Function mixedSecondOrderDerivativeAt

grid_map_core/src/CubicInterpolation.cpp:376–403

}

double mixedSecondOrderDerivativeAt(const Matrix &layerData, const Index &index, double resolution)
{
  /*
   * no need for dimensions since the we have to differentiate w.r.t. x and y
   * the order doesn't matter. Derivative values are the same.
   * Taken from https://www.mathematik.uni-dortmund.de/~kuzmin/cfdintro/lecture4.pdf
   */

  const int numCol = layerData.cols();
  const int numRow = layerData.rows();

  const double f11 = layerData(bindIndexToRange(index.x() - 1, numRow),
                               bindIndexToRange(index.y() - 1, numCol));
  const double f1m1 = layerData(bindIndexToRange(index.x() - 1, numRow),
                                bindIndexToRange(index.y() + 1, numCol));
  const double fm11 = layerData(bindIndexToRange(index.x() + 1, numRow),
                                bindIndexToRange(index.y() - 1, numCol));
  const double fm1m1 = layerData(bindIndexToRange(index.x() + 1, numRow),
                                 bindIndexToRange(index.y() + 1, numCol));

  const double perturbation = resolution;
  // central difference approximation
  // we need to multiply with resolution^2 since we are
  // operating in scaled coordinates. Second derivative scales
  // with the square of the resolution
  return (f11 - f1m1 - fm11 + fm1m1) / (4.0 * perturbation * perturbation) * resolution * resolution;

}

bool getMixedSecondOrderDerivatives(const Matrix &layerData, const IndicesMatrix &indices,
                                    double resolution, DataMatrix *derivatives)