Resultant Vector Of Circle Line Collision

Question

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. vecColl

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); xVel = (float)(mag * Math.cos(angleRad)); yVel = (float)(mag * Math.sin(angleRad)); } }

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
– Gustavo Maciel, Commented Jun 4, 2015 at 10:00

Fooble · Accepted Answer · 2015-05-05 02:36:32Z

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.

For your code

/* 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; } }

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