Conference abstracts

Session A4 - Computational Geometry and Topology

July 12, 18:00 ~ 18:25 - Room B7

Extrinsic Conformal Geometry Processing

Keenan Crane

Carnegie Mellon University, USA   -   kmcrane@cs.cmu.edu

This talk covers fundamental theory and algorithms for manipulating curved surfaces via conformal (i.e., angle-preserving) transformations. Conformal transformations are valuable in applications because they naturally preserve the integrity of geometric data. Until recently, however, there has been no theory of conformal transformations suitable for general-purpose geometry processing algorithms: previous methods for computing conformal maps have been purely intrinsic, with target domains restricted to the flat two-dimensional plane or other spaces of constant curvature. We instead consider a certain time-independent Dirac equation, which replaces the traditional Cauchy-Riemann equation for surfaces immersed in Euclidean 3-space. This equation leads to efficient numerical algorithms that enable processing of surface data via direct manipulation of extrinsic curvature. We will also discuss connections to the recent notion of discrete conformal equivalence based on length cross ratios, including recovery of shape from quantities like lengths and curvatures.

Joint work with Ulrich Pinkall (TU Berlin) and Peter Schröder (Caltech).

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