NDLI: Boundary aligned smooth 3D cross-frame field

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Boundary aligned smooth 3D cross-frame field

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Boundary aligned smooth 3D cross-frame field

Content Provider	ACM Digital Library
Author	Huang, Jin Bao, Hujun Tong, Yiying Wei, Hongyu
Abstract	In this paper, we present a method for constructing a 3D cross-frame field, a 3D extension of the 2D cross-frame field as applied to surfaces in applications such as quadrangulation and texture synthesis. In contrast to the surface cross-frame field (equivalent to a 4-Way Rotational-Symmetry vector field), symmetry for 3D cross-frame fields cannot be formulated by simple one-parameter 2D rotations in the tangent planes. To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2. With such a representation, we can formulate an efficient smoothness measure of the cross-frame field. Through minimization of this measure under certain boundary conditions, we can construct a smooth 3D cross-frame field that is aligned with the surface normal at the boundary. We visualize the resulting cross-frame field through restrictions to the boundary surface, streamline tracing in the volume, and singularities. We also demonstrate the application of the 3D cross-frame field to producing hexahedron-dominant meshes for given volumes, and discuss its potential in high-quality hexahedralization, much as its 2D counterpart has shown in quadrangulation.
Starting Page	1
Ending Page	8
Page Count	8
File Format	PDF
ISBN	9781450308076
DOI	10.1145/2024156.2024177
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-12-12
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	N-rosy frame field Spherical harmonics Hexahedral
Content Type	Text
Resource Type	Article

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