text: // David Eberly, Geometric Tools, Redmond WA 98052
  // Copyright (c) 1998-2021
  // Distributed under the Boost Software License, Version 1.0.
  // https://www.boost.org/LICENSE_1_0.txt
  // https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
  // Version: 4.0.2020.01.11
  
  #pragma once
  
  #include <Mathematics/PdeFilter2.h>
  
  namespace gte
  {
      template <typename Real>
      class CurvatureFlow2 : public PdeFilter2<Real>
      {
      public:
          CurvatureFlow2(int xBound, int yBound, Real xSpacing,
              Real ySpacing, Real const* data, bool const* mask,
              Real borderValue, typename PdeFilter<Real>::ScaleType scaleType)
              :
              PdeFilter2<Real>(xBound, yBound, xSpacing, ySpacing, data, mask,
                  borderValue, scaleType)
          {
          }
  
          virtual ~CurvatureFlow2()
          {
          }
  
      protected:
          virtual void OnUpdateSingle(int x, int y) override
          {
              this->LookUp9(x, y);
  
              Real ux = this->mHalfInvDx * (this->mUpz - this->mUmz);
              Real uy = this->mHalfInvDy * (this->mUzp - this->mUzm);
              Real uxx = this->mInvDxDx * (this->mUpz - (Real)2 * this->mUzz + this->mUmz);
              Real uxy = this->mFourthInvDxDy * (this->mUmm + this->mUpp - this->mUmp - this->mUpm);
              Real uyy = this->mInvDyDy * (this->mUzp - (Real)2 * this->mUzz + this->mUzm);
  
              Real sqrUx = ux * ux;
              Real sqrUy = uy * uy;
              Real denom = sqrUx + sqrUy;
              if (denom > (Real)0)
              {
                  Real numer = uxx * sqrUy + uyy * sqrUx - (Real)0.5 * uxy * ux * uy;
                  this->mBuffer[this->mDst][y][x] = this->mUzz + this->mTimeStep * numer / denom;
              }
              else
              {
                  this->mBuffer[this->mDst][y][x] = this->mUzz;
              }
          }
      };
  }
  