Separating Axis Theorem Research Articles

A case study of virtual CNC machine tool assembly and human-computer interaction techniques

When it comes to the virtual machine tool assembly process, there are problems such as assembly errors. Based on the general idea of correct assembly, it is proposed to innovate the assembly process by utilizing the enclosing box and separating axis theorem and GJK algorithm, so as to monitor the state of the detection process, which verifies the effective feasibility of the monitoring method and provides a new idea for the assembly process of virtual CNC machine tools.

A method for accurately extracting power lines and identifying potential intrusion risks from urban laser scanning data

Timely and accurate monitoring of power line safety is a key step in ensuring urban production and daily life. The rapid development of vehicle-borne mobile laser scanning (MLS) technology has provided an effective solution for intelligent maintenance of power grids. This paper proposes a comprehensive method for accurate extraction, missing completion, and intrusion risk detection of urban power lines. Firstly, local linear geometric features are described using principal component analysis (PCA) covariance matrix, and outliers are accurately separated using a joint Bezier curve distance threshold. Secondly, the statistical inference function estimation method is employed to accurately simulate the complete topology of power lines. Finally, a fast intrusion risk detection method based on the separating axis theorem (SAT) for boundary box neighboring objects is developed. Experimental results demonstrate that our method achieves a recall rate and precision rate of 98.28 % and 98.71 %, respectively, for power line extraction. The root mean square error (RMSE) accuracy and coordinate residual of catenary line fitting are both below 0.04 m, indicating strong noise resistance and robustness. Compared to mainstream geometric extraction methods, our approach exhibits superior performance.

ASIC Design and Implementation of the Real-Time Collision Detection for Machine Tool Automation

Collision detection of two objects plays an essential role for the machine tool automation. Although the collision detection of two objects has been studied in applications like virtual reality, the collision detection for the machine tool requires high precision to avoid overcut damage to the high-cost machine tools. The current collision detection for machine tools is under the soft-ware based computer numerical control (CNC), the low computation capability of which refrains the CNC based approach from real-time collision detection. In this paper, we consider the design of application specific integrated circuit (ASIC) to enhance the collision detection for machine tool automation. Because the bounded objects are represented by meshed triangles, we consider the separating axis theorem (SAT) based detection algorithm. Furthermore, by considering high precision required by machine tool applications, the proposed algorithm includes collision detection of either non-coplanar or coplanar triangles. Following the collision detection algorithm, we design hardware architecture with parallel processing to provide higher throughput rate over the architecture reported in our conference paper. The VLSI implementation results under the TSMC TN40G (45nm) CMOS technology reveal that our architecture requires 1,212K gates and provides detection throughput 38.46M per second for collision detection of two triangles, while operating at 500 MHz. For two objects represented by 400 and 400 meshed triangles, respectively, our hardware architecture can provide collision detection in 0.96 ms, which is smaller than the 1 ms required for real-time processing of collision detection of two objects.

A virtual surgical prototype system based on gesture recognition for virtual surgical training in maxillofacial surgery

BackgroundVirtual reality (VR) technology is an ideal alternative of operation training and surgical teaching. However, virtual surgery is usually carried out using the mouse or data gloves, which affects the authenticity of virtual operation. A virtual surgery system with gesture recognition and real-time image feedback was explored to realize more authentic immersion.MethodGesture recognition technology proposed with an efficient and real-time algorithm and high fidelity was explored. The recognition of hand contour, palm and fingertip was firstly realized by hand data extraction. Then, an Support Vector Machine classifier was utilized to classify and recognize common gestures after extraction of feature recognition. The algorithm of collision detection adopted Axis Aligned Bounding Box binary tree to build hand and scalpel collision models. What’s more, nominal radius theorem (NRT) and separating axis theorem (SAT) were applied for speeding up collision detection. Based on the maxillofacial virtual surgical system we proposed before, the feasibility of integration of the above technologies in this prototype system was evaluated.ResultsTen kinds of signal static gestures were designed to test gesture recognition algorithms. The accuracy of gestures recognition is more than 80%, some of which were over 90%. The generation speed of collision detection model met the software requirements with the method of NRT and SAT. The response time of gesture] recognition was less than 40 ms, namely the speed of hand gesture recognition system was greater than 25 Hz. On the condition of integration of hand gesture recognition, typical virtual surgical procedures including grabbing a scalpel, puncture site selection, virtual puncture operation and incision were carried out with realization of real-time image feedback.ConclusionBased on the previous maxillofacial virtual surgical system that consisted of VR, triangular mesh collision detection and maxillofacial biomechanical model construction, the integration of hand gesture recognition was a feasible method to improve the interactivity and immersion of virtual surgical operation training.

