) % nv), fvarindex, fvarwidth, 0.5f);
        } else if (!fv1IsSmooth || !fv1.IsInitialized()) {
            // Smooth edge subdivision. Add 0.25 of adjacent vertices
            fv1.SetWithWeight(face->GetFVarData(index), fvarindex, fvarwidth, 0.25f);
            fv1.AddWithWeight(face->GetFVarData((index + 1) % nv), fvarindex, fvarwidth, 0.25f);
            // Local subdivided face vertex
            fv1.AddWithWeight(fv2, fvarindex, fvarwidth, 0.25f);
            // Add 0.25 * average of neighboring face vertices
            HbrFace<T>* oppFace = edge->GetRightFace();
            weight = 0.25f / oppFace->GetNumVertices();
            for (int j = 0; j < oppFace->GetNumVertices(); ++j) {
                fv1.AddWithWeight(oppFace->GetFVarData(j), fvarindex, fvarwidth, weight);
            }
        }
		

        // Edge subdivision rule
        edge = edge->GetPrev();

        if (fvarinterp == HbrMesh<T>::k_InterpolateBoundaryNone ||
            edge->GetFVarSharpness(fvaritem) || edge->IsBoundary()) {

            // Sharp edge rule						 
            fv3.SetWithWeight(face->GetFVarData((index + nv - 1) % nv), fvarindex, fvarwidth, 0.5f);
            fv3.AddWithWeight(face->GetFVarData(index), fvarindex, fvarwidth, 0.5f);
        } else if (!fv3IsSmooth || !fv3.IsInitialized()) {
            // Smooth edge subdivision. Add 0.25 of adjacent vertices	
            fv3.SetWithWeight(face->GetFVarData((index + nv - 1) % nv), fvarindex, fvarwidth, 0.25f);
            fv3.AddWithWeight(face->GetFVarData(index), fvarindex, fvarwidth, 0.25f);
            // Local subdivided face vertex
            fv3.AddWithWeight(fv2, fvarindex, fvarwidth, 0.25f);
            // Add 0.25 * average of neighboring face vertices
            HbrFace<T>* oppFace = edge->GetRightFace();
            weight = 0.25f / oppFace->GetNumVertices();
            for (int j = 0; j < oppFace->GetNumVertices(); ++j) {
                fv3.AddWithWeight(oppFace->GetFVarData(j), fvarindex, fvarwidth, weight);
            }
        }

        fvarindex += fvarwidth;
    }
    fv0.SetInitialized();
    fv1.SetInitialized();
    fv3.SetInitialized();

    // Special handling of ptex index for extraordinary faces: make
    // sure the children get their indices reassigned to be
    // consecutive within the block reserved for the parent.
    if (face->GetNumVertices() != 4 && face->GetPtexIndex() != -1) {
        child->SetPtexIndex(face->GetPtexIndex() + index);
    }
}

template <class T>
void
HbrCatmarkSubdivision<T>::transferEditsToChild(HbrFace<T>* face, HbrFace<T>* child, int index) {

    // Hand down pointers to hierarchical edits
    if (HbrHierarchicalEdit<T>** edits = face->GetHierarchicalEdits()) {
	while (HbrHierarchicalEdit<T>* edit = *edits) {
	    if (!edit->IsRelevantToFace(face)) break;
	    if (edit->GetNSubfaces() > face->GetDepth() &&
		(edit->GetSubface(face->GetDepth()) == index)) {
		child->SetHierarchicalEdits(edits);
		break;
	    }
	    edits++;
	}
    }
}


template <class T>
void
HbrCatmarkSubdivision<T>::Refine(HbrMesh<T>* mesh, HbrFace<T>* face) {

