Line Subdivision

  • Hiroshi Kawaharada
  • Kokichi Sugihara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)


This paper proposes a new subdivision scheme based on line geometry. We name the scheme ‘line subdivision’. Line subdivision scheme acts on the line space, and generates two-dimensional manifolds contained in the Klein quadric. The two-dimensional manifolds are the Klein images of line congruences in P 3. So, this new subdivision scheme generates line congruences at the limit. Here, we define the line subdivision surface as an envelope surface which is made by the line congruence. Then, this paper derives basic properties of the surface. Moreover, we show that line subdivision contains ordinary subdivision and dual subdivision.


Tangent Plane Ideal Point Subdivision Scheme Tangent Point Subdivision Surface 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hiroshi Kawaharada
    • 1
  • Kokichi Sugihara
    • 1
  1. 1.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of TokyoJapan

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