godot/thirdparty/embree/kernels/subdiv/gregory_patch.h

// Copyright 2009-2021 Intel Corporation
// SPDX-License-Identifier: Apache-2.0

#pragma once

#include "catmullclark_patch.h"
#include "bezier_patch.h"
#include "bezier_curve.h"
#include "catmullclark_coefficients.h"

namespace embree
{  
  template<typename Vertex, typename Vertex_t = Vertex>
  class __aligned(64) GregoryPatchT
  {
    typedef CatmullClarkPatchT<Vertex,Vertex_t> CatmullClarkPatch;
    typedef GeneralCatmullClarkPatchT<Vertex,Vertex_t> GeneralCatmullClarkPatch;
    typedef CatmullClark1RingT<Vertex,Vertex_t> CatmullClark1Ring;
    typedef BezierCurveT<Vertex> BezierCurve;

  public:
    Vertex v[4][4];
    Vertex f[2][2];

    __forceinline GregoryPatchT() {}

    __forceinline GregoryPatchT(const CatmullClarkPatch& patch) {
      init(patch);
    }

    __forceinline GregoryPatchT(const CatmullClarkPatch& patch, 
                                const BezierCurve* border0, const BezierCurve* border1, const BezierCurve* border2, const BezierCurve* border3) 
    {
      init_crackfix(patch,border0,border1,border2,border3);
    }

    __forceinline GregoryPatchT (const HalfEdge* edge, const char* vertices, size_t stride) { 
      init(CatmullClarkPatch(edge,vertices,stride));
    }
      
    __forceinline Vertex& p0() { return v[0][0]; }
    __forceinline Vertex& p1() { return v[0][3]; }
    __forceinline Vertex& p2() { return v[3][3]; }
    __forceinline Vertex& p3() { return v[3][0]; }
    
    __forceinline Vertex& e0_p() { return v[0][1]; }
    __forceinline Vertex& e0_m() { return v[1][0]; }
    __forceinline Vertex& e1_p() { return v[1][3]; }
    __forceinline Vertex& e1_m() { return v[0][2]; }
    __forceinline Vertex& e2_p() { return v[3][2]; }
    __forceinline Vertex& e2_m() { return v[2][3]; }
    __forceinline Vertex& e3_p() { return v[2][0]; }
    __forceinline Vertex& e3_m() { return v[3][1]; }
    
    __forceinline Vertex& f0_p() { return v[1][1]; }
    __forceinline Vertex& f1_p() { return v[1][2]; }
    __forceinline Vertex& f2_p() { return v[2][2]; }
    __forceinline Vertex& f3_p() { return v[2][1]; }
    __forceinline Vertex& f0_m() { return f[0][0]; }
    __forceinline Vertex& f1_m() { return f[0][1]; }
    __forceinline Vertex& f2_m() { return f[1][1]; }
    __forceinline Vertex& f3_m() { return f[1][0]; }
    
    __forceinline const Vertex& p0() const { return v[0][0]; }
    __forceinline const Vertex& p1() const { return v[0][3]; }
    __forceinline const Vertex& p2() const { return v[3][3]; }
    __forceinline const Vertex& p3() const { return v[3][0]; }
    
    __forceinline const Vertex& e0_p() const { return v[0][1]; }
    __forceinline const Vertex& e0_m() const { return v[1][0]; }
    __forceinline const Vertex& e1_p() const { return v[1][3]; }
    __forceinline const Vertex& e1_m() const { return v[0][2]; }
    __forceinline const Vertex& e2_p() const { return v[3][2]; }
    __forceinline const Vertex& e2_m() const { return v[2][3]; }
    __forceinline const Vertex& e3_p() const { return v[2][0]; }
    __forceinline const Vertex& e3_m() const { return v[3][1]; }
    
    __forceinline const Vertex& f0_p() const { return v[1][1]; }
    __forceinline const Vertex& f1_p() const { return v[1][2]; }
    __forceinline const Vertex& f2_p() const { return v[2][2]; }
    __forceinline const Vertex& f3_p() const { return v[2][1]; }
    __forceinline const Vertex& f0_m() const { return f[0][0]; }
    __forceinline const Vertex& f1_m() const { return f[0][1]; }
    __forceinline const Vertex& f2_m() const { return f[1][1]; }
    __forceinline const Vertex& f3_m() const { return f[1][0]; }
    
    __forceinline Vertex initCornerVertex(const CatmullClarkPatch& irreg_patch, const size_t index) {
      return irreg_patch.ring[index].getLimitVertex();
    }
    
    __forceinline Vertex initPositiveEdgeVertex(const CatmullClarkPatch& irreg_patch, const size_t index, const Vertex& p_vtx) {
      return madd(1.0f/3.0f,irreg_patch.ring[index].getLimitTangent(),p_vtx);
    }
    
    __forceinline Vertex initNegativeEdgeVertex(const CatmullClarkPatch& irreg_patch, const size_t index, const Vertex& p_vtx) {
      return madd(1.0f/3.0f,irreg_patch.ring[index].getSecondLimitTangent(),p_vtx);
    }

    __forceinline Vertex initPositiveEdgeVertex2(const CatmullClarkPatch& irreg_patch, const size_t index, const Vertex& p_vtx) 
    {
      CatmullClark1Ring3fa r0,r1,r2;
      irreg_patch.ring[index].subdivide(r0);
      r0.subdivide(r1);
      r1.subdivide(r2);
      return madd(8.0f/3.0f,r2.getLimitTangent(),p_vtx);
    }
    
    __forceinline Vertex initNegativeEdgeVertex2(const CatmullClarkPatch& irreg_patch, const size_t index, const Vertex& p_vtx) 
    {
      CatmullClark1Ring3fa r0,r1,r2;
      irreg_patch.ring[index].subdivide(r0);
      r0.subdivide(r1);
      r1.subdivide(r2);
      return madd(8.0f/3.0f,r2.getSecondLimitTangent(),p_vtx);
    }
    
    void initFaceVertex(const CatmullClarkPatch& irreg_patch, 
			const size_t index, 
			const Vertex& p_vtx, 
                        const Vertex& e0_p_vtx, 
			const Vertex& e1_m_vtx, 
			const unsigned int face_valence_p1,
 			const Vertex& e0_m_vtx,	
			const Vertex& e3_p_vtx,	
			const unsigned int face_valence_p3,
			Vertex& f_p_vtx, 
			Vertex& f_m_vtx)
    {
      const unsigned int face_valence = irreg_patch.ring[index].face_valence;
      const unsigned int edge_valence = irreg_patch.ring[index].edge_valence;
      const unsigned int border_index = irreg_patch.ring[index].border_index;
      
      const Vertex& vtx     = irreg_patch.ring[index].vtx;
      const Vertex e_i      = irreg_patch.ring[index].getEdgeCenter(0);
      const Vertex c_i_m_1  = irreg_patch.ring[index].getQuadCenter(0);
      const Vertex e_i_m_1  = irreg_patch.ring[index].getEdgeCenter(1);
      
