Determining the topology of real algebraic surfaces

  • Authors:
  • Jin-San Cheng;Xiao-Shan Gao;Ming Li

  • Affiliations:
  • Key Lab of Mathematics Mechanization, Institute of Systems Science, AMSS, Academia Sinica, Beijing, China;Key Lab of Mathematics Mechanization, Institute of Systems Science, AMSS, Academia Sinica, Beijing, China;School of Computer Science, Cardiff University, Cardiff, UK

  • Venue:
  • IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
  • Year:
  • 2005

Quantified Score

Hi-index 0.00

Visualization

Abstract

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.