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Homogeneous Surfaces

  • Fujio Yamaguchi

Abstract

A rational polynomial surface patch is usually defined by the following expressions:
$$ \begin{gathered} p(u,v) = [x(u,v) y(u,v)] = [\frac{{X(u,v)}} {{w(u,v)}}\frac{{Y(u,v)}} {{w(u,v)}}\frac{{Z(u,v)}} {{w(u,v)}}] \hfill \\ = \frac{{\sum\limits_{i = 0}^m {\sum\limits_{j = 0}^n {a_i } (u)a_j (v)w_{ij} q_{ij} } }} {{\sum\limits_{k = 0}^m {\sum\limits_{l = 0}^n {a_k } (u)a_l (v)w_{kl} } }},(0 \leqslant u,v \leqslant 1), \hfill \\ q_{ij} = [x_{ij} y_{ij} z_{ij} ], \hfill \\ \end{gathered} $$
(11.1)
$$ (a_i (u),a_j (v) \geqslant 0 for all i,j) \vee (a_i (u),a_j (u) \leqslant 0 for all i,j), $$
(11.2)
$$ (w > 0 for all i,j) \vee (w < 0 for all i,j), $$
(11.3)
where w ij are called weights.

Keywords

Homogeneous Surface Surface Patch Rational Surface NURBS Surface Homogeneous Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Fujio Yamaguchi
    • 1
  1. 1.Department of Mechanical Engineering School of Science and EngineeringWaseda UniversityTokyoJapan

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