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Curvature‐Domain Shape Processing
Author(s) -
Eigensatz Michael,
Sumner Robert W.,
Pauly Mark
Publication year - 2008
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/j.1467-8659.2008.01121.x
Subject(s) - curvature , smoothing , surface (topology) , geometry processing , gaussian curvature , computer science , principal curvature , feature (linguistics) , domain (mathematical analysis) , algorithm , mean curvature , nonlinear system , geometry , computer vision , artificial intelligence , mathematics , computer graphics (images) , mathematical analysis , polygon mesh , philosophy , physics , quantum mechanics , linguistics
We propose a framework for 3D geometry processing that provides direct access to surface curvature to facilitate advanced shape editing, filtering, and synthesis algorithms. The central idea is to map a given surface to the curvature domain by evaluating its principle curvatures, apply filtering and editing operations to the curvature distribution, and reconstruct the resulting surface using an optimization approach. Our system allows the user to prescribe arbitrary principle curvature values anywhere on the surface. The optimization solves a nonlinear least‐squares problem to find the surface that best matches the desired target curvatures while preserving important properties of the original shape. We demonstrate the effectiveness of this processing metaphor with several applications, including anisotropic smoothing, feature enhancement, and multi‐scale curvature editing.