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++ // Copyright 2009-2021 Intel Corporation
++ // SPDX-License-Identifier: Apache-2.0
++
++ #pragma once
++
++ #include "../common/geometry.h"
++ #include "../common/buffer.h"
++ #include "half_edge.h"
++ #include "catmullclark_coefficients.h"
++
++ namespace embree
++ {
++ struct __aligned(64) FinalQuad {
++ Vec3fa vtx[4];
++ };
++
++ template<typename Vertex, typename Vertex_t = Vertex>
++ struct __aligned(64) CatmullClark1RingT
++ {
++ ALIGNED_STRUCT_(64);
++
++ int border_index; //!< edge index where border starts
++ unsigned int face_valence; //!< number of adjacent quad faces
++ unsigned int edge_valence; //!< number of adjacent edges (2*face_valence)
++ float vertex_crease_weight; //!< weight of vertex crease (0 if no vertex crease)
++ DynamicStackArray<float,16,MAX_RING_FACE_VALENCE> crease_weight; //!< edge crease weights for each adjacent edge
++ float vertex_level; //!< maximum level of all adjacent edges
++ float edge_level; //!< level of first edge
++ unsigned int eval_start_index; //!< topology dependent index to start evaluation
++ unsigned int eval_unique_identifier; //!< topology dependent unique identifier for this ring
++ Vertex vtx; //!< center vertex
++ DynamicStackArray<Vertex,32,MAX_RING_EDGE_VALENCE> ring; //!< ring of neighboring vertices
++
++ public:
++ CatmullClark1RingT ()
++ : eval_start_index(0), eval_unique_identifier(0) {} // FIXME: default constructor should be empty
++
++ /*! calculates number of bytes required to serialize this structure */
++ __forceinline size_t bytes() const
++ {
++ size_t ofs = 0;
++ ofs += sizeof(border_index);
++ ofs += sizeof(face_valence);
++ assert(2*face_valence == edge_valence);
++ ofs += sizeof(vertex_crease_weight);
++ ofs += face_valence*sizeof(float);
++ ofs += sizeof(vertex_level);
++ ofs += sizeof(edge_level);
++ ofs += sizeof(eval_start_index);
++ ofs += sizeof(eval_unique_identifier);
++ ofs += sizeof(vtx);
++ ofs += edge_valence*sizeof(Vertex);
++ return ofs;
++ }
++
++ template<typename Ty>
++ static __forceinline void store(char* ptr, size_t& ofs, const Ty& v) {
++ *(Ty*)&ptr[ofs] = v; ofs += sizeof(Ty);
++ }
++
++ template<typename Ty>
++ static __forceinline void load(char* ptr, size_t& ofs, Ty& v) {
++ v = *(Ty*)&ptr[ofs]; ofs += sizeof(Ty);
++ }
++
++ /*! serializes the ring to some memory location */
++ __forceinline void serialize(char* ptr, size_t& ofs) const
++ {
++ store(ptr,ofs,border_index);
++ store(ptr,ofs,face_valence);
++ store(ptr,ofs,vertex_crease_weight);
++ for (size_t i=0; i<face_valence; i++)
++ store(ptr,ofs,crease_weight[i]);
++ store(ptr,ofs,vertex_level);
++ store(ptr,ofs,edge_level);
++ store(ptr,ofs,eval_start_index);
++ store(ptr,ofs,eval_unique_identifier);
++ Vertex_t::storeu(&ptr[ofs],vtx); ofs += sizeof(Vertex);
++ for (size_t i=0; i<edge_valence; i++) {
++ Vertex_t::storeu(&ptr[ofs],ring[i]); ofs += sizeof(Vertex);
++ }
++ }
++
++ /*! deserializes the ring from some memory location */
++ __forceinline void deserialize(char* ptr, size_t& ofs)
++ {
++ load(ptr,ofs,border_index);
++ load(ptr,ofs,face_valence);
++ edge_valence = 2*face_valence;
++ load(ptr,ofs,vertex_crease_weight);
++ for (size_t i=0; i<face_valence; i++)
++ load(ptr,ofs,crease_weight[i]);
++ load(ptr,ofs,vertex_level);
++ load(ptr,ofs,edge_level);
++ load(ptr,ofs,eval_start_index);