    // Create new quadrilateral children faces from this face
    HbrFace<T>* child;
    HbrVertex<T>* vertices[4];
    HbrHalfedge<T>* edge = face->GetFirstEdge();
    HbrHalfedge<T>* prevedge = edge->GetPrev();
    HbrHalfedge<T>* childedge;
    int nv = face->GetNumVertices();
    float sharpness;
    bool extraordinary = (nv != 4);
    // The funny indexing on vertices is done only for
    // non-extraordinary faces in order to correctly preserve
    // parametric space through the refinement. If we split an
    // extraordinary face then it doesn't matter.
    for (int i = 0; i < nv; ++i) {
	if (!face->GetChild(i)) {
#ifdef HBR_DEBUG
	    std::cerr << "Kid " << i << "\n";
#endif
	    HbrVertex<T>* vertex = edge->GetOrgVertex();
	    if (extraordinary) {
		vertices[0] = vertex->Subdivide();
		vertices[1] = edge->Subdivide();
		vertices[2] = face->Subdivide();
		vertices[3] = prevedge->Subdivide();
	    } else {
		vertices[i] = vertex->Subdivide();
		vertices[(i+1)%4] = edge->Subdivide();
		vertices[(i+2)%4] = face->Subdivide();
		vertices[(i+3)%4] = prevedge->Subdivide();
	    }
	    child = mesh->NewFace(4, vertices, face, i);
#ifdef HBR_DEBUG
	    std::cerr << "Creating face " << *child << " during refine\n";
#endif

	    // Hand down edge sharpnesses
            childedge = vertex->Subdivide()->GetEdge(edge->Subdivide());
            assert(childedge);
	    if ((sharpness = edge->GetSharpness()) > HbrHalfedge<T>::k_Smooth) {
		HbrSubdivision<T>::SubdivideCreaseWeight(
                    edge, edge->GetDestVertex(), childedge);
	    }
            childedge->CopyFVarInfiniteSharpness(edge);

            childedge = prevedge->Subdivide()->GetEdge(vertex->Subdivide());
            assert(childedge);
	    if ((sharpness = prevedge->GetSharpness()) > HbrHalfedge<T>::k_Smooth) {
		HbrSubdivision<T>::SubdivideCreaseWeight(
                    prevedge, prevedge->GetOrgVertex(), childedge);
	    }
            childedge->CopyFVarInfiniteSharpness(prevedge);

	    if (mesh->GetTotalFVarWidth()) {
		transferFVarToChild(mesh, face, child, i);
	    }

	    transferEditsToChild(face, child, i);
	}
	prevedge = edge;
	edge = edge->GetNext();
    }
}

template <class T>
HbrFace<T>*
HbrCatmarkSubdivision<T>::RefineFaceAtVertex(HbrMesh<T>* mesh, HbrFace<T>* face, HbrVertex<T>* vertex) {

#ifdef HBR_DEBUG
    std::cerr << "    forcing refine on " << *face << " at " << *vertex << '\n';
#endif
    
    // Create new quadrilateral children faces from this face
    HbrHalfedge<T>* edge = face->GetFirstEdge();
    HbrHalfedge<T>* prevedge = edge->GetPrev();
    HbrHalfedge<T>* childedge;
    int nv = face->GetNumVertices();
    float sharpness;    
    bool extraordinary = (nv != 4);
    // The funny indexing on vertices is done only for
    // non-extraordinary faces in order to correctly preserve
    // parametric space through the refinement. If we split an
    // extraordinary face then it doesn't matter.
    for (int i = 0; i < nv; ++i) {
	if (edge->GetOrgVertex() == vertex) {
	    if (!face->GetChild(i)) {
		HbrFace<T>* child;
		HbrVertex<T>* vertices[4];
		if (extraordinary) {
		    vertices[0] = vertex->Subdivide();
		    vertices[1] = edge->Subdivide();
		    vertices[2] = face->Subdivide();
		    vertices[3] = prevedge->Subdivide();
		} else {
		    vertices[i] = vertex->Subdivide();
		    vertices[(i+1)%4] = edge->Subdivide();
		    vertices[(i+2)%4] = face->Subdivide();
		    vertices[(i+3)%4] = prevedge->Subdivide();
		}
#ifdef HBR_DEBUG
		std::cerr << "Kid " << i << "\n";
		std::cerr << "  subdivision created " << *vertices[0] << '\n';
		std::cerr << "  subdivision created " << *vertices[1] << '\n';
		std::cerr << "  subdivision created " << *vertices[2] << '\n';
		std::cerr << "  subdivision created " << *vertices[3] << '\n';
#endif
		child = mesh->NewFace(4, vertices, face, i);
#ifdef HBR_DEBUG
		std::cerr << "Creating face " << *child << " during refine\n";
#endif
		// Hand down edge sharpness
                childedge = vertex->Subdivide()->GetEdge(edge->Subdivide());
                assert(childedge);
		if ((sharpness = edge->GetSharpness()) > HbrHalfedge<T>::k_Smooth) {
		    HbrSubdivision<T>::SubdivideCreaseWeight(
                        edge, edge->GetDestVertex(), childedge);
		}
                childedge->CopyFVarInfiniteSharpness(edge);

