java - Wanted to make an object bounce inside a circle, ended up making the object move along the rim of the circle

Question

Here's the code in question:

public void calculate() {
        // Center of circle is at (250, 250).
        //THIS ALGORITHM IS NOW PROVEN TO BE WORSE THAN I FEARED...

        /*      What it does:
         *          Moves object around in a circle.
         *          Does not move the object towards the center.
         *          Object always stays on the rim of the circle.
         * 
         *      Algorithm I used. (DOES NOT WORK):
         *          N is normalized vector. 
         *          R = -2*(V dot N)*N + V
         */

        vx += Accelero.X * 0.1;
        vy += Accelero.Y * 0.1;
        double nx = x - 250;
        double ny = y - 250;
        double nd = Math.hypot(nx, ny);
        if (nd == 0)
            nd = 1;
        nx /= nd;
        ny /= nd;
        double dotProduct = vx * nx + vy * ny;
        vx += (float) (-2 * dotProduct * nx);
        vy += (float) (-2 * dotProduct * ny);
        x -= vx * 2;
        y -= vy * 2;
        vx *= 0.99;
        vy *= 0.99;
    }

And this is what happens.

The black line you see is where the purple object (box) moves. It just so happens to be right on the circle line I drew with Canvas.drawCircle().

I don't understand why reflection didn't work. If an object is to hit a circular wall, shouldn't it reflect the object's direction of velocity, which is what the algorithm was meant to be? Or I used the wrong algorithm?

Any help is appreciated. Thanks in advance.

Answer 1

Can you do bouncing off a straight wall of arbitrary angle? That should be the first step. (You may find that a polar representation of the velocity vector is easier to work with.)

Once you've got that working, it should be fairly straightforward: bouncing off a circle is like bouncing off a tangent of that circle that touches it at the point of contact.

You can calculate this tangent by observing that it's perpendicular to the radius vector in the point of contact (that is the vector that points from where the object is to the centre of the circle)