++ load(ptr,ofs,eval_unique_identifier);
++ vtx = Vertex_t::loadu(&ptr[ofs]); ofs += sizeof(Vertex);
++ for (size_t i=0; i<edge_valence; i++) {
++ ring[i] = Vertex_t::loadu(&ptr[ofs]); ofs += sizeof(Vertex);
++ }
++ }
++
++ __forceinline bool hasBorder() const {
++ return border_index != -1;
++ }
++
++ __forceinline const Vertex& front(size_t i) const {
++ assert(edge_valence>i);
++ return ring[i];
++ }
++
++ __forceinline const Vertex& back(size_t i) const {
++ assert(edge_valence>=i);
++ return ring[edge_valence-i];
++ }
++
++ __forceinline bool has_last_face() const {
++ return (size_t)border_index != (size_t)edge_valence-2;
++ }
++
++ __forceinline bool has_opposite_front(size_t i) const {
++ return (size_t)border_index != 2*i;
++ }
++
++ __forceinline bool has_opposite_back(size_t i) const {
++ return (size_t)border_index != ((size_t)edge_valence-2-2*i);
++ }
++
++ __forceinline BBox3fa bounds() const
++ {
++ BBox3fa bounds ( vtx );
++ for (size_t i = 0; i<edge_valence ; i++)
++ bounds.extend( ring[i] );
++ return bounds;
++ }
++
++ /*! initializes the ring from the half edge structure */
++ __forceinline void init(const HalfEdge* const h, const char* vertices, size_t stride)
++ {
++ border_index = -1;
++ vtx = Vertex_t::loadu(vertices+h->getStartVertexIndex()*stride);
++ vertex_crease_weight = h->vertex_crease_weight;
++
++ HalfEdge* p = (HalfEdge*) h;
++
++ unsigned i=0;
++ unsigned min_vertex_index = (unsigned)-1;
++ unsigned min_vertex_index_face = (unsigned)-1;
++ edge_level = p->edge_level;
++ vertex_level = 0.0f;
++
++ do
++ {
++ vertex_level = max(vertex_level,p->edge_level);
++ crease_weight[i/2] = p->edge_crease_weight;
++ assert(p->hasOpposite() || p->edge_crease_weight == float(inf));
++
++ /* store first two vertices of face */
++ p = p->next();
++ const unsigned index0 = p->getStartVertexIndex();
++ ring[i++] = Vertex_t::loadu(vertices+index0*stride);
++ if (index0 < min_vertex_index) { min_vertex_index = index0; min_vertex_index_face = i>>1; }
++ p = p->next();
++
++ const unsigned index1 = p->getStartVertexIndex();
++ ring[i++] = Vertex_t::loadu(vertices+index1*stride);
++ p = p->next();
++
++ /* continue with next face */
++ if (likely(p->hasOpposite()))
++ p = p->opposite();
++
++ /* if there is no opposite go the long way to the other side of the border */
++ else
++ {
++ /* find minimum start vertex */
++ const unsigned index0 = p->getStartVertexIndex();
++ if (index0 < min_vertex_index) { min_vertex_index = index0; min_vertex_index_face = i>>1; }
++
++ /*! mark first border edge and store dummy vertex for face between the two border edges */
++ border_index = i;
++ crease_weight[i/2] = inf;
++ ring[i++] = Vertex_t::loadu(vertices+index0*stride);
++ ring[i++] = vtx; // dummy vertex
++
++ /*! goto other side of border */
++ p = (HalfEdge*) h;
++ while (p->hasOpposite())
++ p = p->opposite()->next();
++ }
++
++ } while (p != h);
++
++ edge_valence = i;
++ face_valence = i >> 1;
++ eval_unique_identifier = min_vertex_index;
++ eval_start_index = min_vertex_index_face;
++
++ assert( hasValidPositions() );
++ }
++
++ __forceinline void subdivide(CatmullClark1RingT& dest) const
++ {
++ dest.edge_level = 0.5f*edge_level;
++ dest.vertex_level = 0.5f*vertex_level;
++ dest.face_valence = face_valence;
++ dest.edge_valence = edge_valence;
++ dest.border_index = border_index;
++ dest.vertex_crease_weight = max(0.0f,vertex_crease_weight-1.0f);
