The curl radius for children in interpolated mode was calculated using
the total offset from the parent particle. This leads to very large
radii when the distance is large due to sparse parents. Such behavior is
also very unrealistic because the curl radius is mostly constant and
defined by the material properties.
All the child hairs are roughly parallel by default. To simulate the
agglomeration of children into hair wisps the "flatness" parameter is
now used to clump them together.
With the default 5 substeps the simulation can otherwise still become
unstable. This is just a preliminary measure anyway until the length
variance can be fixed properly.
This is more involved than using simple straight bending targets
constructed from the neighboring segments, but necessary for restoring
groomed rest shapes.
The targets are defined by parallel-transporting a coordinate frame
along the hair, which smoothly rotates to avoid sudden twisting (Frenet
frame problem). The rest positions of hair vertices defines the target
vectors relative to the frame. In the deformed motion state the frame
is then recalculated and the targets constructed in world/root space.
derivatives for stabilization.
The bending forces are based on a simplified torsion model where each
neighboring point of a vertex creates a force toward a local goal. This
can be extended later by defining the goals in a local curve frame, so
that natural hair shapes other than perfectly straight hair are
supported.
Calculating the jacobians for the bending forces analytically proved
quite difficult and doesn't work yet, so the fallback method for now
is a straightforward finite difference method. This works very well and
is not too costly. Even the original paper ("Artistic Simulation of
Curly Hair") suggests this approach.
This returns a general status (success/no-convergence/other) along with
basic statistics (min/max/average) for the error value and the number
of iterations. It allows some general estimation of the simulation
quality and detection of critical settings that could become a problem.
Better visualization and extended feedback can follow later.
This makes the bending a truely local effect. Eventually target
directions should be based in a local coordinate frame that gets
parallel transported along the curve. This will allow non-straight
rest shapes for hairs as well as supporting twist forces. However,
calculating locally transformed spring forces is more complicated.
These are much better suited for creating stiff hair. The previous
bending springs are based on "push" type spring along the hypothenuse
of 3 hair vertices. This sort of spring requires a very large force
in the direction of the spring for any angular effect, and is still
unstable in the equilibrium.
The new bending spring model is based on "target" vectors defined in a
local hair frame, which generates a force perpendicular to the hair
segment. For further details see
"Artistic Simulation of Curly Hair" (Pixar technical memo #12-03a)
or
"A Mass Spring Model for Hair Simulation" (Selle, Lentine, Fedkiw 2008)
Currently the implementation uses a single root frame that is not yet
propagated along the hair, so the resulting rest shape is not very
natural. Also damping and derivatives are still missing.
The hair solver needs sane input to converge within reasonable time
steps. In particular the spring lengths must not be too difference
(factor 0.01..100 or so max, this is comparable to rigid body simulation
of vastly different masses, which is also unstable).
The basic hair system generate strands with equally spaced points, which
is good solver material. However, the hair edit operators, specifically
the cutting tool, can move points along the strands, creating tightly
packed hair points. This puts the solver under enormous stress and
causes the "explosions" observed already during the Sintel project.
The simple solution for now is to exclude very short hairs from the
simulation. Later the cutting tool should be modified such that it
keeps the segments roughly at the same length and throws away vertices
when the hair gets too short (same goes for the extension tool).
The hair system should have a general mechanism for making sure that
situations such as this don't occur. This will have to be a design
consideration for replacements in any future hair system.
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.
