Выдержка из оригинальной справки. (NDL Gamebryo 1.1)(С)
Given a leaf node with geometry (represented as a list of triangles), an oriented bounding box tree is built by analyzing the distribution of vertices at that leaf node. At the top level, the vertices are fit with a 3D non-circular Gaussian distribution. The mean of the distribution is used as the center of the box. The eigenvectors of the covariance matrix are used for the box axes. The axis lengths are determined by processing the list of vertices and increasing each axis length as necessary so that the final oriented box contains all the vertices.
The vertices for the entire leaf node are then partitioned into two sets based on the information obtained about the OBB. Each subset is fit with a Gaussian distribution and the corresponding OBBs are built. The algorithm continues recursively until the OBB tree has leaf nodes, each representing a triangle of the original scene graph leaf node. Comparison of two OBB trees is similar to that of NiBound's, but heuristically the number of comparisons is reduced because of the tighter fit on the geometry. Moreover, the game engine allows the application to tune the system by specifying how many triangles should be stored in the OBB tree leaf nodes. One triangle per node gives higher accuracy of intersection tests, but requires more comparisons between OBBs. More triangles per node reduce the accuracy of the intersection tests, but generally the tree comparisons take less time. The engine also allows the application to specify how many levels into the OBB tree the tests should occur.
The static OBB comparisons are fast in that two boxes are tested for intersection by projection onto various separating axes. It can be shown that at most 15 axes are required to determine static intersections and at most 21 axes are required to determine dynamic intersections, but on average, very few are needed to determine non-intersection. Surprisingly, the dynamic OBB comparisons require little additional work. The box projections on a separating axis are intervals. In the static case two intervals are tested for overlap. If there is no overlap on a single separating axis, then the OBBs do not intersect. If there is overlap on all 15 separating axes, then the OBBs do intersect. In the dynamic case, we simply compute the intersections of the OBBs for both starting time and final time of the frame and determine if during that time interval the projected intervals do or do not overlap. The velocities of the OBBs are used directly in determining such overlap.
