Mesh Simplification Method Using Principal Curvatures and Directions

This paper describes an enhancement to Garland and Heckbert's mesh simplification method by using the principal curvatures and directions of each vertex. We calculate the values and directions, before using them to determine the absolute normal curvature in the direction of contraction, and mul...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences 2011, Vol.77 (3-4), p.201-219
Main Authors: Ungvichian, V, Kanongchaiyos, P
Format: Article
Language:English
Subjects:
Algorithms
Counting
Curvature
Distortion
Finite element method
Mathematical analysis
Mathematical models
Simplification
Online Access:Get full text
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Summary:This paper describes an enhancement to Garland and Heckbert's mesh simplification method by using the principal curvatures and directions of each vertex. We calculate the values and directions, before using them to determine the absolute normal curvature in the direction of contraction, and multiplying the curvature with the edge length, the maximum absolute cosine of the angles between the edge and the normals of faces adjacent to either endpoint, and the quadric error of the collapse. We also apply penalties based on compactness and angular and dihedral deviations of the resulting faces. We have implemented these improvements and tested our algorithm on a sample of models from Purdue's Engineering Shape Benchmark. We observe that, while our algorithm tends to produce competitive Hausdorff distances than QEM up to 20% face count, and reduces models to between 20% and 50% of the original face count before significant distortion occurs (at a Hausdorff distance of approximately .05 of the bounding box diagonal), QEM still performs better at more drastic levels of simplification, especially on meshes with already low face count. Future research includes, among others, improving the factors to be more robust towards changes in the model during the simplification process.
ISSN:1526-1492