                childedge = prevedge->Subdivide()->GetEdge(vertex->Subdivide());
                assert(childedge);
		if ((sharpness = prevedge->GetSharpness()) > HbrHalfedge<T>::k_Smooth) {
		    HbrSubdivision<T>::SubdivideCreaseWeight(
                        prevedge, prevedge->GetOrgVertex(), childedge);
		}
                childedge->CopyFVarInfiniteSharpness(prevedge);

		if (mesh->GetTotalFVarWidth()) {
		    transferFVarToChild(mesh, face, child, i);		
		}

		transferEditsToChild(face, child, i);
		return child;
	    } else {
		return face->GetChild(i);
	    }
	}
	prevedge = edge;
	edge = edge->GetNext();
    }
    return 0;
}

template <class T>
void
HbrCatmarkSubdivision<T>::GuaranteeNeighbor(HbrMesh<T>* mesh, HbrHalfedge<T>* edge) {
    if (edge->GetOpposite()) {
	return;
    }

    // For the given edge: if the parent of either of its incident
    // vertices is itself a _face_, then ensuring that this parent
    // face has refined at a particular vertex is sufficient to
    // ensure that both of the faces on each side of the edge have
    // been created.
    bool destParentWasEdge = true;
    HbrFace<T>* parentFace = edge->GetOrgVertex()->GetParentFace();
    HbrHalfedge<T>* parentEdge = edge->GetDestVertex()->GetParentEdge();
    if (!parentFace) {
	destParentWasEdge = false;
	parentFace = edge->GetDestVertex()->GetParentFace();
	parentEdge = edge->GetOrgVertex()->GetParentEdge();
    }
	
    if (parentFace) {

	// Make sure we deal with a parent halfedge which is
	// associated with the parent face
	if (parentEdge->GetFace() != parentFace) {
	    parentEdge = parentEdge->GetOpposite();
	}
	// If one of the vertices had a parent face, the other one MUST
	// have been a child of an edge
	assert(parentEdge && parentEdge->GetFace() == parentFace);
#ifdef HBR_DEBUG
	std::cerr << "\nparent edge is " << *parentEdge << "\n";
#endif

	// The vertex to refine at depends on whether the
	// destination or origin vertex of this edge had a parent
	// edge
	if (destParentWasEdge) {
	    RefineFaceAtVertex(mesh, parentFace, parentEdge->GetOrgVertex());
	} else {
	    RefineFaceAtVertex(mesh, parentFace, parentEdge->GetDestVertex());
	}

	// It should always be the case that the opposite now exists -
	// we can't have a boundary case here
	assert(edge->GetOpposite());
    } else {
	HbrVertex<T>* parentVertex = edge->GetOrgVertex()->GetParentVertex();
	parentEdge = edge->GetDestVertex()->GetParentEdge();
	if (!parentVertex) {
	    parentVertex = edge->GetDestVertex()->GetParentVertex();
	    parentEdge = edge->GetOrgVertex()->GetParentEdge();
	}

	if (parentVertex) {
		
	    assert(parentEdge);

#ifdef HBR_DEBUG
	    std::cerr << "\nparent edge is " << *parentEdge << "\n";
#endif
		
	    // 1. Go up to the parent of my face

	    parentFace = edge->GetFace()->GetParent();
#ifdef HBR_DEBUG
	    std::cerr << "\nparent face is " << *parentFace << "\n";
#endif

	    // 2. Ask the opposite face (if it exists) to refine
	    if (parentFace) {

		// A vertex can be associated with either of two
		// parent halfedges. If the parent edge that we're
		// interested in doesn't match then we should look at
		// its opposite
		if (parentEdge->GetFace() != parentFace)
		    parentEdge = parentEdge->GetOpposite();
		assert(parentEdge->GetFace() == parentFace);

		// Make sure the parent edge has its neighbor as well
		GuaranteeNeighbor(mesh, parentEdge);

		// Now access that neighbor and refine it
		if (parentEdge->GetRightFace()) {
		    RefineFaceAtVertex(mesh, parentEdge->GetRightFace(), parentVertex);

		    // FIXME: assertion?
		    assert(edge->GetOpposite());
		}
	    }
	}
    }
}

template <class T>
void
HbrCatmarkSubdivision<T>::GuaranteeNeighbors(HbrMesh<T>* mesh, HbrVertex<T>* vertex) {

