多面体光线跟踪的两种快速算法

本文提出了适用于凸，凹多面体光线跟踪的两种快带算法。     

Estimating subdivision depth of Catmull-Clark surfaces

In this paper, both general and exponential bounds of the distance between a uniform Catmull-Clark surface and its control polyhedron are derived. The exponential bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Based on the exponential bound, we can predict the depth of subdivision within a user-specified error tolerance. This is quite useful and important for pre-computing the subdivision depth of subdivision surfaces in many engineering applications such as surface/surface intersection,mesh generation, numerical control machining and surface rendering.     

判断两个凸多面体是否相交的一个快速算法

在机器人路径规划中,碰撞检测算法占有十分重要的地位.在智能机器人仿真系统中,碰撞检测耗用的时间在整个路径规划过程所用时间中占有相当大的比例.于是,如何进一步提高碰撞检测的速度在智能机器人路径规划系统中就起到了非常关键的作用.而碰撞检测问题最终转化为判断三维空间中两个凸多面体是否相交的问题.就这一问题,给出了一种新的算法,其思想是取一个从一个凸多面体指向另一个多面体的向量,根据两个多面体中的面与这一向量的相对位置关系来寻找相交的平面.即有两个多面体的交点位于这一平面,若能找到一个相交平面则可以断定两个多面体     

An evolutionary method for general surface-surface intersection problems

A new approach to surface-surface intersection problems is proposed. Surface-surface intersection forms a fundamental function in computational geometry and geometric modeling. A geometric modeler needs to be equipped with a robust and accurate SSI algorithm to deal with a wide range of complex models. Although many methods have been proposed, it is generally known that computation of surface intersections is not an easy task in a computer environment. A new genetic algorithm, called Surface Intersection with Genetic Algorithm (SIGA), is developed. Several steps of an existing genetic algorithm are modified so that the new algorithm can be well suited to the intersection problems. A main advantage of SIGA is that it guarantees probabilistically finding all intersection curves.     

A method of transferring polyhedron between the intersection-form and the sum-form

A bounded polyhedron (or a polyhedral cone) can be given by either an intersection of linear inequalities, which is thus called intersection-form, or a convex combination (or nonnegative linear combination) of some given points, which is thus called sum-form. This paper first proposes a simple and effective method to transfer a bounded polyhedron or a polyhedral cone from the intersection-form to the sum-form. A new method is proposed to transfer a bounded polyhedron (or a polyhedral cone) from the sum-form to the intersection form. Both procedures can be completed in finite number of iterations. Numerical examples are given for illustration.     

碰撞检测技术研究综述

碰撞检测在图形学、仿真、动画和虚拟现实等技术中得到广泛的研究,这些研究具有十分重要的意义。文章对二维空间中多边形等面模型间相交,以及三维空间中多面体等体模型间干涉的角度对碰撞检测技术的研究和发展作了较为全面的论述,并对几种常用的碰撞检测算法进行了分析和比较,最后对碰撞检测算法的发展方向提出了几点建议。     

A quick point-in-polyhedron test

To decide whether a point is contained in a polyhedron, one may use the parity of the number of intersections of a halfline with the boundary of the polyhedron. Difficulties arise if the halfline meets an edge or a vertex. To resolve such singularities, we propose to associate to each point of intersection a certain positive or negative weight and then to consider the sum of these weights.     

Projective Visual Hulls

This article presents a novel method for computing the visual hull of a solid bounded by a smooth surface and observed by a finite set of cameras. The visual hull is the intersection of the visual cones formed by back-projecting the silhouettes found in the corresponding images. We characterize its surface as a generalized polyhedron whose faces are visual cone patches; edges are intersection curves between two viewing cones; and vertices are frontier points where the intersection of two cones is singular, or intersection points where triples of cones meet. We use the mathematical framework of oriented projective differential geometry to develop an image-based algorithm for computing the visual hull. This algorithm works in a weakly calibrated setting–-that is, it only requires projective camera matrices or, equivalently, fundamental matrices for each pair of cameras. The promise of the proposed algorithm is demonstrated with experiments on several challenging data sets and a comparison to another state-of-the-art method.     