++ dest.eval_start_index = eval_start_index;
++ dest.eval_unique_identifier = eval_unique_identifier;
++
++ /* calculate face points */
++ Vertex_t S = Vertex_t(0.0f);
++ for (size_t i=0; i<face_valence; i++)
++ {
++ size_t face_index = i + eval_start_index; if (face_index >= face_valence) face_index -= face_valence; assert(face_index < face_valence);
++ size_t index0 = 2*face_index+0; if (index0 >= edge_valence) index0 -= edge_valence; assert(index0 < edge_valence);
++ size_t index1 = 2*face_index+1; if (index1 >= edge_valence) index1 -= edge_valence; assert(index1 < edge_valence);
++ size_t index2 = 2*face_index+2; if (index2 >= edge_valence) index2 -= edge_valence; assert(index2 < edge_valence);
++ S += dest.ring[index1] = ((vtx + ring[index1]) + (ring[index0] + ring[index2])) * 0.25f;
++ }
++
++ /* calculate new edge points */
++ size_t num_creases = 0;
++ array_t<size_t,MAX_RING_FACE_VALENCE> crease_id;
++
++ for (size_t i=0; i<face_valence; i++)
++ {
++ size_t face_index = i + eval_start_index;
++ if (face_index >= face_valence) face_index -= face_valence;
++ const float edge_crease = crease_weight[face_index];
++ dest.crease_weight[face_index] = max(edge_crease-1.0f,0.0f);
++
++ size_t index = 2*face_index;
++ size_t prev_index = face_index == 0 ? edge_valence-1 : 2*face_index-1;
++ size_t next_index = 2*face_index+1;
++
++ const Vertex_t v = vtx + ring[index];
++ const Vertex_t f = dest.ring[prev_index] + dest.ring[next_index];
++ S += ring[index];
++
++ /* fast path for regular edge points */
++ if (likely(edge_crease <= 0.0f)) {
++ dest.ring[index] = (v+f) * 0.25f;
++ }
++
++ /* slower path for hard edge rule */
++ else {
++ crease_id[num_creases++] = face_index;
++ dest.ring[index] = v*0.5f;
++
++ /* even slower path for blended edge rule */
++ if (unlikely(edge_crease < 1.0f)) {
++ dest.ring[index] = lerp((v+f)*0.25f,v*0.5f,edge_crease);
++ }
++ }
++ }
++
++ /* compute new vertex using smooth rule */
++ const float inv_face_valence = 1.0f / (float)face_valence;
++ const Vertex_t v_smooth = (Vertex_t) madd(inv_face_valence,S,(float(face_valence)-2.0f)*vtx)*inv_face_valence;
++ dest.vtx = v_smooth;
++
++ /* compute new vertex using vertex_crease_weight rule */
++ if (unlikely(vertex_crease_weight > 0.0f))
++ {
++ if (vertex_crease_weight >= 1.0f) {
++ dest.vtx = vtx;
++ } else {
++ dest.vtx = lerp(v_smooth,vtx,vertex_crease_weight);
++ }
++ return;
++ }
++
++ /* no edge crease rule and dart rule */
++ if (likely(num_creases <= 1))
++ return;
++
++ /* compute new vertex using crease rule */
++ if (likely(num_creases == 2))
++ {
++ /* update vertex using crease rule */
++ const size_t crease0 = crease_id[0], crease1 = crease_id[1];
++ const Vertex_t v_sharp = (Vertex_t)(ring[2*crease0] + 6.0f*vtx + ring[2*crease1]) * (1.0f / 8.0f);
++ dest.vtx = v_sharp;
++
++ /* update crease_weights using chaikin rule */
++ const float crease_weight0 = crease_weight[crease0], crease_weight1 = crease_weight[crease1];
++ dest.crease_weight[crease0] = max(0.25f*(3.0f*crease_weight0 + crease_weight1)-1.0f,0.0f);
++ dest.crease_weight[crease1] = max(0.25f*(3.0f*crease_weight1 + crease_weight0)-1.0f,0.0f);
++
++ /* interpolate between sharp and smooth rule */
++ const float v_blend = 0.5f*(crease_weight0+crease_weight1);
++ if (unlikely(v_blend < 1.0f)) {
++ dest.vtx = lerp(v_smooth,v_sharp,v_blend);
