A collisions evaluation method in virtual environment for collaborativeassembly

Collision detection is critical for collaborative assembly simulation to assist design processing. However, collisions between polygonal models may not reflect collisions between real objects in reality because of polygonal approximation and designed tolerance. This problem reduces the reliability of simulation in collaborative assembly and sometimes even results in wrong conclusions. To solve the problem, we propose a novel collision evaluation algorithm based on generalized penetration depth, approximation information, and tolerance information. Given two interfered polygonal models, generalized penetration depth is calculated using relative motion information. Then two thresholds, which are based on approximation information and tolerance information, are integrated to evaluate collisions between polygonal models. In order to distinguish the status of collisions for further analysis, the collisions between polygonal models are categorized into three types by evaluation algorithm, namely real collision, potential collision, and fake collision. Computational efficiency and accuracy of the evaluation algorithm are verified in a virtual collaborative assembly environment.     

Out-of-core real-time haptic interaction on very large models

In this paper we address the problem of fast inclusion tests and distance calculation in very large models, an important issue in the context of environments involving haptic interaction or collision detection. Unfortunately, existing haptic rendering or collision detection toolkits cannot handle polygonal models obtained from 3D digitized point clouds unless the models are simplified up to a few thousand polygons, which leads to an important lack of detail for the scanned pieces. We propose a data structure that is able to manage very large polygonal models (over 25M polygons), and we explain how this can be used in order to compute the inclusion of a point into the solid surface very efficiently, performing several thousand point-in-solid tests per second. Our method uses a data structure called EBP-Octree (Extended Bounding-Planes Octree), which is a very tight hierarchy of convex bounding volumes. Based on a spatial decomposition of the model using an octree, at each node it defines a bounding volume using a subset of the planes of the portion of the polygonal model contained at that node. We use the EBP-Octree in a haptic interaction environment, where distance tests and the orientation of collided triangles must be accurate and fast. We also demonstrate that the proposed algorithm largely meets the interactive query rate demanded by a haptic interaction (1 kHz), despite being executed in a single CPU thread on a commonly available computer.     

基于凸壳的高密度点集物碰撞检测算法

提出了一种基于凸壳的高密度点集物碰撞检测算法。根据高密度点集物紧密性好的特点,设计了一种快速的凸壳算法;当极值比较不能确定待检测点集物未碰撞时,用该算法计算待检测点集物的凸壳,并对凸壳进行求交运算,若不相交,两点集物未发生碰撞,否则在两凸壳的交集区域中寻找碰撞点集。算法简单、高效、可靠,在教育、国防、艺术等方面具有一定应用价值。     

Fast Collision Detection Algorithms with Applications to Particle Flow

In this paper, we present efficient algorithms for collision detection of arbitrarily shaped rigid moving objects in a variety of interactive as well as non-interactive environments. The algorithms primarily consist of two stages. The first stage involves finding candidate objects for possible collisions. The second stage involves detecting exact (within a prespecified tolerance) collision between these candidates. The primary data structure used in the algorithms is an octree. In the first stage, we build an octree for the enclosure containing the objects, which is used to detect possible collisions. Assuming spatial/temporal coherence i.e., that the particles move slowly or that the time sampling is fast enough, the average time complexity of this stage can be shown to be O(n) (excluding the time complexity for a one time octree construction), where n is the number of particles. In the second stage, we build a surface-octree for each object. If the objects are convex and assuming coherence, the expected time complexity to detect precise (within a prespecified tolerance) collision for each pair is a constant (excluding the time complexity for a one time surface-octree construction). Therefore, the overall expected time complexity for convex object collision detection is linear with respect to n. For the concave objects, complexity analysis is nontrivial to perform and instead we provide a very practical (almost linear time) algorithm. We apply our algorithms to particle flow simulations by simulating flow density conditions often arising in granular flows.     

Fast interference detection between geometric models

We present efficient algorithms for interference detection between geometric models described by linear or curved boundaries and undergoing rigid motion. The set of models include surfaces described by rational spline patches or piecewise algebraic functions. In contrast to previous approaches, we first describe an efficient algorithm for interference detection between convex polytopes using coherence and local features. Then an extension using hierarchical representation to concave polytopes is presented. We apply these algorithms along with properties of input models, local and global algebraic methods for solving polynomial equations, and the geometric formulation of the problem to devise efficient algorithms for convex and nonconvex curved objects. Finally, a scheduling scheme to reduce the frequency of interference detection in large environments is described. These algorithms have been successfully implemented and we discuss their performance in various environments.     