      Vertex c_i, e_i_p_1;
      const bool hasHardEdge0 =
        std::isinf(irreg_patch.ring[index].vertex_crease_weight) &&
        std::isinf(irreg_patch.ring[index].crease_weight[0]);
                
      if (unlikely((border_index == edge_valence-2) || hasHardEdge0))
      {
        /* mirror quad center and edge mid-point */
        c_i     = madd(2.0f, e_i - c_i_m_1, c_i_m_1);
        e_i_p_1 = madd(2.0f, vtx - e_i_m_1, e_i_m_1);
      }
      else
      {
        c_i     = irreg_patch.ring[index].getQuadCenter( face_valence-1 );
        e_i_p_1 = irreg_patch.ring[index].getEdgeCenter( face_valence-1 );
      }
      
      Vertex c_i_m_2, e_i_m_2;
      const bool hasHardEdge1 =
        std::isinf(irreg_patch.ring[index].vertex_crease_weight) &&
        std::isinf(irreg_patch.ring[index].crease_weight[1]);
      
      if (unlikely(border_index == 2 || hasHardEdge1))
      {
        /* mirror quad center and edge mid-point */
        c_i_m_2  = madd(2.0f, e_i_m_1 - c_i_m_1, c_i_m_1);
        e_i_m_2  = madd(2.0f, vtx - e_i, + e_i);
      }
      else
      {
        c_i_m_2  = irreg_patch.ring[index].getQuadCenter( 1 );
        e_i_m_2  = irreg_patch.ring[index].getEdgeCenter( 2 );
      }      
      
      const float d = 3.0f;
      //const float c     = cosf(2.0f*M_PI/(float)face_valence);
      //const float c_e_p = cosf(2.0f*M_PI/(float)face_valence_p1);
      //const float c_e_m = cosf(2.0f*M_PI/(float)face_valence_p3);
      
      const float c     = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence);
      const float c_e_p = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence_p1);
      const float c_e_m = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence_p3);

      const Vertex r_e_p = 1.0f/3.0f * (e_i_m_1 - e_i_p_1) + 2.0f/3.0f * (c_i_m_1 - c_i);
      const Vertex r_e_m = 1.0f/3.0f * (e_i     - e_i_m_2) + 2.0f/3.0f * (c_i_m_1 - c_i_m_2);

      f_p_vtx = 1.0f / d * (c_e_p * p_vtx + (d - 2.0f*c - c_e_p) * e0_p_vtx + 2.0f*c* e1_m_vtx + r_e_p);      
      f_m_vtx = 1.0f / d * (c_e_m * p_vtx + (d - 2.0f*c - c_e_m) * e0_m_vtx + 2.0f*c* e3_p_vtx + r_e_m);     
    }

    __noinline void init(const CatmullClarkPatch& patch)
    {
      assert( patch.ring[0].hasValidPositions() );
      assert( patch.ring[1].hasValidPositions() );
      assert( patch.ring[2].hasValidPositions() );
      assert( patch.ring[3].hasValidPositions() );
      
      p0() = initCornerVertex(patch,0);
      p1() = initCornerVertex(patch,1);
      p2() = initCornerVertex(patch,2);
      p3() = initCornerVertex(patch,3);

      e0_p() = initPositiveEdgeVertex(patch,0, p0());
      e1_p() = initPositiveEdgeVertex(patch,1, p1());
      e2_p() = initPositiveEdgeVertex(patch,2, p2());
      e3_p() = initPositiveEdgeVertex(patch,3, p3());

      e0_m() = initNegativeEdgeVertex(patch,0, p0());
      e1_m() = initNegativeEdgeVertex(patch,1, p1());
      e2_m() = initNegativeEdgeVertex(patch,2, p2());
      e3_m() = initNegativeEdgeVertex(patch,3, p3());

      const unsigned int face_valence_p0 = patch.ring[0].face_valence;
      const unsigned int face_valence_p1 = patch.ring[1].face_valence;
      const unsigned int face_valence_p2 = patch.ring[2].face_valence;
      const unsigned int face_valence_p3 = patch.ring[3].face_valence;
      
      initFaceVertex(patch,0,p0(),e0_p(),e1_m(),face_valence_p1,e0_m(),e3_p(),face_valence_p3,f0_p(),f0_m() );
      initFaceVertex(patch,1,p1(),e1_p(),e2_m(),face_valence_p2,e1_m(),e0_p(),face_valence_p0,f1_p(),f1_m() );
      initFaceVertex(patch,2,p2(),e2_p(),e3_m(),face_valence_p3,e2_m(),e1_p(),face_valence_p1,f2_p(),f2_m() );
      initFaceVertex(patch,3,p3(),e3_p(),e0_m(),face_valence_p0,e3_m(),e2_p(),face_valence_p3,f3_p(),f3_m() );

