Game Development Reference

In-Depth Information

Meshless shape matching [Muller et al. 05] discards neighborhood informa-

tion in whole and performs shape matching on the whole point cloud.

This way, each vertex feels the influence of every other vertex, as would a

realistic soft material. The problem with this is that the larger the shape-matching

clusters are, the faster deformations are smoothed out, and the shape will return

to the rigid shape much sooner. If the algorithm is unaltered, the range of motion

is cut drastically. Within the limit of all vertices in one cluster, it will always

try to match all particles to the undeformed mesh. Thus, it will only allow small

deviations from the rigid shape. This comes in handy for simulating rigid-body

dynamics with this algorithm, but this is not in the focus of this chapter.

14.4.1

Extensions to Meshless Shape Matching

Muller [Muller et al. 05] proposes some extensions to the meshless shape-

matching algorithm to allow for bigger derivations from the rigid shape. We

should look at it for completeness, however it is not that well-suited for character

animation.

The idea is to allow the transformation that transforms
x
i

into
c
i
,

c
i
=
Rx
i
+
t
,

to be more general. Sheer and stretch modes can be accounted for by mixing a bit

of the previously calculated linear transformation
A
into the transformation

β
A
+(1

−

β
)
R
.

Here the mixing is controlled by the additional parameter
β
. The transfor-

mation
R
still ensures that there is a tendency towards the undeformed shape.

Volume conservation has to be taken care of by ensuring that det(
A
)=1,which

is not automatically the case.

This can be extended to include quadratic deformations. We will not use this

approach because we will still lose too much realism by discarding the neighbor-

hood information, especially the small, high-frequencymodes we want to achieve.

Extending the range of motion for the shape matching of the neighborhood clus-

ters is not necessary.

14.4.2

Lattice-Based Shape Matching

Another way of simulating volumetric effects is to turn to discrete approximations

of the inside of the mesh. The general idea is to fill the inside with a lattice of

evenly spaced vertices, let them take care of the physics, and reconstruct the de-

formed surface mesh from the deformed lattice after. Unfortunately, these discrete