Convolution Surfaces for Line Skeletons with Polynomial Weight Distributions

Convolution surfaces generalize point-based implicit surfaces to incorporate higherdimensional skeletal elements, of which line segments can be considered the most fundamental since they can approximate curve skeletons. Existing analytical models for line-segment skeletons assumes uniform weight distributions and thus can only produce constant-radius convolution surfaces. This paper presents an analytical solution for convolving line-segment skeletons with a variable kernel modulated by a polynomial function, thus allowing generalized cylindrical convolution surfaces to be conveniently modeled. Its computation requirement is competitive compared with the case of uniform weight distribution. The source code of field computation is available online.