Simulation - Spheres in Collision

This scene models a set of particles representing spheres falling under gravity. Each particle is associated to the following parameters: position \(p\), speed \(v\), forces \(f\), as well as radius and color. The position and speed of each particle is updated through time thanks to a discrete integration

• - \(v^{k+1} = v^{k} + \Delta t\;f^{k}\)

• - \(p^{k+1} = p^{k} + \Delta t\;v^{k+1}\)

Collisions

At the current state of the program, only gravity is took into account.

• > Add collision detection and response between the spheres and the faces of the cube.

• > Add collision detection and response between the sphere themselves.

Note that when multiple spheres are involved in stack, the multiple collisions cannot be solved only by a single pair-wise correction. This can lead to jittering behavior. To limit such effect you can

• - perform several integration steps and collision correction with smaller timer steps before displaying the result
• - avoid bouncing between colliding particles with small relative velocity

Possible extension

• Allow the user to move the box interactively.

• Speed-up the collision detection in building a spatial acceleration structure such as a regular grid storing neighboring particles.