## Abstract

Parameterization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity are not too distorted and do not overlap. Satisfying the non-overlapping requirement is the most difficult and critical component of this process. We describe a generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem, prove its correctness by establishing a connection to spectral graph theory and show how to compute these parameterizations.

Original language | English (US) |
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Pages (from-to) | 358-363 |

Number of pages | 6 |

Journal | ACM Transactions on Graphics |

Volume | 22 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 2003 |

Externally published | Yes |

Event | ACM SIGGRAPH 2003 - San Diego, CA, United States Duration: Jul 27 2003 → Jul 31 2003 |

## All Science Journal Classification (ASJC) codes

- Computer Graphics and Computer-Aided Design

## Keywords

- Embedding
- Parameterization
- Triangle mesh