Browse > Article

Ribs and Fans of $B\ Curves and Surfaces  

Lee, J.H. (한국전자통신연구원, 디지털콘텐츠 연구단)
Park, H.J. (조선대학교, 산업공학과)
Publication Information
Korean Journal of Computational Design and Engineering / v.11, no.4, 2006 , pp. 246-255 More about this Journal
Abstract
Ribs and fans are interesting geometric entities that are derived from an ordinary $B\ curve or surface. A rib itself is a $B\ curve or surface with a lower degree than the given curve or surface. A fan is a vector field whose degree is also lower than its origin. First, we present methods to transform the control points of a $B\ curve or surface into the control points and vectors of its ribs and fans. Then, we show that a $B\ curve of degree n is decomposed into a rib of degree (n-1), a fan of degree (n-2), and a scalar function of degree 2. We also show that a $B\ surface of degree (m, n) is decomposed into a rib of degree (m-1, n-1) and three fans of degrees (m-1, n-2), (m-2, n-1), and (m-2, n-2), respectively. In addition, the lengths of the fans are further controlled by scalar functions of degree 2 and (2, 2). We present relevant notations and definitions, introduce theories, and present some of design examples.
Keywords
Rib; Fan; $B\ curve and surface; Decomposition;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Farin, G. and Hansford, D., The Essentials of CAGD, A K Peters, Natick, MA, 2000
2 Hoschek, J. and Lasser, D., Fundamentals of Computer Aided Geometric Design, A K Peters, Natick, MA, 1993
3 Macromedia Flash MX, http://www.macromedia.com/devnet/devices/, Macromedia, Inc.
4 Farin, G., Curves and Surfaces for CAGD-A Practical Guide, 5th Ed., Morgan Kaufmann, San Francisco, CA, 2002
5 Design Examples of Ribs and Fans, http://joohaeng.etri.re.kr/GeoLix/BezierRibFan
6 Farouki, R. and Rajan, V., 'Algorithms for Polynomials in Bernstein Form', Computer Aided Geometric Design, Vol. 5, No.1, pp. 1-26, 1988   DOI   ScienceOn