“Meshsweeper”: dynamic point-to-polygonal mesh distanceand applications

We introduce a new algorithm for computing the distance from a point to an arbitrary polygonal mesh. Our algorithm uses a multiresolution hierarchy of bounding volumes generated by geometric simplification. Our algorithm is dynamic, exploiting coherence between subsequent queries using a priority process and achieving constant time queries in some cases. It can be applied to meshes that transform rigidly or deform nonrigidly. We illustrate our algorithm with a simulation of particle dynamics and collisions with a deformable mesh, the computation of distance maps and offset surfaces, the computation of an approximation to the expensive Hausdorff distance between two shapes, and the detection of self-intersections. We also report comparison results between our algorithm and an alternative algorithm using an octree, upon which our method permits an order-of-magnitude speed-up     

Collision Detection for Animation using Sphere-Trees

The detection of collisions between moving polyhedral objects is one of the most computationally intensive tasks in the computer animation process. The use of object-oriented techniques to encapsulate data within the objects' structures compounds this problem through the requirement for inter-object message passing in order to obtain geometric information for collision detection. The REALISM system decreases the time for collision detection by using a three stage process. The first stage identifies objects in the same locality using a global bounding volume table. The second stage locates regions of possible collision using a sphere-tree data structure (a hierarchical tree of spheres based on octree-type spatial subdivision). The final stage finds intersections between polygonal faces of the objects that are contained within the intersecting pairs of leaf nodes. Hence the algorithm uses a spherical geometry approximation rapidly to locate regions of potential collisions and then uses a local intersection test with actual object geometry information. The system is therefore fast and accurate. Tests for various geometric objects support this and show performance improvements of jive times over traditional polyhedral intersection tests.     

虚拟环境中的快速碰撞检测算法

该文在Lin-Canny算法的基础上,提出一种虚拟环境下三维实体的动态、实时碰撞检测算法,并应用于柔性制造仿真系统中以检查工作环境中物体间的干涉状况,应用结果表明该算法在物体结构较复杂或运动的连贯性不好的情况下仍有较好的性能。     

基于拓扑层次图的碰撞检测算法

为了提高虚拟环境中碰撞检测的实时性和精确性,提出了一种基于拓扑层次图的碰撞检测方法。利用拓扑结构的连接关系将模型分割成凸集;然后利用凸集较强的适应性和OBB紧密性好的优点构造包围盒的拓扑层次图,提高了剔除不相交包围盒的效率,减少了检测时间;利用智能搜索算法——改进的A*算法搜索潜在碰撞集(PCS),进一步提高相交检测的速度和准确性。实验表明,该算法具有较高的速度和精度,能够满足复杂虚拟环境碰撞检测实时性和精确性的要求。     

Incremental penetration depth estimation between convex polytopes using dual-space expansion

We present a fast algorithm to estimate the penetration depth between convex polytopes in 3D. The algorithm incrementally seeks a "locally optimal solution" by walking on the surface of the Minkowski sums. The surface of the Minkowski sums is computed implicitly by constructing a local dual mapping on the Gauss map. We also present three heuristic techniques that are used to estimate the initial features used by the walking algorithm. We have implemented the algorithm and compared its performance with earlier approaches. In our experiments, the algorithm is able to estimate the penetration depth in about a milli-second on an 1 GHz Pentium PC. Moreover, its performance is almost independent of model complexity in environments with high coherence between successive instances.     

基于线性规划的碰撞检测算法研究

介绍了虚拟环境中一种基于凸多面体面信息对偶线性规划模型(DualModel)的快速旋转和移动物体之间干涉碰撞实时检测方法。该文详细介绍了建模过程和求解步骤,物体由构成凸多面体的三角形面信息表示,而物体的运动由一组虚拟现实环境中的全局移动和旋转矩阵表示。这种数学编程方法具有数据结构简单、算法可靠和速度快等优点,同时能够很好地解决高速(运动帧)碰撞的问题。这一方法通过使用主-对偶(primal-dual)内点方法来解线性规划方程,具有很好的效果,能够检测多物体对之间的碰撞。实验结果表明,基于数学编程的方法相对两种著名的工具包I-COLLIDE和SOLID,具有速度快和稳定可靠的优点,而I-COLLIDE和SOLID工具包基于两种著名的算法:LinCanny(LC)最近特征算法和GJK算法(EnhancedGilbertJohnsonandKeethialgorithm)。     

IBCD: a fast collision detection algorithm based on image space using OBB

Image‐based collision detection algorithms make efficient use of the graphics rendering hardware and reduce the computational cost of CPU. In this article, a fast collision detection algorithm based on image space is presented, which combines graphics hardware capabilities with a simplified geometric representation (oriented bounding box) in order to rapidly detect collisions between complex objects. The method can deal with arbitrary polyhedra, while preserving the merits of image‐based collision detection algorithms. This is achieved by decomposing the surfaces of an object into a list of convex pieces. High efficiency of the algorithm is obtained by organizing the convex pieces into a binary tree with each node representing a convex piece, and by adopting triangle strip compression. The algorithm has been implemented and compared with related algorithms. Copyright © 2003 John Wiley & Sons, Ltd.     

Computation of penetration between smooth convex objects in three-dimensional space

There are many applications in robotics where collision detection, separation distance, and penetration distance between geometrical models of objects are required. Efficient numerical procedures for the computation of these proximal relations are important as they are frequently invoked. A new measure of penetration and separation called the growth distance has been introduced in the literature. It has been shown that the growth distance can be efficiently computed for convex polytopes. This article extends the computation of growth distance to smooth convex objects. Specifically, we introduce a formulation of the growth distance for smooth convex objects that is well suited for numerical computation. By modeling a convex object as union of convex subobjects, the growth distance of a wide family of objects can be computed. However, computation of growth distance for such object models may be expensive. A fast algorithm is introduced that reduces the computational time significantly. In the case where the objects undergo continuous relative motions and the growth distances must be evaluated for a large number of closely-spaced points along the motions, further reduction in computational effort is achieved. Numerical experiments with objects that are found in typical robot applications substantiate the claim. © 1996 John Wiley & Sons, Inc.     

