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Balls Bouncing off Walls

The patterns here are suggested by collisions of colored balls according to the laws of mechanics. Balls with diverse sizes and colors fall under the influence of customizable acceleration due to gravity. They can hit up to three projection walls and bounce back. If a ball leaves the cube, it disappears. Balls interact only with the walls but not with one another. There are several effects that you can set for the projection walls.

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DETAILS

The collision between a ball and a projection wall surface changes only the velocity vector component along the normal direction at the point of collision on . Before the collision, if the ball's velocity vector is and the unit normal at is , then can be written as where and . After collision, the velocity vector becomes . If the projection wall surface is a plane, then determining an accurate collision point is easy; but if is curved surface, this can be somewhat time-consuming and yields little benefit since the ball's radius is relatively small when compared to the simulation region. Therefore to calculate more quickly, we simply use the sphere center's coordinate and a that is obtained by solving the equation as the point of collision.
When a ball hits more than one wall at once, we treat the multiple collisions as follows: if all walls are planes, we write and change it to where or according to which collision happens along the direction. If a wall is a curved surface, then we first deal with the collision on this surface alone using the method described in the previous paragraph and then deal with the remaining collisions on the plane walls.
This Demonstration is inspired by "Create Unique Charts with Different Visualizations" and "Use Symbolic Graphics Primitives to Visualize Results". A few videos of this Demonstration can be downloaded from the author's personal page.
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