### 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) |
---|---|

Title of host publication | SGP 2004 - Symposium on Geometry Processing |

Pages | 103-114 |

Number of pages | 12 |

Volume | 71 |

DOIs | |

State | Published - 2004 |

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

### Other

Other | 2nd Symposium on Geometry Processing, SGP 2004 |
---|---|

Country | France |

City | Nice |

Period | 7/8/04 → 7/10/04 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*SGP 2004 - Symposium on Geometry Processing*(Vol. 71, pp. 103-114) https://doi.org/10.1145/1057432.1057447

**Lofting curve networks using subdivision surfaces.** / Schaefer, S.; Warren, J.; Zorin, Denis.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*SGP 2004 - Symposium on Geometry Processing.*vol. 71, pp. 103-114, 2nd Symposium on Geometry Processing, SGP 2004, Nice, France, 7/8/04. https://doi.org/10.1145/1057432.1057447

}

TY - GEN

T1 - Lofting curve networks using subdivision surfaces

AU - Schaefer, S.

AU - Warren, J.

AU - Zorin, Denis

PY - 2004

Y1 - 2004

N2 - 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 C1 with bounded curvature at these points in the most common cases; empirical results suggest that the surface is also C1 in the general case.

AB - 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 C1 with bounded curvature at these points in the most common cases; empirical results suggest that the surface is also C1 in the general case.

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

UR - http://www.scopus.com/inward/record.url?scp=77954462999&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954462999&partnerID=8YFLogxK

U2 - 10.1145/1057432.1057447

DO - 10.1145/1057432.1057447

M3 - Conference contribution

AN - SCOPUS:77954462999

SN - 3905673134

SN - 9783905673135

VL - 71

SP - 103

EP - 114

BT - SGP 2004 - Symposium on Geometry Processing

ER -