AtomicGameEngine/Source/ThirdParty/embree/kernels/subdiv/bspline_curve.h

// ======================================================================== //
// Copyright 2009-2017 Intel Corporation                                    //
//                                                                          //
// Licensed under the Apache License, Version 2.0 (the "License");          //
// you may not use this file except in compliance with the License.         //
// You may obtain a copy of the License at                                  //
//                                                                          //
//     http://www.apache.org/licenses/LICENSE-2.0                           //
//                                                                          //
// Unless required by applicable law or agreed to in writing, software      //
// distributed under the License is distributed on an "AS IS" BASIS,        //
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. //
// See the License for the specific language governing permissions and      //
// limitations under the License.                                           //
// ======================================================================== //

#pragma once

#include "../common/default.h"
#include "bezier_curve.h"

namespace embree
{
  class BSplineBasis2 // FIXME: make compatible with basis from bspline_patch.h
  {
  public:

    template<typename T>
      static __forceinline Vec4<T>  eval(const T& u) 
    {
      const T t  = u;
      const T s  = T(1.0f) - u;
      const T n0 = s*s*s;
      const T n1 = (4.0f*(s*s*s)+(t*t*t)) + (12.0f*((s*t)*s) + 6.0f*((t*s)*t));
      const T n2 = (4.0f*(t*t*t)+(s*s*s)) + (12.0f*((t*s)*t) + 6.0f*((s*t)*s));
      const T n3 = t*t*t;
      return T(1.0f/6.0f)*Vec4<T>(n0,n1,n2,n3);
    }
    
    template<typename T>
      static __forceinline Vec4<T>  derivative(const T& u)
    {
      const T t  =  u;
      const T s  =  1.0f - u;
      const T n0 = -s*s;
      const T n1 = -t*t - 4.0f*(t*s);
      const T n2 =  s*s + 4.0f*(s*t);
      const T n3 =  t*t;
      return T(0.5f)*Vec4<T>(n0,n1,n2,n3);
    }

    template<typename T>
      static __forceinline Vec4<T>  derivative2(const T& u)
    {
      const T t  =  u;
      const T s  =  1.0f - u;
      const T n0 = s;
      const T n1 = t - 2.0f*s;
      const T n2 = s - 2.0f*t;
      const T n3 = t;
      return Vec4<T>(n0,n1,n2,n3);
    }
  };
  
  struct PrecomputedBSplineBasis
  {
    enum { N = 16 };
  public:
    PrecomputedBSplineBasis() {}
    PrecomputedBSplineBasis(int shift);

    template<typename T>
    __forceinline Vec4<T> eval(const int u, const int size) 
    {
      assert(size <= N);
      assert(u <= size);
      return Vec4<T>(T::loadu(&c0[size][u]),
                     T::loadu(&c1[size][u]),
                     T::loadu(&c2[size][u]),
                     T::loadu(&c3[size][u]));            
    }

    template<typename T>
    __forceinline Vec4<T> derivative(const int u, const int size) 
    {
      assert(size <= N);
      assert(u <= size);
      return Vec4<T>(T::loadu(&d0[size][u]),
                     T::loadu(&d1[size][u]),
                     T::loadu(&d2[size][u]),
                     T::loadu(&d3[size][u]));            
    }
    
    /* basis for bspline evaluation */
  public:
    float c0[N+1][N+1];
    float c1[N+1][N+1];
    float c2[N+1][N+1];
    float c3[N+1][N+1];
    
    /* basis for bspline derivative evaluation */
  public:
    float d0[N+1][N+1];
    float d1[N+1][N+1];
    float d2[N+1][N+1];
    float d3[N+1][N+1];
  };
  extern PrecomputedBSplineBasis bspline_basis0;
  extern PrecomputedBSplineBasis bspline_basis1;

  template<typename Vertex>
    struct BSplineCurveT
    {
      Vertex v0,v1,v2,v3;
      
      __forceinline BSplineCurveT() {}
      
      __forceinline BSplineCurveT(const Vertex& v0, const Vertex& v1, const Vertex& v2, const Vertex& v3)
        : v0(v0), v1(v1), v2(v2), v3(v3) {}

