摘要
为了对复杂物体外形进行快速精确建模,利用多面体样条方法进行物体表面的设计及应用研究.通过对样条函数节点进行分类,给出空间中任意拓扑结构网格上样条函数组的具体构造方法.研究曲线曲面控制点与生成样条函数的节点的相互依赖关系,提出在无单位分解条件下构造具有几何不变性曲线曲面的合理化方法.通过构造控制点处多面体样条函数,生成了任意拓扑结构的连续多面体样条曲面.这样的多面体样条曲面在同样性质要求下曲面次数低,只有张量积NURBS曲面的一半;并且与细分曲面相比,所获取的物体外形表面具有坐标计算准确,中间数据较少等优点,可以用于精确构造电磁射线追踪中物体的外形.
In order to model the complex body surfaces in electronic ray-tracing quickly and accurately,the polyhedron spline method is employed in the research on body surface designing and application.By classifying knots related to spline functions,a method is presented for generate certain spline functions over a mesh with arbitrary topological structure in space.The interdependent relationship between control points for a curve or surface and the mesh knots for spline functions is discussed.The curve or surface with blending functions of non-unit decomposition property is designed,with geometrical invariance and convex hull property.By constructing control polyhedron spline functions at control points distributed in a mesh with arbitrary topology,a continuous polyhedron spline body surface over arbitrary topology is generated.As only half order of the continuous tensor product type NURBS surface,order for the continuous polyhedron spline surface is low.Comparing to subdivision surface which is limiting result,this surface can be obtained exactly,with less processing data,and,can be used for precision complex body surfaces in electromagnetic ray tracing.
出处
《大学数学》
2015年第1期21-25,共5页
College Mathematics
基金
河南省重点科技攻关项目(142102210492
132102210194)
关键词
多面体样条
有理函数
任意网格
物体外形
射线跟踪
polyhedral spline
rational function
arbitrary meshes
body surface
electromagnetic ray tracing
