The Intersection and its Application for Non-Circular Quadric Curved Surface Based on the Theory of Projective Correspondence

Abstract:

Based on the theory of projective correspondence, the principle of affine correspondence and projective correspondence is proposed to resolve the intersection of non-circular quadric curved surface (NCQCS). According to the theory of projective geometry, the intersection that NCQCS intersect with a set of parallel planes is a group of homothetic curves. Taking the homothetic curves as corresponding element, spatial projective correspondence between any two homothetic curves is constructed. Similarly, the intersection that any NCQCS intersected by a set of planes through it axis is a group of similar curves. Taking the similar curves as associated element, spatial affine correspondence between any two similar curves is constructed. The intersection and drawing theory, method, application and technology for the NCQCS provides the theoretical and practice support for the intersection of the NCQCS.

• Periodical: Applied Mechanics and Materials (Volume 389)
• Pages: 860-865
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.389.860
• Online since: August 2013
• Authors: Bin Cheng, Su Liu, Yu Sun, Jie Zhang
• Keywords: Affine Correspondence, Intersection, Non-Circular Quadric Curved Surface, Projective Correspondence, Projective Geometry

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