    }

    __noinline void init_crackfix(const CatmullClarkPatch& patch, 
                                  const BezierCurve* border0, 
                                  const BezierCurve* border1,
                                  const BezierCurve* border2, 
                                  const BezierCurve* border3)
    {
      assert( patch.ring[0].hasValidPositions() );
      assert( patch.ring[1].hasValidPositions() );
      assert( patch.ring[2].hasValidPositions() );
      assert( patch.ring[3].hasValidPositions() );
      
      p0() = initCornerVertex(patch,0);
      p1() = initCornerVertex(patch,1);
      p2() = initCornerVertex(patch,2);
      p3() = initCornerVertex(patch,3);

      e0_p() = initPositiveEdgeVertex(patch,0, p0());
      e1_p() = initPositiveEdgeVertex(patch,1, p1());
      e2_p() = initPositiveEdgeVertex(patch,2, p2());
      e3_p() = initPositiveEdgeVertex(patch,3, p3());

      e0_m() = initNegativeEdgeVertex(patch,0, p0());
      e1_m() = initNegativeEdgeVertex(patch,1, p1());
      e2_m() = initNegativeEdgeVertex(patch,2, p2());
      e3_m() = initNegativeEdgeVertex(patch,3, p3());

      if (unlikely(border0 != nullptr)) 
      {         
        p0()   = border0->v0;
        e0_p() = border0->v1; 
        e1_m() = border0->v2; 
        p1()   = border0->v3;
      }
      
      if (unlikely(border1 != nullptr))
      {          
        p1()   = border1->v0; 
        e1_p() = border1->v1; 
        e2_m() = border1->v2; 
        p2()   = border1->v3; 
      }

      if (unlikely(border2 != nullptr))
      {          
        p2()   = border2->v0; 
        e2_p() = border2->v1; 
        e3_m() = border2->v2; 
        p3()   = border2->v3; 
      }

      if (unlikely(border3 != nullptr))
      {          
        p3()   = border3->v0; 
        e3_p() = border3->v1; 
        e0_m() = border3->v2; 
        p0()   = border3->v3; 
      }

      const unsigned int face_valence_p0 = patch.ring[0].face_valence;
      const unsigned int face_valence_p1 = patch.ring[1].face_valence;
      const unsigned int face_valence_p2 = patch.ring[2].face_valence;
      const unsigned int face_valence_p3 = patch.ring[3].face_valence;
      
      initFaceVertex(patch,0,p0(),e0_p(),e1_m(),face_valence_p1,e0_m(),e3_p(),face_valence_p3,f0_p(),f0_m() );
      initFaceVertex(patch,1,p1(),e1_p(),e2_m(),face_valence_p2,e1_m(),e0_p(),face_valence_p0,f1_p(),f1_m() );
      initFaceVertex(patch,2,p2(),e2_p(),e3_m(),face_valence_p3,e2_m(),e1_p(),face_valence_p1,f2_p(),f2_m() );
      initFaceVertex(patch,3,p3(),e3_p(),e0_m(),face_valence_p0,e3_m(),e2_p(),face_valence_p3,f3_p(),f3_m() );
    }

    
    void computeGregoryPatchFacePoints(const unsigned int face_valence,
				       const Vertex& r_e_p, 
				       const Vertex& r_e_m, 					 
				       const Vertex& p_vtx, 
				       const Vertex& e0_p_vtx, 
				       const Vertex& e1_m_vtx, 
				       const unsigned int face_valence_p1,
				       const Vertex& e0_m_vtx,	
				       const Vertex& e3_p_vtx,	
				       const unsigned int face_valence_p3,
				       Vertex& f_p_vtx, 
				       Vertex& f_m_vtx,
                                       const float d = 3.0f)
    {
      //const float c     = cosf(2.0*M_PI/(float)face_valence);
      //const float c_e_p = cosf(2.0*M_PI/(float)face_valence_p1);
      //const float c_e_m = cosf(2.0*M_PI/(float)face_valence_p3);

      const float c     = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence);
      const float c_e_p = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence_p1);
      const float c_e_m = CatmullClarkPrecomputedCoefficients::table.cos_2PI_div_n(face_valence_p3);


      f_p_vtx = 1.0f / d * (c_e_p * p_vtx + (d - 2.0f*c - c_e_p) * e0_p_vtx + 2.0f*c* e1_m_vtx + r_e_p);      
      f_m_vtx = 1.0f / d * (c_e_m * p_vtx + (d - 2.0f*c - c_e_m) * e0_m_vtx + 2.0f*c* e3_p_vtx + r_e_m);      
      f_p_vtx = 1.0f / d * (c_e_p * p_vtx + (d - 2.0f*c - c_e_p) * e0_p_vtx + 2.0f*c* e1_m_vtx + r_e_p);      
      f_m_vtx = 1.0f / d * (c_e_m * p_vtx + (d - 2.0f*c - c_e_m) * e0_m_vtx + 2.0f*c* e3_p_vtx + r_e_m);
    }

    __noinline void init(const GeneralCatmullClarkPatch& patch)
    {
      assert(patch.size() == 4);
#if 0
      CatmullClarkPatch qpatch; patch.init(qpatch);
      init(qpatch);
#else
      const float face_valence_p0 = patch.ring[0].face_valence;
      const float face_valence_p1 = patch.ring[1].face_valence;
      const float face_valence_p2 = patch.ring[2].face_valence;
      const float face_valence_p3 = patch.ring[3].face_valence;

      Vertex p0_r_p, p0_r_m;
      patch.ring[0].computeGregoryPatchEdgePoints( p0(), e0_p(), e0_m(), p0_r_p, p0_r_m );

      Vertex p1_r_p, p1_r_m;
      patch.ring[1].computeGregoryPatchEdgePoints( p1(), e1_p(), e1_m(), p1_r_p, p1_r_m );
      
      Vertex p2_r_p, p2_r_m;
      patch.ring[2].computeGregoryPatchEdgePoints( p2(), e2_p(), e2_m(), p2_r_p, p2_r_m );

      Vertex p3_r_p, p3_r_m;
      patch.ring[3].computeGregoryPatchEdgePoints( p3(), e3_p(), e3_m(), p3_r_p, p3_r_m );

      computeGregoryPatchFacePoints(face_valence_p0, p0_r_p, p0_r_m, p0(), e0_p(), e1_m(), face_valence_p1, e0_m(), e3_p(), face_valence_p3, f0_p(), f0_m() );
      computeGregoryPatchFacePoints(face_valence_p1, p1_r_p, p1_r_m, p1(), e1_p(), e2_m(), face_valence_p2, e1_m(), e0_p(), face_valence_p0, f1_p(), f1_m() );
      computeGregoryPatchFacePoints(face_valence_p2, p2_r_p, p2_r_m, p2(), e2_p(), e3_m(), face_valence_p3, e2_m(), e1_p(), face_valence_p1, f2_p(), f2_m() );
      computeGregoryPatchFacePoints(face_valence_p3, p3_r_p, p3_r_m, p3(), e3_p(), e0_m(), face_valence_p0, e3_m(), e2_p(), face_valence_p3, f3_p(), f3_m() );

