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
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).
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.
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.
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).
Self collision vertex groups enable artists to exclude selected vertices from getting involved in self collisions. This speeds simulations and it also resolves some self collision issues.
