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Here are some test cases to demonstrate the algorithm.

We implemented the algorithm with C++. Our tests presented below were ran on a Pentium 4 1GB RAM. Addressing the case in which both boxes are moving is unnecessary, because we can always change our coordinate system to be one of the boxes coordinate system, and thus one box is static and the other dynamic.

We tested several degrees of motion including linear, 2nd and 4th degree motions. We shall now present the results in each test case.

Linear Case

Motion Path

Initial Collision Time

Exit Time

In this case we can see an example of a linear motion. The collision type is corner-face (or in SOR - octant-vertex respectively).

This example's motion matrix is given by:

The equation compatible with the colliding vertex and face is:

And the initial collision time is t=0.47.

To run the collision prediction algorithm took us, in this case, 0.0128 seconds on a Pentium 4 with 1Gb RAM.

For further discussion in this example, please refer to the paper in the Download section.

2nd Degree Case

Motion Path

Motion Drag

Initial Collision Time

Exit Time

In this case we can see an example of a 2nd degree motion. The collision type is edge-edge (or in SOR - arc-arc).

This example's motion matrix is given by:

The equation compatible with the colliding edges is:

And the initial collision time is t=0.654, and the exit time is t=0.889.

To run the collision prediction algorithm took us, in this case, 0.052 seconds on a Pentium 4 with 1Gb RAM.

For further discussion in this example, please refer to the paper in the Download section.

4th Degree Case - with no Collision

Motion Path

Motion Drag

This example's motion matrix is given by:

To run the collision prediction algorithm took us, in this case, 0.103 seconds on a Pentium 4 with 1Gb RAM.

For further discussion in this example, please refer to the paper in the Download section.


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 Written by Danny Albocher & Uzi Sarel
Last Update: 21/08/05.