#ifdef HBR_DEBUG
    std::cerr << "\n\nneighbor guarantee at " << *vertex << " invoked\n";
#endif

    // If the vertex is a child of a face, guaranteeing the neighbors
    // of the vertex is simply a matter of ensuring the parent face
    // has refined.
    HbrFace<T>* parentFace = vertex->GetParentFace();
    if (parentFace) {

#ifdef HBR_DEBUG
	std::cerr << "  forcing full refine on parent face\n";
#endif
	Refine(mesh, parentFace);
	return;
    }

    // Otherwise if the vertex is a child of an edge, we need to
    // ensure that the parent faces on either side of the parent edge
    // 1) exist, and 2) have refined at both vertices of the parent
    // edge
    HbrHalfedge<T>* parentEdge = vertex->GetParentEdge();
    if (parentEdge) {

#ifdef HBR_DEBUG
	std::cerr << "  forcing full refine on adjacent faces of parent edge\n";
#endif
	HbrVertex<T>* dest = parentEdge->GetDestVertex();
	HbrVertex<T>* org = parentEdge->GetOrgVertex();
	GuaranteeNeighbor(mesh, parentEdge);
	parentFace = parentEdge->GetLeftFace();
	RefineFaceAtVertex(mesh, parentFace, dest);
	RefineFaceAtVertex(mesh, parentFace, org);

#ifdef HBR_DEBUG
	std::cerr << "    on the right face?\n";
#endif
	parentFace = parentEdge->GetRightFace();
	// The right face may not necessarily exist even after
	// GuaranteeNeighbor
	if (parentFace) {
	    RefineFaceAtVertex(mesh, parentFace, dest);
	    RefineFaceAtVertex(mesh, parentFace, org);
	}
#ifdef HBR_DEBUG
	std::cerr << "  end force\n";
#endif
	return;
    }

    // The last case: the vertex is a child of a vertex. In this case
    // we have to first recursively guarantee that the parent's
    // adjacent faces also exist.
    HbrVertex<T>* parentVertex = vertex->GetParentVertex();
    if (parentVertex) {

#ifdef HBR_DEBUG
	std::cerr << "  recursive parent vertex guarantee call\n";
#endif
	parentVertex->GuaranteeNeighbors();
	
	// And then we refine all the face neighbors of the
	// parentVertex
	HbrHalfedge<T>* start = parentVertex->GetIncidentEdge(), *edge;
	edge = start;
	while (edge) {
	    HbrFace<T>* f = edge->GetLeftFace();
	    RefineFaceAtVertex(mesh, f, parentVertex);
	    edge = parentVertex->GetNextEdge(edge);
	    if (edge == start) break;	    
	}
    }
}

template <class T>
bool
HbrCatmarkSubdivision<T>::HasLimit(HbrMesh<T>* mesh, HbrFace<T>* face) {

    if (face->IsHole()) return false;
    // A limit face exists if all the bounding edges have limit curves
    for (int i = 0; i < face->GetNumVertices(); ++i) {
	if (!HasLimit(mesh, face->GetEdge(i))) {
	    return false;
	}
    }
    return true;
}

template <class T>
bool
HbrCatmarkSubdivision<T>::HasLimit(HbrMesh<T>* mesh, HbrHalfedge<T>* edge) {
    // 	A sharp edge has a limit curve if both endpoints have limits.
    // 	A smooth edge has a limit if both endpoints have limits and
    // 	the edge isn't on the boundary.

    if (edge->GetSharpness() >= HbrHalfedge<T>::k_InfinitelySharp) return true;
    
    if (!HasLimit(mesh, edge->GetOrgVertex()) || !HasLimit(mesh, edge->GetDestVertex())) return false;
    
