Manifold parameterization: mapping the connectivity of a mesh (a) onto another mesh (b) directly to obtain a newmesh (c) that has the connectivity of (a) and geometry of (b). The new mesh (c) looks the same with mesh (b) in shape but has the same connectivity with mesh (a). (d) is the smooth shading of (c).
Abstract
Manifold parameterization
considers the problem of parameterizing a given triangular mesh onto
another mesh surface, which could be particularly plane or sphere
surfaces. In this paper we propose a unified framework for manifold
parameterization between arbitrary meshes with identical genus. Our
approach does this task by directly mapping the connectivity of the
source mesh onto the target mesh surface without any intermediate domain
and partition of the meshes. The connectivity graph of source mesh is
used to approximate the geometry of target mesh using least squares
meshes. A subset of user specified vertices are constrained to have the
geometry information of the target mesh. The geometry of the mesh
vertices is reconstructed while approximating the known geometry of the
subset by positioning each vertex approximately at the center of its
immediate neighbors. This leads to a sparse linear system which can be
effectively solved. Our approach is simple and fast with less user
interactions. Many experimental results and applications are presented
to show the applicability and flexibility of the approach.
This work is highly
inspired by the least-squares meshes and is an extension:
* O. Sorkine and D. Cohen-Or. Least-squares meshes. In Proceedings of
Shape Modeling International, pages 191–199, 2004. [Project
page]
The textured tiger model
used in Fig. 11 is courtesy of Dr. Kun Zhou from Microsoft Research
Asia. This work is supported by the National Natural Science Foundation
of China (No. 60503067, 60333010), Zhejiang Provincial Natural Science
Foundation of China (No. Y105159) and the National Grand Fundamental
Research 973 Program of China (No. 2002CB312101).
title = {Manifold Parameterization},
author = {Lei Zhang and Ligang Liu and Zhongping Ji and Guojin Wang}
journal = {Lecture Notes in Computer Science (Proceedings of CGI)},
volume = {4035},
pages = {160-171},
year = {2006}
}