Technical Papers

Surfaces & Differential Geometry

Tuesday, 23 July 9:00 AM - 10:30 AM
Session Chair: Alyn Rockwood, InterNext Graphics Institute

Globally Optimal Direction Fields

A method for constructing smooth-unit n-direction fields (line fields, cross fields, etc.) on surfaces that is an order of magnitude faster than existing methods, while producing fields of equal or greater quality. Singularity placement is automatic, and fields can be aligned with a given guidance field such as curvature directions.

Felix Knöppel
Technische Universität Berlin

Keenan Crane
California Institute of Technology

Ulrich Pinkall
Technische Universität Berlin

Peter Schröder
California Institute of Technology

Geodesics in Heat: A New Approach to Computing Distance Based on Heat Flow

This paper introduces the heat method for computing the distance to a specified subset (for example, point or curve). The method is simple to implement, can be applied on grids, triangle meshes, point clouds, etc., and updates distance an order of magnitude faster than state-of-the-art methods.

Keenan Crane
California Institute of Technology

Clarisse Weischedel
University of Göttingen

Max Wardetzky
University of Göttingen

Weighted Averages on Surfaces

This paper considers the problem of generalizing affine combinations in Euclidean spaces to triangle meshes. It addresses both the forward problem (computing an average of given anchor points on the mesh with given weights) and the inverse problem (computing the weights given anchor points and a target point).

Daniele Panozzo
ETH Zürich

Ilya Baran
Belmont Technology Incorporated, Adobe Research, Disney Research Zürich

Olga Diamanti
ETH Zürich

Olga Sorkine-Hornung
ETH Zürich

Robust Fairing Via Conformal Curvature Flow

A new algorithm for surface fairing that permits extraordinarily large time steps and naturally preserves the quality of the input mesh, as well as associated textures. The main insight: curvature flow becomes remarkably stable when expressed in curvature space. The paper develops precise conditions under which curvature can evolve.

Keenan Crane
California Institute of Technology

Ulrich Pinkall
Technische Universität Berlin

Peter Schröder
California Institute of Technology