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C ube C over – Parameterization of 3D Volumes
Author(s) -
Nieser M.,
Reitebuch U.,
Polthier K.
Publication year - 2011
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.1467-8659.2011.02014.x
Subject(s) - hexahedron , tetrahedron , boundary (topology) , tessellation (computer graphics) , volume (thermodynamics) , field (mathematics) , frame (networking) , computer science , geometry , surface (topology) , compressibility , topology (electrical circuits) , computational science , computer graphics (images) , mathematics , combinatorics , finite element method , physics , mathematical analysis , engineering , structural engineering , pure mathematics , mechanics , telecommunications , quantum mechanics
Despite the success of quad‐based 2D surface parameterization methods, effective parameterization algorithms for 3D volumes with cubes, i.e. hexahedral elements, are still missing. C ube C over is a first approach for generating a hexahedral tessellation of a given volume with boundary aligned cubes which are guided by a frame field. The input of C ube C over is a tetrahedral volume mesh. First, a frame field is designed with manual input from the designer. It guides the interior and boundary layout of the parameterization. Then, the parameterization and the hexahedral mesh are computed so as to align with the given frame field. C ube C over has similarities to the Q uad C over algorithm and extends it from 2D surfaces to 3D volumes. The paper also provides theoretical results for 3D hexahedral parameterizations and analyses topological properties of the appropriate function space.