共查询到7条相似文献,搜索用时 0 毫秒
1.
Jae Hoon Kong Seung Pil Jeong Sunhong Lee Gwang Il Kim 《Computer Aided Geometric Design》2008,25(4-5):214-229
We introduce a new method of solving C1 Hermite interpolation problems, which makes it possible to use a wider range of PH curves with potentially better shapes. By characterizing PH curves by roots of their hodographs in the complex representation, we introduce PH curves of type K(t−c)2n+1+d. Next, we introduce a speed reparametrization. Finally, we show that, for C1 Hermite data, we can use PH curves of type K(t−c)2n+1+d or strongly regular PH quintics satisfying the G1 reduction of C1 data, and use these curves to solve the original C1 Hermite interpolation problem. 相似文献
2.
Rida T. Farouki Carlotta Giannelli Carla Manni Alessandra Sestini 《Computer Aided Geometric Design》2008,25(4-5):274-297
The problem of specifying the two free parameters that arise in spatial Pythagorean-hodograph (PH) quintic interpolants to given first-order Hermite data is addressed. Conditions on the data that identify when the “ordinary” cubic interpolant becomes a PH curve are formulated, since it is desired that the selection procedure should reproduce such curves whenever possible. Moreover, it is shown that the arc length of the interpolants depends on only one of the parameters, and that four (general) helical PH quintic interpolants always exist, corresponding to extrema of the arc length. Motivated by the desire to improve the fairness of interpolants to general data at reasonable computational cost, three selection criteria are proposed. The first criterion is based on minimizing a bivariate function that measures how “close” the PH quintic interpolants are to a PH cubic. For the second criterion, one of the parameters is fixed by first selecting interpolants of extremal arc length, and the other parameter is then determined by minimizing the distance measure of the first method, considered as a univariate function. The third method employs a heuristic but efficient procedure to select one parameter, suggested by the circumstances in which the “ordinary” cubic interpolant is a PH curve, and the other parameter is then determined as in the second method. After presenting the theory underlying these three methods, a comparison of empirical results from their implementation is described, and recommendations for their use in practical design applications are made. 相似文献
3.
John C. Femiani Chia-Yuan Chuang Anshuman Razdan 《Computer Aided Geometric Design》2012,29(2):141-149
We present a rational Bézier solution to the geometric Hermite interpolation problem. Given two points and respective unit tangent vectors, we provide an interpolant that can reproduce a circle if possible. When the tangents permit an ellipse, we produce one that deviates least from a circle. We cast the problem as a theorem and provide its proof, and a method for determining the weights of the control points of a rational curve. Our approach targets ellipses, but we also present a cubic interpolant that can find curves with inflection points and space curves when an ellipse cannot satisfy the tangent constraints. 相似文献
4.
5.
n degrees of freedom for any given Hermite data on S
n
, n≥2. A method is presented for generating all spherical rational quartic curves on S
n
interpolating given Hermite data. 相似文献
6.
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。 相似文献