## Abstract

Parameterization of 3D mesh data is important for many graphics and mesh processing 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 3D triangle mesh onto the 3D 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 do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways.

Original language | English (US) |
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Pages (from-to) | 185-193 |

Number of pages | 9 |

Journal | Computing (Vienna/New York) |

Volume | 72 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1 2004 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics

## Keywords

- Mesh processing
- Parameterization
- Spherical embedding
- Spherical parametrization