A multi-criteria h-adaptive finite-element framework for industrial part-scale thermal analysis in additive manufacturing processes

This work presents an h-adaptive finite-element (FE) strategy to address the numerical simulation of additive manufacturing (AM) of large-scale parts. The wire-arc additive manufacturing is chosen as the demonstrative technology for its manufacturing capabilities suitable for industrial purposes. The scanning path and processing parameters of the simulation are provided via a RS-274 (GCode) file, being the same as the one delivered to the AM machine. The approach is suitable for industrial applications and can be applied to other AM processes. To identify the location in the FE mesh of the heat affected zone (HAZ), a collision detection algorithm based on the separating axis theorem is used. The mesh is continuously adapted to guarantee the necessary mesh resolution to capture the phenomena inside and outside the HAZ. To do so, a multi-criteria adaptive mesh refinement and coarsening (AMR) strategy is used. The AMR includes a geometrical criterion to guarantee the FE size within the HAZ, and a Zienkiewicz–Zhu-based a-posteriori error estimator to guarantee the solution accuracy elsewhere. Thus, the number of active FEs is controlled and mesh manipulation by the end-user is avoided. Numerical simulations comparing the h-adaptive strategy with the (reference) fixed fine meshes are performed to prove the computational cost efficiency and the solution accuracy.

Collision Detection of Bounding Cylinders in Virtual Environment Systems

The paper proposes methods and algorithms for collision detection of bounding cylinders that surround the geometry of virtual objects. The proposed solutions are based on the separating axis theorem and analysis of possible contact interaction cases between two cylinders. The idea is to approximate the cylinders by prisms with their Gauss map to the unit sphere, which reduces the number of separating axes. Also, to compute contact points, an approach was developed based on fast geometric tests, in which polygon and segment are clipping by a prism, as a common perpendicular between line segments and a point on the circle are found. Based on methods and algorithms proposed in this work, software modules were implemented. Approbation of these modules in the virtual environment system VirSim, which was developed in Scientific Research Institute for System Analysis of the Russian Academy of Sciences, showed the adequacy and effectiveness of created methods and algorithms for real-time simulation of virtual cylindrical objects. The results obtained in this work can be used to solve many practical problems in virtual environment systems, training complexes, educational applications, animation, computer games, etc.

Improved Bidirectional RRT ∗ Path Planning Method for Smart Vehicle

In this paper, an improved bidirectional RRT ∗ vehicle path planning method for smart vehicle is proposed. In this method, the resultant force of the artificial potential field is used to determine the search direction to improve the search efficiency. Different kinds of constraints are considered in the method, including the vehicle constraints and the vehicle driving environment constraints. The collision detection based on separating axis theorem is used to detect the collision between the vehicle and the obstacles to improve the planning efficiency. The cubic B-spline curve is used to optimize the path to make the path’s curvature continuous. Both simulation and experiment are implemented to verify the proposed improved bidirectional RRT ∗ method. In the simulation analysis, this paper’s method can generate the smoothest path and takes the shortest time compared with the other two methods and it can be adaptive to the complicated environment. In the real vehicle experiment, we can see from the test results that this paper’s method can be applied in practice on the smart electric vehicle platform; compared with others’ algorithm, this paper’s algorithm can generate shortest and smoothest path.

