/****

timetodo(PositionList,TA,TB,V1A,V2A,V1B,V2B)

Given the position of colliding particles over time (s), verifies that the time per frame is as given, and calculates the velocities of the particles (cm/s) before and after the collision.

PositionList - Tuple of [FrameNumber, Positions], where Positions is a list of [Position, Letter] tuples, where Letter=a or b
T - time per frame

timetodo([[0,[[0,'a'],[1,''],[2,''],[3,'b']]],
[1,[[0,''],[1,'a'],[2,'b'],[3,'']]],
[2,[[0,'a'],[1,''],[2,''],[3,'b']]]],1,V1A,V2A,V1B,V2B).

V1A = 1,
V2A = V1B, V1B = -1,
V2B = 1 .

timetodo([[0,[[0,'a'],[1,''],[2,'b'],[3,'']]],
[1,[[0,''],[1,'a'],[2,'b'],[3,'']]],
[2,[[0,''],[1,'a'],[2,''],[3,'b']]]],1,V1A,V2A,V1B,V2B).

V1A = 1,
V2A = V1B, V1B = 0,
V2B = 1 ;

****/

timetodo(PositionList,T,V1A,V2A,V1B,V2B) :-
	member([Frame1,Positions1],PositionList),
	member([Frame2,Positions2],PositionList),
	member([Frame3,Positions3],PositionList),
	Frame2 is Frame1 + 1,
	Frame3 is Frame2 + 1,
	selectpositions(Positions1,A1,B1),
	selecttouching(Positions2,A2,B2),
	selectpositions(Positions3,A3,B3),
	V1A is (A2-A1)/T,
        V2A is (A3-A2)/T,
	V1B is (B2-B1)/T,
        V2B is (B3-B2)/T.
selecttouching(Positions,A,B) :-
	selectpositions(Positions,A,B),
	B is A+1.	
selectpositions(Positions,A,B) :-
        member([A,a],Positions),
        member([B,b],Positions).