++ }
++ }
++
++ /* compute new vertex using corner rule */
++ else {
++ dest.vtx = vtx;
++ }
++ }
++
++ __forceinline bool isRegular1() const
++ {
++ if (border_index == -1) {
++ if (face_valence == 4) return true;
++ } else {
++ if (face_valence < 4) return true;
++ }
++ return false;
++ }
++
++ __forceinline size_t numEdgeCreases() const
++ {
++ ssize_t numCreases = 0;
++ for (size_t i=0; i<face_valence; i++) {
++ numCreases += crease_weight[i] > 0.0f;
++ }
++ return numCreases;
++ }
++
++ enum Type {
++ TYPE_NONE = 0, //!< invalid type
++ TYPE_REGULAR = 1, //!< regular patch when ignoring creases
++ TYPE_REGULAR_CREASES = 2, //!< regular patch when considering creases
++ TYPE_GREGORY = 4, //!< gregory patch when ignoring creases
++ TYPE_GREGORY_CREASES = 8, //!< gregory patch when considering creases
++ TYPE_CREASES = 16 //!< patch has crease features
++ };
++
++ __forceinline Type type() const
++ {
++ /* check if there is an edge crease anywhere */
++ const size_t numCreases = numEdgeCreases();
++ const bool noInnerCreases = hasBorder() ? numCreases == 2 : numCreases == 0;
++
++ Type crease_mask = (Type) (TYPE_REGULAR | TYPE_GREGORY);
++ if (noInnerCreases ) crease_mask = (Type) (crease_mask | TYPE_REGULAR_CREASES | TYPE_GREGORY_CREASES);
++ if (numCreases != 0) crease_mask = (Type) (crease_mask | TYPE_CREASES);
++
++ /* calculate if this vertex is regular */
++ bool hasBorder = border_index != -1;
++ if (face_valence == 2 && hasBorder) {
++ if (vertex_crease_weight == 0.0f ) return (Type) (crease_mask & (TYPE_REGULAR | TYPE_REGULAR_CREASES | TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
++ else if (vertex_crease_weight == float(inf)) return (Type) (crease_mask & (TYPE_REGULAR | TYPE_REGULAR_CREASES | TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
++ else return TYPE_CREASES;
++ }
++ else if (vertex_crease_weight != 0.0f) return TYPE_CREASES;
++ else if (face_valence == 3 && hasBorder) return (Type) (crease_mask & (TYPE_REGULAR | TYPE_REGULAR_CREASES | TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
++ else if (face_valence == 4 && !hasBorder) return (Type) (crease_mask & (TYPE_REGULAR | TYPE_REGULAR_CREASES | TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
++ else return (Type) (crease_mask & (TYPE_GREGORY | TYPE_GREGORY_CREASES | TYPE_CREASES));
++ }
++
++ __forceinline bool isFinalResolution(float res) const {
++ return vertex_level <= res;
++ }
++
++ /* computes the limit vertex */
++ __forceinline Vertex getLimitVertex() const
++ {
++ /* return hard corner */
++ if (unlikely(std::isinf(vertex_crease_weight)))
++ return vtx;
++
++ /* border vertex rule */
++ if (unlikely(border_index != -1))
++ {
++ const unsigned int second_border_index = border_index+2 >= int(edge_valence) ? 0 : border_index+2;
++ return (4.0f * vtx + (ring[border_index] + ring[second_border_index])) * 1.0f/6.0f;
++ }
++
++ Vertex_t F( 0.0f );
++ Vertex_t E( 0.0f );
++
++ assert(eval_start_index < face_valence);
++
++ for (size_t i=0; i<face_valence; i++) {
++ size_t index = i+eval_start_index;
++ if (index >= face_valence) index -= face_valence;
++ F += ring[2*index+1];
++ E += ring[2*index];
++ }
++
++ const float n = (float)face_valence;
++ return (Vertex_t)(n*n*vtx+4.0f*E+F) / ((n+5.0f)*n);
++ }
++
++ /* gets limit tangent in the direction of egde vtx -> ring[0] */
++ __forceinline Vertex getLimitTangent() const
