一类定义在球面上的曲面的C^2光滑性

C^2 smoothness of a category of curved surface defined on spherical surface

用三角B样条理论研究了一类定义在球面上的曲面的C2光滑性.为了解决通过定义在球面上的函数构造的一类定义在球面上的封闭参数曲面在球面的南北两个极点处无法达到C2连续的问题,提出将球面上函数用三角B样条张量积形式表示,通过拟合球面上的散乱数据以获得球面上函数.只要在拟合的过程中张量积系数满足文中给出的约束条件,则由此函数构造的定义在球面上封闭参数曲面能够在球面上处处达到C2连续.

C^2 smoothness of a category of curved surface defined on a spherical surface was studied by means of trigonometric B-spline theory.In order to deal with C^2 uncontinuity of a category of closed parametric surface,which is defined on a spherical surface,at both the south and north poles,it was proposed that the function on the sphere be expressed in the form of tensor products of trigonometric B-spline.Then the scattered data on the sphere were fitted to obtain the function on sphere.It only the coefficients of tensor product were satisfied with the constraints specified in this paper,C^2 continuity of so constructed and defined on sphere trigonometric parametric surface would be realized everywhere on the sphere.