simkit.biharmonic_coordinates#

Biharmonic interpolation weights for handle-based deformation.

Functions#

biharmonic_coordinates(→ numpy.ndarray)

Biharmonic coordinates that interpolate values from handle vertices.

Module Contents#

simkit.biharmonic_coordinates.biharmonic_coordinates(X: numpy.ndarray, T: numpy.ndarray, bI: numpy.ndarray) → numpy.ndarray#

Biharmonic coordinates that interpolate values from handle vertices.

Minimizes the discrete biharmonic energy x^T (L^T M^{-1} L) x subject to each handle vertex being held at its indicator value, giving one smooth weight field per handle. The fields sum to one (partition of unity) and reproduce the handle values exactly.

Parameters:

  • X (np.ndarray (n, d)) – Vertex positions.

  • T (np.ndarray (t, s)) – Simplex connectivity.

  • bI (np.ndarray (b,)) – Handle (boundary) vertex indices. Duplicates are ignored.

Returns:

W – Biharmonic weights; column k is the field for the k-th unique handle.

Return type:

np.ndarray (n, b_unique)