# Resultant Vector Of Circle Line Collision

For my game I need to have a circle collide against a wall and bounce off in the appropriate direction. I've looked around for a while and haven't found a good solution to my problem. I have a diagram of what should happen below.

The problem is that I have the vector V, U, and P, but I am unable to calculate the new X and Y vectors after the collision. I have tried using Trig to find the angle of the intersection and get the new X and Y vectors from that but it gives massive numbers. How do I get the new X and Y vectors easily? Source code is posted below.

for (int i = 0; i < collisionList.size(); i++){
Vec2<Integer> c = collisionList.get(i);
int cx = c.getX();
int cy = c.getY();
if (distance(x, y, cx, cy) <= (r - (r / 2))){
float mag = (float)Math.sqrt((Math.pow(x, 2) + Math.pow(y, 2)));
float angleRad = (float)Math.atan(y / x);

}
}

• Get the perpendicular vector of the line direction, mirror the ball velocity to that vector you found. Done! EDIT: in your images, the perpendicular vector of the line direction is U. Q is the mirrored vector of V upon U. – Gustavo Maciel Jun 4 '15 at 10:00

The way I handle these kinds of 2D physics is to process the X and Y components of the vector separately.

That way if a collision occurs, I know which direction the collider was moving along based on the sign and component of the velocity vector I am processing.

Then when a collision occurs, you can modify the velocity on the appropriate axis. Changing the sign simulates a perfectly elastic bounce, while multiplying it by a negative number (eg -0.5) can simluate a bounce where some energy is lost.

/*
Move along X Axis
*/

for (int i = 0; i < collisionList.size(); i++){
Vec2<Integer> c = collisionList.get(i);
int cx = c.getX();
int cy = c.getY();
if (distance(x, y, cx, cy) <= (r - (r / 2))){
xVel = -xVel;
}
}

/*
Move along Y Axis
*/

for (int i = 0; i < collisionList.size(); i++){
Vec2<Integer> c = collisionList.get(i);
int cx = c.getX();
int cy = c.getY();
if (distance(x, y, cx, cy) <= (r - (r / 2))){
yVel = -yVel;
}
}