## Abstract

We present an object-space morphing technique that blends the interiors of given two- or three-dimensional shapes rather than their boundaries. The morph is rigid in the sense that local volumes are least-distorting as they vary from their source to target configurations. Given a boundary vertex correspondence, the source and target shapes are decomposed into isomorphic simplicial complexes. For the simplicial complexes, we find a closed-form expression allocating the paths of both boundary and interior vertices from source to target locations as a function of time. Key points are the identification of the optimal simplex morphing and the appropriate definition of an error functional whose minimization defines the paths of the vertices. Each pair of corresponding simplices defines an affine transformation, which is factored into a rotation and a stretching transformation. These local transformations are naturally interpolated over time and serve as the basis for composing a global coherent least-distorting transformation.

Original language | English |
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Pages | 157-164 |

Number of pages | 8 |

DOIs | |

State | Published - 2000 |

Event | SIGGRAPH 2000 - New Orleans, LA, United States Duration: 23 Jul 2000 → 28 Jul 2000 |

### Conference

Conference | SIGGRAPH 2000 |
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Country/Territory | United States |

City | New Orleans, LA |

Period | 23/07/00 → 28/07/00 |

## Keywords

- Compatible triangulation
- Shape blending
- Vertex path problem