Template Function corners_and_weights

Function Documentation

template<class R, template<class> class T>
int corners_and_weights(const T<R> *that, const double *zero, const double *step, const size_t *ijk, const double *x, size_t *c, double *w, const size_t N, const std::vector<size_t> &dirs)

Find the linear index and weights of interpolation points for a given position.

Linear interpolation in D dimensions requires 2ᴰ points surrounding the position where an interpolated value is to be determined. The value at each of the 2ᴰ points contributes in proportion to how close it is to the interpolation point. This function finds the linear indices for any object which has a sub2map method with signature (const size_t* subscripted_index, size_t* linear_index) and determines the appropriate normalized weights for each of the 2ᴰ points.

Return

An unsigned integer with bits acting as flags to indicate whether a point required for the interpolation is out-of-bounds. The order of bits depends on dirs.size(), see the source if you need to decode this information.

Note

This function supports linear, bilinear, trilinear, and quadralinear interpolation, e.g., 1≤D≤4, in an arbitrary number of dimensions with D≤N; extending it to higher-dimensional interpolation should be possible if ever desired.

Parameters

  • that: A pointer to an object with a sub2map(const size_t*, size_t&) method: MapGrid3, MapGrid4, InterpolateGrid3, InterpolateGrid4, BrillouinZoneGrid3, BrillouinZoneGrid4, etc.

  • zero: Pointer to the zero-point values of the grid, with N elements

  • step: Pointer to the step-size values of the grid, with N elements

  • ijk: Pointer to the nearest grid subscripted index to the interpolation point, with N elements

  • x: Pointer to the coordinates of the interpolation point, with N elements

  • [out] c: Pointer where the linear indices will be stored, with 2ᴺ elements

  • [out] w: Pointer where the weights will be stored, with 2ᴺ elements

  • N: Dimensionality of the gridded space

  • dirs: Directions in the gridded space over which interpolation is to be performed; D=1≤dirs.size()≤N