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_gradients_svd(field)

Arguments

field

A gradient field with the following attributes:

• pts: 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 in space.

• tris: A 2 x D x F array in column-major ordering containing the spatial gradient in expression for each of D latent variables at every triangle in the mesh. Average of the vertices (3 for full triangles, 2 for degenerate triangles).

• edges_pts: A 2 x D x E array in column-major ordering containing the spatial gradient in expression for each of D latent variables at every primal edge (point-to-point) in the mesh. Sum of the two endpoints.

• edges_tris: A 2 x D x E array in column-major ordering containing the spatial gradient in expression for each of D latent variables at every dual edge (triangle-to-triangle) in the mesh. Sum of the two adjacent triangles.

Value

A gradient field with the same attributes as the input, as well as compressed representations pts_svd, tris_svd, edges_pts_svd, and edges_tris_svd. Each of these is a N x 6 matrix with the following columns 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).

len_grad,len_ortho

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