一种基于节点插入技术的B样条曲线平滑方法

三次均匀B样条曲线是工程上广泛采用的曲线绘制方法。提高节点插入算法的效率,实现B样条曲线的平滑效果,是广大学者所关注的问题。文章给出了一种基于Tailor级数展开的三次均匀B样条曲线节点插入的生成算法,并利用该算法提供的节点插入技术来实现三次均匀B样条曲线的平滑效果。与Oslo算法的递推过程相比,该节点插入算法在一定程度上简化了运算过程,提高了算法的生成效率。     

有理Bezier曲线的快速逐点生成算法

该文提出了一种有理Bezier曲线的快速逐点生成算法。该算法不但能够用于低次和高次有理Bezier曲线,而且还能用于均匀有理B样条曲线或NURBUS曲线。该算法具有快速的生成速度、高效率以及广泛的应用价值。     

具有任意自由度的B样条非均匀细分*

为了便于工程实际应用,非均匀细分方法现在已经成为计算机图形学和几何建模中的热点问题。本文提出一个具有任意自由度的B样条非均匀细分算法,其实现与B样条均匀细分即Lane–Riesenfeld细分方法相似。该算法包含了非均匀d环结构生成的双重控制点,其中d环相似于d度均匀B样条曲线的Lane-Riesenfeld算法中均匀的d环结构。Lane-Riesenfeld算法是由B样条曲线基函数的连续卷积公式直接得出的,而本文的算法是blossoming方法的一个扩展。对于非均匀B样条曲线来说,本文的节点插入方法比之前的方法更简单更有效。     

细分生成B样条的几何作图法

研究均匀B样条曲线细分生成的几何作图问题,给出了采用p-nary细分法细分生成任意次均匀B样条曲线的递归细分算法。在此基础上,研究了任意次均匀B样条曲线p-nary细分生成的几何作图方法。利用这种几何作图法,可以直观地在计算机上通过编程来快速准确地绘制B样曲线,更重要的是,可以使基于几何方法的任意次B样曲线的手工绘制成为可能。     

二维手绘草图的非均匀α-B插值样条曲线表示的方法研究*

根据非均匀α-B插值样条曲线的一般形式,结合非均匀α-B插值样条曲线的形状调配方法,产生了一种新方法来解决二维手绘草图的表示问题。在二维草图中,研究了基于非均匀αB插值样条曲线的草图表示、草图生成、草图修改以及草图缩放的算法。这种表示方法模型统一,生成插值点的算法简单,适合分布式网络环境下的实时协作。表示后的草图缩放具有向量图缩放的优点,设计人员可以在缩放后的草图上进行形状调配。     

利用弦长参数插值拟合光滑闭合B样条曲线构造方法

文章针对非均匀采样点拟合光滑B样条曲线构造问题,提出一种基于已知控制点和相邻控制点之间弦长求解控制点方程组系数矩阵来构造光滑B样条曲线的方法。该方法通过控制顶点所在曲线的光顺性提高最终生成曲线的连续性和光滑性。在此基础上,设计了闭合B样条曲线控制点的快速求解算法。首先利用所有控制顶点和相邻点间弦长建立求解系数的参数矩阵,再提出一种基于LU矩阵分解的优化算法。根据方程组系数矩阵的特点,参照追赶法的LU分解,构造了分解后的L、U矩阵结构。最后通过实例说明,采用文中方法所构造的B样条曲线具有较好的光滑性,也证明了该算法的可靠性和有效性。     

一种任意次非均匀B 样条的细分算法

类似于经典的、应用于任意次均匀B 样条的Lane-Riesenfeld 细分算法, 提出了一种任意次非均匀B 样条的细分算法,算法包含加细和光滑两个步骤,可生成任意 次非均匀B 样条曲线。算法是基于于开花方法提出的,不同于以均匀B 样条基函数的卷积 公式为基础的Lane-Riesenfeld 细分算法。通过引入两个开花多项式,给出了算法正确性的 详细证明。算法的时间复杂度优于经典的任意次均匀B 样条细分算法,与已有的任意次非 均匀B 样条细分算法的计算量相当。     

一种n次均匀B样条曲线细分算法

利用 次均匀B样条细分的掩模与Pascal三角形关系,并借助控制多边形在每次加细过程中新旧控制顶点对应的几何位置关系,给出一种新的 次均匀B样条曲线细分算法,基于该算法构造出带有形状参数的局部插值约束的奇次均匀B样条细分曲线。通过理论和算例说明,该算法几何直观性强、新旧点对应明确、应用灵活且能保持良好的参数连续性。     

基于非均匀B样条的船体型线设计软件的研究与应用

文章主要通过对船舶型线设计和非均匀B样条特性的研究,结合船舶型线设计软件,提出了非均匀B样条在船舶型线设计中的应用方法和原理,并提供了必要的数学证明。首先,讨论了利用曲线的分段连接点与控制点或控制多边形的边对应关系,确定非均匀B样条节点矢量的方法,从而解决了用非均匀B样条生成型线的先决问题;其次,提出了K次非均匀B样条曲线的节点插值方法,并讨论了在非封闭曲线和封闭曲线条件下如何反算样条曲线控制点的数学方法;然后,提出了r阶非均匀B样条的导矢算法;最后提出了国内船舶型线辅助设计软件有待进一步研究和发展的一些看法。     

