COLLISION DETECTION FOR VIRTUAL PROTOTYPING ENVIRONMENTS
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1 XIII ADM - XV INGEGRAF International Conference on TOOLS AND METHODS EVOLUTION IN ENGINEERING DESIGN Cassino, June 3th, 2003 Napoli, June 4 th and June 6 th, 2003 Salerno, June 5 th, 2003 COLLISION DETECTION FOR VIRTUAL PROTOTYPING ENVIRONMENTS Mauro Figueiredo (1)(2), Terrence Fernando (1) (1) University of Salford Centre for Virtual Environments {M.Figueiredo, T.Fernando}@salford.ac.uk (2) University of Algarve Escola Superior Tecnologia mfiguei@ualg.pt ABSTRACT The Virtual Prototyping Group at the Center for Virtual Environments at the University of Salford is working in the development of a unified virtual prototyping environment. This environment is a testbed in the development of assembly/disassembly and maintenance verification operations. This paper identifies the requirements and proposes a novel collision detection algorithm for assisting such operations. Virtual prototype models are defined as a collection of surfaces. Available collision detection toolkits for virtual environments are based on polygons. The integration of surface knowledge into the design of the collision detection algorithm contributes for the development of a better real time collision detection algorithm for supporting assembly and maintenance simulations. The algorithm presented in this paper determines, for each pair of colliding objects, the intersecting surfaces. The virtual prototyping environment uses this knowledge for the automatic recognition of geometric constraints during user interaction in assembly and maintenance operations. This paper also introduces the concept of an Overlapping Axis-Aligned Bounding Box (OAABB) for improving the overall complexity of the surface based collision detection algorithm. Keywords: Collision Detection, Assembly/Disassembly and Maintenance Simulation, Virtual Prototyping, Virtual Reality. 1. Introduction Today's development of industrial products faces high requirements. Manufacturing companies need to produce high quality products, at low cost, to be marketed earlier than those of the competitors. Products must satisfy consumer requirements, developed fast and of high quality. To this extent, many manufactures are adopting concurrent engineering in an attempt to reduce the lead-time for new products and improve their quality while reducing manufacturing costs. Concurrent Engineering (CE) is a systematic approach to the integrated concurrent design of products and related processes. It encourages the integration of traditionally separated product development phases in the design of the product. In CE issues of the product life cycle, such as
2 manufacturability and maintainability, are considered and improved at early stages in the design of a product. This reduces unforeseen problems creeping into the design as it progresses through its life cycle, consequently saving both time and money while improving product quality. In this process, different engineering disciplines are considered simultaneously and computer support is required to manage the huge amount of complex product data. The integration of expertise from design, engineering, testing, manufacturing and maintenance in a unified concurrent engineering framework has led to more effective rapid prototyping. Rapid prototyping technology allows the production of a virtual prototype from a three-dimensional CAD drawing. This virtual model gives complete information about the product earlier in the development cycle. Conventional prototyping can take weeks or months. Rapid prototyping is quicker and reduces the cost of building prototypes as opposed to conventional methods. In a virtual prototyping environment, a 3D virtual model of the product is used within the different stages of the product life cycle. As the area of virtual prototyping is developed, it is envisaged that the virtual model will behave as the physical prototype enabling the simulation of all aspects of a product, such as, mechanical design, kinematics, dynamics, testing and maintenance, in a unified framework. In this way, more analyses of the design can be performed before there is a need to build the physical prototype, which is more difficult to modify, thus reducing furthermore the costs and the time to market the product. Current software tools do not fully support all stages of the product development cycle, restricting the applicability of concurrent engineering concepts. There is still a lack of intuitive software tools to address assembly/disassembly operations and maintenance verifications [Sá and Zachmann, 1999], [Fernando et al., 2001]. Development teams continue to build a physical prototype to assess if a human worker can assemble a part or component, and if it can be disassembled later on for service and maintenance. But, a physical prototype is expensive, time consuming and increases the time to market the product. Frequently, a physical prototype is available very late in the design process, making it difficult to integrate any major changes. Pratt [Pratt, 1995] points out that up to 70% of the total life cycle costs of a product are committed by decisions made in the early stages of design. In fact, it has been recognized the benefits of using virtual environments and virtual prototyping for assembly and maintenance verification and it is has been identified has an