Fast Editing of Singularities in Field-Aligned Stripe Patterns

Abstract

Field-aligned parametrization is a method that maps a scalar function onto a surface, such that the gradient vector of the scalar function matches the input vector field. Using this idea, one can produce a stripe pattern that is convenient for various purposes such as remeshing, texture synthesis, and computational fabrication. In the final outcome, the positions of singularities (i.e., bifurcations of the stripe pattern) are essential for functionalities, manufacturability, or aesthetics. In this paper, we propose an algorithm to allow users to interactively edit the singularity positions of field-aligned stripe patterns. The algorithm computes a stripe pattern from a prescribed set of singularities, without generating any unwanted singularities. The solution of the algorithm is formulated as the global minima of a constrained quadratic optimization, whose computation speed is dominated by solving only two sparse linear systems. Furthermore, once the two matrices in the two linear systems are factorized, any update on singularity positions operates in linear time. We showcase several applications feasible with our fast yet simple algorithm.

Nobuyuki Umetani

Associate Professor

My research interests include interactive smart engineering design tool using physics simulation and machine learning.