Control of continuous‐time Markov chains with safety constraints

In this work the controlled continuous‐time finite‐state Markov chain with safety constraints is studied. The constraints are expressed as a finite number of inequalities, whose intersection forms a polyhedron. A probability distribution vector is called safe if it is in the polyhedron. Under the assumptions that the controlled Markov chain is completely observable and the controller induces a unique stationary distribution in the interior of the polyhedron, the author identifies the supreme invariant safety set (SISS) where a set is called an invariant safety set if any probability distribution in the set is initially safe and remains safe as time evolves. In particular, the necessary and sufficient condition for the SISS to be the polyhedron itself is given via linear programming formulations. A closed‐form expression for the condition is also derived as the constraints impose only upper and/or lower bounds on the components of the distribution vectors. If the condition is not satisfied, a finite time bound is identified and used to characterize the SISS. Numerical examples are provided to illustrate the results. Copyright © 2011 John Wiley & Sons, Ltd.     

序列模式挖掘的并行算法研究

序列模式在许多领域都有着重要的应用,大量的数据和模式需要高效的、可扩展的并行算法.针对目前序列模式挖掘算法存在的普遍问题,提出了一个适合无共享并行环境下的算法PMSP,有效地解决了存储受限以及时效性问题,并将它与当前相对较优的并行算法HPSPM做了比较,实验表明PMSP是有效的.     

柔性多面体在遗传算法中的应用研究(I)

文章提出了一种柔性多面体的方向进化算子,并在基本遗传算法中嵌入柔性多面体搜索算法,从而构成了一种基于柔性多面体的新的混合遗传算法(flexiblepolyhedronhybridgeneticalgorithm,FP_HGA)。方向进化算子紧跟基本遗传算法的变异操作之后,其作用是使适应度较低的个体向适应度较高的个体进化;柔性多面体局部搜索算法作用是对当前代所有新个体在进入到下一代之前,使它移动到局部最优点。并用FP_HGA来求解Rosenbrock测试函数的最小值,FP_HGA算法和SGA(SimpleGeneticAlgorithm,SGA)算法的计算结果表明该混合遗传算法在收敛速度和精度方面均得到很大提高。     

重建小凸多面物体面形的新方法

为实现小凸多面物体面形快速重建,提出了基于投影轮廓的新方法。首先处理被测小凸多面物体各平行旋转角度下纵投影轮廓图像,得到对应轮廓序列集及横截面切片投影长度曲线集,然后由该曲线集得到所有疑似被测物体表平面的索引,将该索引对照各轮廓序列进行筛选,最后经计算得到被测物体的各表平面参数,完成面形重建。实验表明,该方法能够精确恢复被测小凸多面物体面形,与现有方法相比具有设备精简、速度快等特点,适用于针对小凸多面体工件的工程应用。     

多个凹凸形多面体的深度优先消隐算法研究

为了对多个凹凸形多面体进行消隐处理,应首先对单个凹凸形多面体进行可见性测试。对多个凹凸形多面体间可能出现的遮蔽进行屏幕投影多边形的重叠排除验证,对可能出现重叠的多边形边进行交点计算、包容性测试和深度检查。本文指出,凹凸形多面体在可见性测试及投影多边形包容性测试方面应采用不同的处理方法。实践结果表明,此算
算法可以取得较好的效果。     

Computation of probabilities of survival/failure of technical,economic systems/structures by means of piecewise linearization of the performance function