      __forceinline Vertex begin() const {
        return madd(1.0f/6.0f,v0,madd(2.0f/3.0f,v1,1.0f/6.0f*v2));
      }

      __forceinline Vertex end() const {
        return madd(1.0f/6.0f,v1,madd(2.0f/3.0f,v2,1.0f/6.0f*v3));
      }
      
      __forceinline Vertex eval(const float t) const 
      {
        const Vec4<float> b = BSplineBasis2::eval(t);
        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
      }
      
      __forceinline Vertex eval_du(const float t) const
      {
        const Vec4<float> b = BSplineBasis2::derivative(t);
        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
      }
      
      __forceinline Vertex eval_dudu(const float t) const 
      {
        const Vec4<float> b = BSplineBasis2::derivative2(t);
        return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
      }
      
      __forceinline void eval(const float t, Vertex& p, Vertex& dp, Vertex& ddp) const
      {
        p = eval(t);
        dp = eval_du(t);
        ddp = eval_dudu(t);
      }
      
      friend inline std::ostream& operator<<(std::ostream& cout, const BSplineCurveT& curve) {
        return cout << "BSplineCurve { v0 = " << curve.v0 << ", v1 = " << curve.v1 << ", v2 = " << curve.v2 << ", v3 = " << curve.v3 << " }";
      }
    };

  template<typename Vertex>
    __forceinline void convert(const BezierCurveT<Vertex>& icurve, BezierCurveT<Vertex>& ocurve) {
     ocurve = icurve;
   }

   template<typename Vertex>
    __forceinline void convert(const BSplineCurveT<Vertex>& icurve, BSplineCurveT<Vertex>& ocurve) {
     ocurve = icurve;
   }

  template<typename Vertex>
    __forceinline void convert(const BezierCurveT<Vertex>& icurve, BSplineCurveT<Vertex>& ocurve)
  {
    const Vertex v0 = madd(6.0f,icurve.v0,madd(-7.0f,icurve.v1,2.0f*icurve.v2));
    const Vertex v1 = msub(2.0f,icurve.v1,icurve.v2);
    const Vertex v2 = msub(2.0f,icurve.v2,icurve.v1);
    const Vertex v3 = madd(2.0f,icurve.v1,madd(-7.0f,icurve.v2,6.0f*icurve.v3));
    ocurve = BSplineCurveT<Vertex>(v0,v1,v2,v3);
  }

  template<typename Vertex>
    __forceinline void convert(const BSplineCurveT<Vertex>& icurve, BezierCurveT<Vertex>& ocurve)
  {
    const Vertex v0 = madd(1.0f/6.0f,icurve.v0,madd(2.0f/3.0f,icurve.v1,1.0f/6.0f*icurve.v2));
    const Vertex v1 = madd(2.0f/3.0f,icurve.v1,1.0f/3.0f*icurve.v2);
    const Vertex v2 = madd(1.0f/3.0f,icurve.v1,2.0f/3.0f*icurve.v2);
    const Vertex v3 = madd(1.0f/6.0f,icurve.v1,madd(2.0f/3.0f,icurve.v2,1.0f/6.0f*icurve.v3));
    ocurve = BezierCurveT<Vertex>(v0,v1,v2,v3);
  }

  struct BSplineCurve3fa : public BSplineCurveT<Vec3fa>
  {
    //using BSplineCurveT<Vec3fa>::BSplineCurveT; // FIXME: not supported by VS2010
    
    __forceinline BSplineCurve3fa() {}

    __forceinline BSplineCurve3fa(const Vec3fa& v0, const Vec3fa& v1, const Vec3fa& v2, const Vec3fa& v3)
      : BSplineCurveT<Vec3fa>(v0,v1,v2,v3) {}
    
    __forceinline Vec4vfx eval_(const vfloatx& t) const 
    {
      const Vec4vfx b = BSplineBasis2::eval(t);
      return madd(b.x, Vec4vfx(v0), madd(b.y, Vec4vfx(v1), madd(b.z, Vec4vfx(v2), b.w * Vec4vfx(v3))));
    }

    __forceinline Vec4vfx derivative(const vfloatx& t) const 
    {
      const Vec4vfx b = BSplineBasis2::derivative(t);
      return madd(b.x, Vec4vfx(v0), madd(b.y, Vec4vfx(v1), madd(b.z, Vec4vfx(v2), b.w * Vec4vfx(v3))));
    }

