Central and non-central kick

kick.c

//
// Here is some illustration of central kick:
// https://commons.wikimedia.org/wiki/File:Elastischer_stoß3.gif
//
//         V       -V
// [m = 2]--->    <---[m = 1]
//    [m = 2]      [m = 1]
//       [m = 2][m = 1]
//      [m = 2]      [m = 1]
//   <-[m = 2]            [m = 1]----->
// -1/3 V                        5/3 V
//
void centralKick(double m1, double m2, double u1, double u2, double *v1, double *v2)
{
    *v1 = (2*m2*u2 + (m2 - m1)*u1)/(m1 + m2);
    *v2 = (2*m1*u1 + (m1 - m2)*u2)/(m1 + m2);
}

// This kick is not central :)
void notCentralKick(double x1, double y1, double m1, double u1x, double u1y,
                    double x2, double y2, double m2, double u2x, double u2y,
                    double *v1x, double *v1y,
                    double *v2x, double *v2y)
{
    double angle = atan2(y2-y1,x2-x1);
    double sprite1Speed = sqrt(u1x*u1x + u1y*u1y);
    double sprite2Speed = sqrt(u2x*u2x + u2y*u2y);
    double sprite1Angle = atan2(u1y,u1x);
    double sprite2Angle = atan2(u2y,u2x);
    
    double alpha = sprite1Angle - angle;
    double beta = sprite2Angle - angle;
    double sprite1SpeedX = sprite1Speed*cos(alpha);
    double sprite2SpeedX = sprite2Speed*cos(beta);
    double sprite1SpeedY = sprite1Speed*sin(alpha);
    double sprite2SpeedY = sprite2Speed*sin(beta);
    
    double vx1, vx2;
    centralKick(m1, m2, sprite1SpeedX, sprite2SpeedX, &vx1, &vx2);
    
    double newSpeed1 = sqrt(sprite1SpeedY*sprite1SpeedY + vx1*vx1);
    double newSpeed2 = sqrt(sprite2SpeedY*sprite2SpeedY + vx2*vx2);
    double newAplha = atan2(sprite1SpeedY,vx1);
    double newBeta = atan2(sprite2SpeedY,vx2);
    
    *v1x = newSpeed1*cos(newAplha + angle);
    *v1y = newSpeed1*sin(newAplha + angle);
    *v2x = newSpeed2*cos(newBeta + angle);
    *v2y = newSpeed2*sin(newBeta + angle);
}