opportunity to improve the development process and a topic of ongoing research [Fernando et al., 2001], [Loock and Schömer, 2001], [Sá and Zachmann, 1999]. The Virtual Prototyping Group at the Centre for Virtual Environments at the University of Salford has been exploring the applicability of virtual reality in different product development stages such as maintenance simulation, which involves complex object interaction and control [Fernando et al., 2001]. Work is being carried on in the development of a simulation environment that allows designers and engineers to assess maintenance tasks before any physical prototype is built. In a maintenance simulation scenario, it is necessary to allow the user to interactively carry out assembly and disassembly operations on the virtual prototypes in a realistic way. In such environment, the three-dimensional virtual prototypes need to simulate physical properties realistic and interactively. In this paper, we present a collision detection algorithm focused in the development of a better real time collision detection algorithm for supporting assembly and maintenance simulation in an unified virtual prototyping environment, using effectively the available surface data from the CAD model. In the interactive simulation of assembly and disassembly operations, it is automatically established, or removed, a set of geometric
3 constraint relationships between surfaces as the user manipulates the assembly components. These operations rely on the determination of intersecting surfaces between colliding objects to: provide collision response; stop object penetration; simulate constrained motion; simulate kinematics motion and sliding; assist users to carry out precise object manipulations; automatically recognize constraints. Current collision detection algorithms simply discard the surface data and are unable to determine intersecting surfaces. Available collision detection approaches for virtual environments are based on polygons [Figueiredo et al., 2002]. They are very effective in determining intersecting polygons, but cannot determine intersecting surfaces. The approach that we present uses the surface knowledge to build an effective novel collision detection algorithm that provides information about colliding surfaces to be used by the constraint manager. We also introduce the Overlapping Axis-Aligned Bounding Box (OAABB) concept in the collision detection algorithm to improve performance. The complexity of the proposed algorithm is reduced from a square factor to a linear factor. This paper is organized as follows. Section 2 presents our view of a unified virtual prototyping environment that is under development at the Center for Virtual Environments. Several case study scenarios from industrial partners contributed for the identification of the requirements for a collision detection manager for virtual prototyping applications, presented in section 3. Section 4 presents the architecture for the proposed collision detection manager. Conclusions are discussed in section Virtual prototyping framework The ongoing research at the Center for Virtual Environments at the University of Salford is concerned in the development of a unified platform for virtual prototyping. A goal of this research is to integrate expertise from design, engineering, testing, manufacturing and maintenance in a unified concurrent engineering framework in a virtual environment. The architecture of the proposed unified virtual prototyping environment is shown in figure 1. The framework for the virtual prototyping environment consists of three main components: visualization; interaction and behavior simulation. These components are commonly present in virtual environments applications. The function of each of these components is as follows: Visualization: This component is responsible for the presentation of high-level 3D graphical and multimedia scenes. Interaction: This module gives to the user the feeling of direct interaction with the application, rather than with a computer. The user is able to interact naturally in 3D by touching, feeling, grabbing, moving and manipulating objects, as he/she would do in the physical world. Behavior: This module supplies the functionality that helps in the simulation of the reality. It contributes to the enrichment of the creation of the sensation of manipulating a real world. Three modules can be identified: 1) Physical Realism : This component is responsible for the simulation of physical properties such as: solidity, gravity, elastic collisions, and others. The physical realism manager includes generic behaviors that contribute to the simulation of reality. When an object is dropped, it falls according to the gravity laws until it stops on the floor. An object like a balloon rises in the air until it reaches the virtual room
