Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting

Data fitting with B-splines is a challenging problem in reverse engineering for CAD/CAM, virtual reality, data visualization, and many other fields. It is well-known that the fitting improves greatly if knots are considered as free variables. This leads, however, to a very difficult multimodal and multivariate continuous nonlinear optimization problem, the so-called knot adjustment problem. In this context, the present paper introduces an adapted elitist clonal selection algorithm for automatic knot adjustment of B-spline curves. Given a set of noisy data points, our method determines the number and location of knots automatically in order to obtain an extremely accurate fitting of data. In addition, our method minimizes the number of parameters required for this task. Our approach performs very well and in a fully automatic way even for the cases of underlying functions requiring identical multiple knots, such as functions with discontinuities and cusps. To evaluate its performance, it has been applied to three challenging test functions, and results have been compared with those from other alternative methods based on AIS and genetic algorithms. Our experimental results show that our proposal outperforms previous approaches in terms of accuracy and flexibility. Some other issues such as the parameter tuning, the complexity of the algorithm, and the CPU runtime are also discussed.     

Education-driven research in CAD

We argue for a new research category, named education-driven research (EDR), which fills the gap between traditional field-specific research that is not concerned with educational objectives and research in education that focuses on fundamental teaching and learning principles and possibly on their customization to broad areas (such as mathematics or physics), but not to specific disciplines (such as CAD). The objective of EDR is to simplify the formulation of the underlying theoretical foundations and of specific tools and solutions in a specialized domain, so as to make them easy to understand and internalize. As such, EDR is a difficult and genuine research activity, which requires a deep understanding of the specific field and can rarely be carried out by generalists with primary expertise in broad education principles. We illustrate the concept of EDR with three examples in CAD: (1) the Split and Tweak subdivisions of a polygon and its use for generating curves, surfaces, and animations; (2) the construction of a topological partition of a plane induced by an arbitrary arrangement of edges; and (3) a romantic definition of the minimal and Hausdorff distances. These examples demonstrate the value of using analogies, of introducing evocative terminology, and of synthesizing the simplest fundamental building blocks. The intuitive understanding provided by EDR enables the students (and even the instructor) to better appreciate the limitations of a particular solution and to explore alternatives. In particular, in these examples, EDR has allowed the author to: (1) reduce the cost of evaluating a cubic B-spline curve; (2) develop a new subdivision curve that is better approximated by its control polygon than either a cubic B-spline or an interpolating 4-point subdivision curve; (3) discover how a circuit inclusion tree may be used for identifying the faces in an arrangement; and (4) rectify a common misconception about the computation of the Hausdorff error between triangle meshes. We invite the scientific community to encourage the development of EDR by publishing its results as genuine research contributions in peer-reviewed professional journals.     

参数三次B样条曲线的一种整体光顺方法

本文在能量法的基础上，提出了一种新的目标函数，给出了参数三次Ｂ样条曲线的一种新的整体光顺方法。利用这种方法得到的曲线不仅具有较小的应变能，而且曲率变化比较均匀，具有很好的光顺效果。该方法能推广到对曲面的光顺。     

一种等高线自动加密算法

本文给出的算法可以在间距较大的等高线之间形成新的等高线，该算法以任意直线与B-样条曲线求变算法为基础。新等高践的形成建立在原有等高线和已知的离散点等客观信息基础之上，等高线加密效果好。     

Spline-based meshfree method with extended basis

In this work, an extension has been performed on the analysis basis of spline-based meshfree method (SBMFM) to stabilize its solution. The potential weakness of the SBMFM is its numerical instability from using regular grid background mesh. That is, if an extremely small trimmed element is produced by the trimming curves that represent boundaries of the analysis domain, it can induce an excessively large condition number in global system matrix. To resolve the instability problem, the extension technique of the weighted extended B-spline (WEB-spline) is implemented in the SBMFM. The basis functions with very small trimmed supports are extrapolated by neighboring basis functions with some special scheme so that those basis functions can be condensed in the solution process. In order to impose essential boundary conditions in the SBMFM with extended basis, Nitsche's method is implemented. Using numerical examples, the presented SBMFM with extended basis is shown to be valid and effective. Moreover, the condition number of the system is well-managed guaranteeing the stability of the numerical analysis.     

Total curvature variation fairing for medial axis regularization

We present a new fairing method for planar curves, which is particularly well suited for the regularization of the medial axis of a planar domain. It is based on the concept of total variation regularization. The original boundary (given as a closed B-spline curve or several such curves for multiply connected domains) is approximated by another curve that possesses a smaller number of curvature extrema. Consequently, the modified curve leads to a smaller number of branches of the medial axis. In order to compute the medial axis, we use the state-of-the-art algorithm from [1] which is based on arc spline approximation and a domain decomposition approach. We improve this algorithm by using a different decomposition strategy that allows to reduce the number of base cases from 13 to only 5. Moreover, the algorithm reduces the number of conic arcs in the output by approx. 50%.     

自适应B样条小波函数模糊距离测量方法

目的 双目测距和单目测距是目前常用的两种基于光学传感器的测距方法,双目测距需要相机标定和图像配准,计算量大且测量范围有限,而单目测距减少了对设备和场地的要求,加快了计算时间。为了解决现有的单目测距方法存在精度低、鲁棒性差等缺点,本文提出了一种基于单模糊图像和B样条小波变换的自适应距离测量方法。方法 引入拉普拉斯算子量化评估图像模糊程度,并根据模糊程度值自动定位阶跃边缘;利用B样条小波变换代替高斯滤波器主动模糊化目标图像,并通过分析图像模糊程度、模糊次数以及测量误差之间的关系模型,自适应地计算不同景物图像的最优模糊次数;根据最优模糊图像中阶跃边缘两侧模糊程度变化求解目标边缘和相机之间的相对距离。结果 本文方法与基于高斯模糊图像的距离测量方法相比精度更高,平均相对误差降低5%。使用不同模糊次数对同样的图像进行距离测量时,本文算法能够自适应选取最优模糊次数,保证所测量距离的精度更高。结论 本文提出的单视觉测距方法,综合了传统的方法和B样条小波的优点,测距结果更准确,自适应性和鲁棒性更高。     

平面铰链四杆机构的轨迹综合方法

为提高平面铰链四杆机构轨迹综合的速度与精度,提出基于B样条曲线的综合方法.采用三次非均匀B样条曲线对连杆曲线进行拟合,将B样条曲线控制多边形各相邻两边的夹角作为连杆曲线的特征参数,将大量连杆曲线特征参数和对应的机构尺寸参数存入计算机以建立电子图谱库;当输入一定数目的有序离散数据点时,通过B样条曲线拟合得到期望曲线,提取期望曲线的特征参数;再利用神经网络将期望曲线的特征参数与电子图谱库中特征参数进行匹配,从而找到满足要求的机构,最终达到轨迹综合的目的.设计实例表明,该方法可快速实现四杆机构的轨迹综合,综合的精度高且所提取的特征参数与连杆曲线方位、缩放比例无关,减少了图谱库的数据冗余.     

基于三次B样条有限元法的BBMB方程数值解

对空间和时间坐标分别采用三次B样条有限法和Crank-Nicolson差分法求得非线性BBMB方程的数值解,应用Von-Neumann稳定性理论证明了此方法的无条件稳定性,并且通过两个例子验证了该方法的有效性与可行性.