### Abstract

We present an efficient and robust approach for computing the minimum distance between two sphere-swept surfaces. As examples of sphere-swept surfaces, we consider canal surfaces and bivariate sphere-swept surfaces. For computing the minimum distance between two parametric surfaces, a simple technique is to find the two closest points from the given surfaces using the normal vector information. We suggest a novel approach that efficiently computes the minimum distance between two sphere-swept surfaces by treating each surface as a family of spheres. Rather than computing the complicated normal vectors for given surfaces, our method solves the problem by computing the minimum distance between two moving spheres. We prove that the minimum distance between two sphere-swept surfaces is identical to that between two moving spheres. Experimental results of minimum distance computation are given. We also reproduce the result of Kim [Kim K-J. Minimum distance between a canal surface and a simple surface. Computer-Aided Design 2003;35:871-9] based on the suggested approach.

Original language | English |
---|---|

Pages (from-to) | 452-459 |

Number of pages | 8 |

Journal | CAD Computer Aided Design |

Volume | 39 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2007 Jun 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bivariate sphere-swept surface
- Canal surface
- Distance
- Sphere geometry

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering
- Geometry and Topology

### Cite this

*CAD Computer Aided Design*,

*39*(6), 452-459. https://doi.org/10.1016/j.cad.2007.01.002

**Minimum distance between two sphere-swept surfaces.** / Lee, Kwanhee; Seong, Jun Kyung; Kim, Ku Jin; Hong, Sung Je.

Research output: Contribution to journal › Article

*CAD Computer Aided Design*, vol. 39, no. 6, pp. 452-459. https://doi.org/10.1016/j.cad.2007.01.002

}

TY - JOUR

T1 - Minimum distance between two sphere-swept surfaces

AU - Lee, Kwanhee

AU - Seong, Jun Kyung

AU - Kim, Ku Jin

AU - Hong, Sung Je

PY - 2007/6/1

Y1 - 2007/6/1

N2 - We present an efficient and robust approach for computing the minimum distance between two sphere-swept surfaces. As examples of sphere-swept surfaces, we consider canal surfaces and bivariate sphere-swept surfaces. For computing the minimum distance between two parametric surfaces, a simple technique is to find the two closest points from the given surfaces using the normal vector information. We suggest a novel approach that efficiently computes the minimum distance between two sphere-swept surfaces by treating each surface as a family of spheres. Rather than computing the complicated normal vectors for given surfaces, our method solves the problem by computing the minimum distance between two moving spheres. We prove that the minimum distance between two sphere-swept surfaces is identical to that between two moving spheres. Experimental results of minimum distance computation are given. We also reproduce the result of Kim [Kim K-J. Minimum distance between a canal surface and a simple surface. Computer-Aided Design 2003;35:871-9] based on the suggested approach.

AB - We present an efficient and robust approach for computing the minimum distance between two sphere-swept surfaces. As examples of sphere-swept surfaces, we consider canal surfaces and bivariate sphere-swept surfaces. For computing the minimum distance between two parametric surfaces, a simple technique is to find the two closest points from the given surfaces using the normal vector information. We suggest a novel approach that efficiently computes the minimum distance between two sphere-swept surfaces by treating each surface as a family of spheres. Rather than computing the complicated normal vectors for given surfaces, our method solves the problem by computing the minimum distance between two moving spheres. We prove that the minimum distance between two sphere-swept surfaces is identical to that between two moving spheres. Experimental results of minimum distance computation are given. We also reproduce the result of Kim [Kim K-J. Minimum distance between a canal surface and a simple surface. Computer-Aided Design 2003;35:871-9] based on the suggested approach.

KW - Bivariate sphere-swept surface

KW - Canal surface

KW - Distance

KW - Sphere geometry

UR - http://www.scopus.com/inward/record.url?scp=34248530671&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248530671&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2007.01.002

DO - 10.1016/j.cad.2007.01.002

M3 - Article

VL - 39

SP - 452

EP - 459

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 6

ER -