4 ceiling. Each object has its individual behavior, knowing how to react to various stimuli the environment exerts upon it. 2) Constraint-based Geometric : This component is responsible for modeling interactive assembly and disassembly tasks. This manager automatically recognizes geometric constraint relationships between the assembly components. It also automatically removes the constraint relationships appropriately, when the user is disassembling a model. The constraint-based geometric module also manages constraint relationships while simulating constrained motion. 3) Collision Detection : This module is responsible for finding precisely and interactively collisions between the geometric surfaces. The collision detection manager checks if any objects are colliding in the world at any moment. For objects that do collide, the system determines appropriate behavior to simulate reality. For assembly/disassembly and maintenance simulations, the collision detection manager determines the colliding surfaces passed to the constraint-based geometric manager. This information is used for the automatic recognition of geometric constraint relationships among the assembly components and to remove the geometric constraint relationships appropriately during user interaction. Behaviour Visualization Physical Realism Constraint-based Geometric Virtual Prototyping System Collision Detection Interaction Figure 1. Architecture of the unified virtual prototyping environment. 3. Collision detection requirements for virtual prototyping This section presents the characteristics of a collision detection manager to be developed for assisting in assembly and maintenance operations in virtual prototyping environments. Wimalaratne [Wimalaratne, 2002] identifies the need of developing efficient surfacebased collision software to integrate a virtual prototyping system for assembly simulation. Virtual prototyping models, generated by Computer-Aided Design (CAD) systems, are surface-based. There are several publicly available collision detection toolkits for virtual environments: I-COLLIDE [Cohen et al., 1995]; RAPID [Gottschalk et al., 1996]; V-COLLIDE [Hudson et al., 1997]; SOLID [Van Der Bergen, 1997];
5 QuickCD [Klosowski et al., 1998]. These collision detection managers support polygonal models [Figueiredo et al., 2002], disregarding all the surface data of the CAD model. The knowledge of all the colliding surfaces is valuable information for the constraint manager, enabling the automatic recognition of constraints and avoiding penetrating objects. In the simulation of assembly and disassembly operations, finding precise collisions is an important task for achieving realistic behavior [Munlin, 1995]. When assembling two components, it is necessary to find precisely which parts are colliding, to determine possible constraints and simulate solidity. When simulating the dynamic behavior of a virtual prototype, collision detection determines again the exact interactions between different components. If a user wants to grab a virtual prototype, a precise collision check must be done to guarantee that he is touching it. Figure 2 shows an example that emphasizes the importance of exactly finding collisions for the recognition of constraints in assembly operations. (a) (b) Figure 2. In the digger case study scenario it is used the concept of virtual sensor based on bounding volumes. (a) Identification of a constraint between the two highlighted surfaces. (b) The two components are assembled unrealistically. Figure 2-a presents a situation where there is no contact between the two highlighted surfaces. However, it is automatically recognized a constraint between the two surfaces, as a result of the determination of an overlap between the two corresponding bounding volumes. If the user accepts the recognized constraint, the two components are unrealistically assembled as it is presented in figure 2-b. Collision detection algorithms implemented only with bounding volumes are ineffective in automatically identifying geometric constraints correctly. Finding collisions in a three-dimensional environment can be a very demanding task. In some environments it can easily consume up to 50% of the total run time [Wieland et al., 2001]. In real industrial case studies tested and evaluated at the Center for Virtual Environments at the University of Salford, 3D virtual prototypes can be very complex with thousands of primitives. Developing collision detection algorithms for complex environments is an open research issue [Lin and Gottschalk, 1998]. Furthermore, maintaining the user of a virtual prototyping application engaged and providing the illusion of being immersed and working interactively in the system requires a constant high frame rate. In the worst case, it is required an update rate of at least 10 Hz. In summary, we can say that a collision detection component for assisting in assembly/disassembly and maintenance operations in virtual prototyping environments should: (a) determine collisions based on surfaces; (b) determine collisions precisely; (c) determine collisions interactively.
6 4. Collision detection architecture This section presents a novel algorithm for finding collisions in a virtual prototyping environment. The collision detection manager described, in the following paragraphs, takes advantage of the scene graph structure (figure 3) available from CAD models. For each pair of objects it determines the colliding surfaces. Scene Graph Objects Ob 1... Ob m Surfaces S 1... S i Polygons P 1 P 2... P j P 1 P 2... P k Figure 3. Virtual prototyping scene graph. The proposed algorithm for the determination of colliding objects and surfaces in a virtual prototyping scene graph is done in three steps (figure 4): 1) Filter Objects ; 2) Filter Surfaces ; 3) Polygons Intersection. Scene Graph Filter Objects Ob i, Ob j, OAABB(i,j) Filter Surfaces S i, S j, OAABB(i,j) Polygons Intersection Colliding Surfaces S i, S j Figure 4. Collision detection architecture.