#endif
    }
   
    
    __forceinline void convert_to_bezier()
    {
      f0_p() = (f0_p() + f0_m()) * 0.5f;
      f1_p() = (f1_p() + f1_m()) * 0.5f;
      f2_p() = (f2_p() + f2_m()) * 0.5f;
      f3_p() = (f3_p() + f3_m()) * 0.5f;
      f0_m() = Vertex( zero );
      f1_m() = Vertex( zero );
      f2_m() = Vertex( zero );
      f3_m() = Vertex( zero );      
    }
    
    static __forceinline void computeInnerVertices(const Vertex matrix[4][4], const Vertex f_m[2][2], const float uu, const float vv,
						   Vertex_t& matrix_11, Vertex_t& matrix_12, Vertex_t& matrix_22, Vertex_t& matrix_21)
    {
      if (unlikely(uu == 0.0f || uu == 1.0f || vv == 0.0f || vv == 1.0f)) 
      {
	matrix_11 = matrix[1][1];
	matrix_12 = matrix[1][2];
	matrix_22 = matrix[2][2];
	matrix_21 = matrix[2][1];	 
      }
      else
      {
	const Vertex_t f0_p = matrix[1][1];
	const Vertex_t f1_p = matrix[1][2];
	const Vertex_t f2_p = matrix[2][2];
	const Vertex_t f3_p = matrix[2][1];
        
	const Vertex_t f0_m = f_m[0][0];
	const Vertex_t f1_m = f_m[0][1];
	const Vertex_t f2_m = f_m[1][1];
	const Vertex_t f3_m = f_m[1][0];
        
	matrix_11 = (      uu  * f0_p +       vv  * f0_m)*rcp(uu+vv);
	matrix_12 = ((1.0f-uu) * f1_m +       vv  * f1_p)*rcp(1.0f-uu+vv);
	matrix_22 = ((1.0f-uu) * f2_p + (1.0f-vv) * f2_m)*rcp(2.0f-uu-vv);
	matrix_21 = (      uu  * f3_m + (1.0f-vv) * f3_p)*rcp(1.0f+uu-vv);
      }
    } 

    template<typename vfloat>
    static __forceinline void computeInnerVertices(const Vertex v[4][4], const Vertex f[2][2], 
                                                   size_t i, const vfloat& uu, const vfloat& vv, vfloat& matrix_11, vfloat& matrix_12, vfloat& matrix_22, vfloat& matrix_21) 
    {
      const auto m_border = (uu == 0.0f) | (uu == 1.0f) | (vv == 0.0f) | (vv == 1.0f);

      const vfloat f0_p = v[1][1][i];
      const vfloat f1_p = v[1][2][i];
      const vfloat f2_p = v[2][2][i];
      const vfloat f3_p = v[2][1][i];
      
      const vfloat f0_m = f[0][0][i];
      const vfloat f1_m = f[0][1][i];
      const vfloat f2_m = f[1][1][i];
      const vfloat f3_m = f[1][0][i];
      
      const vfloat one_minus_uu = vfloat(1.0f) - uu;
      const vfloat one_minus_vv = vfloat(1.0f) - vv;      
      
      const vfloat f0_i = (          uu * f0_p +           vv * f0_m) * rcp(uu+vv);
      const vfloat f1_i = (one_minus_uu * f1_m +           vv * f1_p) * rcp(one_minus_uu+vv);
      const vfloat f2_i = (one_minus_uu * f2_p + one_minus_vv * f2_m) * rcp(one_minus_uu+one_minus_vv);
      const vfloat f3_i = (          uu * f3_m + one_minus_vv * f3_p) * rcp(uu+one_minus_vv);
      
      matrix_11 = select(m_border,f0_p,f0_i);
      matrix_12 = select(m_border,f1_p,f1_i);
      matrix_22 = select(m_border,f2_p,f2_i);
      matrix_21 = select(m_border,f3_p,f3_i);
    }

    static __forceinline Vertex eval(const Vertex matrix[4][4], const Vertex f[2][2], const float& uu, const float& vv) 
    {
      Vertex_t v_11, v_12, v_22, v_21;
      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
      
      const Vec4<float> Bu = BezierBasis::eval(uu);
      const Vec4<float> Bv = BezierBasis::eval(vv);
      
      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
    }

    static __forceinline Vertex eval_du(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
    {
      Vertex_t v_11, v_12, v_22, v_21;
      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
      
      const Vec4<float> Bu = BezierBasis::derivative(uu);
      const Vec4<float> Bv = BezierBasis::eval(vv);

      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
    }

    static __forceinline Vertex eval_dv(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
    {
      Vertex_t v_11, v_12, v_22, v_21;
      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
      
      const Vec4<float> Bu = BezierBasis::eval(uu);
      const Vec4<float> Bv = BezierBasis::derivative(vv);
 
      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
    }

    static __forceinline Vertex eval_dudu(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
    {
      Vertex_t v_11, v_12, v_22, v_21;
      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
      
      const Vec4<float> Bu = BezierBasis::derivative2(uu);
      const Vec4<float> Bv = BezierBasis::eval(vv);
 
      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
     }

    static __forceinline Vertex eval_dvdv(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
    {
      Vertex_t v_11, v_12, v_22, v_21;
      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
      
      const Vec4<float> Bu = BezierBasis::eval(uu);
      const Vec4<float> Bv = BezierBasis::derivative2(vv);

      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
    }

    static __forceinline Vertex eval_dudv(const Vertex matrix[4][4], const Vertex f[2][2], const float uu, const float vv) // approximative derivative
    {
      Vertex_t v_11, v_12, v_22, v_21;
      computeInnerVertices(matrix,f,uu,vv,v_11, v_12, v_22, v_21);
      
      const Vec4<float> Bu = BezierBasis::derivative(uu);
      const Vec4<float> Bv = BezierBasis::derivative(vv);

      return madd(Bv.x,madd(Bu.x,matrix[0][0],madd(Bu.y,matrix[0][1],madd(Bu.z,matrix[0][2],Bu.w * matrix[0][3]))), 
                  madd(Bv.y,madd(Bu.x,matrix[1][0],madd(Bu.y,v_11        ,madd(Bu.z,v_12        ,Bu.w * matrix[1][3]))), 
                       madd(Bv.z,madd(Bu.x,matrix[2][0],madd(Bu.y,v_21        ,madd(Bu.z,v_22        ,Bu.w * matrix[2][3]))), 
                            Bv.w*madd(Bu.x,matrix[3][0],madd(Bu.y,matrix[3][1],madd(Bu.z,matrix[3][2],Bu.w * matrix[3][3])))))); 
    }

