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.     

基于双三次B样条插值的空间结构自由曲面

双三次B样条插值曲面方法是工业造型、机械制造领域应用成熟的一种自由曲面设计方法，本在分析空间结构曲面设计现状、需求以及不足的基础上，提出了应用C^2连续的双三次B样条插值曲面方法进行空间结构自由曲面设计算法，并通过实例论证了该算法的可行性和有效性。     

利用曲线面变形提取产品形态体特征的方法研究

在变形设计理论的基础上,提出了将产品主体形态分解为子形态。研究了基于超椭圆方程和三次带参均匀B样条曲线构造技术提取影响产品艺术风格子形态横截面造型特征的方法,并结合曲面构造变形技术实现产品形态体特征的提取。以电动手工具为例研究了产品形态体特征提取与形态优化设计效果,得出超椭圆方程提取算法参数少,可较好地提取对称图形、非倒角图形的造型特征;基于三次带参均匀B样条曲线构造技术的算法参数较多,可较好地提取多种图形。     

Shape transformer nets: Generating viewpoint-invariant 3D shapes from a single image

Single-view 3D shapes generation has achieved great success in recent years. However, current methods always blind the learning of shapes and viewpoints. The generated shape only fit the observed viewpoints and would not be optimal from unknown viewpoints. In this paper, we propose a novel encoder–decoder based network which contains a disentangled transformer to generate the viewpoint-invariant 3D shapes. The differentiable and parametric Non-uniform B-spline (NURBS) surface generation and 3D-to-3D viewpoint transformation are incorporated to learn the viewpoint-invariant shape and the camera viewpoint, respectively. Our new framework allows us to learn the latent geometric parameters of shapes and viewpoints without knowing the ground truth viewpoint. That can simultaneously generate camera-viewpoint and viewpoint-invariant 3D shapes of the object. We analyze the effects of disentanglement and show both quantitative and qualitative results of shapes generated at various unknown viewpoints.     

Offshore wind turbine blades measurement using Coherent Laser Radar

To maximize aerodynamic efficiency, large-scale offshore wind turbine blades require inspection during the production stage to ensure strict tolerance requirements are met. During production, the blade is fixed at the root, restricting movement in the Z direction. X, Y, Rx, Ry and Rz remain unconstrained causing blade flex due to gravity. This deforms the blade away from the theoretical CAD blade location, causing measurement results that do not accurately represent the blade profile. Measurement error can be minimized using rigorous B-spline data alignment. Such alignment compensates for blade flex by varying the constrained Degrees of Freedom (DoF), and provides manufacturers with confidence in the design process. This paper used Coherent Laser Radar and Spatial Analyzer to establish the optimal constrained DoF variation, giving the most accurate data alignment solution. Of the constraints investigated, the optimal data transformation solution was found with a double B-spline alignment method, whilst constraining movement in Y, Z and Ry.     

Exponential splines and minimal-support bases for curve representation

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show that the minimal-support basis functions of that subspace are linear combinations of derivatives of exponential B-splines. These minimal-support basis functions form a natural multiscale hierarchy, which we utilize to design fast multiresolution algorithms and subdivision schemes for the representation of closed geometric curves. This makes them attractive from a computational point of view. Finally, we illustrate our scheme by constructing minimal-support bases that reproduce ellipses and higher-order harmonic curves.     

B-spline method for solving Bratu's problem

In this paper, we propose a B-spline method for solving the one-dimensional Bratu's problem. The numerical approximations to the exact solution are computed and then compared with other existing methods. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where two solutions occur.     

基于二维小波变换的爆堆矿岩边缘检测

根据爆堆图像灰度分布的特点,并结合小波变换应用于边缘检测的基本原理,采用能够检测局部突变能力的B样条小波用于爆堆岩石的边缘检测。通过推导,给出B样条小波滤波器,并根据滤波器设计出了基于二维小波边缘检测算法。在小波边缘分割中自主设计了自适应阈值检测算法,该算法能很好地去除图像的噪声,并保留了图像的边缘。     

四参数宽带B样条子波

本文基于地震尖脉冲的小波分解及其重构原理,提出一种基于部分尺度下信号重构理论的宽带子波构成方法,利用此方法可以形成一系列各具特色的地震子波。基于复B样条小波,具体讨论四参数宽带B样条地震子波的构成,推导出四参数宽带B样条子波的时间域和频率域的解析表达式。四参数宽带B样条地震子波不仅具有可直接调节旁瓣衰减的参数,而且还可以直接调节相位的个数,与相同主瓣等效频率的雷克子波和俞氏子波相比,四参数宽带B样条子波旁瓣小,非零时间点的延续时间短。楔形模型制作的合成地震记录表明,四参数宽带B样条子波的分辨率更高且参数选择更为灵活,可为地震资料处理提供一个更方便、更灵活的地震理论子波。     

Damage identification in composite plates using two-dimensional B-spline wavelets

In this paper the construction of general order two-dimensional B-spline wavelets was presented and applied for damage identification in polymeric composite plates. At the very beginning the algorithm of one- and two-dimensional discrete wavelet transform and formulation of one- and two-dimensional B-spline wavelets with examples were presented. The fully clamped square layered composite plate was modeled using finite element-based software. Estimated natural modes of vibration with various damage configurations were analyzed using the two-dimensional sixth-order B-spline wavelet, and the method of damage identification was presented. The effective damage identification is based on the evaluation of the singularities in horizontal, vertical and diagonal details coefficients. Results obtained based on the numerical data were verified experimentally. Research results show the effectiveness of B-spline wavelets in application to the diagnostics and structural health monitoring.