    __forceinline void evalN(const vfloatx& t, Vec4vfx& p, Vec4vfx& dp) const
    {
      p = eval_(t);
      dp = derivative(t);
    }

#if 0
    
    template<int M>
      __forceinline Vec4<vfloat<M>> eval0(const int ofs, const int size) const
    {
      const Vec4<vfloat<M>> b = bspline_basis0.eval<vfloat<M>>(ofs,size);
      return madd(b.x, Vec4<vfloat<M>>(v0), madd(b.y, Vec4<vfloat<M>>(v1), madd(b.z, Vec4<vfloat<M>>(v2), b.w * Vec4<vfloat<M>>(v3))));
    }
    
    template<int M>
      __forceinline Vec4<vfloat<M>> eval1(const int ofs, const int size) const
    {
      const Vec4<vfloat<M>> b = bspline_basis1.eval<vfloat<M>>(ofs,size);
      return madd(b.x, Vec4<vfloat<M>>(v0), madd(b.y, Vec4<vfloat<M>>(v1), madd(b.z, Vec4<vfloat<M>>(v2), b.w * Vec4<vfloat<M>>(v3))));
    }

    template<int M>
      __forceinline Vec4<vfloat<M>> derivative0(const int ofs, const int size) const
    {
      const Vec4<vfloat<M>> b = bspline_basis0.derivative<vfloat<M>>(ofs,size);
      return madd(b.x, Vec4<vfloat<M>>(v0), madd(b.y, Vec4<vfloat<M>>(v1), madd(b.z, Vec4<vfloat<M>>(v2), b.w * Vec4<vfloat<M>>(v3))));
    }

    template<int M>
      __forceinline Vec4<vfloat<M>> derivative1(const int ofs, const int size) const
    {
      const Vec4<vfloat<M>> b = bspline_basis1.derivative<vfloat<M>>(ofs,size);
      return madd(b.x, Vec4<vfloat<M>>(v0), madd(b.y, Vec4<vfloat<M>>(v1), madd(b.z, Vec4<vfloat<M>>(v2), b.w * Vec4<vfloat<M>>(v3))));
    }

#else

    template<int M>
      __forceinline Vec4<vfloat<M>> eval0(const int ofs, const int size) const
    {
      assert(size <= PrecomputedBSplineBasis::N);
      assert(ofs <= size);
      return madd(vfloat<M>::loadu(&bspline_basis0.c0[size][ofs]), Vec4<vfloat<M>>(v0),
                  madd(vfloat<M>::loadu(&bspline_basis0.c1[size][ofs]), Vec4<vfloat<M>>(v1),
                       madd(vfloat<M>::loadu(&bspline_basis0.c2[size][ofs]), Vec4<vfloat<M>>(v2),
                            vfloat<M>::loadu(&bspline_basis0.c3[size][ofs]) * Vec4<vfloat<M>>(v3))));
    }
    
    template<int M>
      __forceinline Vec4<vfloat<M>> eval1(const int ofs, const int size) const
    {
      assert(size <= PrecomputedBSplineBasis::N);
      assert(ofs <= size);
      return madd(vfloat<M>::loadu(&bspline_basis1.c0[size][ofs]), Vec4<vfloat<M>>(v0), 
                  madd(vfloat<M>::loadu(&bspline_basis1.c1[size][ofs]), Vec4<vfloat<M>>(v1),
                       madd(vfloat<M>::loadu(&bspline_basis1.c2[size][ofs]), Vec4<vfloat<M>>(v2),
                            vfloat<M>::loadu(&bspline_basis1.c3[size][ofs]) * Vec4<vfloat<M>>(v3))));
    }

    template<int M>
      __forceinline Vec4<vfloat<M>> derivative0(const int ofs, const int size) const
    {
      assert(size <= PrecomputedBSplineBasis::N);
      assert(ofs <= size);
      return madd(vfloat<M>::loadu(&bspline_basis0.d0[size][ofs]), Vec4<vfloat<M>>(v0),
                  madd(vfloat<M>::loadu(&bspline_basis0.d1[size][ofs]), Vec4<vfloat<M>>(v1),
                       madd(vfloat<M>::loadu(&bspline_basis0.d2[size][ofs]), Vec4<vfloat<M>>(v2),
                            vfloat<M>::loadu(&bspline_basis0.d3[size][ofs]) * Vec4<vfloat<M>>(v3))));
    }