    __forceinline Vertex eval(const float uu, const float vv) const {
      return eval(v,f,uu,vv);
    }

    __forceinline Vertex eval_du( const float uu, const float vv) const {
      return eval_du(v,f,uu,vv);
    }

    __forceinline Vertex eval_dv( const float uu, const float vv) const {
      return eval_dv(v,f,uu,vv);
    }

    __forceinline Vertex eval_dudu( const float uu, const float vv) const {
      return eval_dudu(v,f,uu,vv);
    }

    __forceinline Vertex eval_dvdv( const float uu, const float vv) const {
      return eval_dvdv(v,f,uu,vv);
    }

    __forceinline Vertex eval_dudv( const float uu, const float vv) const {
      return eval_dudv(v,f,uu,vv);
    }

    static __forceinline Vertex normal(const Vertex matrix[4][4], const Vertex f_m[2][2], const float uu, const float vv)  // FIXME: why not using basis functions
    {
      /* interpolate inner vertices */
      Vertex_t matrix_11, matrix_12, matrix_22, matrix_21;
      computeInnerVertices(matrix,f_m,uu,vv,matrix_11, matrix_12, matrix_22, matrix_21);
      
      /* tangentU */
      const Vertex_t col0 = deCasteljau(vv, (Vertex_t)matrix[0][0], (Vertex_t)matrix[1][0], (Vertex_t)matrix[2][0], (Vertex_t)matrix[3][0]);
      const Vertex_t col1 = deCasteljau(vv, (Vertex_t)matrix[0][1], (Vertex_t)matrix_11   , (Vertex_t)matrix_21   , (Vertex_t)matrix[3][1]);
      const Vertex_t col2 = deCasteljau(vv, (Vertex_t)matrix[0][2], (Vertex_t)matrix_12   , (Vertex_t)matrix_22   , (Vertex_t)matrix[3][2]);
      const Vertex_t col3 = deCasteljau(vv, (Vertex_t)matrix[0][3], (Vertex_t)matrix[1][3], (Vertex_t)matrix[2][3], (Vertex_t)matrix[3][3]);
      
      const Vertex_t tangentU = deCasteljau_tangent(uu, col0, col1, col2, col3);
      
      /* tangentV */
      const Vertex_t row0 = deCasteljau(uu, (Vertex_t)matrix[0][0], (Vertex_t)matrix[0][1], (Vertex_t)matrix[0][2], (Vertex_t)matrix[0][3]);
      const Vertex_t row1 = deCasteljau(uu, (Vertex_t)matrix[1][0], (Vertex_t)matrix_11   , (Vertex_t)matrix_12   , (Vertex_t)matrix[1][3]);
      const Vertex_t row2 = deCasteljau(uu, (Vertex_t)matrix[2][0], (Vertex_t)matrix_21   , (Vertex_t)matrix_22   , (Vertex_t)matrix[2][3]);
      const Vertex_t row3 = deCasteljau(uu, (Vertex_t)matrix[3][0], (Vertex_t)matrix[3][1], (Vertex_t)matrix[3][2], (Vertex_t)matrix[3][3]);
      
      const Vertex_t tangentV = deCasteljau_tangent(vv, row0, row1, row2, row3);
      
      /* normal = tangentU x tangentV */
      const Vertex_t n = cross(tangentU,tangentV);
      
      return n;     
    }
   
    __forceinline Vertex normal( const float uu, const float vv) const {
      return normal(v,f,uu,vv);
    }    
    
    __forceinline void eval(const float u, const float v, 
                            Vertex* P, Vertex* dPdu, Vertex* dPdv, 
                            Vertex* ddPdudu, Vertex* ddPdvdv, Vertex* ddPdudv,
                            const float dscale = 1.0f) const
    {
      if (P) {
        *P = eval(u,v); 
      }
      if (dPdu) {
        assert(dPdu); *dPdu = eval_du(u,v)*dscale; 
        assert(dPdv); *dPdv = eval_dv(u,v)*dscale; 
      }
      if (ddPdudu) {
        assert(ddPdudu); *ddPdudu = eval_dudu(u,v)*sqr(dscale); 
        assert(ddPdvdv); *ddPdvdv = eval_dvdv(u,v)*sqr(dscale); 
        assert(ddPdudv); *ddPdudv = eval_dudv(u,v)*sqr(dscale); 
      }
    }

    template<class vfloat>
    static __forceinline vfloat eval(const Vertex v[4][4], const Vertex f[2][2], 
                                     const size_t i, const vfloat& uu, const vfloat& vv, const Vec4<vfloat>& u_n, const Vec4<vfloat>& v_n,
                                     vfloat& matrix_11, vfloat& matrix_12, vfloat& matrix_22, vfloat& matrix_21)
    {
      const vfloat curve0_x = madd(v_n[0],vfloat(v[0][0][i]),madd(v_n[1],vfloat(v[1][0][i]),madd(v_n[2],vfloat(v[2][0][i]),v_n[3] * vfloat(v[3][0][i]))));
      const vfloat curve1_x = madd(v_n[0],vfloat(v[0][1][i]),madd(v_n[1],vfloat(matrix_11 ),madd(v_n[2],vfloat(matrix_21 ),v_n[3] * vfloat(v[3][1][i]))));
      const vfloat curve2_x = madd(v_n[0],vfloat(v[0][2][i]),madd(v_n[1],vfloat(matrix_12 ),madd(v_n[2],vfloat(matrix_22 ),v_n[3] * vfloat(v[3][2][i]))));
      const vfloat curve3_x = madd(v_n[0],vfloat(v[0][3][i]),madd(v_n[1],vfloat(v[1][3][i]),madd(v_n[2],vfloat(v[2][3][i]),v_n[3] * vfloat(v[3][3][i]))));
      return madd(u_n[0],curve0_x,madd(u_n[1],curve1_x,madd(u_n[2],curve2_x,u_n[3] * curve3_x)));
    }
    
