Enhancing Bounding Volumes using Support Plane Mappings for Collision Detection

Abstract

In this paper we present a new method for improving the performance of the widely used Bounding Volume Hierarchies for collision detection. The major contribution of our work is a culling algorithm that serves as a generalization of the Separating Axis Theorem for non parallel axes, based on the well-known concept of support planes. We also provide a rigorous definition of support plane mappings and implementation details regarding the application of the proposed method to commonly used bounding volumes. The paper describes the theoretical foundation and an overall evaluation of the proposed algorithm. It demonstrates its high culling efficiency and in its application, significant improvement of timing performance with different types of bounding volumes and support plane mappings for rigid body simulations.

A path planning method for large-aperture non-spherical surface detection profilometer

“…If the projections overlap in all four directions, it is considered that there is an overlapping area between boxes A and B, indicating a collision. In contrast, if there is a straight line perpendicular to them can be drawn between box A and box B as the separation axis [10] to separate them, indicating no collision. Figure 2 illustrates this process.…”

Compact Union of Disjoint Boxes: An Efficient Decomposition Model for Binary Volumes

“…Sometimes we want to determine if two or more objects collide or are adjacent. In collision detection [30] when exact accuracy is not required, typical bounding volumes like axis-aligned bounding boxes (AABB) [59], spheres [22], oriented polytopes [13] or hybrid bounding volumes are used [56].…”

Six Degrees of Freedom Implicit Haptic Rendering

“…The importance of support planes is intuitively apparent: they provide an explicit way of deciding whether another object could possibly intersect with the one that the support planes refers to. Based on this simple but important feature of support planes, a slightly more generalized formulation has been derived [14] introducing the concept of support plane mappings for collision detection. The approach described in [14] is used in the proposed framework for collision detection.…”

“…Based on this simple but important feature of support planes, a slightly more generalized formulation has been derived [14] introducing the concept of support plane mappings for collision detection. The approach described in [14] is used in the proposed framework for collision detection.…”

“…Referring to Figure 2 that for simplicity depicts the 2D case, let M 1 and M 2 be the mesh areas of two different objects possibly involved in collision and S 1 and S 2 their respective support planes. Based on the approach presented in [14] it can be decided whether M 1 and M 2 are probably involved in collisions using their SPMs S 1 and S 2 . Now the question is: Is it possible to identify the collisions and calculate 6DoF force feedback without entering the computationally intensive narrow-phase [14] of the collision detection algorithm?…”