Collision algorithms

First also in the implementation there are the object to the same object collision which are described here:

Sphere2Sphere

The collision of 2 spheres is the most simple algorithms. Important is the distance between the two center points. If this distance is larger than the sum of the two radii then there is no collision. If the distance is equal as the radii sum both spheres has one contact point. If there is are real overlapping one can define a contact circle (not implemented yet!).

Box2Box

The collision of two boxes is based on a simple algorithm approach. One has a collision of at least one corner of one box is touching or is inside the other box. For a complete test one has to check for all corners of all boxes! Before describing the test of a corner is touching or inside a box it is necessary to describe a helper algorithm, the calculation of the box volume. Generally the volume of a box even if the box is not rectangular is calculated by multiplying the base of a box with the height. For our purpose we need another slightly complicated algorithm. We cut the box into 6 pyramids where all pyramids have the same top point, which is naturally the center point of the box. However, if one move this center point around inside the box the calculated volume will not change (in the computational world the volume will be the same within accuracy value!). So coming back to the corner test. Assume that the test point is outside the box if we now use the same volume algorithm and exchange the center point with the test point the volume is now larger than the original volume of the box. If the new calculated volume is equal to the original volume then the corner is touching is laying inside the box which indicated a collision. Please keep always in mind to check every corner of both boxes since there is one test case in which one corner of one box is inside the other box. The corner of this box are far away from the other box, so checking only this box is not sufficient!