    template<typename vbool, typename vfloat>
    static __forceinline void eval(const Vertex v[4][4], const Vertex f[2][2], 
                                   const vbool& valid, const vfloat& uu, const vfloat& vv, 
                                   float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv,
                                   const float dscale, const size_t dstride, const size_t N) 
    {
      if (P) {
        const Vec4<vfloat> u_n = BezierBasis::eval(uu); 
        const Vec4<vfloat> v_n = BezierBasis::eval(vv); 
        for (size_t i=0; i<N; i++) {
          vfloat matrix_11, matrix_12, matrix_22, matrix_21;
          computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21); // FIXME: calculated multiple times
          vfloat::store(valid,P+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21));
        }
      }
      if (dPdu)
      {
        {
          assert(dPdu);
          const Vec4<vfloat> u_n = BezierBasis::derivative(uu); 
          const Vec4<vfloat> v_n = BezierBasis::eval(vv);
          for (size_t i=0; i<N; i++) {
            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
            vfloat::store(valid,dPdu+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*dscale);
          }
        }
        {
          assert(dPdv);
          const Vec4<vfloat> u_n = BezierBasis::eval(uu); 
          const Vec4<vfloat> v_n = BezierBasis::derivative(vv);
          for (size_t i=0; i<N; i++) {
            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
            vfloat::store(valid,dPdv+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*dscale);
          }
        }
      }
      if (ddPdudu)
      {
        {
          assert(ddPdudu);
          const Vec4<vfloat> u_n = BezierBasis::derivative2(uu); 
          const Vec4<vfloat> v_n = BezierBasis::eval(vv);
          for (size_t i=0; i<N; i++) {
            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
            vfloat::store(valid,ddPdudu+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*sqr(dscale));
          }
        }
        {
          assert(ddPdvdv);
          const Vec4<vfloat> u_n = BezierBasis::eval(uu); 
          const Vec4<vfloat> v_n = BezierBasis::derivative2(vv);
          for (size_t i=0; i<N; i++) {
            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
            vfloat::store(valid,ddPdvdv+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*sqr(dscale));
          }
        }
        {
          assert(ddPdudv);
          const Vec4<vfloat> u_n = BezierBasis::derivative(uu); 
          const Vec4<vfloat> v_n = BezierBasis::derivative(vv);
          for (size_t i=0; i<N; i++) {
            vfloat matrix_11, matrix_12, matrix_22, matrix_21;
            computeInnerVertices(v,f,i,uu,vv,matrix_11,matrix_12,matrix_22,matrix_21);  // FIXME: calculated multiple times
            vfloat::store(valid,ddPdudv+i*dstride,eval(v,f,i,uu,vv,u_n,v_n,matrix_11,matrix_12,matrix_22,matrix_21)*sqr(dscale));
          }
        }
      }
    }

    template<typename vbool, typename vfloat>
    __forceinline void eval(const vbool& valid, const vfloat& uu, const vfloat& vv, 
                            float* P, float* dPdu, float* dPdv, float* ddPdudu, float* ddPdvdv, float* ddPdudv,
                            const float dscale, const size_t dstride, const size_t N) const {
      eval(v,f,valid,uu,vv,P,dPdu,dPdv,ddPdudu,ddPdvdv,ddPdudv,dscale,dstride,N);
    }

    template<class T>
      static __forceinline Vec3<T> eval_t(const Vertex matrix[4][4], const Vec3<T> f[2][2], const T& uu, const T& vv) 
    {
      typedef typename T::Bool M;
      const M m_border = (uu == 0.0f) | (uu == 1.0f) | (vv == 0.0f) | (vv == 1.0f);

      const Vec3<T> f0_p = Vec3<T>(matrix[1][1].x,matrix[1][1].y,matrix[1][1].z);
      const Vec3<T> f1_p = Vec3<T>(matrix[1][2].x,matrix[1][2].y,matrix[1][2].z);
      const Vec3<T> f2_p = Vec3<T>(matrix[2][2].x,matrix[2][2].y,matrix[2][2].z);
      const Vec3<T> f3_p = Vec3<T>(matrix[2][1].x,matrix[2][1].y,matrix[2][1].z);
      
      const Vec3<T> f0_m = f[0][0];
      const Vec3<T> f1_m = f[0][1];
      const Vec3<T> f2_m = f[1][1];
      const Vec3<T> f3_m = f[1][0];
      
      const T one_minus_uu = T(1.0f) - uu;
      const T one_minus_vv = T(1.0f) - vv;      
      
      const Vec3<T> f0_i = (          uu * f0_p +           vv * f0_m) * rcp(uu+vv);
      const Vec3<T> f1_i = (one_minus_uu * f1_m +           vv * f1_p) * rcp(one_minus_uu+vv);
      const Vec3<T> f2_i = (one_minus_uu * f2_p + one_minus_vv * f2_m) * rcp(one_minus_uu+one_minus_vv);
      const Vec3<T> f3_i = (          uu * f3_m + one_minus_vv * f3_p) * rcp(uu+one_minus_vv);
      
      const Vec3<T> F0( select(m_border,f0_p.x,f0_i.x), select(m_border,f0_p.y,f0_i.y), select(m_border,f0_p.z,f0_i.z) );
      const Vec3<T> F1( select(m_border,f1_p.x,f1_i.x), select(m_border,f1_p.y,f1_i.y), select(m_border,f1_p.z,f1_i.z) );
      const Vec3<T> F2( select(m_border,f2_p.x,f2_i.x), select(m_border,f2_p.y,f2_i.y), select(m_border,f2_p.z,f2_i.z) );
      const Vec3<T> F3( select(m_border,f3_p.x,f3_i.x), select(m_border,f3_p.y,f3_i.y), select(m_border,f3_p.z,f3_i.z) );

      const T B0_u = one_minus_uu * one_minus_uu * one_minus_uu;
      const T B0_v = one_minus_vv * one_minus_vv * one_minus_vv;
      const T B1_u = 3.0f * (one_minus_uu * uu * one_minus_uu);
      const T B1_v = 3.0f * (one_minus_vv * vv * one_minus_vv);
      const T B2_u = 3.0f * (uu * one_minus_uu * uu);
      const T B2_v = 3.0f * (vv * one_minus_vv * vv);
      const T B3_u = uu * uu * uu;
      const T B3_v = vv * vv * vv;

