等距曲面的NURBS放样插值方法

本文给出了等距曲面的一种NURBS放样插值生成方法，该方法主要是在原始NURBS曲面上取得一个能较好反映曲面特征的型值点阵，再交这个型值点阵按某种算法矢方向外推，从而得到原始曲面的等距曲面上的型值点阵，然后，再用NURBS放样插值曲面来逼近等距曲面，本文给出的算法几何意义明显，易于编程实现，且得到的等距曲面其u向和v向参数曲线仍是NURBS曲线，且具有C^2连续性，最后，给出了一个实例。     

曲率单调Bézier曲线G1插值算法及应用

基于曲率单调的 Bézier 曲线,提出了一种精确而高效的满足 G1 约束的样条曲线插值算法。给定首 尾插值数据点位置及方向角,利用曲率单调 Bézier 曲线的几何设计准则,求解非线性方程组,构造满足 G1 插值条 件的曲率单调 Bézier 曲线。与基于欧拉螺旋线的插值算法相比,本文方法构造简单、插值精确,与现有的 NURBS 方法兼容。基于分段拼接,该算法能够处理给定点列及首尾切线方向的插值问题,具有较强的适应性与通用性。     

带约束的B 样条曲线曲面延伸技术

论文提出了一种带光滑有序点列约束的B 样条曲线延伸方法。该算法能 够根据约束点列的情况对曲线延伸部分所对应的节点值进行优化,通过插值尽量少的约束 点,使得延伸曲线与约束点列之间的最大距离小于预先给定的误差值,并且延伸曲线与原始 曲线之间自然达到最大阶连续。该方法也同样适用于带曲线约束的B 样条曲面延伸。实例 表明,所提出的算法是可行且有效的。     

基于AIWCPSO算法的三次样条气动参数插值方法

针对飞行仿真建模过程中气动参数以矩阵的形式给出, 大都存在着非线性关系, 提出一种基于自适应惯性权重的混沌粒子群优化(AIWCPSO) 算法的三次样条气动参数插值方法. 首先建立粒子与三次样条插值函数中系数的映射关系; 然后利用AIWCPSO 算法对三次样条插值函数的系数进行寻优, 将获得的最优解近似看作三次样条插值函数的系数; 最后计算得到离散点的气动参数. 仿真实验结果表明, 所提出的方法能有效地解决飞行气动参数插值问题.     

基于Delaunay三角网的克里金并行算法优化

当采样点数据量较大时, 可以采用Delaunay三角剖分建立三角网来使用局部邻域采样点进行克里金插值. 但是该算法需要对每个插值点拟合半变异函数, 插值点规模大时造成巨大开销. 为此, 本文提出了一种以三角形为单位拟合半变异函数的克里金插值方法, 采用CPU-GPU负载均衡将部分计算优化, 充分考虑不均匀样本对克里金插值效果的影响. 结果表明, 本文算法能够保证不均匀样本集的插值效果, 提升了计算性能且能够保证较高的精度.     

基于模糊区域检测的手写汉字笔画提取方法

针对手写汉字笔画提取的重点和难点--模糊区域的识别和解析问题,提出了一种新的基于模糊区域检测的笔画提取算法.该算法首先利用细化算法提取的fork候选点和fork候选点附近的轮廓信息来检测模糊区域;然后利用图模型来对子笔画和模糊区域进行建模,同时通过构造贝叶斯分类器来分析子笔画对的连续性,并通过路径搜索来得到子笔画序列;最后通过进行B样条插值来提取细化后的笔画.对比实验结果表明,该算法不仅能够有效地用于模糊区域检测和笔画提取,而且能够避免细化结果在模糊区域内的形状畸变.     

基于边界约束的空间复杂曲面重构算法

针对克里金(Kriging)算法在复杂地质构造应用中的局限性,提出了一种基于边界约束的复杂曲面插值方法.其基本思想是将断层多边形作为层面边界的约束条件,根据种子点与待插值点穿越多边形的关系为依据,判断待插值点与控制点之间的空间拓扑关系,并将满足条件的种子点利用克里金算法进行插值计算.通过实际数据的测试,解决了传统的网格化插值方案层位与断层无法严格相交以及多重逆掩断层构造的层面拟合等难题,为等值线绘制、地质块状模型构建等提供了新的思路.     