    return !edge->IsBoundary();
}

template <class T>
bool
HbrCatmarkSubdivision<T>::HasLimit(HbrMesh<T>* /* mesh */, HbrVertex<T>* vertex) {
    vertex->GuaranteeNeighbors();
    switch (vertex->GetMask(false)) {
	case HbrVertex<T>::k_Smooth:
	case HbrVertex<T>::k_Dart:
	    return !vertex->OnBoundary();
	    break;
	case HbrVertex<T>::k_Crease:
	case HbrVertex<T>::k_Corner:
	default:
	    if (vertex->IsVolatile()) {
		// Search for any incident semisharp boundary edge
                HbrHalfedge<T>* start = vertex->GetIncidentEdge(), *edge, *next;
                edge = start;
                while (edge) {
		    if (edge->IsBoundary() && edge->GetSharpness() < HbrHalfedge<T>::k_InfinitelySharp) {
			return false;
		    }
                    next = vertex->GetNextEdge(edge);
                    if (next == start) {
                        break;
                    } else if (!next) {
                        edge = edge->GetPrev();
                        if (edge->IsBoundary() && edge->GetSharpness() < HbrHalfedge<T>::k_InfinitelySharp) {
                            return false;
                        }
                        break;
                    } else {
                        edge = next;
                    }
		}
	    }
	    return true;
    }
}

template <class T>
HbrVertex<T>*
HbrCatmarkSubdivision<T>::Subdivide(HbrMesh<T>* mesh, HbrFace<T>* face) {

    // Face rule: simply average all vertices on the face
    HbrVertex<T>* v = mesh->NewVertex();    
    T& data = v->GetData();
    int nv = face->GetNumVertices();
    float weight = 1.0f / nv;

    HbrHalfedge<T>* edge = face->GetFirstEdge();
    for (int i = 0; i < face->GetNumVertices(); ++i) {
	HbrVertex<T>* w = edge->GetOrgVertex();
	// If there are vertex edits we have to make sure the edit
	// has been applied
	if (mesh->HasVertexEdits()) {
	    w->GuaranteeNeighbors();
	}
	data.AddWithWeight(w->GetData(), weight);
	data.AddVaryingWithWeight(w->GetData(), weight);
	edge = edge->GetNext();
    }
#ifdef HBR_DEBUG
    std::cerr << "Subdividing at " << *face << "\n";
#endif

    // Set the extraordinary flag if the face had anything other than
    // 4 vertices
    if (nv != 4) v->SetExtraordinary();
    
#ifdef HBR_DEBUG
    std::cerr << "  created " << *v << "\n";
#endif
    return v;
}

#if 0
// The "old" triangle subdivision method modifies the face subdivision
// rule. Unfortunately we can't put simply put this code into the
// standard face Subdivide method, because that would disrupt the
// averages computed for adjacent edges and vertices (which rely on
// face averages computed using the standard Catmull-Clark method).
// Instead we must call this after a face has been Subdivided using
// the normal rule; this code will modify that face's subdivided
// vertex value only.
template <class T>
HbrVertex<T>*
HbrCatmarkSubdivision<T>::OldTriangleSubdivide(HbrMesh<T>* mesh, HbrFace<T>* face) {
    assert(face->GetNumVertices() == 3 && triangleSubdivision == k_Old);
    HbrVertex<T>* w = face->Subdivide();
    NgpVVectorItem& data = w->GetData();
    data.Clear();

    float weight = 1.0f / 6.0f;
    
    for (int i = 0; i < 3; ++i) {
	HbrVertex<T>* w = face->GetVertex(i);
	HbrHalfedge<T>* e = face->GetEdge(i);
	data.AddWithWeight(w->Subdivide()->GetData(), weight);
	data.AddWithWeight(e->Subdivide()->GetData(), weight);
    }
}
#endif

/* This comment describe the "new" triangle subdivision method, which
   modifies only the edge subdivision rule:

   The "smoothtriangles" tag makes triangular faces smoother.  This is done
   by modifying the first level of subdivision in order to generate a limit
   surface that is closer to what Loop subdivision would yield.  Note that
   there is no extra expense in forcing one level of subdivision, since
   extraordinary faces need to be subdivided at least once anyway.

   We have two degrees of freedom to play with, namely the weight assigned
   to each neighbouring vertex when subdividing a vertex, and the weight
   assigned to each neighbouring face vertex when subdividing an edge.  Our
   initial strategy for choosing these parameters was to derive the limit
   masks (position and tangent) for the Catmull-Clark and Loop schemes at
   three representative points: each original vertex, the center of each
   original edge, and the center of each original face.  The parameter
   values were then optimized to get the best least-squares match to the
   limit positions and tangents of the Loop surface at these chosen points.
   (In the case of tangents an extra scale factor was used so that only the
   tangent direction is optimized rather than its magnitude.)  All this was
   done using Mathematica.

