This paper presents an efficient method for collision detection in complex environments using bounding volume hierarchies (BV-trees) of discrete orientation polytopes (k-dops). The authors propose a careful study of effective methods for constructing BV-trees and an efficient algorithm for maintaining these trees as objects move and rotate. They also develop a fast collision detection algorithm using BV-trees of moving objects and the environment. The algorithms are implemented and tested, showing that they significantly outperform previous methods in terms of speed. The paper discusses various design choices, such as the degree of the tree, the choice of k-dops, and splitting rules, and provides experimental results to support their findings. The authors conclude with a discussion of extensions and future work.This paper presents an efficient method for collision detection in complex environments using bounding volume hierarchies (BV-trees) of discrete orientation polytopes (k-dops). The authors propose a careful study of effective methods for constructing BV-trees and an efficient algorithm for maintaining these trees as objects move and rotate. They also develop a fast collision detection algorithm using BV-trees of moving objects and the environment. The algorithms are implemented and tested, showing that they significantly outperform previous methods in terms of speed. The paper discusses various design choices, such as the degree of the tree, the choice of k-dops, and splitting rules, and provides experimental results to support their findings. The authors conclude with a discussion of extensions and future work.