Gabriel Zachmann

Collision Detection for Deformable Objects

Interactive environments for dynamically deforming objects play an important role in surgery simulation and entertainment technology. These environments require fast deformable models and very efficient collision handling techniques. While collision detection for rigid bodies is well investigated, collision detection for deformable objects introduces additional challenging problems. This paper focuses on these aspects and summarizes recent research in the area of deformable collision detection. Various approaches based on bounding volume hierarchies, distance fields and spatial partitioning are discussed. In addition, image‐space techniques and stochastic methods are considered. Applications in cloth modeling and surgical simulation are presented.

Virtual reality as a tool for verification of assembly and maintenance processes

Abstract Business process re-engineering is becoming a main focus in todays efforts to overcome problems and deficits in the automotive and aerospace industries (e.g., integration in international markets, product complexity, increasing number of product variants, reduction in product development time and cost). In this paper, we investigate the steps needed to apply virtual reality (VR) for virtual prototyping (VP) to verify assembly and maintenance processes. After a review of todays business process in vehicle prototyping, we discuss CAD-VR data integration and identify new requirements for design quality. We present several new interaction paradigms so that engineers and designers can experiment naturally with the prototype. Finally, a user survey evaluates some of the paradigms and the acceptance and feasability of virtual prototyping for our key process. The results show that VR will play an important role for VP in the near future.

Rapid collision detection by dynamically aligned DOP-trees

Based on a general hierarchical data structure, we present a fast algorithm for exact collision detection of arbitrary polygonal rigid objects. Objects consisting of hundreds of thousands of polygons can be checked for collision at interactive rates. The pre-computed hierarchy is a tree of discrete oriented polytopes (DOPs). An efficient way of realigning DOPs during the traversal of such trees allows us to use simple interval tests for determining the overlap between DOPs. The data structure is very efficient in terms of memory and construction time. Extensive experiments with synthetic and real-world CAD data have been carried out to analyze the performance and memory usage of the data structure. A comparison with oriented bounding box (OBB) trees indicates that DOP-trees are as efficient in terms of collision query time and more efficient in memory usage and construction time.

GPU-ABiSort: optimal parallel sorting on stream architectures

In this paper, we present a novel approach for parallel sorting on stream processing architectures. It is based on adaptive bitonic sorting. For sorting n values utilizing p stream processor units, this approach achieves the optimal time complexity O((n log n)/p). While this makes our approach competitive with common sequential sorting algorithms not only from a theoretical viewpoint, it is also very fast from a practical viewpoint. This is achieved by using efficient linear stream memory accesses (and by combining the optimal time approach with algorithms optimized for small input sequences). We present an implementation on modern programmable graphics hardware (GPUs). On GPUs, our optimal parallel sorting approach has shown to be remarkably faster than sequential sorting on the CPU, and it is also faster than previous non-optimal sorting approaches on the GPU for sufficiently large input sequences. Because of the excellent scalability of our algorithm with the number of stream processor units p (up to n/log/sup 2/ n or even n/log n units, depending on the stream architecture), our approach profits heavily from the trend of increasing number of fragment processor units on GPUs, so that we can expect further speed improvement with upcoming GPU generations.

Minimal hierarchical collision detection

We present a novel bounding volume hierarchy that allows for extremely small data structure sizes while still performing collision detection as fast as other classical hierarchical algorithms in most cases. The hierarchical data structure is a variation of axis-aligned bounding box trees. In addition to being very memory efficient, it can be constructed efficiently and very fast.We also propose a criterion to be used during the construction of the BV hierarchies is more formally established than previous heuristics. The idea of the argument is general and can be applied to other bounding volume hierarchies as well. Furthermore, we describe a general optimization technique that can be applied to most hierarchical collision detection algorithms.Finally, we describe several box overlap tests that exploit the special features of our new BV hierarchy. These are compared experimentally among each other and with the DOP tree using a benchmark suite of real-world CAD data.

Point Cloud Collision Detection

In the past few years, many efficient rendering and surface reconstruction algorithms for point clouds have been developed. However, collision detection of point clouds has not been considered until now, although this is a prerequisite to use them for interactive or animated 3D graphics.

A unified approach for physically-based simulations and haptic rendering

Based on our new geometric data structure, the inner sphere trees, we present fast and stable algorithms for different kinds of collision detection queries between rigid objects at haptic rates. Namely, proximity queries and the penetration volume, which is related to the water displacement of the overlapping region and thus corresponds to a physically motivated force. The latter allows us to define a novel penalty-based collision response scheme that provides continuous forces and torques which are applicable to physically-based simulations as well as to haptic rendering scenarios. Moreover, we present a time-critical version of the penetration volume computation that is able to achieve very tight bounds within a fixed budget of query time. The main idea of our new data structure is to bound the object from the inside with a set of non-overlapping bounding volumes. The results show performance at haptic rates both for proximity and penetration volume queries, independent from the polygon count of the objects.

Point cloud surfaces using geometric proximity graphs

We present a new definition of an implicit surface over a noisy point cloud, based on the weighted least-squares approach. It can be evaluated very fast, but artifacts are significantly reduced. We propose to use a different kernel function that approximates geodesic distances on the surface by utilizing a geometric proximity graph. From a variety of possibilities, we have examined the Delaunay graph and the sphere-of-influence graph (SIG), for which we propose several extensions. The proximity graph also allows us to estimate the local sampling density, which we utilize to automatically adapt the bandwidth of the kernel and to detect boundaries. Consequently, our method is able to handle point clouds of varying sampling density without manual tuning. Our method can be integrated into other surface definitions, such as moving least squares, so that these benefits carry over.

Inner sphere trees for proximity and penetration queries

We present a novel geometric data structure for approximate collision detection at haptic rates between rigid objects. Our data structure, which we call inner sphere trees, supports different kinds of queries, namely, proximity queries and a new method for interpenetration computation, the penetration volume, which is related to the water displacement of the overlapping region and, thus, corresponds to a physically motivated force. The main idea is to bound objects from the inside with a set of non-overlapping spheres. Based on such sphere packings, a “inner bounding volume hierarchy” can be constructed. In order to do so, we propose to use an AI clustering algorithm, which we extend and adapt here. The results show performance at haptic rates both for proximity and penetration volume queries for models consisting of hundreds of thousands of polygons.

Kinetic bounding volume hierarchies for deformable objects

We present novel algorithms for updating bounding volume hierarchies of objects undergoing arbitrary deformations. Therefore, we introduce two new data structures, the kinetic AABB tree and the kinetic BoxTree.The event-based approach of the kinetic data structures framework enables us to show that our algorithms are optimal in the number of updates. Moreover, we show a lower bound for the total number of BV updates, which is independent of the number of frames.We used our kinetic bounding volume hierarchies for collision detection and performed a comparison with the classical bottom-up update method. The results show that our algorithms perform up to ten times faster in practically relevant scenarios.