postPerspective

Meshes & Fields

Thursday, 28 July, 10:45 am - 12:15 pm, Anaheim Convention Center, Ballroom C
Session Chair: Etienne Vouga, University of Texas

Discrete Connection and Covariant Derivative for Vector-Field Analysis and Design

This paper introduces a discrete definition of connection on simplicial manifolds, from which a covariant derivative is directly constructed. The resulting explicit expressions of basis functions and local derivatives of vertex-based vector fields are leveraged for various applications.

Beibei Liu
California Institute of Technology

Fernando de Goes
PIxar Animation Studios

Yiying Tong
Michigan State University

Mathieu Desbrun
California Institute of Technology

Subdivision Exterior Calculus for Geometry Processing

A numerical framework to compute discrete differential operators tailored to subdivision surfaces. By leveraging the refinability of subdivision basis functions, the approach offers significant improvements in accuracy compared to polygonal methods, while retaining core properties of the smooth theory.

Fernando de Goes
Pixar Animation Studios

Mathieu Desbrun
California Institute of Technology

Mark Meyer
Pixar Animation Studios

Tony DeRose
Pixar Animation Studios

Accelerated Quadratic Proxy for Geometric Optimization

This paper proposes a first-order algorithm for optimization of problems defined over triangular and tetrahedral meshes. The algorithm combines acceleration with a local quadratic approximation of the energy to be minimized, resulting in a substantial improvement in both effectiveness and computational efficiency.

Shahar Kovalsky
Weizmann Institute of Science

Meirav Galun
Weizmann Institute of Science

Yaron Lipman
Weizmann Institute of Science

G1 Non-Uniform Catmull-Clark Surfaces

This paper develops refinement rules for non-uniform Catmull-Clark surfaces. The method consists of designing an “eigen polyhedron” in R2 for each extraordinary point and formulating refinement rules for which refinement of the eigen polyhedron reduces to a scale and translation. These refinement rules yield G1 extraordinary points.

Xin Li
University of Science and Technology of China

G. Thomas Finnigan
Autodesk, Inc.

Thomas Sederberg
Brigham Young University