We present an improved parallel Sweep and Prune algorithm that solves the dynamic box intersection problem in three dimensions. It scales up to very large datasets, which makes it suitable for broad phase collision detection in complex moving body simulations. Our algorithm gracefully handles high-density scenarios, including challenging clustering behavior, by using a double-axis sweeping approach and a cache-friendly succinct data structure. The algorithm is realized by three parallel stages for sorting, candidate generation, and object pairing. By the use of temporal coherence, our sorting stage runs with close to optimal load balancing. Furthermore, our approach is characterized by a work-division strategy that relies on adaptive partitioning, which leads to almost ideal scalability. In addition, for scenarios that involves intense clustering along several axes simultaneously, we propose an enhancement that increases the context-awareness of the algorithm. By exploiting information gathered along three orthogonal axes, an efficient choice of what range query to perform can be made per object during run-time. Experimental results show high performance for up to millions of objects on modern multi-core CPUs.

Abstract In this paper, an algorithm is introduced that computes an arbitrarily fine approximation of the smallest enclosing ball of a point set in any dimension. This operation is important in, for example, classification, clustering, and data mining. The algorithm is very simple to implement, gives reliable results, and gracefully handles large problem instances in low and high dimensions, as confirmed by both theoretical arguments and empirical evaluation. For example, using a CPU with eight cores, it takes less than two seconds to compute a 1.001‐approximation of the smallest enclosing ball of one million points uniformly distributed in a hypercube in dimension 200. Furthermore, the presented approach extends to a more general class of input objects, such as ball sets.

Abstract We introduce a bounding volume hierarchy based on the Slab Cut Ball. This novel type of enclosing shape provides an attractive balance between tightness of fit, cost of overlap testing, and memory requirement. The hierarchy construction algorithm includes a new method for the construction of tight bounding volumes in worst case O(n) time, which means our tree data structure is constructed in O(n log n) time using traditional top‐down building methods. A fast overlap test method between two slab cut balls is also proposed, requiring as few as 28–99 arithmetic operations, including the transformation cost. Practical collision detection experiments confirm that our tree data structure is amenable for high performance collision queries. In all the tested benchmarks, our bounding volume hierarchy consistently gives performance improvements over the sphere tree, and it is also faster than the OBB tree in five out of six scenes. In particular, our method is asymptotically faster than the sphere tree, and it also outperforms the OBB tree, in close proximity situations.