Implicit Equations of Non-degenerate Rational Bezier Quadric Triangles

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• 关键词：Quadric ; Steiner surfaces ; Rational Bézier triangles
• 刊名：Lecture Notes in Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：9213
• 期：1
• 页码：70-79
• 全文大小：519 KB
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• 作者单位：Alicia Cantón (20)
  L. Fernández-Jambrina (20)
  E. Rosado María (20)
  M. J. Vázquez-Gallo (20)
  
  20. Universidad Politécnica de Madrid, 28040, Madrid, Spain
  
• 丛书名：Curves and Surfaces
• ISBN：978-3-319-22804-4
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bézier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is grounded on the pencil of quadrics circumscribed to a tetrahedron formed by vertices of the control net and an additional point which is required for the Steiner surface to be a non-degenerate quadric.