catmullclark_ring.h

// 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 edge 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 edge 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 edge 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 edge 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;
    } 
  };  
}