7 Filter Objects This manager determines possible objects candidates for collisions. This stage uses the axis-aligned bounding box (AABB) of each object. If a pair of axis-aligned bounding boxes do not overlap, then the corresponding two objects cannot intersect and this pair of objects is filtered out. Two objects are candidates for collision if the corresponding axis-aligned bounding boxes overlap. In this case, the collision detection manager determines the Overlapping Axis-Aligned Bounding Box (OAABB) (figure 5). This is determined as the volume that is common to the two overlapping axis-aligned bounding boxes. A novelty of the proposed algorithm is the use of the OAABB of the two objects in the next steps of the collision detection process. OAABB(Ob 1,Ob 2 ) AABB(Ob 2 ) S 2 S' 1 Ob 1 S 1 S' 2 Ob 2 S' 3 S 3 S 4 AABB(Ob 1 ) Figure 5. The Overlapping Axis-Aligned Bounding Box (OAABB) concept shown in 2D. Filter Surfaces This process determines possible surfaces candidates for intersection. For every pair of objects candidates for collision determined in the previous step, the algorithm filters out surfaces that cannot intersect. This is a novelty of the present algorithm. The determination of precise collisions in a virtual prototyping environment considers the available surface data from the CAD model. The proposed algorithm uses the axisaligned bounding box of each surface and the overlapping axis-aligned bounding box determined in the first step (figure 6a). A straightforward implementation for finding pairs of surfaces from the two objects candidates for collision, checks for intersection every AABB of each surface from one object against every AABB of each surface from the other object (figure 6b). This approach is of complexity O(n 2 ), n is the number of surfaces of each object. To achieve a better performance, it is proposed the use of the OAABB determined from the two candidates objects for intersection. Two surfaces are candidate for intersection if they also intersect the OAABB (figure 6). In this way, surfaces whose AABBs do not intersect the OAABB are filtered out. The remaining m surfaces of each object are than intersected to find if their corresponding AABBs are overlapping. This step is also of complexity O(m 2 ), but m is the small number of remaining surfaces of each object. In the example shown in figure 6, there is an overhead of 50% of the straightforward implementation over the approach based on OAABB. A list of pairs of surfaces candidates for collision is the output of the filter surface manager. Polygons Intersection This manager is responsible for determining precisely intersecting polygons. For every pair of objects candidates for collision, the previous stage determined a set of pairs of surfaces that can possible collide. Finding precisely if two objects intersect, needs
8 checking for collision every pair of polygons from this set of surfaces. Intersecting two polygons is an expensive computational operation. Axis-aligned bounding boxes of each polygon can be used to reduce the number of such operations in a process for filtering polygons (figure 7). Pairs of polygons whose AABBs do not overlap, cannot intersect and are discarded. At this point, the proposed algorithm introduces the novelty of using again the overlapping axis-aligned bounding box. Two polygons can possible collide if and only if their AABBs intersect the OAABB. Therefore, the first operation accomplished in this stage consists in, testing for each polygon, if its AABB intersects the OAABB. If there is no intersection then the corresponding polygon is filtered out. AABBs pairs of the remaining polygons are then intersected. Those non-intersecting pairs are filtered out. These previous steps filter out every pair of polygons that do not intersect, because theirs corresponding axis-aligned bounding box do not overlap. In the end, there are a small number of pairs of polygons candidates for collision. The final step is to proceed with the intersection of pairs of polygons. If there is a pair of intersecting polygons then the corresponding surfaces intersect. A list of colliding surfaces is constructed. AABB(S 2 ) Ob 1 S 2 OAABB(Ob 1,Ob 2 ) S' 2 S AABB(S' 1 2 ) AABB(S 1 ) S S 4 3 AABB(S 3 ) AABB(S 4 ) Ob 2 AABB(S' 1 ) S' 1 S' 3 AABB(S' 3 ) Straightforward Approach O(n 2 ) Intersect (AABB(S 1 ), AABB(S' 1 )) Intersect (AABB(S 1 ), AABB(S' 2 )) Intersect (AABB(S 1 ), AABB(S' 3 )) Intersect (AABB(S 2 ), AABB(S' 1 )) Intersect (AABB(S 2 ), AABB(S' 2 )) Intersect (AABB(S 2 ), AABB(S' 3 )) Intersect (AABB(S 3 ), AABB(S' 1 )) Intersect (AABB(S 3 ), AABB(S' 2 )) Intersect (AABB(S 3 ), AABB(S' 3 )) Intersect (AABB(S 4 ), AABB(S' 1 )) Intersect (AABB(S 4 ), AABB(S' 2 )) Intersect (AABB(S 4 ), AABB(S' 3 )) Surface Filter Implementation OAABB Approach Intersect (AABB(S 1 ), OAABB) Intersect (AABB(S 2 ), OAABB) Intersect (AABB(S 3 ), OAABB) Intersect (AABB(S 4 ), OAABB) Intersect (AABB(S' 1 ), OAABB) Intersect (AABB(S' 2 ), OAABB) Intersect (AABB(S' 3 ), OAABB) Intersect (AABB(S 1 ), AABB(S' 2 )) Figure 6. (a) The filtering surface process shown in 2D. (b) Comparison of two approaches for filtering surfaces. OAABB(Ob 1,Ob 2 ) S 2 S' 1 S' 2 P' 1 Ob 1 S 1 P' 2 P 1 P 2 P 3 P' 3 Ob 2 P' 4 P' 5 P 4 P 5 S' 3 S 3 S 4 Figure 7. Filtering polygons using AABBs and OAABB in 2D.
