Efficient Collision Detection among Moving Spheres with Unknown Trajectories

Collision detection is critical for applications that demand a great deal of spatial interaction among objects. In such applications the trajectory of an object is often not known in advance either since a user is allowed to move an object at his/her will, or since an object moves under the rules that are hard to describe by exact mathematical formulas. In this paper we present a new algorithm that efficiently detects the collisions among moving spheres with unknown trajectories. We assume that the current position and velocity of every sphere can be probed at any time although its trajectory is unknown. We also assume that the magnitude of the acceleration of each sphere is bounded. Under these assumptions, we represent the bounding volume of the sphere as a moving sphere of variable radius, called a time-varying bound. Whenever the time-varying bounds of two spheres collide with each other, they are checked for actual collision. Exploiting these bounds, the previous event-driven approach for detecting the collisions among multiple moving spheres with ballistic trajectories is generalized for those with unknown trajectories. The proposed algorithm shows an interactive performance for thousands of moving spheres with unknown trajectories without any hardware help.     

Fast collision detection among multiple moving spheres

This paper presents an event-driven approach that efficiently detects collisions among multiple ballistic spheres moving in the 3D space. Adopting a hierarchical uniform space subdivision scheme, we are able to trace the trajectories of spheres and their time-varying spatial distribution. We identify three types of events to detect the sequence of all collisions during our simulation: collision, entering, and leaving. The first type of event is due to actual collisions, and the other two types occur when spheres move from subspace to subspace in the space. Tracing all such events in the order of their occurring times, we are able to avoid fixed time step simulation. When the size of the largest sphere is bounded by a constant multiple of that of the smallest, it takes O(n¯_c log n+n¯_e log n) time with O(n) space after O(n log n) time preprocessing to simulate n moving spheres, where n¯_c and n¯_e are the number of actual collisions and that of entering and leaving events during the simulation, respectively. Since n¯_e, depends on the size of subspaces, we modify the collision model from kinetic theory for molecular gas to determine the subspace sizes for the space subdivision scheme, that minimize simulation time. Experimental results show that collision detection can be done in linear time in n over a large range     

数控仿真中的实时碰撞检测算法的研究

碰撞干涉检测是数控加工仿真中的重要组成,文章提出了一种实现数控仿真加工的实时碰撞检测算法,该方法是通过测试线与刀具扫掠体包络面求交的交点来判断刀具或刀柄在加工过程中是否和夹具发生了碰撞,以及碰撞发生在哪些控制代码所对应的刀具移动上;算法的关键在于实时性,满足了数控加工过程中的实时碰撞检测,同时也给出了实例说明了算法的有效性。     

Generalization of the collision cone approach for motion safety in 3-D environments

Avoidance of collision between moving objects in a 3-D environment is fundamental to the problem of planning safe trajectories in dynamic environments. This problem appears in several diverse fields including robotics, air vehicles, underwater vehicles and computer animation. Most of the existing literature on collision prediction assumes objects to be modelled as spheres. While the conservative spherical bounding box is valid in many cases, in many other cases, where objects operate in close proximity, a less conservative approach, that allows objects to be modelled using analytic surfaces that closely mimic the shape of the object, is more desirable. In this paper, a collision cone approach (previously developed only for objects moving on a plane) is used to determine collision between objects, moving in 3-D space, whose shapes can be modelled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained and used to derive dynamic inversion based avoidance strategies.     

Obstacle avoidance in a dynamic environment: a collision coneapproach

A novel collision cone approach is proposed as an aid to collision detection and avoidance between irregularly shaped moving objects with unknown trajectories. It is shown that the collision cone can be effectively used to determine whether collision between a robot and an obstacle (both moving in a dynamic environment) is imminent. No restrictions are placed on the shapes of either the robot or the obstacle, i.e., they can both be of any arbitrary shape. The collision cone concept is developed in a phased manner starting from existing analytical results that enable prediction of collision between two moving point objects. These results are extended to predict collision between a point and a circular object, between a point and an irregularly shaped object, between two circular objects, and finally between two irregularly shaped objects. Using the collision cone approach, several strategies that the robot can follow in order to avoid collision, are presented. A discussion on how the shapes of the robot and obstacles can be approximated in order to reduce computational burden is also presented. A number of examples are given to illustrate both collision prediction and avoidance strategies of the robot     