      const T x = madd(B0_v,madd(B0_u,matrix[0][0].x,madd(B1_u,matrix[0][1].x,madd(B2_u,matrix[0][2].x,B3_u * matrix[0][3].x))), 
                  madd(B1_v,madd(B0_u,matrix[1][0].x,madd(B1_u,F0.x          ,madd(B2_u,F1.x          ,B3_u * matrix[1][3].x))), 
                  madd(B2_v,madd(B0_u,matrix[2][0].x,madd(B1_u,F3.x          ,madd(B2_u,F2.x          ,B3_u * matrix[2][3].x))), 
                       B3_v*madd(B0_u,matrix[3][0].x,madd(B1_u,matrix[3][1].x,madd(B2_u,matrix[3][2].x,B3_u * matrix[3][3].x)))))); 

      const T y = madd(B0_v,madd(B0_u,matrix[0][0].y,madd(B1_u,matrix[0][1].y,madd(B2_u,matrix[0][2].y,B3_u * matrix[0][3].y))),
                  madd(B1_v,madd(B0_u,matrix[1][0].y,madd(B1_u,F0.y          ,madd(B2_u,F1.y          ,B3_u * matrix[1][3].y))),
                  madd(B2_v,madd(B0_u,matrix[2][0].y,madd(B1_u,F3.y          ,madd(B2_u,F2.y          ,B3_u * matrix[2][3].y))),
                       B3_v*madd(B0_u,matrix[3][0].y,madd(B1_u,matrix[3][1].y,madd(B2_u,matrix[3][2].y,B3_u * matrix[3][3].y))))));
      
      const T z = madd(B0_v,madd(B0_u,matrix[0][0].z,madd(B1_u,matrix[0][1].z,madd(B2_u,matrix[0][2].z,B3_u * matrix[0][3].z))),
                  madd(B1_v,madd(B0_u,matrix[1][0].z,madd(B1_u,F0.z          ,madd(B2_u,F1.z          ,B3_u * matrix[1][3].z))),
                  madd(B2_v,madd(B0_u,matrix[2][0].z,madd(B1_u,F3.z          ,madd(B2_u,F2.z          ,B3_u * matrix[2][3].z))),
                       B3_v*madd(B0_u,matrix[3][0].z,madd(B1_u,matrix[3][1].z,madd(B2_u,matrix[3][2].z,B3_u * matrix[3][3].z))))));
      
      return Vec3<T>(x,y,z);
    }

    template<class T>
    __forceinline Vec3<T> eval(const T& uu, const T& vv) const 
    {
      Vec3<T> ff[2][2];
      ff[0][0] = Vec3<T>(f[0][0]);
      ff[0][1] = Vec3<T>(f[0][1]);
      ff[1][1] = Vec3<T>(f[1][1]);
      ff[1][0] = Vec3<T>(f[1][0]);
      return eval_t(v,ff,uu,vv);
    }

    template<class T>
      static __forceinline Vec3<T> normal_t(const Vertex matrix[4][4], const Vec3<T> f[2][2], const T& uu, const T& vv) 
    {
      typedef typename T::Bool M;
      
      const Vec3<T> f0_p = Vec3<T>(matrix[1][1].x,matrix[1][1].y,matrix[1][1].z);
      const Vec3<T> f1_p = Vec3<T>(matrix[1][2].x,matrix[1][2].y,matrix[1][2].z);
      const Vec3<T> f2_p = Vec3<T>(matrix[2][2].x,matrix[2][2].y,matrix[2][2].z);
      const Vec3<T> f3_p = Vec3<T>(matrix[2][1].x,matrix[2][1].y,matrix[2][1].z);

      const Vec3<T> f0_m = f[0][0];
      const Vec3<T> f1_m = f[0][1];
      const Vec3<T> f2_m = f[1][1];
      const Vec3<T> f3_m = f[1][0];
      
      const T one_minus_uu = T(1.0f) - uu;
      const T one_minus_vv = T(1.0f) - vv;      
      
      const Vec3<T> f0_i = (          uu * f0_p +           vv * f0_m) * rcp(uu+vv);
      const Vec3<T> f1_i = (one_minus_uu * f1_m +           vv * f1_p) * rcp(one_minus_uu+vv);
      const Vec3<T> f2_i = (one_minus_uu * f2_p + one_minus_vv * f2_m) * rcp(one_minus_uu+one_minus_vv);
      const Vec3<T> f3_i = (          uu * f3_m + one_minus_vv * f3_p) * rcp(uu+one_minus_vv);

#if 1
      const M m_corner0 = (uu == 0.0f) & (vv == 0.0f);
      const M m_corner1 = (uu == 1.0f) & (vv == 0.0f);
      const M m_corner2 = (uu == 1.0f) & (vv == 1.0f);
      const M m_corner3 = (uu == 0.0f) & (vv == 1.0f);      
      const Vec3<T> matrix_11( select(m_corner0,f0_p.x,f0_i.x), select(m_corner0,f0_p.y,f0_i.y), select(m_corner0,f0_p.z,f0_i.z) );
      const Vec3<T> matrix_12( select(m_corner1,f1_p.x,f1_i.x), select(m_corner1,f1_p.y,f1_i.y), select(m_corner1,f1_p.z,f1_i.z) );
      const Vec3<T> matrix_22( select(m_corner2,f2_p.x,f2_i.x), select(m_corner2,f2_p.y,f2_i.y), select(m_corner2,f2_p.z,f2_i.z) );
      const Vec3<T> matrix_21( select(m_corner3,f3_p.x,f3_i.x), select(m_corner3,f3_p.y,f3_i.y), select(m_corner3,f3_p.z,f3_i.z) );
#else
      const M m_border = (uu == 0.0f) | (uu == 1.0f) | (vv == 0.0f) | (vv == 1.0f);
      const Vec3<T> matrix_11( select(m_border,f0_p.x,f0_i.x), select(m_border,f0_p.y,f0_i.y), select(m_border,f0_p.z,f0_i.z) );
      const Vec3<T> matrix_12( select(m_border,f1_p.x,f1_i.x), select(m_border,f1_p.y,f1_i.y), select(m_border,f1_p.z,f1_i.z) );
      const Vec3<T> matrix_22( select(m_border,f2_p.x,f2_i.x), select(m_border,f2_p.y,f2_i.y), select(m_border,f2_p.z,f2_i.z) );
      const Vec3<T> matrix_21( select(m_border,f3_p.x,f3_i.x), select(m_border,f3_p.y,f3_i.y), select(m_border,f3_p.z,f3_i.z) );
#endif
      
