The Homogeneous Representation of Quadratic Rational Bezier Curve and NURBS.

DOI Web Site 1 Citations 8 References

Bibliographic Information

Other Title
  • ２次有理Ｂｅｚｉｅｒ曲線および２次ＮＵＲＢＳの同次表現について
  • 2ジ ユウリ Bezier キョクセン オヨビ 2ジ NURBS ノ ドウジ

Search this article

Description

Rational curves such as rational Bézier curves and NURBS are widely being used in CAD and CAGD, and defining them as homogeneous curves in homogeneous space has many advantages in geometric processing. In this paper, some properties of quadratic rational Bézier curves and NURBS defined in homogeneous space are discussed. First, the relationship between the two kinds of homogeneous curves is studied. Secondly, the implicit form of quadratic homogeneous Bézier curves is derived, and by using the implicit form, the inclusion test and the conic classification (hyperbola, parabola, and ellipse) are performed. Finally, the fact that a whole conic can be represented as one homogenized NURBS is shown. The properties discussed here are more general than those of conventional rational curves.

Journal

Citations (1)*help

See more

References(8)*help

See more

Keywords

Details 詳細情報について

Report a problem

Back to top