ROCA: Auto‐resolving overlapping and conflicts in Access Control List policies for Software Defined Networking

SummarySoftware‐defined networking (SDN) is a new networking architecture that decouples both the control and management planes from the data plane of forwarding devices. Control and management planes are implemented at a logically centralized entity called the controller. Despite numerous advantages, SDN is more prone to logical errors like loops, black holes, network reachability problems, and access control list (ACL) policies violation. In the existing approaches, the network requirements are specified by different network administrators using the ACL policies. SDN allows multiple network administrators to specify the ACL policies simultaneously, which may lead to conflicts and overlaps among the ACL policies. In this research work, a novel technique, called auto‐resolving overlapping and conflicts in ACL policies (ROCA), is proposed to efficiently detect and solve both the conflicts and the overlaps among the ACL policies by using the techniques of set theory, 3D structure, and separating axis theorem. It is shown by simulation and testing on the real network traces that ROCA outperforms the existing approaches in terms of computation time avoiding conflicts and overlapping among the ACL policies.

Research on local path planning based on improved RRT algorithm

In order to solve the local path planning of self-driving car in the structured road environment, an improved path planning algorithm named Regional-Sampling RRT (RS-RRT) algorithm was proposed for obstacle avoidance conditions. Gaussian distribution sampling and local biasing sampling were integrated to improve the search efficiency in the sampling phase. In the expansion phase, considering the actual size of the vehicle and obstacles, combined with the goal of safety and comfort, the separating axis theorem (SAT) method and vehicle dynamics were used to detect the collision among vehicle and surrounding obstacles in real time. In the post-processing stage, the driver’s driving consensus and path smoothing algorithm were combined to correct the planning path. In order to track the generated path, the MPC tracking algorithm was designed based on the Four-Wheel-Independent Electric Vehicle (FWIEV) model. The co-simulation software platform of CarSim and MATLAB/Simulink was employed to verify the effectiveness and feasibility of the path planning and tracking algorithm. The results show that compared with basic RRT and Goal-biasing RRT, the proposed RS-RRT algorithm has advantages in terms of number of nodes, path length and running time. The generated path can meet the FWIEV dynamics and path tracking requirements.

Collision detection of virtual plant based on bounding volume hierarchy: A case study on virtual wheat

Visualization of simulated crop growth and development is of significant interest to crop research and production. This study aims to address the phenomenon of organs cross-drawing by developing a method of collision detection for improving vivid 3D visualizations of virtual wheat crops. First, the triangular data of leaves are generated with the tessellation of non-uniform rational B-splines surfaces. Second, the bounding volumes (BVs) and bounding volume hierarchies (BVHs) of leaves are constructed based on the leaf morphological characteristics and the collision detection of two leaves are performed using the Separating Axis Theorem. Third, the detecting effect of the above method is compared with the methods of traditional BVHs, Axis-Aligned Bounding Box (AABB) tree, and Oriented Bounding Box (OBB) tree. Finally, the BVs of other organs (ear, stem, and leaf sheath) in virtual wheat plant are constructed based on their geometric morphology, and the collision detections are conducted at the organ, individual and population scales. The results indicate that the collision detection method developed in this study can accurately detect collisions between organs, especially at the plant canopy level with high collision frequency. This collision detection-based virtual crop visualization method could reduce the phenomenon of organs cross-drawing effectively and enhance the reality of visualizations.

