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Two Simple Methods for Improving a Triangle Mesh Surface
Author(s) -
Renka Robert J.
Publication year - 2016
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12731
Subject(s) - triangle mesh , vertex (graph theory) , curvature , surface (topology) , simple (philosophy) , tangent , mathematics , tangent space , geometry , plane (geometry) , quadratic equation , algorithm , computer science , combinatorics , polygon mesh , graph , philosophy , epistemology
We present two simple and efficient local methods that reposition vertices of a triangle mesh surface with the goal of producing good triangle shapes while preserving the enclosed volume and sharp features. The methods involve minimizing a quadratic energy functional with respect to variations in a tangent plane (or in the direction of a crease) at each free vertex. One of the methods is aimed at producing uniform angles, while the other method is designed to produce uniform triangle areas, or more generally, to force relative triangle areas to conform to curvature estimates or estimates of local feature size so that vertex density is low in flat spots and relatively high in regions of large curvature. Test results demonstrate the effectiveness of both methods, especially when combined.