function [value, isterminal, direction] = check_billiards_collisions(~,state)
% This function determines whether two billiard balls have hit the walls or
% each other. There are nine possible collisions that can occur: each ball
% with each wall, plus the two balls together.
%
% The input t is time in seconds.
% The input state is our state vector. It has eight elements, arranged in a column.
% The state vector's first element, state(1), is the horizontal position of the white ball's center, in meters.
% The state vector's second element, state(2), is the vertical position of the white ball's center, in meters.
% The state vector's third element, state(3), is the horizontal velocity of the white ball's center, in m/s.
% The state vector's fourth element, state(4), is the vertical velocity of the white ball's center, in m/s.
% The state vector's fifth element, state(5), is the horizontal position of the black ball's center, in meters.
% The state vector's sixth element, state(6), is the vertical position of the black ball's center, in meters.
% The state vector's seventh element,state(7), is the horizontal velocity of the black ball's center, in m/s.
% The state vector's eigth element, state(8), is the vertical velocity of the black ball's center, in m/s.

% Declare wall locations as global.
global leftWallX rightWallX lowerWallY upperWallY
global whiteBallRadius blackBallRadius
global whiteLeft whiteRight whiteLower whiteUpper blackLeft blackRight blackLower blackUpper whiteBlack

% Pull our positions out of the state vector. They are all we need.
xw = state(1);
yw = state(2);
xb = state(5);
yb = state(6);

% The value of each test is the distance from the ball in question to the
% object with which we are checking, making sure to subtract out the ball
% radius. These are all positive values that become zero when the
% collision occurs.
value(whiteLeft,1) = xw - leftWallX - whiteBallRadius;
value(whiteRight,1) = rightWallX - xw - whiteBallRadius;
value(whiteLower,1) = yw - lowerWallY - whiteBallRadius;
value(whiteUpper,1) = upperWallY - yw - whiteBallRadius;
value(blackLeft,1) = xb - leftWallX - blackBallRadius;
value(blackRight,1) = rightWallX - xb - blackBallRadius;

Part 1 The state of the spacecraft is the position and the velocit...