Incremental algorithms for collision detection between polygonalmodels

Fast and accurate collision detection between general polygonal models is a fundamental problem in physically based and geometric modeling, robotics, animation, and computer-simulated environments. Most earlier collision detection algorithms are either restricted to a class of models (such as convex polytopes) or are not fast enough for practical applications. The authors present an incremental algorithm for collision detection between general polygonal models in dynamic environments. The algorithm combines a hierarchical representation with incremental computation to rapidly detect collisions. It makes use of coherence between successive instances to efficiently determine the number of object features interacting. For each pair of objects, it tracks the closest features between them on their respective convex hulls. It detects the objects' penetration using pseudo internal Voronoi cells and constructs the penetration region, thus identifying the regions of contact on the convex hulls. The features associated with these regions are represented in a precomputed hierarchy. The algorithm uses a coherence based approach to quickly traverse the precomputed hierarchy and check for possible collisions between the features. They highlight its performance on different applications     

Fast collision detection between complex solids using rasterizing graphics hardware

We present an efficient method for detecting collisions between complex solid objects. The method features a stable processing time and low sensitivity to the complexity of contact between objects. The algorithm handles both concave and convex objects; however, the best performance is achieved when at least one object is convex in the proximity of the collision zone (our techniques check the required convexity property as a byproduct of the calculations). The method achieves real-time performance when calculations are supported by the standard functionality of graphics hardware available on high-end workstations.     

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.     

Proximity Queries Between Convex Objects: An Interior Point Approach for Implicit Surfaces

This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulations and in haptic interactions. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem. We use an interior point method to solve the optimization problem and demonstrate that, for general convex objects represented as implicit surfaces, interior point approaches are globally convergent, and fast in practice. Further, they provide polynomial-time guarantees for implicit surface objects when the implicit surfaces have self-concordant barrier functions. We use a primal-dual interior point algorithm that solves the Karush-Kuhn-Tucker (KKT) conditions obtained from the convex programming formulation. For the case of polyhedra and quadrics, we establish a theoretical time complexity of O(n^1.5), where n is the number of constraints. We present implementation results for example implicit surface objects, including polyhedra, quadrics, and generalizations of quadrics such as superquadrics and hyperquadrics, as well as intersections of these surfaces. We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved. We also extend the approach to proximity queries between deforming convex objects. Finally, we show that continuous collision detection for linearly translating objects can be performed by solving two related convex optimization problems. For polyhedra and quadrics, we establish that the computational complexity of this problem is also O(n^1.5).     

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)。     

基于深度纹理的实时碰撞检测算法

结合层次包围盒和基于图形硬件的方法,以带深度纹理的包围盒替代物体的几何模型,利用图形硬件在纹理映射时进行深度比较,以实现碰撞检测.实验结果表明,与CULLIDE算法相比,文中算法执行效率更高且执行时间固定,具有较高的实时性.     

Octree generation from object silhouettes in perspective views

Octrees are useful for object representation when fast access to coarse spatial occupancy information is necessary. This paper presents an efficient algorithm for generating octrees from multiple perspective views of an object. The algorithm first obtains a polygonal approximation of the object silhouette. This polygon is then decomposed into convex components. For each convex component, a pyramid is formed treating the view point as its apex and the convex components as a cross section. The octree representation of each of these pyramids is obtained by performing intersection detection of the object with the cubes corresponding to octree nodes. The intersection detection step is made efficient by decomposing it into a coarse-to-fine sequence of intersection tests. The octree for one silhouette is obtained by taking the union of octrees obtained for each component. An intersection of octrees corresponding to different viewing directions gives the final octree of the object. An implementation of the algorithm is given. The accuracy of the octree representation of the objects is evaluated. The ratio of the actual volume of the object to the volume of the object reconstructed from the octree representation is used as a performance index of the algorithm.     

CPU–GPU Parallel Framework for Real‐Time Interactive Cutting of Adaptive Octree‐Based Deformable Objects

A software framework taking advantage of parallel processing capabilities of CPUs and GPUs is designed for the real‐time interactive cutting simulation of deformable objects. Deformable objects are modelled as voxels connected by links. The voxels are embedded in an octree mesh used for deformation. Cutting is performed by disconnecting links swept by the cutting tool and then adaptively refining octree elements near the cutting tool trajectory. A surface mesh used for visual display is reconstructed from disconnected links using the dual contour method. Spatial hashing of the octree mesh and topology‐aware interpolation of distance field are used for collision. Our framework uses a novel GPU implementation for inter‐object collision and object self collision, while tool‐object collision, cutting and deformation are assigned to CPU, using multiple threads whenever possible. A novel method that splits cutting operations into four independent tasks running in parallel is designed. Our framework also performs data transfers between CPU and GPU simultaneously with other tasks to reduce their impact on performances. Simulation tests show that when compared to three‐threaded CPU implementations, our GPU accelerated collision is 53–160% faster; and the overall simulation frame rate is 47–98% faster.     

COLLISION DETECTION AMONG MOVING OBJECTSIN MACHINING PROCESS SIMULATION

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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.     

