一类代数-三角函数表示的空间PH 曲线及其应用

在代数-三角函数空间Ω=span{1,θ ···, θm+1, sinθ, cosθ, θsinθ, ···, θn cosθ}定义了一类 空间曲线。通过选取合适的积分核函数，该曲线在xy-平面上的投影具有内蕴表示或整条曲线是 PH 曲线。曲线的笛卡尔坐标可由预定义的核函数通过积分计算得到。此外，给出了不同核函数 表示的积分曲线的Hermite 插值算法。对给定的边界条件，积分核函数系数可通过求解方程组 得到。最后，利用PH 曲线设计了一族标架，并用于构造有理形式的扫掠曲面。实验表明，分 片定义的扫掠曲面在脊线处G1 连续，在其余连接处达到近似G1 连续。

A Family of Spacial PH Curves Represented by Algebraic-Trigonometric Functions and Their Applications

A class of spacial curves are defined over the algebraic-trigonometric space Ω=span{1,θ ···, θm+1, sinθ, cosθ, θsinθ, ···, θn cosθ}. By choosing proper integral kernels, the projection of the spacial integral curve on the xy-plane has intrinsic definition, or the whole spacial curve is a PH curve. The Cartesian coordinates of the curve can be explicitly evaluated by integrals of the predefined kernels. Besides, techniques of interpolation of integral curves with different integral kernels have been studied. Given the boundary data, the coefficients within the kernel functions are obtained by solving a system. Finally, we use PH curves to design a family of frames, which can be used to construct a rational swept surface. Experimental results show that the piecewise swept surface is G1 continuous at the ridge line and is nearly G1 continuous at the remaining junctions.