Linear Rotation-invariant Coordinates for Meshes

Yaron Lipman Olga Sorkine David Levin Daniel Cohen-Or

Abstract:

We introduce a rigid motion invariant mesh representation based on discrete forms defined on the mesh. The reconstruction of mesh geometry from this representation requires solving two linear systems that arise from the discrete

forms: the first system defines the relationship between local frames on the mesh, and the second encodes the position of the vertices via the local frames. The reconstructed geometry is unique up to a rigid transformation of the mesh.

We define surface editing operations by placing user-defined constraints on the local frames and the vertex positions. These constraints are incorporated in the two linear reconstruction systems, and their solution produces a deformed surface geometry that preserves the local differential properties in the least-squares sense. Linear combination of shapes that are expressed with our representation enables linear shape interpolation that correctly

handles rotations. We demonstrate the effectiveness of the new representation with various detail-preserving editing operators and shape morphing.

BibTeX entry:

@inproceedings{lipman2005,
author = {Yaron Lipman and Olga Sorkine and David Levin and Daniel Cohen-Or},
title = {Linear Rotation-invariant Coordinates for Meshes},
 booktitle = {Proceedings of ACM SIGGRAPH 2005},
year = {2005},
 pages = {479--487},
 location = {Los Angeles, California, USA},
 publisher = {ACM Press}
}

Video (some shape interpolation examples):
QuickTime,  34.4MB

Paper:
Acrobat PDF, 7.7MB

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