Determining the Topology of Real Algebraic Surfaces

  • Jin-San Cheng
  • Xiao-Shan Gao
  • Ming Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)


An algorithm is proposed to determine the topology of an implicit real algebraic surface in ℝ3. The algorithm consists of three steps: surface projection, projection curve topology determination and surface patches composition. The algorithm provides a curvilinear wireframe of the surface and the surface patches of the surface determined by the curvilinear wireframe, which have the same topology as the surface. Most of the surface patches are curvilinear polygons. Some examples are used to show that our algorithm is effective.


Boundary Point Rational Number Real Root Plane Curve Surface Patch 
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-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jin-San Cheng
    • 1
  • Xiao-Shan Gao
    • 1
  • Ming Li
    • 2
  1. 1.Key Lab of Mathematics Mechanization, Institute of Systems Science, AMSSAcademia SinicaBeijingChina
  2. 2.School of Computer ScienceCardiff UniversityCardiffUK

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