A novel random forests based class incremental learning method for activity recognition

Automatic activity recognition is an active research topic which aims to identify human activities automatically. A significant challenge is to recognize new activities effectively. In this paper, we propose an effective class incremental learning method, named Class Incremental Random Forests (CIRF), to enable existing activity recognition models to identify new activities. We design a separating axis theorem based splitting strategy to insert internal nodes and adopt Gini index or information gain to split leaves of the decision tree in the random forests (RF). With these two strategies, both inserting new nodes and splitting leaves are allowed in the incremental learning phase. We evaluate our method on three UCI public activity datasets and compare with other state-of-the-art methods. Experimental results show that the proposed incremental learning method converges to the performance of batch learning methods (RF and extremely randomized trees). Compared with other state-of-the-art methods, it is able to recognize new class data continuously with a better performance.

Random Sequential Adsorption of Unoriented Cuboids with a Square Base and a Comparison of Cuboid--Cuboid Intersection Tests

In the paper, packings built of identical cuboids with a square base created by random sequential adsorption are studied. The result of the study show that the packing of the highest density are obtained for oblate and prolate cuboids of the edge-edge length ratios of $0.7$ and $1.4$. For both cases, the packing fraction is $0.400 \pm 0.002$, which is approximately 8% higher than the value reported for cubes. Additionally, because the crucial part of the packing generation algorithm is the cuboid-cuboid intersection detection, several methods were tested. It appears that the fastest one is based on the separating axis theorem.

A stepwise approach for 3D fracture intersection analysis and application to a hydropower station in Southwest China

A stepwise algorithm for determining the intersections between fractures is presented. The stepwise approach is based on the bounding volume technology and separating axis theorem. The length and orientation distribution of the fracture intersections can be obtained by the stepwise approach. The stepwise approach is used to study the connectivity of the rock mass at Songta hydropower station. According to the traces data acquired from a tunnel namely PD231, a DFN model was generated for intersection analysis and connectivity analysis. The results of intersection analysis show that the stepwise approach is effective. Connectivity parameters such as the average number of fracture intersections per fracture, and the length of intersection lines per unit volume, can be calculated. The mean length of intersections is 1.184m and the variance is 0.622m. The self-intersection behavior and direction vector of the intersections are studied. The simulations show that the sub-vertical joint set 3 and the shallow joint set 1 constitute the main flow pathways in the fractured rock at dam site. Besides, the results suggest that the sub-vertical joint sets (joint set 2 and 3) are more connected than the shallow joint set (joint set 1).

Abnormal Event Detection of Traffic Intersection Based on SAT Algorithm

SAT (Separating Axis Theorem) is an algorithm applied in two-dimensional games of collision detection in the convex polygon. This paper applied SAT algorithm into video monitoring at intersections to detect the vehicles collision incidents. Established separation axis to extracted vehicles and projected the target vehicles into separation axis. Through comparing the scalar value in separation axis to determine whether the target vehicles collision. It's proved that the method is effective by using Matlab software to the simulation test in this algorithm.

A new approach to real-time mosaicing of aerial images

We present a new image mosaicing technique that uses sequential aerial images captured from a camera and is capable of creating consistent large scale mosaics in real-time. To find the alignment of every new image, we use all the available images in the mosaic that have intersection with the new image instead of using only the previous one. To detect image intersections in an efficient manner, we utilize ‘Separating Axis Theorem’, a geometric tool from computer graphics which is used for collision detection. Moreover, after a certain number of images are added to the mosaic, a novel affine refinement procedure is carried out to increase global consistency. Finally, gain compensation and multi-band blending are optionally used as offline steps to compensate for photometric defects and seams caused by misregistrations. Proposed approach is tested on some public datasets and it is compared with two state-of-the-art algorithms. Results are promising and show the potential of our algorithm in various practical scenarios.

Enhancing Bounding Volumes using Support Plane Mappings for Collision Detection

In this paper we present a new method for improving the performance of the widely used Bounding Volume Hierarchies for collision detection. The major contribution of our work is a culling algorithm that serves as a generalization of the Separating Axis Theorem for non parallel axes, based on the well-known concept of support planes. We also provide a rigorous definition of support plane mappings and implementation details regarding the application of the proposed method to commonly used bounding volumes. The paper describes the theoretical foundation and an overall evaluation of the proposed algorithm. It demonstrates its high culling efficiency and in its application, significant improvement of timing performance with different types of bounding volumes and support plane mappings for rigid body simulations.

