Convolution Surfaces for Line Skeletons with Polynomial Weight Distributions

Abstract

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