++ {
++ if (unlikely(std::isinf(vertex_crease_weight)))
++ return ring[0] - vtx;
++
++ /* border vertex rule */
++ if (unlikely(border_index != -1))
++ {
++ if (border_index != (int)edge_valence-2 ) {
++ return ring[0] - vtx;
++ }
++ else
++ {
++ const unsigned int second_border_index = border_index+2 >= int(edge_valence) ? 0 : border_index+2;
++ return (ring[second_border_index] - ring[border_index]) * 0.5f;
++ }
++ }
++
++ Vertex_t alpha( 0.0f );
++ Vertex_t beta ( 0.0f );
++
++ const size_t n = face_valence;
++
++ assert(eval_start_index < face_valence);
++
++ Vertex_t q( 0.0f );
++ for (size_t i=0; i<face_valence; i++)
++ {
++ size_t index = i+eval_start_index;
++ if (index >= face_valence) index -= face_valence;
++ const float a = CatmullClarkPrecomputedCoefficients::table.limittangent_a(index,n);
++ const float b = CatmullClarkPrecomputedCoefficients::table.limittangent_b(index,n);
++ alpha += a * ring[2*index];
++ beta += b * ring[2*index+1];
++ }
++
++ const float sigma = CatmullClarkPrecomputedCoefficients::table.limittangent_c(n);
++ return sigma * (alpha + beta);
++ }
++
++ /* gets limit tangent in the direction of egde vtx -> ring[edge_valence-2] */
++ __forceinline Vertex getSecondLimitTangent() const
++ {
++ if (unlikely(std::isinf(vertex_crease_weight)))
++ return ring[2] - vtx;
++
++ /* border vertex rule */
++ if (unlikely(border_index != -1))
++ {
++ if (border_index != 2) {
++ return ring[2] - vtx;
++ }
++ else {
++ const unsigned int second_border_index = border_index+2 >= int(edge_valence) ? 0 : border_index+2;
++ return (ring[border_index] - ring[second_border_index]) * 0.5f;
++ }
++ }
++
++ Vertex_t alpha( 0.0f );
++ Vertex_t beta ( 0.0f );
++
++ const size_t n = face_valence;
++
++ assert(eval_start_index < face_valence);
++
++ for (size_t i=0; i<face_valence; i++)
++ {
++ size_t index = i+eval_start_index;
++ if (index >= face_valence) index -= face_valence;
++
++ size_t prev_index = index == 0 ? face_valence-1 : index-1; // need to be bit-wise exact in cosf eval
++ const float a = CatmullClarkPrecomputedCoefficients::table.limittangent_a(prev_index,n);
++ const float b = CatmullClarkPrecomputedCoefficients::table.limittangent_b(prev_index,n);
++ alpha += a * ring[2*index];
++ beta += b * ring[2*index+1];
++ }
++
++ const float sigma = CatmullClarkPrecomputedCoefficients::table.limittangent_c(n);
++ return sigma* (alpha + beta);
++ }
++
++ /* gets surface normal */
++ const Vertex getNormal() const {
++ return cross(getLimitTangent(),getSecondLimitTangent());
++ }
++
++ /* returns center of the n-th quad in the 1-ring */
++ __forceinline Vertex getQuadCenter(const size_t index) const
++ {
++ const Vertex_t &p0 = vtx;
++ const Vertex_t &p1 = ring[2*index+0];
++ const Vertex_t &p2 = ring[2*index+1];
++ const Vertex_t &p3 = index == face_valence-1 ? ring[0] : ring[2*index+2];
++ const Vertex p = (p0+p1+p2+p3) * 0.25f;
++ return p;
++ }
++
++ /* returns center of the n-th edge in the 1-ring */
++ __forceinline Vertex getEdgeCenter(const size_t index) const {
++ return (vtx + ring[index*2]) * 0.5f;
++ }
++
++ bool hasValidPositions() const
++ {
++ for (size_t i=0; i<edge_valence; i++) {
++ if (!isvalid(ring[i]))
++ return false;
++ }
++ return true;
++ }
++
++ friend __forceinline embree_ostream operator<<(embree_ostream o, const CatmullClark1RingT &c)
++ {
