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- Publications
- Influence

Discrete exterior calculus

- Mathieu Desbrun, A. Hirani, M. Leok, J. Marsden
- Mathematics
- 18 August 2005

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 complex… Expand

Discrete shells

- E. Grinspun, A. Hirani, Mathieu Desbrun, P. Schröder
- Computer Science, Physics
- SCA '03
- 26 July 2003

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 undeformed… Expand

Discrete multiscale vector field decomposition

- Y. Tong, S. Lombeyda, A. Hirani, Mathieu Desbrun
- Computer Science
- SIGGRAPH '03
- 1 July 2003

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-difference… Expand

Barycentric coordinates for convex sets

- J. Warren, Scott Schaefer, A. Hirani, Mathieu Desbrun
- Computer Science, Mathematics
- Adv. Comput. Math.
- 20 August 2007

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 various… Expand

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 equations… Expand

Discrete exterior calculus for variational problems in computer vision and graphics

- Mathieu Desbrun, A. Hirani, J. Marsden
- Computer Science
- 42nd IEEE International Conference on Decision…
- 1 December 2003

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 includes… Expand

Well-Centered Triangulation

- Evan VanderZee, A. Hirani, Damrong Guoy, E. Ramos
- Computer Science, Mathematics
- SIAM J. Sci. Comput.
- 14 February 2008

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. We… Expand

Combining frequency and spatial domain information for fast interactive image noise removal

- A. Hirani, T. Totsuka
- Computer Science
- SIGGRAPH '96
- 1 August 1996

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 production… Expand

Least Squares Ranking on Graphs

- A. Hirani, Kaushik Kalyanaraman, S. Watts
- Computer Science, Mathematics
- 8 November 2010

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 the… Expand

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 both… Expand