Algorithms for some geometric properties of tangential intersection of two surfaces in Euclidean 3-spaces
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we study the geodesic curvature of intersection curve of two regular parametric and two regular implicit surfaces in R3. Here the intersection curve will be of tangential type, i.e., the normal vectors of the two surfaces at the given intersection point are linearly dependent, while in case of transversal intersection, the normals of the intersecting surfaces at the intersection point are linearly independent.
Abstract
In this paper, we study the geodesic curvature of intersection curve of two regular parametric and two regular implicit surfaces in R3. Here the intersection curve will be of tangential type, i.e., the normal vectors of the two surfaces at the given intersection point are linearly dependent, while in case of transversal intersection, the normals of the intersecting surfaces at the intersection point are linearly independent.
참고문헌 (14)
- B. U. Duldul, "On the geodesic torsion of a tangential intersection curve of two surfaces in R3", Acta Math. Univ. Comenianae, 2, pp.177~189 (2013)
- E. Hartmann, "Interpolation and bending on surfaces", Visual Comput., 12, pp.181~192 (1996)
- E. Kreyszig, "Differential geometry" (1991), Dover Publication Inc.
- G. Farin, "Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide" (2002), Academic Press, Inc.
- H. Gluck, "Higher curvatures of curves in Euclidean space", Am. Math. Mon., 73(7), pp.699~704 (1966)
- J. Hoschek, "Fundamentals of Computer Aided Geometric Design" (1993), A.K. Peters, Wellesley
- M. A. Soliman, "Intersection curves of implicit and parametric surfaces in R3", Applied Mathematics, 2(8), pp.1019~1026 (2011)
- N. H. Abdel-Alld, "Intersection curves of two implicit surfaces in R3", J. Math Comput. Sci., 2(2), pp.152~171 (2012)
- N. M. Patrikalakis, "Shape Interrogation for Computer Aided Design and Manufacturing" (2002), Springer-Verlag, Berlin, Heidelberg
- P.M. do Carmo, "Differential Geometry of Curves and Surfaces" (1976), Prentice-Hall
- R. Goldman, "Curvature formulas for implicit curves and surfaces", Computer Aided Geometric Design, 22, pp.632~658 (2005)
- T. J. Willmore, "An Introduction to Differential Geometry" (1959), Clarendon Press
- W. Klingenberg, "A Course in Differential Geometry" (1978), Springer-Verlag
- Y. Xiuzi, "Differential geometry of intersection curves of two surfaces", Computer Aided Geometric Design, 16, pp.767~788 (1999)