Closed-form solutions for lowpass filtering of 3D digital geometry

Closed-form solutions for lowpass filtering of 3D digital geometry are presented. Conventional signal processing is difficult to apply since 3D digital geometry does not usually satisfy the prerequisites of regular sampling and global parameterisation. Representing digital geometry as a level set of a 3D scalar field fitted with Gaussians and polynomials, derived are closed-form solutions of convolution with Gaussian smoothing kernels and lowpass filtering without the pitfalls of other approaches are analytically achieved.