9 5. Conclusions The main contribution of the present paper is the presentation of a novel collision detection algorithm that determines precisely collisions between surfaces of 3D assembly models in virtual prototype environments. Initially, we present our view about the development of a unified virtual prototyping environment at the Center for Virtual Environments at the University of Salford. The collision detection manager plays an important role in this framework. We identify the requirements for a collision detection manager for a virtual prototyping environment. Current virtual prototype environments base the collision detection manager on polygonal models. The available surface data from the CAD model is not used. The novel collision detection algorithm presented in this paper uses the surface knowledge to determine intersecting surfaces for assisting in assembly and maintenance operations in a unified virtual prototyping environment. This algorithm determines precisely intersecting surfaces. This knowledge can be used, more effectively, by the constraintbased geometric manager, in the automatic recognition of geometric constraints during user interaction. In this paper, it is also introduced the novel concept of overlapping axis-aligned bounding boxes OAABB for improving the overall performance. A straightforward collision detection algorithm is of complexity O(n 2 ). The use of an OAABB can significantly improve performance to a linear factor. References Cohen, J., Lin, M., Manocha, D. and Ponamgi, K., I-COLLIDE: An Interactive and Exact Collision Detection System for Large-Scale Environments, In Proceedings of ACM Int. 3D Graphics Conference, vol. 1, 1995, pp Fernando, T, Marcelino, L, Wimalaratne, P., Constraint-based Immersive Virtual Environment for Supporting Assembly and Maintenance Tasks, HCII 2001, New Orleans, Vol.1, 2001,pp Figueiredo, M., Marcelino, L., Fernando, T., A Survey on Collision Detection Techniques for Virtual Environments. In Proc. of V Symposium in Virtual Reality, Brasil, 2002, pp Gottschalk, S., Lin, M. C. and Manocha, D., Obb-tree: A hierarchical structure for rapid interference detection, In Proc. of ACM Siggraph'96, 1996, pp Hudson, T. C., Lin, M. C., Cohen, J., Gottschalk, S. and Manocha, D., V-COLLIDE: Accelerated Collision Detection for VRML, In Proc. of VRML, 1997, pp Klosowski, J., Held, M., Mitchell, J., Sowizral, H. and Zikan, K., Efficient Collision Detection using Bounding Volume Hierarchies of k-dops, IEEE Trans. On Visualization and Computer Graphics, 4, 1, 1998, pp
10 Lin, M. C. and Gottschalk, S., Collision Detection between Geometric Models: A Survey, In Proc. of IMA Conference on Mathematics of Surfaces (San Diego (CA)), vol. 1, 1998, pp Loock, A., and Schömer, E., A Virtual Environment for Interactive Assembly Simulation: From Rigid Bodies to Deformable Cables. In 5 th World Multiconference on Systemics, Cybernetics and Informatics (SCI'01), Vol. 3 (Virtual Engineering and Emergent Computing), 2001, pp Munlin, M., Interactive assembly modeling within a virtual environment. PhD thesis, University of Leeds, Leeds, UK, Pratt, M. J., Virtual prototypes and product models in mechanical engineering. In J. Rix, S. Haas & J. Teixeira (Eds.), Virtual prototyping virtual environments and the product design process, 1995, pp. 113 Sá, A. G., and Zachmann, G., Virtual reality as a tool for verification of assembly and maintenance processes. Computers & Graphics, Vol. 23, No. 3, 1999, pp Van Der Bergen, G., Efficient Collision Detection of Complex Deformable Models using AABB Trees, In Journal of Graphics Tools, 2, 4, 1997, pp Wieland, F., Carnes, D. and Schultz, G., Using Quad Trees for Parallelizing Conflict Detection in a Sequencial Simulation. In Proc. of the 15th Workshop on Parallel and Distributed Simulation, 2001, pp Wimalaratne, P., Constraint-based functional virtual prototyping for assembly simulation. PhD thesis, University of Salford, Salford, UK, 2002.
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