Simple and parallel proximity algorithms for general polygonal models

AbstractWe present simple and fast parallel proximity algorithms for rigid polygonal models. Given two polygon‐soup models in space, if they overlap, our algorithm can find all the intersected primitives between them; otherwise, it reports their Euclidean minimum distance. Our algorithm is performed in a parallel fashion and shows scalable performance in terms of the number of available computing cores. The key ingredient of our algorithm is a simple load‐balancing metric based on the penetration depth (PD) (for collision detection) and approximate Euclidean distance (for Euclidean distance computation) between bounding volumes. To compute the PD between oriented bounding boxes (OBBs), we present a novel algorithm based on the well‐known separating axis theorem (SAT) and also shows that the PD can be trivially obtained as a byproduct of SAT. We have implemented these algorithms on a commodity PC with eight cores and benchmarked their performance on complicated geometric models. In practice, the performance of our algorithm shows up to 5 and 9.7 times improvement for collision and distance queries, respectively, compared to single core computation. Copyright © 2010 John Wiley & Sons, Ltd.

Real‐time collision detection and response techniques for deformable objects based on hybrid bounding volume hierarchy

PurposeThe purpose of this paper is to propose a physically plausible solution based on hybrid bounding volume (BV) hierarchy for real‐time collision detection (CD) and response between a deformable and a rigid object.Design/methodology/approachHybrid BV can be used to build BV hierarchy for the deformable object. The overlapping tests based on separating axis theorem (SAT) can be used to deal with CD. The physics conception of restitution coefficient and other important forces can be used to more real collision response.FindingsMany methods focus on a specific application, but none of them gives an approach to physically plausible, real‐time simulation of CD and response up to 10,000 of deforming primitives. The paper finds that hybrid BV AABB‐Sphere for deformable object could increase the efficiency for CD, and restitution coefficient and other important physical concepts could provide more real collision response.Research limitations/implicationsThe paper does not deal with all types of CD, such as CD for two deformable objects.Originality/valueUsing AABB‐Sphere hybrid BV to build hierarchical BV tree for deformable object, and OBB‐Sphere hybrid BV for rigid object. Owing to the variety of hybrid BV structures, during different phases of CD, different overlapping tests are used to accelerate CD effectively. Using important physics conceptions provides a good solution to simulate more real collision response.

Oriented bounding box and octree based global interference detection in 5-axis machining of free-form surfaces

Global interference detection is a critical problem in 5-axis NC machining of free-form surfaces. Based on the hierarchical oriented bounding box (OBB) which is used in virtual reality to detect spatial collisions between 3D objects, a new global interference detection method is developed in this paper. In this method, in order to simplify the computation process of updating tool positions and orientations in 5-axis machining, the cutter and cutter holder are modeled by a hierarchical OBB structure, whereas the workpiece surfaces are approximated by an octree. Interference detection is conducted between the tool OBBs and the gray octants of the surface octree with the separating axis theorem. With the hierarchical structure of octree, if interference is found in one octant, its sub-octants are further processed to locate the exact colliding leaf nodes and the discretized surface points contained in these leaf nodes are tested with a conventional vector calculation method for exact interference detection; if no interference is detected, all the sub-octants are then considered as interference free and are not processed further. Meanwhile, with the hierarchical structure of the tool OBBs, should interference occur between octants and the OBBs in the first level of the hierarchical structure, the sub-OBBs in the second level would be further tested. Otherwise it could be determined with certainty that there is no interference between the tool and the octant.

Fast Tetrahedron-Tetrahedron Overlap Algorithm

Abstract We present an algorithm to test two tetrahedra for overlap. The algorithm is based on a dimension reduction technique that allows the application of the Separating Axis Theorem, thus avoid...