code.
The implicit solver itself should remain agnostic to the specifics of
the Blender data (cloth vs. hair). This way we could avoid the bloated
data conversion chain from particles/hair to derived mesh to cloth
modifier to implicit solver data and back. Every step in this chain adds
overhead as well as rounding errors and a possibility for bugs, not to
speak of making the code horribly complicated.
The new subfolder is named "physics" since it should be the start of a
somewhat "unified" physics systems combining all the various solvers in
the same place and managing things like synchronized time steps.
handle only one collision contact at a time.
Collision still randomly explodes, even with differing results on the
same file. This could indicate a threading issue, possibly also related
to the dependency graph since multiple objects are involved in
collisions.
This reverts commit c52b8ae818844965d56714a71255408873275dc1.
Sadly, at this point solver convergence is an exception rather than the
rule... Individual hairs can "explode" easily and thus disable the whole
simulation, which isn't helpful either.
This helps keep the simulation stable as long as there are only a few
substeps that become too constrained for the solver.
Eventually we need better feedback about these solver results, so that
artists can tweak situations specifically to resolve bad solver results.
This is somewhat similar to the camera tracker, which also can run into
cases that cannot be resolved and have to be fixed manually.
The Eigen solver is not quite stable currently (possibly due to
incorrect porting of force calculations). It also still lacks threading
support and optimized matrix construction, making it slower in
comparison. Eventually would still like to switch, but fixing these
issues takes time.
This adds transformations for each hair from world to "root space".
Currently positions and velocities are simply transformed for the solver
data and inverse-transformed when copying the results back to the cloth
data. This way the hair movement becomes independent from the movement
of the emitter object. Eventually the "fictitious" forces originating
from emitter movement can be added back in a controlled way.
http://en.wikipedia.org/wiki/Fictitious_force
Ignoring these fictitious forces or scaling their effect is physically
correct, because in the absence of external forces the hair will always
return to rest position in this root frame.
External forces currently are not yet transformed into the root space.
mode.
Eigen can become very slow in debug mode, which is a bit of a problem.
It relies heavily on compiler optimizations to remove function calls
etc. More optimizations may be desirable, possibly putting the implicit
solver into its own little library and enabling optimizations in debug
mode there could help.
This will allow us to implement moving reference frames for hair and
make "fictitious" forces optional, aiding in creating stable and
controllable hair systems.
Adding data in this place is a nasty hack, but it's too difficult to
encode as a DM data layer and the whole cloth modifier/DM intermediate
data copying for hair should be removed anyway.
This is not nice at all, but for some reason (possibly time scale) the
old force values are much too high and cause the solver to become
unstable. These will be revisited later anyway, so for now such scaling
should be fine.
constraining.
The algorithm is described in the paper "Large Steps in Cloth Simulation"
(Baraff/Witkin 1998). The same method was (incorrectly) implemented in
the old cloth solver.
It is based on restricting the degrees of freedom (ndof) of vertices
using a block matrix and a vector of target velocity deltas.
See chapter 5 of the paper for details.
Note that goal springs currently are really bad ... They have a factor
on hairs that "fades" goal influence from the root to the tip. The last
point on the hair is completely free, which makes the goal springs
pretty much useless on their own without supporting bend stiffness.
Can only assume this was added to compensate unphysical behavior of
goal springs when using uniform weight, but it's a poor replacement for
true localized bending forces ...
a custom built solver.
The old cloth solver is broken unfortunately. Eigen is a designated
linear algebra library and very likely their implementation is a lot
better (can't compare until it's implemented though).
Only basic gravity is active atm, spring forces, external force fields,
damping and volumetric friction have to be added back by converting
the data into the Eigen format.
responses.
The S matrix together with the z Vector encodes the degrees of freedom
of a colliding hair point and the target velocity change. In a collision
the hair vertex is restricted in the normal direction (when moving
toward the collider) and the collision dynamics define target velocity.
This simply uses the position above the triangle instead of the
intersection point of the vertex path. The other method was broken
anyway, but also has a problem catching all the contacts reliably. The
new method might have a few false positives but that is acceptable.
solver that properly supports constraints with some degrees-of-freedom.
The previous solver implementation only used the S matrix (constraint
filter matrix) for pinning vertices, in which case all elements are
zero and the error doesn't show up. With partial constraints (useful for
collision contacts) the matrix has non-zero off-diagonal elements and
the algorithm easily diverges.
There are also initial steps for implementing collision prevention as
described in the Baraff/Witkin paper "Large Steps in Cloth Simulation"
(http://www.cs.cmu.edu/~baraff/papers/sig98.pdf).
This is a first test, the contacts are very explosive atm because they
basically pin hair vertices globally on collision, which leads to
stretching of the springs which is then suddenly released in the next
frame.
