Graphics Reference
In-Depth Information
to the root; also, it maintains the hair style more eciently without bringing
unnecessary extra stiffness to overall hair simulation.
The benefit of global shape constraints is that it keeps the global shape with
minimum cost. Combined with local shape constraints, it takes almost no time to
settle the simulation and there is no visual perturbation when simulation starts.
Designers can expect that their authored hair shape will be the initial shape.
Global shape constraints also ensure that hair does not get tangled in weird
shapes during fast-moving gameplay.
1.5.3 Local Shape Constraint
Even though GSC can effectively manage the hair shape, we need a way to
simulate bending and twisting forces for individual hair strands. In real-time cloth
simulation, the bending effect is often represented as a soft distance constraint
connecting two vertices across the bent edge. It is also possible to use the same
approach for a bending effect in hair, but twisting is not really easy.
For simplicity and high performance, we combine bending and twisting effects
as one soft distance constraint. To define this constraint, the target goal positions
are computed using the local frames as in Figures 1.2 and 1.3.
Equation (1.2) may look complex due to its subscripts and superscripts but
the concept is the same as ELC. The first equation computes
i−
1
d
i
,whichis
a distance between the current position and its target goal position. The left
superscript
i
1 indicates that those positions are defined within the local frames.
In the end, when we calculate the position correction, we actually use world frame
but equation (1.2) is written in local frame to simplify it:
−
i
−
1
d
i
=
i−
1
P
i
−
i
−
1
P
i
=
1
i−
1
P
i−
1
−
2
S
L
i−
1
d
i
(1.2)
i−
1
P
i
+=
1
2
S
L
i−
1
d
i
.
As explained in ELC, we divide the position correction by the mass ratio and
apply it to two connected vertices (
i−
1
P
i−
1
and
i−
1
P
i
). Here, we already assume
that all mass is equal so the ratio is 1/2.
1.6 Wind and Collision
Wind is an important part of simulation since it makes the hair interact with the
environment and gives the game character dynamics even during idle states. To
generate more randomized effects and prevent hair from getting clumped, a single
wind input gets converted to four cone-shape directions as in Figure 1.5. Also,
