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Journal Article
베지어 곡선과 곡면의 립과 팬
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- Authors
- 이주행, 박형준
- Issue Date
- 2006-08
- Citation
- 한국CAD/CAM학회논문집, v.11, no.4, pp.246-255
- ISSN
- 1226-0606
- Publisher
- 한국CAD/CAM학회 (SCCE)
- Language
- Korean
- Type
- Journal Article
- Abstract
- Ribs and fans are interesting geometric entities that are derived from an ordinary Bzier curve or surface. A rib itself is a Bzier 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 Bezier curve or surface into the control points and vectors of its ribs and fans. Then, we show that a Bzier 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 Bzier 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.
- KSP Keywords
- Bezier curve, Control Points, M-, N 2, N-1, vector field