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ESTIMATING CURVATURE ON TRIANGULAR MESHES

Dept. of Computer Science and Engineering, Washington University in St. Louis, One Brookings Drive, St. Louis, MO 63130, USA

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CINDY M. GRIMM

Dept. of Computer Science and Engineering, Washington University in St. Louis, One Brookings Drive, St. Louis, MO 63130, USA

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https://doi.org/10.1142/S0218654306000810Cited by:100 (Source: Crossref)

Abstract

This paper takes a systematic look at methods for estimating the curvature of surfaces represented by triangular meshes. We have developed a suite of test cases for assessing both the detailed behavior of these methods, and the error statistics that occur for samples from a general mesh. Detailed behavior is represented by the sensitivity of curvature calculation methods to noise, mesh resolution, and mesh regularity factors. Statistical analysis breaks out the effects of valence, triangle shape, and curvature sign. These tests are applied to existing discrete curvature approximation techniques and common surface fitting methods. We provide a summary of existing curvature estimation methods, and also look at alternatives to the standard parameterization techniques. The results illustrate the impact of noise and mesh related issues on the accuracy of these methods and provide guidance in choosing an appropriate method for applications requiring curvature estimates.

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AMSC: 22E46, 53C35, 57S20

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ESTIMATING CURVATURE ON TRIANGULAR MESHES

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