Quadrangulating a Mesh using Laplacian Eigenvectors

Dong, Shen; Bremer, Peer-Timo; Garland, Michael; Pascucci, Valerio; Hart, John C.

Permalink

https://hdl.handle.net/2142/11036 Copy

Description

Title

Quadrangulating a Mesh using Laplacian Eigenvectors

Author(s)

• Dong, Shen
• Bremer, Peer-Timo
• Garland, Michael
• Pascucci, Valerio
• Hart, John C.

Issue Date

2005-06

Keyword(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.

Type of Resource

text

Permalink

http://hdl.handle.net/2142/11036

Copyright and License 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).

Owning Collections