      const Vec3<T> matrix_00 = Vec3<T>(matrix[0][0].x,matrix[0][0].y,matrix[0][0].z);
      const Vec3<T> matrix_10 = Vec3<T>(matrix[1][0].x,matrix[1][0].y,matrix[1][0].z);
      const Vec3<T> matrix_20 = Vec3<T>(matrix[2][0].x,matrix[2][0].y,matrix[2][0].z);
      const Vec3<T> matrix_30 = Vec3<T>(matrix[3][0].x,matrix[3][0].y,matrix[3][0].z);
      
      const Vec3<T> matrix_01 = Vec3<T>(matrix[0][1].x,matrix[0][1].y,matrix[0][1].z);
      const Vec3<T> matrix_02 = Vec3<T>(matrix[0][2].x,matrix[0][2].y,matrix[0][2].z);
      const Vec3<T> matrix_03 = Vec3<T>(matrix[0][3].x,matrix[0][3].y,matrix[0][3].z);
      
      const Vec3<T> matrix_31 = Vec3<T>(matrix[3][1].x,matrix[3][1].y,matrix[3][1].z);
      const Vec3<T> matrix_32 = Vec3<T>(matrix[3][2].x,matrix[3][2].y,matrix[3][2].z);
      const Vec3<T> matrix_33 = Vec3<T>(matrix[3][3].x,matrix[3][3].y,matrix[3][3].z);
      
      const Vec3<T> matrix_13 = Vec3<T>(matrix[1][3].x,matrix[1][3].y,matrix[1][3].z);
      const Vec3<T> matrix_23 = Vec3<T>(matrix[2][3].x,matrix[2][3].y,matrix[2][3].z);
      
      /* tangentU */
      const Vec3<T> col0 = deCasteljau(vv, matrix_00, matrix_10, matrix_20, matrix_30);
      const Vec3<T> col1 = deCasteljau(vv, matrix_01, matrix_11, matrix_21, matrix_31);
      const Vec3<T> col2 = deCasteljau(vv, matrix_02, matrix_12, matrix_22, matrix_32);
      const Vec3<T> col3 = deCasteljau(vv, matrix_03, matrix_13, matrix_23, matrix_33);
      
      const Vec3<T> tangentU = deCasteljau_tangent(uu, col0, col1, col2, col3);
      
      /* tangentV */
      const Vec3<T> row0 = deCasteljau(uu, matrix_00, matrix_01, matrix_02, matrix_03);
      const Vec3<T> row1 = deCasteljau(uu, matrix_10, matrix_11, matrix_12, matrix_13);
      const Vec3<T> row2 = deCasteljau(uu, matrix_20, matrix_21, matrix_22, matrix_23);
      const Vec3<T> row3 = deCasteljau(uu, matrix_30, matrix_31, matrix_32, matrix_33);
      
      const Vec3<T> tangentV = deCasteljau_tangent(vv, row0, row1, row2, row3);
      
      /* normal = tangentU x tangentV */
      const Vec3<T> n = cross(tangentU,tangentV);
      return n;
    }

     template<class T>
    __forceinline Vec3<T> normal(const T& uu, const T& vv) const 
    {
      Vec3<T> ff[2][2];
      ff[0][0] = Vec3<T>(f[0][0]);
      ff[0][1] = Vec3<T>(f[0][1]);
      ff[1][1] = Vec3<T>(f[1][1]);
      ff[1][0] = Vec3<T>(f[1][0]);
      return normal_t(v,ff,uu,vv);
    }

    __forceinline BBox<Vertex> bounds() const
    {
      const Vertex *const cv = &v[0][0];
      BBox<Vertex> bounds (cv[0]);
      for (size_t i=1; i<16; i++) 
        bounds.extend( cv[i] );
      bounds.extend(f[0][0]);
      bounds.extend(f[1][0]);
      bounds.extend(f[1][1]);
      bounds.extend(f[1][1]);
      return bounds;
    }
    
    friend embree_ostream operator<<(embree_ostream o, const GregoryPatchT& p)
    {
      for (size_t y=0; y<4; y++)
	for (size_t x=0; x<4; x++)
	  o << "v[" << y << "][" << x << "] " << p.v[y][x] << embree_endl;
      
      for (size_t y=0; y<2; y++)
	for (size_t x=0; x<2; x++)
	  o << "f[" << y << "][" << x << "] " << p.f[y][x] << embree_endl;
      return o;
    } 
  };

  typedef GregoryPatchT<Vec3fa,Vec3fa_t> GregoryPatch3fa;

  template<typename Vertex, typename Vertex_t>
    __forceinline  BezierPatchT<Vertex,Vertex_t>::BezierPatchT (const HalfEdge* edge, const char* vertices, size_t stride) 
  {
    CatmullClarkPatchT<Vertex,Vertex_t> patch(edge,vertices,stride);
    GregoryPatchT<Vertex,Vertex_t> gpatch(patch); 
    gpatch.convert_to_bezier(); 
    for (size_t y=0; y<4; y++)
      for (size_t x=0; x<4; x++)
        matrix[y][x] = (Vertex_t)gpatch.v[y][x];
  }
  
   template<typename Vertex, typename Vertex_t>
    __forceinline BezierPatchT<Vertex,Vertex_t>::BezierPatchT(const CatmullClarkPatchT<Vertex,Vertex_t>& patch) 
    {
      GregoryPatchT<Vertex,Vertex_t> gpatch(patch); 
      gpatch.convert_to_bezier(); 
      for (size_t y=0; y<4; y++)
	for (size_t x=0; x<4; x++)
	  matrix[y][x] = (Vertex_t)gpatch.v[y][x];
    }

   template<typename Vertex, typename Vertex_t>
     __forceinline BezierPatchT<Vertex,Vertex_t>::BezierPatchT(const CatmullClarkPatchT<Vertex,Vertex_t>& patch, 
                                                               const BezierCurveT<Vertex>* border0,
                                                               const BezierCurveT<Vertex>* border1,
                                                               const BezierCurveT<Vertex>* border2,
                                                               const BezierCurveT<Vertex>* border3) 
    {
      GregoryPatchT<Vertex,Vertex_t> gpatch(patch,border0,border1,border2,border3); 
      gpatch.convert_to_bezier(); 
      for (size_t y=0; y<4; y++)
	for (size_t x=0; x<4; x++)
	  matrix[y][x] = (Vertex_t)gpatch.v[y][x];
    }
}