   Although the resulting surfaces were much smoother, there was still some
   degree of "ringing" (probably due to the fact that the surface was
   optimized at a discrete set of points, rather than by integrating over
   the surface).  We then tried a second strategy, namely choosing the
   vertex weights to minimize surface curvature.  This was done by setting
   up test cases for extraordinary vertices of each degree, rendering an
   animation using a range of parameter values, and integrating the
   curvature over each surface (with a shader and some scripts).  We chose
   to minimize the squared mean curvature, which seemed to have the best
   correspondence to surfaces that look "smooth".

   Surprisingly, the vertex weights obtained in this way were not
   significantly different than the standard Catmull-Clark weights.
   Thus the final "smooth triangles" technique only modifies the edge
   subdivision rule: the adjacent face vertices are weighted by
   HBR_SMOOTH_TRI_EDGE_WEIGHT rather than the standard CC value of 0.25.
   If there is a mixture of triangular and non-triangular faces, the
   weights are interpolated. */

#define HBR_SMOOTH_TRI_EDGE_WEIGHT	0.470f	/* from Mathematica */

template <class T>
HbrVertex<T>*
HbrCatmarkSubdivision<T>::Subdivide(HbrMesh<T>* mesh, HbrHalfedge<T>* edge) {

    // Ensure the opposite face exists.
    GuaranteeNeighbor(mesh, edge);

    float esharp = edge->GetSharpness();

#ifdef HBR_DEBUG
    std::cerr << "Subdividing at " << *edge << " (sharpness = " << esharp << ")";
#endif
    
    HbrVertex<T>* v = mesh->NewVertex();
    T& data = v->GetData();

    // If there's the possibility of vertex edits on either vertex, we
    // have to make sure the edit has been applied
    if (mesh->HasVertexEdits()) {
	edge->GetOrgVertex()->GuaranteeNeighbors();
	edge->GetDestVertex()->GuaranteeNeighbors();
    }
    
    if (!edge->IsBoundary() && esharp <= 1.0f) {

	// Of the two half-edges, pick one of them consistently such
	// that the left and right faces are also consistent through
	// multi-threading. It doesn't matter as far as the
	// theoretical calculation is concerned, but it is desirable
	// to be consistent about it in the face of the limitations of
	// floating point commutativity. So we always pick the
	// half-edge such that its incident face is the smallest of
	// the two faces, as far as the face paths are concerned.
	if (edge->GetOpposite() && edge->GetOpposite()->GetFace()->GetPath() < edge->GetFace()->GetPath()) {
	    edge = edge->GetOpposite();
	}
	
	// Handle both the smooth and fractional sharpness cases.  We
	// lerp between the sharp case (average of the two end points)
	// and the unsharp case (average of two end points plus two
	// face averages).

	float leftWeight, rightWeight, faceWeight, vertWeight;
	HbrFace<T>* rf = edge->GetRightFace();
	HbrFace<T>* lf = edge->GetLeftFace();

	// The standard catmull-clark rule for face weights is 0.25.
	// The modified, new triangle subdivision rule uses a value of
	// SMOOTH_TRI_EDGE_WEIGHT as defined above. We lerp between
	// the right and left weights as needed.
	leftWeight = (triangleSubdivision == k_New && lf->GetNumVertices() == 3) ? HBR_SMOOTH_TRI_EDGE_WEIGHT : 0.25f;
	rightWeight = (triangleSubdivision == k_New && rf->GetNumVertices() == 3) ? HBR_SMOOTH_TRI_EDGE_WEIGHT : 0.25f;
	faceWeight = 0.5f * (leftWeight + rightWeight);	
	vertWeight = 0.5f * (1.0f - 2.0f * faceWeight);

	// Lerp the face weight between non sharp contribution and
	// sharp contribution (which is zero)
	faceWeight *= (1.0f - esharp);
	
	// Lerp the vert weight between non sharp contribution and
	// sharp contribution of 0.5f
	vertWeight = 0.5f * esharp + (1.0f - esharp) * vertWeight;
	
	data.AddWithWeight(edge->GetOrgVertex()->GetData(), vertWeight);
	data.AddWithWeight(edge->GetDestVertex()->GetData(), vertWeight);

	data.AddWithWeight(lf->Subdivide()->GetData(), faceWeight);
	data.AddWithWeight(rf->Subdivide()->GetData(), faceWeight);
    } else {
	// Fully sharp edge, just average the two end points
	data.AddWithWeight(edge->GetOrgVertex()->GetData(), 0.5f);
	data.AddWithWeight(edge->GetDestVertex()->GetData(), 0.5f);
    }

