In my physics engine I give a body a value for restitution between 0 and 1. When two bodies collide there seems to be different views on how the restitution of the collision should be calculated. To me the most intuitive seems to be to take the average of the two but some seem to take only the largest one.
Are there other ways to do it? Also, could the closing velocity or some other parameter come into effect?
Also, could the closing velocity or some other parameter come into effect?
According to Wikipedia,
in a series of experiments performed at Florida State University in 1955, it was shown that the COR varies as the collision speed approaches zero, first rising significantly as the speed drops, then dropping significantly as the speed drops to about 1 cm/s and again as the collision speed approaches zero.
Sadly the link to the paper on this is dead.
To answer the main question, Cholesky's suggestion of a table is a good one, but if you want to reduce the number of cases you have to select values for then one approach would be to store for each material a base restitution and a weight with which to take a weighted average. What restitution is really about is how much of the energy of the collision is converted into forms other than the post-collision kinetic energy of the bodies. Sound can be neglected: what you're interested in is deformation. So give easily deformed materials such as soft sand a high weight and a low restitution and you have a model which should be good enough.
After all, games only have to feel right to the player: they don't have to be accurate simulations of the real world.
I personally think that taking the largest one make the most sense: (throwing a bouncy ball at a brick bounces even though a brick has no restitution to speak of), but if you have a game where you need to model complex bouncy interactions you could store a "material" per body and build up a materialA vs. materialB lookup table.
BulletPhysics seems to just multiply the restitution factors. This might not be a universal solution, but it satisfies the "everything just works" approach when adding new materials.
From a physics standpoint, the minimum restitution between two bodies should be used.
Think of gel hitting a rubber ball. The rubber ball has high restitution, but the gel has low. The rubber ball will not bounce off the gel. In the case of bounciness, lowest wins.
However, gel has low density, which allows the ball to penetrate it and hit something with higher restitution, such as the ground.
The gel will absorb some of the kinetic energy of the ball, how far the ball bounces, often considerably. But that's a bit off topic.
Restitution is a representation of loss of kinetic energy through collisions, so the lowest value is the most accurate. Throw a golf ball at a block of soft clay and you will see what I mean.
