This allows setting a target density which the fluid simulation will
take into account as an additional term in the pressure Poisson
equation. Based on two papers
"Detail Preserving Continuum Simulation of Straight Hair" (McAdams et al. 2009)
and
"Two-way Coupled SPH and Particle Level Set Fluid Simulation" (Losasso et al. 2008)
Currently the target pressure is specified directly, but it will be
a lot more convenient to define this in terms of a geometric value such
as "number of hairs per area" (combined with hair "thickness").
Conflicts:
source/blender/physics/intern/BPH_mass_spring.cpp
on the grid.
This uses the Eigen conjugate-gradient solver to solve the implicit
Poisson equation for the pressure Laplacian:
div(grad(p)) = div(v)
As described in "Detail Preserving Continuum Simulation of Straight Hair"
(McAdams, Selle, 2009).
Conflicts:
source/blender/physics/intern/BPH_mass_spring.cpp
This is a bit more awkward for artists to use, but necessary for
a stable solution of the hair continuum calculation. The grid size is
defined by the user, the extent of the grid is then calculated based on
the hair geometry. A hard upper limit prevents bad memory allocation
in case too small values are entered.
Conflicts:
source/blender/physics/intern/BPH_mass_spring.cpp
This is an artifact of earlier attempts to implement velocity smoothing,
but doesn't work anyway.
Conflicts:
source/blender/physics/intern/BPH_mass_spring.cpp
This is a leftover from previous approach of hair collisions (with
insufficient results). The hair volumetrics actually implements
"collision" with solid objects as well, but uses a Neumann boundary
condition on the main grid for this purpose.
This is based on the paper
"Detail Preserving Continuum Simulation of Straight Hair"
(McAdams, Selle, Ward, 2009)
The main difference is that hair line segments are used rather than only
rasterizing velocity at the vertices. This gives a much better coverage
of the hair volume grid, otherwise gaps can be produced at smaller grid
cell sizes and the distribution is uneven along the hair curve.
The algorithm for rasterizing is a variation of Bresenham's algorithm
extended onto 3D grids.
Conflicts:
source/blender/physics/intern/BPH_mass_spring.cpp
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).
