Spin Transformations of Discrete Surfaces - Conference Presentation
Channel: Keenan Crane
Date: 2011-08-13

This video is a conference presentation of the paper, "Spin Transformations of Discrete Surfaces" given by Keenan Crane in August 2011 -- see http://keenan.is/spin for more information.

Spin Transformations of Discrete Surfaces
Keenan Crane, Ulrich Pinkall, Peter Schröder
SIGGRAPH 2011

Abstract: We introduce a new method for computing conformal transformations of triangle meshes in R3. Conformal maps are desirable in digital geometry processing because they do not exhibit shear, and therefore preserve texture fidelity as well as the quality of the mesh itself. Traditional discretizations consider maps into the complex plane, which are useful only for problems such as surface parameterization and planar shape deformation where the target surface is flat. We instead consider maps into the quaternions, which allows us to work directly with surfaces sitting in R3. In particular, we introduce a quaternionic Dirac operator and use it to develop a novel integrability condition on conformal deformations. Our discretization of this condition results in a sparse linear system that is simple to build and can be used to efficiently edit surfaces by manipulating curvature and boundary data, as demonstrated via several mesh processing applications.