++ o << "vtx " << c.vtx << " size = " << c.edge_valence << ", " <<
++ "hard_edge = " << c.border_index << ", face_valence " << c.face_valence <<
++ ", edge_level = " << c.edge_level << ", vertex_level = " << c.vertex_level << ", eval_start_index: " << c.eval_start_index << ", ring: " << embree_endl;
++
++ for (unsigned int i=0; i<min(c.edge_valence,(unsigned int)MAX_RING_FACE_VALENCE); i++) {
++ o << i << " -> " << c.ring[i];
++ if (i % 2 == 0) o << " crease = " << c.crease_weight[i/2];
++ o << embree_endl;
++ }
++ return o;
++ }
++ };
++
++ typedef CatmullClark1RingT<Vec3fa,Vec3fa_t> CatmullClark1Ring3fa;
++
++ template<typename Vertex, typename Vertex_t = Vertex>
++ struct __aligned(64) GeneralCatmullClark1RingT
++ {
++ ALIGNED_STRUCT_(64);
++
++ typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClark1Ring;
++
++ struct Face
++ {
++ __forceinline Face() {}
++ __forceinline Face (int size, float crease_weight)
++ : size(size), crease_weight(crease_weight) {}
++
++ // FIXME: add member that returns total number of vertices
++
++ int size; // number of vertices-2 of nth face in ring
++ float crease_weight;
++ };
++
++ Vertex vtx;
++ DynamicStackArray<Vertex,32,MAX_RING_EDGE_VALENCE> ring;
++ DynamicStackArray<Face,16,MAX_RING_FACE_VALENCE> faces;
++ unsigned int face_valence;
++ unsigned int edge_valence;
++ int border_face;
++ float vertex_crease_weight;
++ float vertex_level; //!< maximum level of adjacent edges
++ float edge_level; // level of first edge
++ bool only_quads; // true if all faces are quads
++ unsigned int eval_start_face_index;
++ unsigned int eval_start_vertex_index;
++ unsigned int eval_unique_identifier;
++
++ public:
++ GeneralCatmullClark1RingT()
++ : eval_start_face_index(0), eval_start_vertex_index(0), eval_unique_identifier(0) {}
++
++ __forceinline bool isRegular() const
++ {
++ if (border_face == -1 && face_valence == 4) return true;
++ return false;
++ }
++
++ __forceinline bool has_last_face() const {
++ return border_face != (int)face_valence-1;
++ }
++
++ __forceinline bool has_second_face() const {
++ return (border_face == -1) || (border_face >= 2);
++ }
++
++ bool hasValidPositions() const
++ {
++ for (size_t i=0; i<edge_valence; i++) {
++ if (!isvalid(ring[i]))
++ return false;
++ }
++ return true;
++ }
++
++ __forceinline void init(const HalfEdge* const h, const char* vertices, size_t stride)
++ {
++ only_quads = true;
++ border_face = -1;
++ vtx = Vertex_t::loadu(vertices+h->getStartVertexIndex()*stride);
++ vertex_crease_weight = h->vertex_crease_weight;
++ HalfEdge* p = (HalfEdge*) h;
++
++ unsigned int e=0, f=0;
++ unsigned min_vertex_index = (unsigned)-1;
++ unsigned min_vertex_index_face = (unsigned)-1;
++ unsigned min_vertex_index_vertex = (unsigned)-1;
++ edge_level = p->edge_level;
++ vertex_level = 0.0f;
++ do
++ {
++ HalfEdge* p_prev = p->prev();
++ HalfEdge* p_next = p->next();
++ const float crease_weight = p->edge_crease_weight;
++ assert(p->hasOpposite() || p->edge_crease_weight == float(inf));
++ vertex_level = max(vertex_level,p->edge_level);
++
++ /* find minimum start vertex */
++ unsigned vertex_index = p_next->getStartVertexIndex();
++ if (vertex_index < min_vertex_index) { min_vertex_index = vertex_index; min_vertex_index_face = f; min_vertex_index_vertex = e; }
++
++ /* store first N-2 vertices of face */
++ unsigned int vn = 0;
++ for (p = p_next; p!=p_prev; p=p->next()) {
