Stripe Patterns on Surfaces

Abstract

Stripe patterns are ubiquitous in nature, describing macroscopic phenomena such as stripes on plants and animals, down to material impurities on the atomic scale. We propose a method for synthesizing stripe patterns on triangulated surfaces, where singularities are automatically inserted in order to achieve user-specified orientation and line spacing. Patterns are characterized as global minimizers of a convex-quadratic energy which is well-defined in the smooth setting. Computation amounts to finding the principal eigenvector of a symmetric positive-definite matrix with the same sparsity as the standard graph Laplacian. The resulting patterns are globally continuous, and can be applied to a variety of tasks in design and texture synthesis.