### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*CAD Computer Aided Design*,

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

**Interpolation by geometric algorithm.** / Maekawa, Takashi; Matsumoto, Yasunori; Namiki, Ken.

Research output: Contribution to journal › Article

*CAD Computer Aided Design*, vol. 39, no. 4, pp. 313-323. https://doi.org/10.1016/j.cad.2006.12.008

}

TY - JOUR

T1 - Interpolation by geometric algorithm

AU - Maekawa, Takashi

AU - Matsumoto, Yasunori

AU - Namiki, Ken

PY - 2007/4/1

Y1 - 2007/4/1

N2 - 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.

AB - 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.

KW - B-spline curves and surfaces

KW - Catmull-Clark subdivision surface

KW - Geometric algorithm

KW - Geometric modeling

KW - Loop subdivision surface

KW - Surface interpolation

UR - http://www.scopus.com/inward/record.url?scp=34147179068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34147179068&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2006.12.008

DO - 10.1016/j.cad.2006.12.008

M3 - Article

VL - 39

SP - 313

EP - 323

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 4

ER -