++ ring[e++] = Vertex_t::loadu(vertices+p->getStartVertexIndex()*stride);
++ vn++;
++ }
++ faces[f++] = Face(vn,crease_weight);
++ only_quads &= (vn == 2);
++
++ /* continue with next face */
++ if (likely(p->hasOpposite()))
++ p = p->opposite();
++
++ /* if there is no opposite go the long way to the other side of the border */
++ else
++ {
++ /* find minimum start vertex */
++ unsigned vertex_index = p->getStartVertexIndex();
++ if (vertex_index < min_vertex_index) { min_vertex_index = vertex_index; min_vertex_index_face = f; min_vertex_index_vertex = e; }
++
++ /*! mark first border edge and store dummy vertex for face between the two border edges */
++ border_face = f;
++ faces[f++] = Face(2,inf);
++ ring[e++] = Vertex_t::loadu(vertices+p->getStartVertexIndex()*stride);
++ ring[e++] = vtx; // dummy vertex
++
++ /*! goto other side of border */
++ p = (HalfEdge*) h;
++ while (p->hasOpposite())
++ p = p->opposite()->next();
++ }
++
++ } while (p != h);
++
++ edge_valence = e;
++ face_valence = f;
++ eval_unique_identifier = min_vertex_index;
++ eval_start_face_index = min_vertex_index_face;
++ eval_start_vertex_index = min_vertex_index_vertex;
++
++ assert( hasValidPositions() );
++ }
++
++ __forceinline void subdivide(CatmullClark1Ring& dest) const
++ {
++ dest.edge_level = 0.5f*edge_level;
++ dest.vertex_level = 0.5f*vertex_level;
++ dest.face_valence = face_valence;
++ dest.edge_valence = 2*face_valence;
++ dest.border_index = border_face == -1 ? -1 : 2*border_face; // FIXME:
++ dest.vertex_crease_weight = max(0.0f,vertex_crease_weight-1.0f);
++ dest.eval_start_index = eval_start_face_index;
++ dest.eval_unique_identifier = eval_unique_identifier;
++ assert(dest.face_valence <= MAX_RING_FACE_VALENCE);
++
++ /* calculate face points */
++ Vertex_t S = Vertex_t(0.0f);
++ for (size_t face=0, v=eval_start_vertex_index; face<face_valence; face++) {
++ size_t f = (face + eval_start_face_index)%face_valence;
++
++ Vertex_t F = vtx;
++ for (size_t k=v; k<=v+faces[f].size; k++) F += ring[k%edge_valence]; // FIXME: optimize
++ S += dest.ring[2*f+1] = F/float(faces[f].size+2);
++ v+=faces[f].size;
++ v%=edge_valence;
++ }
++
++ /* calculate new edge points */
++ size_t num_creases = 0;
++ array_t<size_t,MAX_RING_FACE_VALENCE> crease_id;
++ Vertex_t C = Vertex_t(0.0f);
++ for (size_t face=0, j=eval_start_vertex_index; face<face_valence; face++)
++ {
++ size_t i = (face + eval_start_face_index)%face_valence;
++
++ const Vertex_t v = vtx + ring[j];
++ Vertex_t f = dest.ring[2*i+1];
++ if (i == 0) f += dest.ring[dest.edge_valence-1];
++ else f += dest.ring[2*i-1];
++ S += ring[j];
++ dest.crease_weight[i] = max(faces[i].crease_weight-1.0f,0.0f);
++
++ /* fast path for regular edge points */
++ if (likely(faces[i].crease_weight <= 0.0f)) {
++ dest.ring[2*i] = (v+f) * 0.25f;
++ }
++
++ /* slower path for hard edge rule */
++ else {
++ C += ring[j]; crease_id[num_creases++] = i;
++ dest.ring[2*i] = v*0.5f;
++
++ /* even slower path for blended edge rule */
++ if (unlikely(faces[i].crease_weight < 1.0f)) {
++ dest.ring[2*i] = lerp((v+f)*0.25f,v*0.5f,faces[i].crease_weight);
++ }
++ }
++ j+=faces[i].size;
++ j%=edge_valence;
++ }
++
++ /* compute new vertex using smooth rule */
++ const float inv_face_valence = 1.0f / (float)face_valence;
++ const Vertex_t v_smooth = (Vertex_t) madd(inv_face_valence,S,(float(face_valence)-2.0f)*vtx)*inv_face_valence;