    // Varying data is always the average of two end points
    data.AddVaryingWithWeight(edge->GetOrgVertex()->GetData(), 0.5f);
    data.AddVaryingWithWeight(edge->GetDestVertex()->GetData(), 0.5f);

#ifdef HBR_DEBUG
    std::cerr << "  created " << *v << "\n";
#endif
    return v;
}

template <class T>
HbrVertex<T>*
HbrCatmarkSubdivision<T>::Subdivide(HbrMesh<T>* mesh, HbrVertex<T>* vertex) {

    // Ensure the ring of faces around this vertex exists before
    // we compute the valence
    vertex->GuaranteeNeighbors();
    
    float valence = static_cast<float>(vertex->GetValence());
    float invvalencesquared = 1.0f / (valence * valence);


    HbrVertex<T>* v = mesh->NewVertex();
    T& data = v->GetData();

    // Due to fractional weights we may need to do two subdivision
    // passes
    int masks[2];
    float weights[2];
    int passes;
    masks[0] = vertex->GetMask(false);
    masks[1] = vertex->GetMask(true);
    // If the masks are different, we subdivide twice: once using the
    // current mask, once using the mask at the next level of
    // subdivision, then use fractional mask weights to weigh
    // each weighing
    if (masks[0] != masks[1]) {
	weights[1] = vertex->GetFractionalMask();
	weights[0] = 1.0f - weights[1];
	passes = 2;
    } else {
	weights[0] = 1.0f;
	weights[1] = 0.0f;
	passes = 1;
    }
    for (int i = 0; i < passes; ++i) {
	switch (masks[i]) {
	    case HbrVertex<T>::k_Smooth:
	    case HbrVertex<T>::k_Dart: {
		// Compute n-2/n of the old vertex value
		data.AddWithWeight(vertex->GetData(), weights[i] * invvalencesquared * valence * (valence - 2));
		// Add 1 / n^2 * surrounding edge vertices and surrounding face
		// subdivided vertices
                HbrSubdivision<T>::AddSurroundingVerticesWithWeight(
                    mesh, vertex, weights[i] * invvalencesquared, &data);

		HbrHalfedge<T>* start = vertex->GetIncidentEdge(), *edge;
		edge = start;
		while (edge) {
		    HbrFace<T>* f = edge->GetLeftFace();
		    data.AddWithWeight(f->Subdivide()->GetData(), weights[i] * invvalencesquared);
		    edge = vertex->GetNextEdge(edge);
		    if (edge == start) break;
		}
		break;
	    }
	    case HbrVertex<T>::k_Crease: {
		// Compute 3/4 of old vertex value
		data.AddWithWeight(vertex->GetData(), weights[i] * 0.75f);

		// Add 0.125f of the (hopefully only two!) neighbouring
		// sharp edges
                HbrSubdivision<T>::AddCreaseEdgesWithWeight(
                    mesh, vertex, i == 1, weights[i] * 0.125f, &data);
		break;
	    }
	    case HbrVertex<T>::k_Corner:
	    default: {
		// Just copy the old value
		data.AddWithWeight(vertex->GetData(), weights[i]);
		break;
	    }
	}
    }

    // Varying data is always just propogated down
    data.AddVaryingWithWeight(vertex->GetData(), 1.0f);
    
#ifdef HBR_DEBUG
    std::cerr << "Subdividing at " << *vertex << "\n";    
    std::cerr << "  created " << *v << "\n";
#endif
    // Inherit extraordinary flag and sharpness
    if (vertex->IsExtraordinary()) v->SetExtraordinary();
    float sharp = vertex->GetSharpness();
    if (sharp >= HbrVertex<T>::k_InfinitelySharp) {
	v->SetSharpness(HbrVertex<T>::k_InfinitelySharp);
    } else if (sharp > HbrVertex<T>::k_Smooth) {
	sharp -= 1.0f;
	if (sharp < (float) HbrVertex<T>::k_Smooth) {
	    sharp = (float) HbrVertex<T>::k_Smooth;
	}
	v->SetSharpness(sharp);
    } else {
	v->SetSharpness(HbrVertex<T>::k_Smooth);
    }
    return v;    
}

#endif /* HBRCATMARK_H */