### Abstract

We herein propose a novel method for removing irregularities of B-spline surfaces via smoothing circular highlight lines. A circular highlight line is defined as a set of points on a surface such that the distance between a circular light source and an extended surface normal to be zero. Circular highlight lines allow us to capture the surface fairness in all directions, whereas conventional method, which uses a family of parallel straight lines for light sources, can capture the surface irregularity only in one direction. This method of correcting surface irregularities through circular highlight lines is intuitive and allows non-skilled persons to generate surfaces that can satisfy requirements imposed by downstream applications. Nonlinear equations that relate the difference between the circular highlight lines of the current surface and the target curves in the parameter space are formulated in terms of control points of the surface to be modified. The nonlinear governing equations are solved by Newton’s method. The effectiveness of these algorithms is demonstrated through examples.

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

Pages (from-to) | 405-414 |

Number of pages | 10 |

Journal | Computer-Aided Design and Applications |

Volume | 4 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - 2007 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- B-spline surface
- Circular highlight lines
- Surface fairing
- Surface interrogation

### ASJC Scopus subject areas

- Computational Mechanics
- Computer Graphics and Computer-Aided Design
- Computational Mathematics

### Cite this

*Computer-Aided Design and Applications*,

*4*(1-4), 405-414. https://doi.org/10.1080/16864360.2007.10738560

**Surface Faring Using Circular Highlight Lines.** / Nishiyama, Yu; Nishimura, Yoh; Sasaki, Takayuki; Maekawa, Takashi.

Research output: Contribution to journal › Article

*Computer-Aided Design and Applications*, vol. 4, no. 1-4, pp. 405-414. https://doi.org/10.1080/16864360.2007.10738560

}

TY - JOUR

T1 - Surface Faring Using Circular Highlight Lines

AU - Nishiyama, Yu

AU - Nishimura, Yoh

AU - Sasaki, Takayuki

AU - Maekawa, Takashi

PY - 2007/1/1

Y1 - 2007/1/1

N2 - We herein propose a novel method for removing irregularities of B-spline surfaces via smoothing circular highlight lines. A circular highlight line is defined as a set of points on a surface such that the distance between a circular light source and an extended surface normal to be zero. Circular highlight lines allow us to capture the surface fairness in all directions, whereas conventional method, which uses a family of parallel straight lines for light sources, can capture the surface irregularity only in one direction. This method of correcting surface irregularities through circular highlight lines is intuitive and allows non-skilled persons to generate surfaces that can satisfy requirements imposed by downstream applications. Nonlinear equations that relate the difference between the circular highlight lines of the current surface and the target curves in the parameter space are formulated in terms of control points of the surface to be modified. The nonlinear governing equations are solved by Newton’s method. The effectiveness of these algorithms is demonstrated through examples.

AB - We herein propose a novel method for removing irregularities of B-spline surfaces via smoothing circular highlight lines. A circular highlight line is defined as a set of points on a surface such that the distance between a circular light source and an extended surface normal to be zero. Circular highlight lines allow us to capture the surface fairness in all directions, whereas conventional method, which uses a family of parallel straight lines for light sources, can capture the surface irregularity only in one direction. This method of correcting surface irregularities through circular highlight lines is intuitive and allows non-skilled persons to generate surfaces that can satisfy requirements imposed by downstream applications. Nonlinear equations that relate the difference between the circular highlight lines of the current surface and the target curves in the parameter space are formulated in terms of control points of the surface to be modified. The nonlinear governing equations are solved by Newton’s method. The effectiveness of these algorithms is demonstrated through examples.

KW - B-spline surface

KW - Circular highlight lines

KW - Surface fairing

KW - Surface interrogation

UR - http://www.scopus.com/inward/record.url?scp=34250748407&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250748407&partnerID=8YFLogxK

U2 - 10.1080/16864360.2007.10738560

DO - 10.1080/16864360.2007.10738560

M3 - Article

VL - 4

SP - 405

EP - 414

JO - Computer-Aided Design and Applications

JF - Computer-Aided Design and Applications

SN - 1686-4360

IS - 1-4

ER -