++ dest.vtx = v_smooth;
++
++ /* compute new vertex using vertex_crease_weight rule */
++ if (unlikely(vertex_crease_weight > 0.0f))
++ {
++ if (vertex_crease_weight >= 1.0f) {
++ dest.vtx = vtx;
++ } else {
++ dest.vtx = lerp(vtx,v_smooth,vertex_crease_weight);
++ }
++ return;
++ }
++
++ if (likely(num_creases <= 1))
++ return;
++
++ /* compute new vertex using crease rule */
++ if (likely(num_creases == 2)) {
++ const Vertex_t v_sharp = (Vertex_t)(C + 6.0f * vtx) * (1.0f / 8.0f);
++ const float crease_weight0 = faces[crease_id[0]].crease_weight;
++ const float crease_weight1 = faces[crease_id[1]].crease_weight;
++ dest.vtx = v_sharp;
++ dest.crease_weight[crease_id[0]] = max(0.25f*(3.0f*crease_weight0 + crease_weight1)-1.0f,0.0f);
++ dest.crease_weight[crease_id[1]] = max(0.25f*(3.0f*crease_weight1 + crease_weight0)-1.0f,0.0f);
++ const float v_blend = 0.5f*(crease_weight0+crease_weight1);
++ if (unlikely(v_blend < 1.0f)) {
++ dest.vtx = lerp(v_sharp,v_smooth,v_blend);
++ }
++ }
++
++ /* compute new vertex using corner rule */
++ else {
++ dest.vtx = vtx;
++ }
++ }
++
++ void convert(CatmullClark1Ring& dst) const
++ {
++ dst.edge_level = edge_level;
++ dst.vertex_level = vertex_level;
++ dst.vtx = vtx;
++ dst.face_valence = face_valence;
++ dst.edge_valence = 2*face_valence;
++ dst.border_index = border_face == -1 ? -1 : 2*border_face;
++ for (size_t i=0; i<face_valence; i++)
++ dst.crease_weight[i] = faces[i].crease_weight;
++ dst.vertex_crease_weight = vertex_crease_weight;
++ for (size_t i=0; i<edge_valence; i++) dst.ring[i] = ring[i];
++
++ dst.eval_start_index = eval_start_face_index;
++ dst.eval_unique_identifier = eval_unique_identifier;
++
++ assert( dst.hasValidPositions() );
++ }
++
++
++ /* gets limit tangent in the direction of egde vtx -> ring[0] */
++ __forceinline Vertex getLimitTangent() const
++ {
++ CatmullClark1Ring cc_vtx;
++
++ /* fast path for quad only rings */
++ if (only_quads)
++ {
++ convert(cc_vtx);
++ return cc_vtx.getLimitTangent();
++ }
++
++ subdivide(cc_vtx);
++ return 2.0f * cc_vtx.getLimitTangent();
++ }
++
++ /* gets limit tangent in the direction of egde vtx -> ring[edge_valence-2] */
++ __forceinline Vertex getSecondLimitTangent() const
++ {
++ CatmullClark1Ring cc_vtx;
++
++ /* fast path for quad only rings */
++ if (only_quads)
++ {
++ convert(cc_vtx);
++ return cc_vtx.getSecondLimitTangent();
++ }
++
++ subdivide(cc_vtx);
++ return 2.0f * cc_vtx.getSecondLimitTangent();
++ }
++
++
++ /* gets limit vertex */
++ __forceinline Vertex getLimitVertex() const
++ {
++ CatmullClark1Ring cc_vtx;
++
++ /* fast path for quad only rings */
++ if (only_quads)
++ convert(cc_vtx);
++ else
++ subdivide(cc_vtx);
++ return cc_vtx.getLimitVertex();
++ }
++
++ friend __forceinline embree_ostream operator<<(embree_ostream o, const GeneralCatmullClark1RingT &c)
++ {
++ o << "vtx " << c.vtx << " size = " << c.edge_valence << ", border_face = " << c.border_face << ", " << " face_valence = " << c.face_valence <<
++ ", edge_level = " << c.edge_level << ", vertex_level = " << c.vertex_level << ", ring: " << embree_endl;
++ for (size_t v=0, f=0; f<c.face_valence; v+=c.faces[f++].size) {
++ for (size_t i=v; i<v+c.faces[f].size; i++) {
++ o << i << " -> " << c.ring[i];
++ if (i == v) o << " crease = " << c.faces[f].crease_weight;
++ o << embree_endl;
++ }
++ }
++ return o;
++ }
++ };
++ }