skshapes.morphing.intrinsic_deformation.shell_energy_metric

skshapes.morphing.intrinsic_deformation.shell_energy_metric(points_sequence, velocities_sequence, edges=None, triangles=None, bending_weight=0.001)

Shell energy metric.

This metric is the sum of a membrane contribution, measuring the local stretching and a bending contribution, measuring the change in curvature. The parameter weight controls the importance of the bending energy.

Parameters:

  • points_sequence (Float32[Tensor, '_ _ _']) – Sequence of points

  • velocities_sequence (Float32[Tensor, '_ _ _']) – Sequence of velocities.

  • edges (Int64[Tensor, '_ 2'] | None) – Edges.

  • triangles (Int64[Tensor, '_ 3'] | None) – Triangles.

  • bending_weight (int | float) – The weight of the bending energy.

Raises:

AttributeError – This metric requires triangles to be defined:

Return type:

Float32[Tensor, '']

Returns:

FloatScalar: the mean velocities metric

References

[HEEREN, Behrend, RUMPF, Martin, SCHRÖDER, Peter, et al. Exploring the geometry of the space of shells. In : Computer Graphics Forum. 2014. p. 247-256.](https://ddg.math.uni-goettingen.de/pub/HeRuSc14.pdf)