Collision detection in motion simulation

This paper describes a method of detecting collisions in motion simulation. In motion simulation, objects occasionally share a sphere in the simulated world. This would not occur in the real world, since objects would have collided before they shared a common sphere. In order to avoid such sharing and to accurately simulate collisions, a collision detection method called the Space Occupancy Method is proposed here, in which the detection of collisions between free form objects in 3-D space can be made quickly and precisely. An implementation design of the collision detection method and some results of simulations are shown.     

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.     

The sweep plane algorithm for global collision detection with workpiece geometry update for five-axis NC machining

A new algorithm based on the sweep plane approach for global collision detection for five-axis NC machining is presented. This algorithm takes into account not only collisions between the tool and workpiece, but also collisions between the other parts of the CNC machine, especially the change of the workpiece geometry is included in the detection process. The workpiece and machine bodies are firstly approximated by an octree of bounding spheres. Collision detection is conducted between these spheres. If there is any interference between these bounding spheres, their subspheres are further tested. The subdivision process is recursively performed until the resolution reaches the desired precision level. If there is no interference between the spheres, there is no need to subdivide any more. When the interference is detected between the spheres in the last octree level, the slices within these colliding spheres are further checked by using the sweep plane algorithm to determine whether the enclosed objects really collide with each other. In the sweep plane algorithm, most of the slices of the moving bodies stay parallel and their collisions are detected by checking the interference between these parallel slices using 2D polygon clipping. Whereas, if the slices are not parallel to the reference slicing direction (due to the rotary axes), the interference detection is conducted by examining overlaps of the projections of these slices on the three perpendicular planes XY,YZ, and ZX. The accuracy of the algorithm can be adjusted by changing the distance between the sweep planes. The algorithm can be applied to any five-axis CNC machines.     

Computing rational bisectors

Bisector construction plays an important role in many geometric computations. This article explains how to compute rational bisectors of point-surface and sphere-surface pairs. This article shows that the bisector of a point and a rational surface in R³ (3D space) is also a rational surface. This result implies that the bisector of a sphere and a surface with a rational offset is also a rational surface. Even a simple rational bisector between two spheres and that between a point and a sphere have many important applications in practice. The bisector between a cube and a sphere consists of various surface patches, some of them are the bisectors between portions of the sphere and the corners of the cube. An application that uses the bisector of two spheres (of different radii) occurs in computing an optimal path for an airplane trying to avoid radar detection. Assuming each radar has different intensity, we can model the influence regions with spheres of different radii. The optimal path must lie on the bisector surface of the spheres     

基于角色几何碰撞体估计的实时服装仿真

提出了一种快速处理三维服装仿真中角色与服装碰撞的方法.该方法能够满足交互式实时仿真环境的需求.在预处理阶段,根据蒙皮动画的特点,将角色的几何形状以球和简化凸包等简单碰撞体进行估计.在实时模拟阶段,这些碰撞体跟随骨架运动并代替角色模型网格完成与虚拟服装之间的碰撞处理.此外,为了能够快速计算碰撞响应信息,该方法还利用外围映射机制进一步开发了相交测试的空间局部性.实验结果表明,应用该方法可以有效避免衣片与角色模型之间的相互穿透,同时大幅度地减少碰撞处理计算量.实时仿真系统对于复杂服装网格仍然保持了较高的模拟帧速率.     

A scalable parallel method for large collision detection problems

This paper discusses a parallel collision detection algorithm. Implemented using software executed on ubiquitous Graphics Processing Unit (GPU) cards, the algorithm demonstrates two orders of magnitude speedup over a state-of-the art sequential implementation when handling multimillion object collision detection tasks. GPUs are composed of many (on the order of hundreds) scalar processors that can simultaneously execute an operation; this strength is leveraged in the proposed algorithm, which combines the use of multiple CPU cores with multiple GPUs. The software implementation of the algorithm can be used to detect collisions between five million objects in less than two seconds and was used to detect 1.4 billion contact events in less than 40 seconds. A spherical padding approach is used to represent surface geometries as large collections of spheres when dealing with collision detection between bodies with complex geometries. The proposed methodology is expected to be relevant in computational mechanics with applications in granular flow dynamics and smoothed particle hydrodynamics (SPH), where the number of contact events ranges from millions to billions.     