基于误差控制的自适应3次B样条曲线插值

针对现有曲线插值算法不能有效压缩型值点的缺陷,研究了一种自适应三次B样条曲线插值算法。从型值点序列中选用最少的点插值一条初始曲线,基于提出的点到曲线的最小距离计算方法,分别计算各非插值点对应的插值误差,并从中提取最大插值误差。若最大误差大于给定的误差阈值,则将其对应的型值点加入插值型值点序列,重新插值曲线,直到最大插值误差满足误差要求。与现有曲线插值算法相比,该算法可以在保证插值精度的前提下有效压缩数据量。     

Interpolatory Model Order Reduction Method for Second Order Systems

In this paper, we propose a structure‐preserving model reduction method for second‐order systems based on H₂ optimal interpolation. In the iterative process of the proposed method, an algorithm is presented for selecting interpolation points in order to control the dimension of the reduced system. Result about error analysis of the interpolation points selection algorithm is obtained and the property of the new model reduction method is also given. Finally, three numerical examples are performed to illustrate the effectiveness of the new method.     

离散点重构车身曲面的一种方法

基于激光无触点式三坐标测量仪所测得的曲面离散数据点 ,论文给出了一种用双三次B样条曲面插值来重构车身曲面的方法。该方法首先介绍B样条曲线和曲面的插值算法 ,接着对曲面离散点进行预处理 ,最后对离散点进行曲面插值。论文所生成的曲面网格 ,不仅适用于车身曲面设计 ,而且能用作车身覆盖件冲压仿真计算有限元模型     

基于Delaunay三角剖分和高斯小波函数插值的三维表面重建算法

在稀疏数据的三维表面重建中,通过插值的方法得到更为稠密的数据点是一个很重要的环节。该文在比较其它插值算法的基础上,提出了一种三维表面重建算法。该算法在对原始数据进行Delaunay三角剖分的基础上采用二维高斯小波函数插值,它不仅能有效地处理非均匀采样的三维稀疏数据,而且能克服其它插值算法中需要定义权重或估计参数的缺点。最终的实验结果验证了该算法的有效性和实用性。     

基于对应点匹配的眼球切片图像插值算法

图像插值是三维重建的一个关键步骤。针对眼球切片图像的特点，研究和分析了传统的图像插值方法，并在此基础上提出了一种改进的对应点匹配插值方法。先根据改进的对应点匹配准则在相邻层间建立点对点的对应关系，然后利用这些对应点进行插值，得到插值图像数据。实验结果表明，该算法能有效减少插值误差，获得令人满意的效果。     

Double- and triple-step incremental linear interpolation

Incremental linear interpolation determines the set of n+1 equidistant points on an interval [a,b] where all variables involved (n, a, b, and the set of equidistant points) are integers and n>0. Our method of linear interpolation generalizes the findings of a variable-step line-drawing algorithm. The resulting interpolation algorithm has as many loops as the line-drawing algorithm, but fewer restrictions on its input variables. Furthermore, its benefits over the fixed-step interpolation algorithms are similar to those of the variable-step line-drawing algorithm. That is, the double- and triple-step interpolation algorithm can reduce the number of loop iterations of the double-step interpolation algorithm (by 12.5% on average) while keeping the code complexity, initialization costs, and worst-case performance the same. The improvement in speed over the single-step B5 algorithm is even greater     

基于对应点匹配的眼球切片图像插值算法

图像插值是三维重建的一个关键步骤。针对眼球切片图像的特点,研究和分析了传统的图像插值方法,并在此基础上提出了一种改进的对应点匹配插值方法。先根据改进的对应点匹配准则在相邻层间建立点对点的对应关系,然后利用这些对应点进行插值,得到插值图像数据。实验结果表明,该算法能有效减少插值误差,获得令人满意的效果。     

空间插值分析算法综述

空间插值分析算法是一种应用于将离散点的测量数据转换为连续数据表面的算法,能够将连续数据曲面与其他空间现象的分布情况进行比较,它在空间信息方面具有广泛的应用场景,尤其是地理信息方面.对泰森多边形法、反距离权重插值法、样条函数插值法、克里金插值法等空间插值算法的插值原理和应用场景进行综述,对空间插值分析算法的进展和未来研究方向进行了探讨.     