隐多项式曲线的快速逐点生成算法

隐多项式曲线一直没有理想的生成算法,给出了一种针对二维n次隐多项式曲线的快速逐点生成算法,该算法思路简洁,在逐点生成过程中,只用到整数加减法,故速度快,效率高,具有广泛的应用价值。最后,运用算法给出了曲线生成实例和对算法效率的比较,比较结果表明本文提出的算法有效的提高了生成曲线的效率。     

2D affine-invariant contour matching using B-spline model

This paper presents a new affine-invariant matching algorithm based on B-Spline modeling, which solves the problem of the non-uniqueness of B-Spline in curve matching. This method first smoothes the B-Spline curve by increasing the degree of the curve. It is followed by a reduction of the curve degree using the Least Square Error (LSE) approach to construct the Curvature Scale Space (CSS) image. CSS matching is then carried out. Our method combines the advantages of B-Spline that are continuous curve representation and the robustness of CSS matching with respect to noise and affine transformation. It avoids the need for other matching algorithms that have to use the re-sampled points on the curve. Thus, the curve matching error is reduced. The proposed algorithm has been tested by matching similar shapes from a prototype database. The experimental results showed the robustness and accuracy of the proposed method in B-Spline curve matching.     

基于B-样条曲线的线缆变形仿真

线缆变形仿真是线缆辅助设计和维修过程仿真需要解决的核心问题,也是目前虚拟现实技术研究的热点之一。B-样条曲线是计算几何学的重要理论成果,已经广泛应用于计算机辅助设计。本文首先对B-样条函数的概念进行了简单介绍,分析了用三次开放B-样条曲线进行线缆变形仿真的优越性;然后将全局能量优化方法与高度坐标置零法结合求解曲线控制点的坐标,建立关于已知两端点位置和通过指定点的线缆模型;用Lagrange乘子法建立指定点有切矢约束的线缆模型。这种方法描述的是处于平衡状态的线缆变形,计算量小,模型逼真,而且形状控制方便,能够实现线缆布线指导和维修过程仿真。     

一种B样条曲线局部修改算法

针对B样条曲线局部修改的问题,提出一种双正交非均匀B样条小波与外部能量约束相结合的算法。与传统能量约束法相比,该算法使曲线除局部修改外整体形变较小,具有一定的保形效果。     

重心坐标下曲线的像素级生成算法

对重心坐标下的曲线方程以及重心坐标下曲线的生成进行了研究,提出一和像素级的生成算法,由于只涉及到加减法,效率极高。     

Supervised training algorithms for B-Spline neural networks and neuro-fuzzy systems

Complete supervised training algorithms for B-Spline neural networks and fuzzy rule-based systems are discussed. By introducing the relationships between B-Spline neural networks and Mamdani (satisfying certain assumptions) and Takagi-Kang-Sugeno fuzzy models, training algorithms developed initially for neural networks can be adapted to fuzzy systems. The standard training criterion is reformulated, by separating its linear and nonlinear parameters. By employing this reformulated criterion with the Levenberg-Marquardt algorithm, a new training method, offering a fast rate of convergence is obtained. It is also shown that the standard Error-Back Propagation algorithm, the most common training method for this class of systems, exhibits a very poor and unreliable performance.     

参数多项式曲线的快速逐点生成算法

给出了参数多项曲线（包括Ｂｅｚｉｅｒ曲线、Ｂ样条曲线等）的一种快速逐点生成算法．在曲线的逐点生成过程中,只用到加减法,故效率极高．而且,此方法可在两３方面加以推广,一是推广到有理参数曲线（包括非均匀有理Ｂ样条曲线）,一是推广到多项式参数曲面以及更高维的多项式参数函数．     

B-Spline Curve Approximation by Utilizing Big Bang-Big Crunch Method

The location of knot points and estimation of the number of knots are undoubtedly known as one of the most difficult problems in B-Spline curve approximation. In the literature, different researchers have been seen to use more than one optimization algorithm in order to solve this problem. In this paper, Big Bang-Big Crunch method (BB-BC) which is one of the evolutionary based optimization algorithms was introduced and then the approximation of B-Spline curve knots was conducted by this method. The technique of reverse engineering was implemented for the curve knot approximation. The detection of knot locations and the number of knots were randomly selected in the curve approximation which was performed by using BB-BC method. The experimental results were carried out by utilizing seven different test functions for the curve approximation. The performance of BB-BC algorithm was examined on these functions and their results were compared with the earlier studies performed by the researchers. In comparison with the other studies, it was observed that though the number of the knot in BB-BC algorithm was high, this algorithm approximated the B-Spline curves at the rate of minor error.     

Genetic B-Spline approximation on combined B-reps

We present a genetic algorithm for approximating densely sampled curves with uniform cubic B-Splines suitable for Combined B-reps. A feature of this representation is altering the continuity property of the B-Spline at any knot, allowing to combine freeform curves and polygonal parts within one representation. Naturally there is a trade-off between different approximation properties like accuracy and the number of control points needed. Our algorithm creates very accurate B-Splines with few control points, as shown in Fig.?1. Since the approximation problem is highly nonlinear, we approach it with genetic methods, leading to better results compared to classical gradient based methods. Parallelization and adapted evolution strategies are used to create results very fast.