flipcode - Collision Question

Collision Question
Question submitted by (16 July 1999)


	I'm writing collision routines for a very simple game, and need to determine the outcome of a collision of two spherical objects, both of which are the same size. One of the objects will remain stationary, and the other is in motion. I have calculated the vector between the two objects, and have a vector of the direction of motion for the moving object. Is there an easy way to calculate the new direction of the moving object?

let P be the point of contact on the stationary sphere. the vector from the centre of this sphere toward P is PO. the tangent at P is perpendicular to PO. also, suppose the direction of motion of the moving sphere is labeled D.



			\  D
			 \
			  \
			   \
			    \
			-----P--------  tangent on the stationary sphere at P
			     |
			     |
			     |
			     |
			     | PO
			     |

the moving sphere will bounce away from P along the direction D' such that the angle between D and PO is the same as the angle between D' and PO.



			\  D      /  D'
			 \       /
			  \     /
			   \   /
			    \ /
			-----P-------- tangent on the stationary sphere at P
			     |
			     |
			     |
			     |
			     | PO
			     |

extending D "into" the sphere and projecting the endpoint onto the tangent yields the vector XP, the component of D' parallel to the tangent.



                        \  D      /  D'
                         \       /
                          \     /
                           \   /
                            \ /
                        -----P----X--- tangent on the stationary sphere at P
                             |\   |
                             | \  |
                             |  \ |
                             |   \|
                             | PO
                             |

of course, if the vectors D and PO are colinear, the moving sphere will simply bounce back in the direction of -kD where k is some constant.

Response provided by Hin Jang

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