针对三维有限元数据场的精确后处理算法

为了描述有限元模型中数据场的分布规律，发展与完善了基于单元局部插值的母单元绘制算法，提出了以高斯积分点作为插值基准点的有限元应力云图绘制算法，并给出了具体的基于母单元的等值线绘制算法．与传统三角形算法做系统的比较表明，文中算法使有限元后处理功能充分达到了有限元数值分析的精度，尤其针对高阶插值数据场有更好的效果．     

基于断层图像分割的三维匹配插值

CT和MRI图像断层之间的距离远大于断层内部像素间的距离,三维剂量场的计算等工作通常需要等间隔分布的三维图像数据。目前常用的基于灰度插值方法会引起图像边界模糊,而基于形状的插值方法不能得到整个图像的数据。为解决这一问题,文中提出了一种基于断层图像分割的三维匹配插值算法。通过对断层图像进行分割,获得断层图像的空气、软组织和骨骼等区域信息。对相同密度区域采用匹配插值,不同密度区域采用缩放区域大小作为插值数据,使新的图像不仅在灰度上,而且在组织形状上介于原来的断层图像之间,满足了医学图像插值要求。和线性插值方法相比,新算法提高了插值图像的质量,插值结果可有效地应用于构建三维体模型。     

The Cubic Trigonometric Automatic Interpolation Spline

A class of cubic trigonometric interpolation spline curves with two parameters is presented in this paper. The spline curves can automatically interpolate the given data points and become C2 interpolation curves without solving equations system even if the interpolation conditions are fixed. Moreover, shape of the interpolation spline curves can be globally adjusted by the two parameters. By selecting proper values of the two parameters, the optimal interpolation spline curves can be obtained.      

Efficient circular arc interpolation based on active tolerance control

In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G¹ arc splines. To fit a parametric curve by an arc spline within a prescribed tolerance, we first sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct new biarc curves interpolating local triarc spirals explicitly based on the control of permitted tolerances. To reduce the segment number of fitting arc spline as much as possible, we replace the corresponding parts of the spline by the new biarc curves and compute active tolerances for new interpolation steps. By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end. Even more, the fitting arc spline has the same end points and end tangents with the original curve, and the arcs will be jointed smoothly if the original curve is composed of several smooth connected pieces. The algorithm is easy to be implemented and generally applicable to circular arc interpolation problem of all kinds of smooth parametric curves. The method can be used in wide fields such as geometric modeling, tool path generation for NC machining and robot path planning, etc. Several numerical examples are given to show the effectiveness and efficiency of the method.     

Performance Evaluation of GPU-Accelerated Spatial Interpolation Using Radial Basis Functions for Building Explicit Surfaces

This paper focuses on evaluating the computational performance of parallel spatial interpolation with Radial Basis Functions (RBFs) that is developed by utilizing modern GPUs. The RBFs can be used in spatial interpolation to build explicit surfaces such as Discrete Elevation Models. When interpolating with large-size of data points and interpolated points for building explicit surfaces, the computational cost would be quite expensive. To improve the computational efficiency, we specifically develop a parallel RBF spatial interpolation algorithm on many-core GPUs, and compare it with the parallel version implemented on multi-core CPUs. Five groups of experimental tests are conducted on two machines to evaluate the computational efficiency of the presented GPU-accelerated RBF spatial interpolation algorithm. Experimental results indicate that: in most cases, the parallel RBF interpolation algorithm on many-core GPUs does not have any significant advantages over the parallel version on multi-core CPUs in terms of computational efficiency. This unsatisfied performance of the GPU-accelerated RBF interpolation algorithm is due to: (1) the limited size of global memory residing on the GPU, and (2) the need to solve a system of linear equations in each GPU thread to calculate the weights and prediction value of each interpolated point.