基于遗传算法的曲面最短路径求解

对曲面上两点间最短路径的求解是一个应用非常广泛,但理论求解困难的问题。遗传算法是一种新型的、较成熟的全局随机搜索算法,具有优良的性态。该文将遗传算法引入到曲面最短路径寻优的问题中。首先在离散化的模拟数字高程上依据起点和终点,以实数编码产生一系列初始群体,定义相应的适应度函数,然后对群体进行复制、交叉和变异等操作,求解出一条曲面上两点间的最短路径。在文章的最后给出了一个数值仿真实例来了证明该算法的有效性和实用性。     

求解曲面距离问题的模拟退火遗传算法

提出计算曲面距离的统一方法——退火遗传算法。该算法将模拟退火算法和遗传算法相结合,解决了曲面之间的距离问题。该方法将工业中常用的曲面统一用参数形式表示,利用遗传算法求解曲面的距离问题。该方法通过引入模拟退火机制和人为地加入一定数目的特殊个体,大大增强了算法的爬山性能。     

基于人类繁殖现象的遗传算法研究

标准遗传算法（SGA）只是对自然界遗传进化过程的比较简单的模拟,较少考虑人类特有的繁殖方式。提出一种基于人类繁殖现象的遗传算法（HRGA）,该算法的遗传算子包括选择算子、助长算子、交叉算子和变异算子,遗传个体具有雄性和雌性两种不同的性别,融合了个体的年龄和个体间的亲缘关系两种特征,在允许的年龄范围内,异性个体进行严格的远缘繁殖,从而克服了标准遗传算法容易出现的早熟收敛现象,提高了算法的收敛速度。通过对函数最优化问题的求解试验,证明了该算法具有很强的跳出局部收敛的能力,其全局收敛速度和最优解的质量明显高于标准遗传算法,同时也证明了该算法的有效性。     

元胞遗传算法的全局优化性能仿真分析

元胞遗传算法将遗传操作限制在邻域内进行,减缓了优势个体在群体中的扩散速度,具有更好的全局探索能力,在求解复杂优化问题中显示出优越性.与传统遗传算法对比,以选择压力作为分析手段,对元胞遗传算法进行定性分析.通过求解具有不同特征的函数,分析进化过程群体多样性变化.从进化过程群体分布图,直观得出元胞遗传算法具有较好的维持群体多样性能力;统计结果表明,元胞遗传算法能极大提高全局收敛率,并且求解稳定性更好.     

基于选择压力的全局优化元胞遗传算法分析

元胞遗传算法将遗传操作限制在邻域内进行,减缓了优势个体在群体中的扩散速度,具有更好的全局收敛性,在求解复杂优化问题中显示出优越性。与传统遗传算法对比,以选择压力作为分析手段,对元胞遗传算法进行定性分析。通过求解具有不同特征的函数,分析进化过程群体多样性变化,从进化过程群体分布图,直观得出元胞遗传算法具有较好的维持群体多样性能力;从计算的统计结果,得出元胞遗传算法能极大提高全局收敛率,并且求解稳定性更好。     

病毒进化遗传算法的车辆调度优化模型

为了提高车辆调度优化效率,提出一种病毒进化遗传算法的车辆调度优化模型。建立车辆调度的数学模型,采用遗传算法对模型进行求解,并采用病毒群体感染主群体,主群体在历代个体间纵向传递信息以利于全局优化,病毒群体通过感染操作在同代个体间横向传递信息利于局部搜索,进行仿真对比实验。结果表明,病毒进化遗传算法较好地解决了标准遗传算法存在的不足,加快了车辆调度优化问题的求解效率,获得了更优的车辆调度方案,具有较高的应用价值。     

直觉模糊小生境的自适应遗传算法求解旅行商问题

提出一种基于直觉模糊距离测度的小生境技术,结合模糊控制的自适应遗传算法求解旅行商问题。运用个体在遗传算法迭代寻优中的适应度值,通过直觉模糊集的距离测度确定个体之间的相似性,使用共享函数和惩罚函数对适应度低的个体进行惩罚和淘汰,维护了种群个体的多样性;建立模糊推理系统,以自适应调节遗传算法迭代中的交叉率和变异率,使遗传算法能在局部寻优和全局寻优之间达到平衡,弥补遗传算法易早熟收敛和后期寻优能力差的缺陷;通过求解TSPLIB中的多组实例并进行对比,结果表明所提算法的收敛速度、优化精度、效率均具有明显优势。     

