### Abstract

Lofting is a traditional technique for creating a curved shape by first specifying a network of curves that approximates the desired shape and then interpolating these curves with a smooth surface. This paper addresses the problem of lofting from the viewpoint of subdivision. First, we develop a subdivision scheme for an arbitrary network of cubic B-splines capable of being interpolated by a smooth surface. Second, we provide a quadrangulation algorithm to construct the topology of the surface control mesh. Finally, we extend the Catmull-Clark scheme to produce surfaces that interpolate the given curve network. Near the curve network, these lofted subdivision surfaces are C ^{2} bicubic splines, except for those points where three or more curves meet. We prove that the surface is C^{1} with bounded curvature at these points in the most common cases; empirical results suggest that the surface is also C^{1} in the general case.

Original language | English (US) |
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Title of host publication | SGP 2004 - Symposium on Geometry Processing |

Pages | 103-114 |

Number of pages | 12 |

DOIs | |

State | Published - 2004 |

Event | 2nd Symposium on Geometry Processing, SGP 2004 - Nice, France Duration: Jul 8 2004 → Jul 10 2004 |

### Publication series

Name | ACM International Conference Proceeding Series |
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Volume | 71 |

### Other

Other | 2nd Symposium on Geometry Processing, SGP 2004 |
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Country | France |

City | Nice |

Period | 7/8/04 → 7/10/04 |

### Keywords

- I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling

### ASJC Scopus subject areas

- Software
- Human-Computer Interaction
- Computer Vision and Pattern Recognition
- Computer Networks and Communications

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## Cite this

*SGP 2004 - Symposium on Geometry Processing*(pp. 103-114). (ACM International Conference Proceeding Series; Vol. 71). https://doi.org/10.1145/1057432.1057447