论文信息 - Design of developable surfaces using duality between plane and point geometries

Design of developable surfaces using duality between plane and point geometries

Abstract The concept of duality between points and planes in 3D projective space is used to develop a new representation for developable surfaces in terms of plane geometry. In this manner, a developable surface is designed using control planes with appropriate basis functions. The use of rational Bezier and B-spline bases is focused on, and a technique for the geometric design of developable surfaces is developed that has all the characteristics of existing methods for curve design. It is shown that some of the geometric constructions that exist for curves also generalize to the design of developable surfaces. In particular, de Casteljau- and Farin-Boehm-type construction algorithms are developed for Bezier developable surfaces.

[1] Gerald Farin,et al. Curves and surfaces for computer aided geometric design , 1990 .

[2] J. Semple,et al. Introduction to Algebraic Geometry , 1949 .

[3] D. M. Y. Sommerville,et al. An Introduction to The Geometry of N Dimensions , 2022 .

[4] Tony DeRose,et al. Geometric continuity of parametric curves: constructions of geometrically continuous splines , 1990, IEEE Computer Graphics and Applications.

[5] Bahram Ravani,et al. Bertrand offsets of ruled and developable surfaces , 1991, Comput. Aided Des..

[6] Günter Aumann,et al. Interpolation with developable Bézier patches , 1991, Comput. Aided Geom. Des..

[7] I. Faux,et al. Computational Geometry for Design and Manufacture , 1979 .

[8] Bahram Ravani,et al. Computer Aided Geometric Design of Line Constructs , 1991 .

[9] D. Struik. Lectures on classical differential geometry , 1951 .

[10] T J Nolan. Computer-Aided Design of Developable Hull Surfaces , 1970 .

[11] P. Redont. Representation and deformation of developable surfaces , 1989 .

[12] L. W. Ferris. A Standard Series of Developable Surfaces , 1968 .