CRGA--一种基于保留全局公共模式和约束交叉位置的遗传算法

提出了一种基于保留全局公共模式和约束交叉位置的遗传算法CRGA,该算法解决了标准交叉算子容易破坏高阶、长而好的模式及其在相似个体之间低效的问题,CRGA通过对适应度高于群体平均适应度的个体模式基因值的统计来估算父个体基因值在子个体中保留的概率,从而达到对高阶、长而好的模式的保护;同时通过约束交叉位置,保证了交叉操作一定能产生新个体．实验结果表明,CRGA算法在收敛精度和收敛速度上都要明显优于基于标准交叉算子的遗传算法．     

单纯形搜索在遗传算法中的融合研究

构造了单纯形混合遗传算法SM-HGA⁺。分析单纯形搜索算法,提出了单纯形交叉算子和K步随机单纯形搜索算子,并将单纯形搜索算法和这两个算子分别融入到最优微群体μP_B（t）、最差微群体μP_W（t）和普通群体P_C（t）,形成SM-HGA⁺。最优微群体中的单纯搜索算法提高算法的精度;最差微群体中的单纯形交叉算子加速最差个体向优秀个体进化;普通群体中K步随机单纯性搜索提高全局搜索速度,同时在普通群体采用大交叉概率的标准遗传算法,提高全局搜索能力。遗传算法测试函数验证算法SM-HGA⁺的正确性、效率。     

求解NURBS曲面间最小距离的人工势场算法

针对Newton-Raphson(NR)法对初值要求苛刻的缺点,结合人工势场法和Verlet算法,提出一种求解NURBS曲面间最小距离的人工势场算法.该算法构建了小球势力场模型,通过分析小球受力情况,采用Verlet算法模拟小球在势力场中的运动过程,两球平衡位置即为曲面间最小距离处.将曲面边界问题用统一的算法描述,通过...     

Minimum distance between two sphere-swept surfaces

We present an efficient and robust approach for computing the minimum distance between two sphere-swept surfaces. As examples of sphere-swept surfaces, we consider canal surfaces and bivariate sphere-swept surfaces. For computing the minimum distance between two parametric surfaces, a simple technique is to find the two closest points from the given surfaces using the normal vector information. We suggest a novel approach that efficiently computes the minimum distance between two sphere-swept surfaces by treating each surface as a family of spheres. Rather than computing the complicated normal vectors for given surfaces, our method solves the problem by computing the minimum distance between two moving spheres. We prove that the minimum distance between two sphere-swept surfaces is identical to that between two moving spheres. Experimental results of minimum distance computation are given. We also reproduce the result of Kim [Kim K-J. Minimum distance between a canal surface and a simple surface. Computer-Aided Design 2003;35:871-9] based on the suggested approach.     

Computing minimum distance between two implicit algebraic surfaces

The minimum distance computation problem between two surfaces is very important in many applications such as robotics, CAD/CAM and computer graphics. Given two implicit algebraic surfaces, a new method based on the offset technique is presented to compute the minimum distance and a pair of points where the minimum distance occurs. The new method also works where there are an implicit algebraic surface and a parametric surface. Quadric surfaces, tori and canal surfaces are used to demonstrate our new method. When the two surfaces are a general quadric surface and a surface which is a cylinder, a cone or an elliptic paraboloid, the new method can produce two bivariate equations where the degrees are lower than those of any existing method.     

自由曲面之间最短距离的一种新的改进遗传算法

遗传算法具有独有的特性,它采用选择、交叉和变异等策略,获取的解为全局最优解,而且无需计算函数的导数,是一种只考虑输入与输出关系的黑箱方法,因而适用于处理各种复杂问题。由于自由曲面的不规则性,自由曲面最短距离是CAD/CAM领域一个最重要的研究课题之一,也是一个难题。文章基于自由曲面的特性,在遗传算法中引入新的特殊个体,通过大量的计算与分析,提出了求自由曲面之间最短距离的一种新的改进遗传算法,并给出了计算实例,效果显著。     

Finding Starting Points for Tracing Surface Intersections

1 Introduction Finding out proper starting points for all the intersection curves between two surfaces is a key process in numerical tracing methods for surface-surface intersection (SSI) problems. A number of methods [1] are introduced to calculate the starting points. Cugini et al. [2] introduced the concept of shrinking bounding boxes to calculate starting points. This method is simple and in some cases effective, but it may miss some intersection components. Muellenheim [3] presented an…     

Finding Starting Points for Tracing Surface Intersections

To find starting points for all the intersection curves, one of the surfaces is subdivided into some small surface patches. Based on a correlative algorithm of computing the minimum distance of two surfaces, the intersections of every patch with another surface are detected, and starting points are calculated by dichotomy. This algorithm shows superior efficiency in the computational complexity and number of iterations needed. It can be used to determine exact starting points on all possible solution curves between any kinds of parametric sculptured surfaces.     

