Separation-Sensitive Collision Detection for Convex Objects

We develop a class of new kinetic data structures for collision detection between moving convex polytopes; the performance of these structures is sensitive to the separation of the polytopes during their motion. For two convex polygons in the plane, let $D$ be the maximum diameter of the polygons, and let $s$ be the minimum distance between them during their motion. Our separation certificate changes $O(\log(D/s))$ times when the relative motion of the two polygons is a translation along a straight line or convex curve, $O(\sqrt{D/s})$ for translation along an algebraic trajectory, and $O(D/s)$ for algebraic rigid motion (translation and rotation). Each certificate update is performed in $O(\log(D/s))$ time. Variants of these data structures are also shown that exhibit \emph{hysteresis}---after a separation certificate fails, the new certificate cannot fail again until the objects have moved by some constant fraction of their current separation. We can then bound the number of events by the combinatorial size of a certain cover of the motion path by balls.Comment: 10 pages, 8 figures; to appear in Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms, 1999; see also http://www.uiuc.edu/ph/www/jeffe/pubs/kollide.html ; v2 replaces submission with camera-ready versio

Mochi: Fast \& Exact Collision Detection

Collision Detection (CD) has several applications across the domains such as robotics, visual graphics, and fluid mechanics. Finding exact collisions between the objects in the scene is quite computationally intensive. To quickly filter the object pairs that do not result in a collision, bounding boxes are built on the objects, indexed using a Bounding Volume Hierarchy(BVH), and tested for intersection before performing the expensive object-object intersection tests. In state-of-the-art CD libraries, accelerators such as GPUs are used to accelerate BVH traversal by building specialized data structures. The recent addition of ray tracing architecture to GPU hardware is designed to do the same but in the context of implementing a Ray Tracing algorithm to render a graphical scene in real-time. We present Mochi, a fast and exact collision detection engine that accelerates both the broad and narrow phases by taking advantage of the capabilities of Ray Tracing cores. We introduce multiple new reductions to perform generic CD to support three types of objects for CD: simple spherical particles, objects describable by mathematical equations, and complex objects composed of a triangle mesh. By implementing our reductions, Mochi achieves several orders of magnitude speedups on synthetic datasets and 5x-28x speedups on real-world triangle mesh datasets. We further evaluate our reductions thoroughly and provide several architectural insights on the ray tracing cores that are otherwise unknown due to their proprietorship

Hybrid Hierarchical Collision Detection Based on Data Reuse

To improve the efficiency of collision detection between rigid bodies in complex scenes, this paper proposes a method based on hybrid bounding volume hierarchies for collision detection. In order to improve the simulation performance, the method is based on weighted oriented bounding box and makes dense sampling on the convex hulls of the geometric models. The hierarchical bounding volume tree is composed of many layers. The uppermost layer adopts a cubic bounding box, while lower layers employ weighted oriented bounding box. In the meantime, the data of weighted oriented bounding box is reused for triangle intersection check. We test the method using two scenes. The first scene contains two Buddha models with totally 361,690 triangle facets. The second scene is composed of 200 models with totally 115, 200 triangle facets. The experiments verify the effectiveness of the proposed method

Simple and Robust Boolean Operations for Triangulated Surfaces

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the inter-section lines for all pairs of triangles with parallel algorithm; (2) We form closed or open intersection-loops, sub-surfaces and sub-blocks quite robustly only according to the cleared and updated topology of meshes while without coordinate computations for geometric enti-ties. A novel technique instead of inside/outside classification is also proposed to distinguish the resulting union, subtraction and intersection. Several examples have been given to illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio

The Double Hierarchy Method: a parallel 3D contact method for the interaction of spherical particles with rigid FE boundaries using the DEM

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-016-0109-4In this work, we present a new methodology for the treatment of the contact interaction between rigid boundaries and spherical discrete elements (DE). Rigid body parts are present in most of large-scale simulations. The surfaces of the rigid parts are commonly meshed with a finite element-like (FE) discretization. The contact detection and calculation between those DE and the discretized boundaries is not straightforward and has been addressed by different approaches. The algorithm presented in this paper considers the contact of the DEs with the geometric primitives of a FE mesh, i.e. facet, edge or vertex. To do so, the original hierarchical method presented by Horner et al. (J Eng Mech 127(10):1027–1032, 2001) is extended with a new insight leading to a robust, fast and accurate 3D contact algorithm which is fully parallelizable. The implementation of the method has been developed in order to deal ideally with triangles and quadrilaterals. If the boundaries are discretized with another type of geometries, the method can be easily extended to higher order planar convex polyhedra. A detailed description of the procedure followed to treat a wide range of cases is presented. The description of the developed algorithm and its validation is verified with several practical examples. The parallelization capabilities and the obtained performance are presented with the study of an industrial application example.Peer ReviewedPostprint (author's final draft

A Motion Planning Processor on Reconfigurable Hardware

Motion planning algorithms enable us to find feasible paths for moving objects. These algorithms utilize feasibility checks to differentiate valid paths from invalid ones. Unfortunately, the computationally expensive nature of such checks reduces the effectiveness of motion planning algorithms. However, by using hardware acceleration to speed up the feasibility checks, we can greatly enhance the performance of the motion planning algorithms. Of course, such acceleration is not limited to feasibility checks; other components of motion planning algorithms can also be accelerated using specially designed hardware. A Field Programmable Gate Array (FPGA) is a great platform to support such an acceleration. An FPGA is a collection of digital gates which can be reprogrammed at run time, i.e., it can be used as a CPU that reconfigures itself for a given task. In this paper, we study the feasibility of an FPGA based motion planning processor and evaluate its performance. In order to leverage its highly parallel nature and its modular structure, our processor utilizes the probabilistic roadmap method at its core. The modularity enables us to replace the feasibility criteria with other ones. The reconfigurability lets us run our processor in different roles, such as a motion planning co-processor, an autonomous motion planning processor or dedicated collision detection chip. Our experiments show that such a processor is not only feasible but also can greatly increase the performance of current algorithms

Quad Axis Separation Framework for Bounding-Volume Hierarchies Construction

The construction of Bounding-Volume Hierarchies (BVH) for Virtual Environment application has been varied from the rigid bodies application type to the deformable bodies application. Numerous technique and specific instruction has been given from several researchers in order to make sure that the BVH can suite their application without any restriction. In this paper, we explore the capability of BVH using a technique called Quad Axis Separation Technique (QAS) that could efficiently create full-blown hierarchical tree using approximation of separating axes theorem for Virtual Environment. A theoretical implementation is carried out with standard experimental that is also been used by researcher to test their BVH in the Virtual Environment. We also believed that QAS could provide fast and efficient hierarchical tree construction and also enhance the speed and accuracy of the collision detection technique