Bounding Volume Hierarchies of Slab Cut Balls

We introduce a bounding volume hierarchy based on the Slab Cut Ball. This novel type of enclosing volume 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. For example, in all the tested benchmarks, our bounding volume hierarchy consistently gives performance improvements over both the sphere tree and the OBB tree data structure. In particular, our method is asymptotically faster than the sphere tree, and it also outperforms the OBB tree, in close proximity situations.