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Discrete exterior calculus
This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our approach is to develop DEC using only discrete combinatorial and geometric operations on a simplicial complexExpand
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Discrete shells
In this paper we introduce a discrete shell model describing the behavior of thin flexible structures, such as hats, leaves, and aluminum cans, which are characterized by a curved undeformedExpand
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Discrete multiscale vector field decomposition
While 2D and 3D vector fields are ubiquitous in computational sciences, their use in graphics is often limited to regular grids, where computations are easily handled through finite-differenceExpand
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Barycentric coordinates for convex sets
In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in variousExpand
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A Posteriori Error Estimates for Finite Element Exterior Calculus: The de Rham Complex
Finite element exterior calculus (FEEC) has been developed over the past decade as a framework for constructing and analyzing stable and accurate numerical methods for partial differential equationsExpand
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Discrete exterior calculus for variational problems in computer vision and graphics
The paper demonstrates how discrete exterior calculus (DEC) tools may be useful in computer vision and graphics. A variational approach provides a link with mechanics. Our development of DEC includesExpand
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Well-Centered Triangulation
Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. WeExpand
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Combining frequency and spatial domain information for fast interactive image noise removal
Scratches on old films must be removed since these are more noticeable on higher definition and digital televisions. Wires that suspend actors or cars must be carefully erased during post productionExpand
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Least Squares Ranking on Graphs
Given a set of alternatives to be ranked, and some pairwise comparison data, ranking is a least squares computation on a graph. The vertices are the alternatives, and the edge values comprise theExpand
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PyDEC: Software and Algorithms for Discretization of Exterior Calculus
This article describes the algorithms, features, and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into bothExpand
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