solver step.
Calculating forces and jacobians from linearly interpolated grid values
is problematic due to discontinuities at the grid boundaries. The new
approach of modifying velocities after the backward euler solver step
was suggested in a newer paper
"Detail Preserving Continuum Simulation of Straight Hair"
(McAdams, Selle 2009)
Conflicts:
source/blender/physics/intern/BPH_mass_spring.cpp
This is not necessary: the implicit solver data can keep track instead
of how many off-diagonal matrix blocks are in use (provided the
allocation limit is calculated correctly). Every time a spring is
created it then simply increments this counter and uses the block index
locally - no need to store this persistently.
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.
single transform matrix.
Dynamic properties of the transformation are only needed during the
setup phase when they should be read from external data (hair system
roots) and generate fictitious forces on each point.
This is part of the original method from "Volumetric Methods for
Simulation and Rendering of Hair". The current filter is a simple box
filter. Other energy-preserving filters such as gaussian filtering
can be implemented later.
The filter size is currently given as a cell count. This is not ideal,
rather it should use a geometrical length value, but this is too
abstract for proper artistical use. Eventually defining the whole grid
in terms of spatial size might work better (possibly using an external
object).
at a the margin distance ("outer" softbody margin).
This has to be clamped arbitrarily unfortunately, otherwise the
repulsion force can add too much energy into the system. A factor of
4 * restitution impulse seems to give good results for now, this can
be refined later on if necessary.
This is now also decoupled from the internal solver data. The grid is
created as an opaque structure, filled with vertex or collider data
(todo), and then forces can be calculated by interpolating the grid at
random locations. These forces and derivatives are then fed into the
solver.
moving hair root reference frames.
This calculates Euler, Coriolis and Centrifugal forces which result
from describing hair in a moving reference frame.
http://en.wikipedia.org/wiki/Fictitious_force
frames.
These forces don't have to be calculated for each individual
contribution. Rather they can be split off and be calculated on top of
the basic force vector rotation (todo).
There are currently 3 types of springs: basic linear springs, goal
springs toward a fixed global target (not recommended, but works) and
bending springs.
These are agnostic to the specific spring definition in the cloth system
so hair systems can use the same API without converting everything to
cloth first.
Conflicts:
source/blender/physics/intern/implicit_blender.c
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.