The computation of the probability of survival/failure of technical/economic structures and systems is based on an appropriate performance or so-called (limit) state function separating the safe and unsafe states in the space of random model parameters. Starting with the survival conditions, hence, the state equation and the condition for the admissibility of states, an optimizational representation of the state function can be given in terms of the minimum value function of a closely related minimization problem. Selecting a certain number of boundary points of the safe/unsafe domain, hence, on the limit state surface, the safe/unsafe domain is approximated by a convex polyhedron. This convex polyhedron is defined by the intersection of the half spaces in the parameter space generated by the tangent hyperplanes to the safe/unsafe domain at the selected boundary points on the limit state surface. The approximative probability functions are then defined by means of the resulting probabilistic linear constraints in the parameter space. After an appropriate transformation, the probability distribution of the parameter vector can be assumed to be normal with zero mean vector and unit covariance matrix. Working with separate linear constraints, approximation formulas for the probability of survival of the structure are obtained immediately. More exact approximations are obtained by considering joint probability constraints. In a second approximation step, these approximations can be evaluated by using probability inequalities and/or discretizations of the underlying probability distribution.     

Finding the intersection of two convex polyhedra

Given two convex polyhedra in three-dimensional space, we develop an algorithm to (i) test whether their intersection is empty, and (ii) if so to find a separating plane, while (iii) if not to find a point in the intersection and explicitly construct their intersection polyhedron. The algorithm runs in timeO (nlogn), where n is the sum of the numbers of vertices of the two polyhedra. The part of the algorithm concerned with (iii) (constructing the intersection) is based upon the fact that if a point in the intersection is known, then the entire intersection is obtained from the convex hull of suitable geometric duals of the two polyhedra taken with respect to this point.     

运动曲面求交优化算法

运动曲面求交通常采用曲面求交算法，通过反复迭代求取曲面交线，没有考虑运动曲面自身的特性进行求交简化．由于运动曲面不同运动瞬间的曲面交线之间存在必然联系，因此通过对曲面内在属性分析，提出了运用运动曲面不同运动瞬间曲面交线相似性进行运动曲面求交的优化算法．首先对两个运动曲面的基曲面进行预处理。获取表征曲面交线拓扑的特征点；根据特征点分布图确定不同运动瞬间曲面交线起始点搜索策略，采用跟踪法动态调整步长和跟踪方向求解整个交线环．采用文中方法可以有效地解决运动曲面的子环、奇点遗漏、分支跳跃、乱序跟踪和初始点求取问题，精确、鲁棒、快速地计算出交线．     

云环境下方差定向变异遗传算法的任务调度

云环境下遗传算法（GA）的任务调度存在寻优能力差、结果不稳定等问题。对于上述问题,提出了一种基于方差与定向变异的遗传算法（V-DVGA）。在选择部分,在每一次迭代的过程中进行多次选择,利用数学方差来保证种群的多样性并扩大较优解的搜索范围。在交叉部分,建立新的交叉机制,丰富种群的多样性并提高种群整体的适应度。在变异部分,优化变异机制,在传统变异的基础上采用定向变异来提高算法的寻优能力。通过workflowSim平台进行云环境仿真实验,将此算法与经典的遗传算法和当前的基于遗传算法的工作流调度算法（CWTS-GA）进行比较。实验结果表明,在相同的设置条件下,该算法在执行效率、寻优能力和稳定性等方面优于其他两个算法,是一种云计算环境下有效的任务调度算法。     

Kinematics of grasping and manipulation of a B‐spline surface object by a multifingered robot hand

Kinematics of grasping and manipulation by a multifingered robotic hand where multifinger surfaces are in contact with an object is solved. The surface of the object was represented by B‐spline surfaces to model objects of various shapes. The fingers were modeled by cylindrical links and a half ellipsoid fingertip. Geometric contact equations have been solved for all possible contact combinations between the finger surface and the object. The simulation system calculated joint displacements and contact locations for a given trajectory of the object. Since there are no closed form solutions for contact or intersection between these surfaces, kinematics of grasping was solved by recursive numerical calculation. The initial estimate of the contact point was obtained by approximating the B‐spline surface by a polyhedron. As for the simulation of manipulation, exact contact locations were updated by solving the contact equations according to the given contact conditions such as pure rolling, twist‐rolling, or slide‐twist‐rolling. Several examples of simulation of grasping and manipulation are presented. ©1999 John Wiley & Sons, Inc.