虚拟装配中基于精确模型的碰撞检测算法

针对目前虚拟装配中由多边形模型引起的碰撞检测准确性低的问题,提出一种考虑公差信息的精确碰撞检测算法.首先进行分层的多边形碰撞检测,获得发生碰撞的多边形;然后基于层次图像数据将发生碰撞的多边形映射到零件相应的几何上;再依据几何的公差信息计算碰撞阈值;最后根据碰撞阈值进行精确碰撞判定.实例验证结果表明,文中算法在保证虚拟装配系统实时性的同时,提高了碰撞检测的准确性.     

Efficient Collision Detection for Moving Ellipsoids Using Separating Planes

We present a simple, accurate and efficient algorithm for collision detection among moving ellipsoids. Its efficiency is attributed to two results: (i) a simple algebraic test for the separation of two ellipsoids, and (ii) an efficient method for constructing a separating plane between two disjoint ellipsoids. Inter-frame coherence is exploited by using the separating plane to reduce collision detection to simpler subproblems of testing for collision between the plane and each of the ellipsoids. Compared with previous algorithms (such as the GJK method) which employ polygonal approximation of ellipsoids, our algorithm demonstrates comparable computing speed and much higher accuracy.     

虚拟坦克装甲车运动仿真中的碰撞检测算法研究

提出了一种新的虚拟坦克装甲车运动仿真的混合碰撞检测算法，该算法是先用帧与帧之间的画面连贯性进行判断，若帧与帧之间的物体不一致，则用方向包围盒来进行碰撞检测，为了避免两帧之间发生穿透，则有线段与包围盒的重叠测试进行穿透测试。此算法可以很好解决坦克装甲车的运动仿真中的碰撞检测。满足实时性要求。     

基于凸分解与OBB层次结构的碰撞检测方法

目前的碰撞检测方法大部分是基于简单的包围盒方法和简单的搜索算法的,这种算法精确度低且效率不高。基于凸分解与OBB层次结构的碰撞检测方法是对传统碰撞检测算法的一种改进,该方法继承了传统碰撞检测算法的优点,同时又对传统算法进行了必要的改进。实验证明,利用物体表面凸分解的方法解决了传统碰撞检测算法不能测试非凸物体相交的问题,拓宽了碰撞检测算法的应用范围;根据物体前后碰撞点的相关性,运用加速搜索提高了碰撞检测效率,降低了算法复杂度。     

基于凸分解与OBB层次结构的碰撞检测方法

目前的碰撞检测方法大部分是基于简单的包围盒方法和简单的搜索算法的，这种算法精确度低且效率不高。基于凸分解与OBB层次结构的碰撞检测方法是对传统碰撞检测算法的一种改进，该方法继承了传统碰撞检测算法的优点，同时又对传统算法进行了必要的改进。实验证明，利用物体表面凸分解的方法解决了传统碰撞检测算法不能测试非凸物体相交的问题，拓宽了碰撞检测算法的应用范围；根据物体前后碰撞点的相关性，运用加速搜索提高了碰撞检测效率，降低了算法复杂度。     

基于Sphere-OBB的改进碰撞检测算法及其应用

静态或动态环境中两个或者多个几何模型之间的碰撞检测是计算机图形学基础问题之一,基于层次包围盒的碰撞检测算法是一种比较有效的碰撞检测算法。提出了OBB包围盒与球包围盒相结合的高效碰撞检测算法,该算法既具有OBB的包围紧密性,又具有球包围盒的测试简便性。用高效的球包围盒排除大量距离远的不相交物体,剩下距离近的物体用分离轴测试,其中一些分离轴效率更高应该优先被测试。将该算法用于虚拟针灸训练系统,实验结果表明算法减少了查询时间并增强了实时性。     

Fast Penetration Volume for Rigid Bodies

Handling collisions among a large number of bodies can be a performance bottleneck in video games and many other real‐time applications. We present a new framework for detecting and resolving collisions using the penetration volume as an interpenetration measure. Given two non‐convex polyhedral bodies, a new sampling paradigm locates their near‐contact configurations in advance, and stores associated contact information in a compact database. At runtime, we retrieve a given configuration's nearest neighbors. By taking advantage of the penetration volume's continuity, cheap geometric methods can use the neighbors to estimate contact information as well as a translational gradient. This results in an extremely fast, geometry‐independent, and trivially parallelizable computation, which constitutes the first global volume‐based collision resolution. When processing multiple collisions simultaneously on a 4‐core processor, the average running cost is as low as 5 μs. Furthermore, no additional proximity or contact‐regions queries are required. These results are orders of magnitude faster than previous penetration volume approaches.