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 |
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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
Surface Faring Using Circular Highlight Lines. / Nishiyama, Yu; Nishimura, Yoh; Sasaki, Takayuki; Maekawa, Takashi.
In: Computer-Aided Design and Applications, Vol. 4, No. 1-4, 01.01.2007, p. 405-414.Research output: Contribution to journal › Article
}
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 -