Compress a gradient field using SVD

Expresses the 2 x D total derivative at each location as a pair of 2-dimensional vectors in the gradient and orthogonal directions.

Usage

compress_field_cpp(field)

Arguments

field

A 2 x D x N array in column-major ordering containing the spatial gradient in expression for each of D latent variables at every point, edge, or triangle.

Value

A N x 6 matrix with the following attributes for each location:

dx grad,dy grad

x,y directions of unit vector in the direction of greatest change (first singular vector).

dx ortho,dy ortho

x,y directions of unit vector orthogonal to the direction of greatest change (second singular vector).

|grad|,|ortho|

Magnitude of directional derivative in the gradient and orthogonal directions (singular values).