### Abstract

We present a novel geometric algorithm to construct a smooth surface that interpolates a triangular or a quadrilateral mesh of arbitrary topological type formed by n vertices. Although our method can be applied to B-spline surfaces and subdivision surfaces of all kinds, we illustrate our algorithm focusing on Loop subdivision surfaces as most of the meshes are in triangular form. We start our algorithm by assuming that the given triangular mesh is a control net of a Loop subdivision surface. The control points are iteratively updated globally by a simple local point-surface distance computation and an offsetting procedure without solving a linear system. The complexity of our algorithm is O (m n) where n is the number of vertices and m is the number of iterations. The number of iterations m depends on the fineness of the mesh and accuracy required.

Original language | English |
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Pages (from-to) | 313-323 |

Number of pages | 11 |

Journal | CAD Computer Aided Design |

Volume | 39 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2007 Apr 1 |

Externally published | Yes |

### Keywords

- B-spline curves and surfaces
- Catmull-Clark subdivision surface
- Geometric algorithm
- Geometric modeling
- Loop subdivision surface
- Surface interpolation

### ASJC Scopus subject areas

- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering

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## Cite this

*CAD Computer Aided Design*,

*39*(4), 313-323. https://doi.org/10.1016/j.cad.2006.12.008