Harmonic Functions for Quadrilateral Remeshing of Arbitrary Manifolds

Dong, Shen; Kircher, Scott I.; Garland, Michael

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https://hdl.handle.net/2142/10896 Copy

Description

Title

Harmonic Functions for Quadrilateral Remeshing of Arbitrary Manifolds

Author(s)

• Dong, Shen
• Kircher, Scott I.
• Garland, Michael

Issue Date

2004-08

Keyword(s)

Computer Graphics

Abstract

In this paper, we propose a new quadrilateral remeshing method for manifolds of arbitrary genus that is at once general, flexible, and efficient. Our technique is based on the use of smooth harmonic scalar fields defined over the mesh. Given such a field, we compute its gradient field and a second vector field that is everywhere orthogonal to the gradient. We then trace integral lines through these vector fields to sample the mesh. The two nets of integral lines together are used to form the polygons of the output mesh. Curvature-sensitive spacing of the lines provides for anisotropic meshes that adapt to the local shape. Our scalar field construction allows users to exercise extensive control over the structure of the final mesh. The entire process is performed without computing a parameterization of the surface, and is thus applicable to manifolds of any genus without the need for cutting the surface into patches.

Type of Resource

text

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http://hdl.handle.net/2142/10896

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