Generic collisions

A large part of this book was dedicated to finding the most efficient way of determining whether two shapes intersect. The most robust, general purpose algorithm we have talked about so far has been Separating Axis Theorem (SAT). SAT has several limitations, the biggest one being curved surfaces. The execution time of SAT also gets out of hand when a complex mesh has many faces.

In this section, we will discuss a different generic algorithm--the Gilbert Johnson Keerthi or GJK algorithm. GJK runs in near linear time, often outperforming SAT. However, it is difficult to achieve the stability SAT provides using GJK. GJK should be used to find intersection data with complex meshes that have many faces. The GJK algorithm needs a support function to work, and this support function is called Minkowski Sum.

Note

For an algorithm to run in linear time, adding an iteration increases the execution time of the algorithm by the same amount every time, regardless of the size of the dataset...