Gaussian Splat Covariance

Problem

Build the 3D covariance of a Gaussian splat.

The covariance is R * diag(scale^2) * R^T, where rot is a 3x3 rotation matrix and scale holds the per-axis standard deviations. Return the 3x3 symmetric matrix with every entry rounded to 4 decimal places.

Hint

Compute M = R * diag(scale) first, then cov = M * M^T.

Test cases

case 1

in: [[[1,0,0],[0,1,0],[0,0,1]],[1,2,3]]

expected: [[1,0,0],[0,4,0],[0,0,9]]

case 2

in: [[[1,0,0],[0,1,0],[0,0,1]],[0,0,0]]

expected: [[0,0,0],[0,0,0],[0,0,0]]

case 3

in: [[[0,-1,0],[1,0,0],[0,0,1]],[1,2,3]]

expected: [[4,0,0],[0,1,0],[0,0,9]]

case 4

in: [[[1,0,0],[0,1,0],[0,0,1]],[1,1,1]]

expected: [[1,0,0],[0,1,0],[0,0,1]]

Starter codePython

def splat_covariance(rot, scale):
    # Your code here
    pass

4 test cases · run your code against them in the editor