Curvature-based anisotropic geodesic distance computation for parametric and implicit surfaces

Distribution of geometric features varies with direction, including, for example, normal curvature. In this paper, this characteristic of shape is used to define a new anisotropic geodesic (AG) distance for both parametric and implicit surfaces. Local distance (LD) from a point is defined as a function of both the point and a unit tangent plane directions, and a total distance is defined as an integral of that local distance. The AG distance between points on the surface is the minimum total distance between them. The path between the points that attains the minimum is called the anisotropic geodesic path. Minimization of total distance to attain the AG distance is performed by associating the LD function with a tensor speed function that controls wave propagation in the convex Hamilton–Jacobi (H–J) equation solver. We present new distance metrics for both parametric and implicit surfaces based on the curvature tensor. In order to solve for the implicit AG, a bounded 3D H–J equation solver was developed. We present a second metric for the AG distance, a difference curvature tensor, for parametric surfaces. Some properties of both new AG distances are presented, including parameterization invariance. This AG path differs from the usual geodesic in that minimal path, i.e., lowest cost path, roughly speaking, minimizes an integral of curvature along the curve. Then, the effectiveness of the proposed AG distances as shape discriminators is demonstrated in several applications, including surface segmentation and partial shape matching.

三维带符号的欧氏距离变换及其应用

距离变换是图像处理中历史悠久的研究课题．该文将二维带符号的欧氏距离变换推广到三维，对其进行了优化，分析了它的计算复杂度，并应用于解决计算机图形学中的两个重要问题：第一，将图形对象的三角网格表示转换为它的距离场表示．即首先将三角网格模型离散为体素表示，利用三维带符号的距离变换，将求空间一点到图形对象的最短距离的全局搜索过程，转化为求这一点到离它最近的特征体素所包含的图形对象部分的局部搜索过程；第二，利用类似的思想，求两张空间曲面之间的最短距离．     

GPU-accelerated Hausdorff distance computation between dynamic deformable NURBS surfaces

We present a parallel GPU-accelerated algorithm for computing the directed Hausdorff distance from one NURBS surface to another, within a bound. We make use of axis-aligned bounding-box hierarchies that bound the NURBS surfaces to accelerate the computations. We dynamically construct as well as traverse the bounding-box hierarchies for the NURBS surfaces using operations that are optimized for the GPU. To compute the Hausdorff distance, we traverse this hierarchy after culling bounding-box pairs that do not contribute to the Hausdorff distance. Our contribution includes two-sided culling tests that can be performed in parallel using the GPU. The culling, based on the minimum and maximum distance ranges between the bounding boxes, eliminates bounding-box pairs from both surfaces that do not contribute to the Hausdorff distance simultaneously. We calculate accuracy bounds for our computed Hausdorff distance based on the curvature of the surfaces. Our algorithm runs in real-time with very small guaranteed error bounds for complex NURBS surfaces. Since we dynamically construct our bounding-box hierarchy, our algorithm can be used to interactively compute the Hausdorff distance for models made of dynamic deformable surfaces.     

Minimum distance between a canal surface and a simple surface

The computation of the minimum distance between two objects is an important problem in the applications such as haptic rendering, CAD/CAM, NC verification, robotics and computer graphics. This paper presents a method to compute the minimum distance between a canal surface and a simple surface (i.e. a plane, a natural quadric, or a torus) by finding roots of a function of a single parameter. We utilize the fact that the normals at the closest points between two surfaces are collinear. Given the spine curve C(t), t_min≤t≤t_max, and the radius function r(t) for a canal surface, a point on the spine curve uniquely determines a characteristic circle on the surface. Normals to the canal surface at points on form a cone with a vertex and an axis which is parallel to Then we construct a function of t which expresses the condition that the perpendicular from C(t) to a given simple surface is embedded in the cone of normals to the canal surface at points on K(t). By solving this equation, we find characteristic circles which contain the points of locally minimum distance from the simple surface. Based on these circles, we can compute the minimum distance between given surfaces.     

基于曲率特征的自由曲面匹配算法

针对无任何预知联系下的自由曲面匹配问题,提出了一种简捷、快速的匹配方法.该方法以曲面的曲率为联系特征,在测量数据与模型曲面之间建立起满足角度、距离约束的对应关系,利用三点旋转平移变换法生成旋转平移变换列表;然后通过最小距离目标函数选取正确的三维坐标变换,实现测量数据与模型曲面之间的准确匹配.实验结果表明:该方法简捷、可靠且容易实现,特别适用于工件的测量定位和多视数据的融合.