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.
Instead of handling contact tests and collision response in the same
function in collision.c, first generate contact points and return them
as a list, then free at the end of the stepping function. This way the
contact response can be integrated into the conjugate gradient method
properly instead of using the hackish and unstable double evaluation
that is currently used.
The original BLI method for line/triangle intersection returns false
in case the line does not actually intersect, but in order to generate
repulsion forces we need to also handle contacts inside the margin.
timestep segment.
This ensures the distance for a collision pair is the one of the current
point position, and the response gets calculated accordingly.
simulation.
Note that this currently generates an extreme amount of points, by
making a edit pathcache curve for each hair in every frame! But at least
doesn't simply crash now.
This implements a penalty force as well as a repulsion force to avoid
further penetration, as suggested in
"Simulating Complex Hair with Robust Collision Handling"
(http://graphics.snu.ac.kr/publications/2005-choe-HairSim/Choe_2005_SCA.pdf)
Friction forces are still missing. More problematic is handling of
moving colliders, when face swap places with the hair vertex and a
collision is missed, putting the vertex inside the mesh volume. Larger
margins might help, but ultimately using Bullet collision detection is
probably more reliable and failsafe.
as forces, velocities, contact points etc.
This uses a hash table to store debug elements (dots, lines, vectors at
this point). The hash table allows continuous display of elements that
are generated only in certain time steps, e.g. contact points, while
avoiding massive memory allocation. In any case, this system is really
a development feature, but very helpful in finding issues with the
internal solver data.
This is still using the old BVH tree collision methods to generate
contact points, similar to what cloth does. This should be replaced
by a Bullet collision check, but generating contacts in this way is
easier for now, and lets us test responses and stability (although in
more complex collision cases the BVH method fails utterly, beside being
terribly inefficient with many colliders).
on itself.
This uses the same voxel structure as the hair smoothing algorithm.
A slightly different method was suggested in the original paper
(Volumetric Methods for Simulation and Rendering of Hair), but this is
based on directing hair based on a target density, which is another
way of implementing global goals. Our own approach is to define a
pressure threshold above which the hair is repelled in the density
gradient direction to simulate internal pressure from collisions.
This is an important hair interaction feature that simulates friction
between hairs in an efficient way. The method is based on the paper
"Volumetric Methods for Simulation and Rendering of Hair"
( http://graphics.pixar.com/library/Hair/paper.pdf )
It was partially implemented already, but didn't work in this simplified
version. The same voxel structure can be used for implemeting repelling
forces on hair based on density, which can help a hair system maintain
volume instead of collapsing in on itself.
the suggested tent function from the original paper.
Plain float->int conversion for the grid location otherwise leads to
skewed data and unnecessary loss of information.