    template<int M>
      __forceinline Vec4<vfloat<M>> derivative1(const int ofs, const int size) const
    {
      assert(size <= PrecomputedBSplineBasis::N);
      assert(ofs <= size);
      return madd(vfloat<M>::loadu(&bspline_basis1.d0[size][ofs]), Vec4<vfloat<M>>(v0),
                  madd(vfloat<M>::loadu(&bspline_basis1.d1[size][ofs]), Vec4<vfloat<M>>(v1),
                       madd(vfloat<M>::loadu(&bspline_basis1.d2[size][ofs]), Vec4<vfloat<M>>(v2),
                            vfloat<M>::loadu(&bspline_basis1.d3[size][ofs]) * Vec4<vfloat<M>>(v3))));
    }

#endif

    /* calculates bounds of bspline curve geometry */
    __forceinline BBox3fa accurateBounds() const
    {
      const int N = 7;
      const float scale = 1.0f/(3.0f*(N-1));
      Vec4vfx pl(pos_inf), pu(neg_inf);
      for (int i=0; i<=N; i+=VSIZEX)
      {
        vintx vi = vintx(i)+vintx(step);
        vboolx valid = vi <= vintx(N);
        const Vec4vfx p  = eval0<VSIZEX>(i,N);
        const Vec4vfx dp = derivative0<VSIZEX>(i,N);
        const Vec4vfx pm = p-Vec4vfx(scale)*select(vi!=vintx(0),dp,Vec4vfx(zero));
        const Vec4vfx pp = p+Vec4vfx(scale)*select(vi!=vintx(N),dp,Vec4vfx(zero));
        pl = select(valid,min(pl,p,pm,pp),pl); // FIXME: use masked min
        pu = select(valid,max(pu,p,pm,pp),pu); // FIXME: use masked min
      }
      const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
      const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
      const Vec3fa upper_r = Vec3fa(reduce_max(max(abs(pl.w),abs(pu.w))));
      return enlarge(BBox3fa(lower,upper),upper_r);
    }

    /* calculates bounds when tessellated into N line segments */
    __forceinline BBox3fa tessellatedBounds(int N) const
    {
      if (likely(N == 4))
      {
        const Vec4vf4 pi = eval0<4>(0,4);
        const Vec3fa lower(reduce_min(pi.x),reduce_min(pi.y),reduce_min(pi.z));
        const Vec3fa upper(reduce_max(pi.x),reduce_max(pi.y),reduce_max(pi.z));
        const Vec3fa upper_r = Vec3fa(reduce_max(abs(pi.w)));
        const Vec3fa pe = end();
        return enlarge(BBox3fa(min(lower,pe),max(upper,pe)),max(upper_r,Vec3fa(abs(pe.w))));
      } 
      else
      {
        Vec3vfx pl(pos_inf), pu(neg_inf); vfloatx ru(0.0f);
        for (int i=0; i<=N; i+=VSIZEX)
        {
          vboolx valid = vintx(i)+vintx(step) <= vintx(N);
          const Vec4vfx pi = eval0<VSIZEX>(i,N);
          
          pl.x = select(valid,min(pl.x,pi.x),pl.x); // FIXME: use masked min
          pl.y = select(valid,min(pl.y,pi.y),pl.y); 
          pl.z = select(valid,min(pl.z,pi.z),pl.z); 
          
          pu.x = select(valid,max(pu.x,pi.x),pu.x); // FIXME: use masked min
          pu.y = select(valid,max(pu.y,pi.y),pu.y); 
          pu.z = select(valid,max(pu.z,pi.z),pu.z); 

          ru = select(valid,max(ru,abs(pi.w)),ru); 
        }
        const Vec3fa lower(reduce_min(pl.x),reduce_min(pl.y),reduce_min(pl.z));
        const Vec3fa upper(reduce_max(pu.x),reduce_max(pu.y),reduce_max(pu.z));
        const Vec3fa upper_r(reduce_max(ru));
        return enlarge(BBox3fa(lower,upper),upper_r);
      }
    }
  };
  
#if defined(EMBREE_NATIVE_CURVE_BSPLINE)
  #define CurveT BSplineCurveT
  typedef BSplineCurve3fa Curve3fa;
#endif
}