ACM Transactions on Graphics· 2013Q1
Geodesics in heat
- 408citations
- Q1SCImago
- 2013year
Short summary
The "heat method" computes geodesic distances to subsets of domains 10x faster than prior methods, using standard linear solvers.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces the "heat method" for computing geodesic distances to domain subsets.
- Method is robust, efficient, and simple, based on solving two linear elliptic problems.
- Prefactored systems allow updates in near-linear time, 10x faster than state-of-the-art.
- Maintains comparable accuracy to existing methods.
- Applicable to grids, triangle meshes, point clouds, and other domains using standard differential operators.
AI-generated from the title and abstract; the full text is not read.
Abstract
We introduce the heat method for computing the geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting systems can be prefactored once and subsequently solved in near-linear time. In practice, distance is updated an order of magnitude faster than with state-of-the-art methods, while maintaining a comparable level of accuracy. The method requires only standard differential operators and can hence be applied on a wide variety of domains (grids, triangle meshes, point clouds, etc.). We provide numerical evidence that the method converges to the exact distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where greater regularity is required.
The authors' abstract, as published at the source. ACM Transactions on Graphics, 2013 · DOI ↗
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Field: Computer Graphics and Computer-Aided Design
Computer Graphics and Computer-Aided DesignComputer Science