运用改进的八叉树算法实现精确碰撞检测

提出一种精确碰撞检测算法,通过计算空间多面体之间距离实现碰撞检测功能.在计算2个多面体之间距离时,运用空间层次划分技术高效地寻找多面体中充分接近的三角面片,然后在这些三角面片中进行距离计算,以提高算法效率;同时运用改进的八叉树层次分割算法,与基本八叉树算法相比,减少了算法的空间复杂度.文中算法已经在超导Tokamak实验装置（EAST）虚拟装配仿真系统的碰撞检测模块中得到应用,通过实验比较,证明了该算法的可行性.     

An Adaptive Spatial Subdivision of the Object Space for Fast Collision Detection of Animated Rigid Bodies

Collision detection tests between objects dominate run time simulation of rigid body animation. Traditionally, hierarchical bounding box tests are used to minimize collision detection time. But the bounding boxes do not take shapes of the objects into account which results in a large number of collision detection tests. We propose an adaptive spatial subdivision of the object space based on octree structure to rectify this problem. We also present a technique for efficiently updating this structure periodically during the simulation.     

Symmetry identification of a 3-D object represented by octree

An algorithm for identifying symmetry of a 3-D object given by its octree is presented, and the symmetry degree (a measure of object symmetry) is proposed. The algorithm is based on traversals of the octree obtained by the principal axis transform of an input octree. An object can be in an arbitrary position and with arbitrary orientation within the octree space, and a wide range of symmetries represented by groups of proper and improper rotations can be identified. It is shown that the octree data structure supports these operations well, especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry. The operation of the algorithm is illustrated using some synthetic test objects. The results, which are composed of identified symmetry types and the corresponding symmetry degrees, were satisfactory     

Collision-free object movement using vector fields

Presents a technique for automatically providing animation and collision avoidance in a general-purpose computer graphics system. The technique, which relies on an expanded notion of vector fields, allows users to set up and animate objects easily, then prevents objects from colliding as the animation proceeds. This technique automatically generates volume octree vector fields around objects in a scene. These vector fields affect object motion and animation, and also provide for automatic collision avoidance for arbitrary objects. Applications of collision avoidance in an animation system encompass any scene containing object movement above or around other objects     

复杂场景中基于拓扑空间网格的碰撞检测算法

为了提高复杂场景的碰撞检测效率,提出一种基于拓扑空间网格的碰撞检测算法. 由于场景中存在众多形状复杂、尺寸不一且运动状态不同的物体,首先采取场景预处理对空间进行均匀八叉树网格划分,建立物体方向包围盒层次树与空间网格拓扑结构,利用静态大尺寸物体分割策略提升定位精确性,然后在实时检测中利用拓扑空间网格及投影相交测试排除大量不相交物体对,利用层次包围盒算法对潜在碰撞对进行精确检测并计算出碰撞点. 实验结果表明,本算法有效地提高了实时检测的效率,适用于复杂虚拟场景中的碰撞检测.     

一种基于八叉树与流水线技术的快速碰撞检测算法

针对存在大量运动物体的虚拟环境,提出一种基于空间八叉树剖分与流水线技术的并行碰撞检测算法.通过八叉树剖分,把虚拟空间剖分成一系列的子空间,然后只对同一空间中的结点进行碰撞检测.对空间内的每个物体构建包围盒树,同一空间中的任意两棵包围盒树遍历构成任务树,把任务树中的任务分配给不同的进程进行碰撞检测,并采用流水线与多线程技...     

Computation of a penetration measure between 3D convex polyhedral objects for collision detection

Measures to characterize the penetration between a pair of intersecting objects are given, based on translating one object to separate from the other. Algorithms to compute a measure between convex polyhedral objects in ?³ are presented for two different input representations. These algorithms have linear expected running time. Details of experiments in collision detection for 3D objects using the penetration measure are also presented. © 2001 John Wiley & Sons, Inc.     

适用于复杂场景的碰撞检测算法研究

创建虚拟场景不仅要进行静态建模,更重要的是进行动态建模。而且物体之间的实时碰撞检测是关键。首先对常用检测算法的检测效率进行了分析和比较。然后重点针对复杂虚拟场景中吉有大量物体的特点,提出了混合包围盒碰撞检测算法。该算法利用帧与帧之间的时间和几何相关性,把对（cn^2＋m）个对象的动态跟踪转化为它们在三个坐标轴上的投影的排序问题,把时间复杂度由O（n^2）降低为O（n）。并引入树的深度的概念,根据不同的应用场合合理控制检测深度以加快检测速度。理论分析和仿真计算都表明,该算法能够满足多达几百个运动物体的实时交互碰撞检测。     

From A Medial Surface To A Mesh

Medial surfaces are well‐known and interesting surface skeletons. As such, they can describe the topology and the geometry of a 3D closed object. The link between an object and its medial surface is also intuitively understood by people. We want to exploit such skeletons to use them in applications like shape creation and shape deformation. For this purpose, we need to define medial surfaces as Shape Representation Models (SRMs). One of the very first task of a SRM is to offer a visualization of the shape it describes. However, achieving this with a medial surface remains a challenging problem. In this paper, we propose a method to build a mesh that approximates an object only described by a medial surface. To do so, we use a volumetric approach based on the construction of an octree. Then, we mesh the boundary of that octree to get a coarse approximation of the object. Finally, we refine this mesh using an original migration algorithm. Quantitative and qualitative studies, on objects coming from digital modeling and laser scans, shows the efficiency of our method in providing high quality surfaces with a reasonable computational complexity.