Feature-Sized Sampling for Vector Line Art

Abstract

By introducing a first-of-its-kind quantifiable sampling algorithm based on feature size, we present a fresh perspective on the practical aspects of planar curve sampling. Following the footsteps of ε-sampling, which was originally proposed in the context of curve reconstruction to offer provable topological guarantees [ABE98] under quantifiable bounds, we propose an arbitrarily precise ε-sampling algorithm for sampling smooth planar curves (with a prior bound on the minimum feature size of the curve). This paper not only introduces the first such algorithm which provides user-control and quantifiable precision but also highlights the importance of such a sampling process under two key contexts: 1) To conduct a first study comparing theoretical sampling conditions with practical sampling requirements for reconstruction guarantees that can further be used for analysing the upper bounds of ε for various reconstruction algorithms with or without proofs, 2) As a feature-aware sampling of vector line art that can be used for applications such as coloring and meshing.