Design And Research On CE-Bezier Developable Surfaces And λ,μ-B Spline Developable Surfaces

Geometric modeling method focuses on the denotation, design, display, and analysis of surface under the environment of computer graphics system. The major research issues of the thesis are the critical technology in the field of surface modeling, include presenting new effective methods of computer aided geometric design for developable surfaces. The extension of Bezier developable surface and B-spline developable surface with parameters has become a hotspot in CAGD recently, partially influenced by the enormous growing computing technologies. Its main contents and achievements are as follows:Based on the important idea of duality between plane and point geometries in 3D space, two direct explicit methods of computer-aided design for developable surfaces are used:(1)a developable surface is considered as envelope of the one-parameter set of its tangent planes; (2)a developable surface is considered as the surface composed of the tangent lines to a spline curve. In these manners, the developable surfaces are designed using control planes with CE-Bezier basis function,λ,μ-B spline basis function. The shape of developable surface can be adjusted using a control parameter on the condition of the control planes given. When adjusting the parameter, a family of developable surface can be constructed and they can keep the characteristics of Bezier surfaces and B-spline surfaces. In the particular value case of the parameter, the developable surface is a uniform Bezier surface and B-spline surface. The thesis also discusses respectively properties of designed developable surface. Meanwhile it shows that the techniques for the geometric design of developable surface in this paper have all the characteristics of existing methods for curves design.