DDG: Trivial Connections on Discrete Surfaces, Video

Video Description: Real time editing of a surface vector field using discrete connections.
This video demonstrates a new algorithm for editing direction fields on discrete surfaces that are as smooth as possible everywhere but on a set of isolated singularities of given index. Direction fields are represented via a "discrete connection," i.e., an angle associated with each (dual) edge. These angles are determined by the solution to a linear system, and are globally optimal in the sense that they describe the trivial connection closest to Levi-Civita among all solutions with a prescribed set of singularities. Relative to previous methods our algorithm is highly efficient and surprisingly simple, and can be implemented using standard operations from mesh processing and linear algebra. The solution can be used to construct rotationally symmetric direction fields with a prescribed set of singularities and directional constraints, which are essential in applications such as quadrilateral remeshing, texture synthesis, and "fur" design.

This video is supplementary material from the paper "Trivial Connections on Discrete Surfaces" by Keenan Crane, Mathieu Desbrun, and Peter Schröder, Symposium on Geometry Processing SPG 2010. Source: California Institute of Technology, Keenan Crane.