Sweep and Prune Algorithm - Introduction

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本文详细介绍了逐维递归分组法（Sweep and Prune）在碰撞检测中的原理和实现过程，通过检测轴对齐边界框的重叠来快速筛选可能相撞的对象，有效减少不必要的碰撞检查，提高效率。

在第一阶段的检测(BroadPhase)中所需要的算法就是 Sweep and Prune,因为从未接触过此类的东西,所以不知道到底是个什么东西,今天终于找到具体资料了,一看,晕倒掉了.原来就是<游戏编程精粹2>里面所提及到的逐维递归分组法...
貌似如果有人搜索相关词汇是能够搜索到我的blog的,特别留下此文以防止有哥们走我同样的弯路了...

顺便放一个英文东西:
来自于:http://parallel.vub.ac.be/documentation/pvm/Example/Marc_Ramaekers/node3.html
Sweep and Prune
Given a number N of objects, O( N²) object pairs have to be checked for collision. In general, the objects in most of the pairs aren't even close to each other so we should be able to eliminate them quickly. To do this we use a technique called Sweep and Prune ([ CLMP95]). In this section I will briefly introduce this technique.

To determine whether two objects are close enough to potentially collide, the Sweep and Prune checks whether the axis aligned bounding boxes of the respective objects overlap. If they do, further investigation is necessary. If not, the objects can't possibly collide and the algorithm can move on. To determine whether two bounding boxes overlap, the algorithm reduces the 3D problem to three simpler 1D problems. It does so by determining the intervals occupied by the bounding volume along each of the x,y and z axes. If and only if the intervals of two bounding volumes overlap in all of the three dimensions, the objects corresponding to these bounding volumes must overlap. To determine which intervals of the objects along an axis overlap, the list of the intervals is sorted. Normally, using quick-sort, this would be an $O(N \log N)$ process. However, by exploiting frame coherence (the similarity between situations in two subsequent frames) we can sort the lists in an expected (O(N), using insertion sort.

Another difficult part in the Sweep and Prune approach is the maintenance of the bounding volume. If the objects in the scene move or rotate, the previously calculated bounding boxes are invalid. It is important to be able to update the boxes as quickly as possible. Again, we can do this by exploiting frame coherence.

The algorithm's performance is of course dependent on the application and the typical situations that occur in that application. Many variations exists, such as reducing the overlap problem by only 1 dimension and using a rectangle intersection test. It is also possible to choose other types of bounding volumes that might be faster to update but produce a less accurate approximation of the object.