On Sun, 20 Oct 2002 17:18:29 +0200, "Rune"
<run### [at] mobilixnetdk> wrote:

>This can in no way be compared to the complexity it is to define any
>given surface in the term of a function. With the object approach you
>can have a CSG object with hundreds of primitives in it and make the
>particles collide with it, or you can use a mesh object for that matter.

Meshes are quite easy to define in terms of functions. Besides, what
Christoph is describing are force fields while what you are describing
are penalty functions. They are different and have different uses.

>That is next to impossible with functions. I don't see why you seem to
>think that it is such a great advantage to use function based
>environments, if you compare the pros and cons.

As I said, they are different approaches to the same problem.
Collision is a complex problem because it involves instant change in
momentum (which is never instant in reality), energy loss, extreme
stress gradients and whatever you can think of. Even for a pure
particle system, where you don't deal with volumes or deformable
bodies, collision is quite a challenge.

Using penalty functions (as you do) has the advantage that it is
generally simpler to implement and faster to compute. The problem is
that due to the infinite gradient of the penalty function (the
function being 0 outside the object and non-zero inside), it is
impossible to use higher-order integration methods.

With force fields (usually based on proximity functions), you always
get prolonged collisions. This can be problematic with steep collision
angles because the particle may actually gain energy from the field,
which is quite impossible, so care should be taken. On the bright
side, you can predict quite well the behavior of particles in such an
environment due to the well-defined energy gradients, so you can use
implicit integration methods for higher step sizes (see Baraff, David
and Witkin, Andrew."Large Steps in Cloth Simulation."
http://www-2.cs.cmu.edu/~baraff/papers/sig98.pdf)

One could combine the best of both worlds, as Xavier Provot is doing
in his cloth simulations.

One could also use adaptive time steps. I haven't read anything on the
subject and so can't give you any links, but it seems like a pretty
obvious thing to do so I guess someone must have implemented it
already :)

Looking forward to further development.


Peter Popov ICQ : 15002700
Personal e-mail : pet### [at] vipbg
TAG      e-mail : pet### [at] tagpovrayorg

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