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Quadrangulating a Mesh using Laplacian Eigenvectors

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Title: Quadrangulating a Mesh using Laplacian Eigenvectors
Author(s): Dong, Shen; Bremer, Peer-Timo; Garland, Michael; Pascucci, Valerio; Hart, John C.
Subject(s): Computer graphics
Abstract: Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing systems. The vast majority of work in the past has focused on triangular remeshing; the equally important problem of resampling surfaces with quadrilaterals has remained largely unaddressed. Despite the relative lack of attention, the need for quality quadrangular resampling methods is of central importance in a number of important areas of graphics. Quadrilaterals are the preferred primitive in many cases, such as Catmull-Clark subdivision surfaces, fluid dynamics, and texture atlasing. We propose a fundamentally new approach to the problem of quadrangulating manifold polygon meshes. By applying a Morse-theoretic analysis to the eigenvectors of the mesh Laplacian, we have developed an algorithm that can correctly quadrangulate any manifold, no matter its genus. Because of the properties of the Laplacian operator, the resulting quadrangular patches are well-shaped and arise directly from intrinsic properties of the surface, rather than from arbitrary heuristics. We demonstrate that this quadrangulation of the surface provides a base complex that is well-suited to semi-regular remeshing of the initial surface into a fully conforming mesh composed exclusively of quadrilaterals.
Issue Date: 2005-06
Genre: Technical Report
Type: Text
URI: http://hdl.handle.net/2142/11036
Other Identifier(s): UIUCDCS-R-2005-2583
Rights Information: You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS: 2009-04-17
 

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