Collision detection methodologies for rigid body assembly in a virtual environment

In this paper, a simulated three-dimensional virtual environment is created with a virtual 3D track ball for virtual object control. We propose a new technique called HV Partition to detect accurate collision in the assembly of two polyhedral solids in virtual simulation. This is a solid interference detection methodology achieved by automatically partitioning the object into smaller solid boxes. An important advantage of this methodology compared with other approaches is that it can deal with non-convex objects. This means that mechanical components, represented by non-convex polyhedra, traversing any degree of freedom, can be used in this virtual environment. Using this HV Partition method, the precise interference between two polyhedral solid objects can be found. The HV Partition methodology is applied following initial approximate collision detection using traditional bounding box and bounding sphere methods. The smaller the number of smaller boxes, the quicker is the performance of the collision algorithm. An optimal partition method is also given to reduce the number of smaller boxes in an object.     

Efficient collision detection using a dual OBB-sphere bounding volume hierarchy

We present an efficient algorithm for collision detection between static rigid objects using a dual bounding volume hierarchy which consists of an oriented bounding box (OBB) tree enhanced with bounding spheres. This approach combines the compactness of OBBs and the simplicity of spheres. The majority of distant objects are separated using the simpler sphere tests. The remaining objects are in close proximity, where some separation axes are significantly more effective than others. We select 5 from among the 15 potential separating axes for OBBs. Experimental results show that our algorithm achieves considerable speedup in most cases with respect to the existing OBB algorithms.     

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.     

基于混合包围盒的碰撞检测算法

提出了一种基于k-dops包围盒与包围球相结合的碰撞检测算法。预处理阶段为几何对象构造包围盒二叉树,其中节点的内层构造k-dops包围盒,节点的外层构造包围球。碰撞检测阶段,首先利用包围球快速排除不可能发生相交的物体,然后利用k-dops包围盒进一步精确地判断物体对是否发生相交。通过与QuickCD算法的性能进行比较,证明了这种混合包围盒能够有效地提高复杂结构几何体之间碰撞检测的效率。     

可变形物体间的精确碰撞检测方法研究

针对可变形物体,提出了一种基于粒子的精确碰撞检测算法。首先用LBG矢量量化技术将物体的表面划分成几个小区域,然后在每个区域中分别选择一个点作为检测粒子。当一个物体接近另一个物体时,找出两物体上靠得最近的粒子对。为了得到精确的碰撞位置坐标,进一步计算靠得最近的顶点的相关三角面片之间的最短距离。若此距离小于某个给定的阈值,则可认为两物体在相关三角面片上的最近点处发生了碰撞。仿真实验验证了该算法能有效处理虚拟力交互仿真中的可变形物体的碰撞检测。     

Intelligent collision avoidance planning of a robot manipulator whose workspace includes moving objects

The collision avoidance problem of a robot manipulator whose workspace includes moving objects is considered in this paper. It is shown that the proposed computer simulation system can be used in a dialogue mode with a designer to check whether or not collision with obstacles is avoided and to determine the appropriate movement.     

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。     

一种用于群体模拟的分层次避障法

个体避障是实现基于主体的(agent-based)群体模拟中一个很重要的问题,为了实现个体间以及个体和环境间的碰撞避免并杜绝穿透,人们提出了大量避障方法.但是,这些方法面临的挑战在于:如何杜绝穿透现象并最大程度地减少由于避障需求而带来的个体行为模拟上的空间限制和失真.针对这一问题,提出了一种分层次避障方法,从静态避障、动态避障、穿透矫正3个不同的层次对避障进行处理.静态避障层和动态避障层通过对物体的划分和分别避障,极大地减少了各层次避障时需要考虑的各种复杂情形;而基于可变包围盒和原位置的穿透矫正层则有效地杜绝了模拟中出现的穿透现象,也消除了现有模拟中由于避免穿透而引入的空间限制和失真.