Method FunctionGradient

Common/DataModel/vtkImplicitFunction.cxx:176–212

Evaluate function gradient at position x-y-z and pass back vector. Point x[3] is transformed through transform (if provided).

// Evaluate function gradient at position x-y-z and pass back vector. Point
// x[3] is transformed through transform (if provided).
void vtkImplicitFunction::FunctionGradient(const double x[3], double g[3])
{
  if (!this->Transform)
  {
    this->EvaluateGradient(const_cast<double*>(x), g);
  }
  else // pass point through transform
  {
    double pt[3];
    double A[3][3];
    this->Transform->Update();
    this->Transform->InternalTransformDerivative(x, pt, A);
    this->EvaluateGradient(static_cast<double*>(pt), g);

    // The gradient must be transformed using the same math as is
    // use for a normal to a surface: it must be multiplied by the
    // inverse of the transposed inverse of the Jacobian matrix of
    // the transform, which is just the transpose of the Jacobian.
    vtkMath::Transpose3x3(A, A);
    vtkMath::Multiply3x3(A, g, g);

    /* If the determinant of the Jacobian matrix is negative,
       then the gradient points in the opposite direction.  This
       behaviour is actually incorrect, but is necessary to
       balance the incorrect behaviour of FunctionValue.  Otherwise,
       if you feed certain VTK filters a transform with a flip
       the gradient will point in the wrong direction and they
       will never converge to a result */

    if (vtkMath::Determinant3x3(A) < 0)
    {
      g[0] = -g[0];
      g[1] = -g[1];
      g[2] = -g[2];
    }
  }
}

// Overload standard modified time function. If Transform is modified,
// then this object is modified as well.