Game Development Reference

In-Depth Information

the renderer. Therefore, we do not need to update the surface mesh each time we

update the volumetric mesh.

Storing
ξ
requires four floating-point values per surface-mesh vertex. If the

surface mesh is dense, a tetrahedron may have many associated vertices. In this

case, we can save memory by computing the transformation
T
(
p
) of a point
p
,as

shown in Equation (10.19).

Therefore, each time we want to update the surface mesh, we compute
T

once for each tetrahedron
e
and the new position
T
(
p
) of all the surface vertices

associated with
e
using Equation (10.19). It should be noticed that
C
e
changes

in every iteration step and
P
−
e
can be precomputed and stored. Now we have

to save 16 floating-point values per tetrahedron instead of four values per surface

vertex.

Thanks to the nature of the operations used by the two processes described

above, we can dramatically speed-up our system if we perform all the operations

in the GPU. Due to space constraints, we are not going to describe the GPU algo-

rithm, but it can be obtained quite straightforwardly from the description made in

this section.

Bibliography

[Etzmuss et al. 03] O. Etzmuss, M. Keckeisen, and W. Strasser. “A Fast Finite

Element Solution for Cloth Modelling.” In
Proceedings of 11th Pacific Con-

ference on Computer Graphics and Applications
, pp. 244-251. Washington,

DC: IEEE Computer Society, 2003.

[Garcia et al. 06] M. Garcia, C. Mendoza, A. Rodriguez, and L. Pastor. “Opti-

mized Linear FEM for Modeling Deformable Objects.”
Comput. Animat.

Virtual Worlds
17: 3-4 (2006), 393-402.

[Muller and Gross 04] M. Muller and M. Gross. “Interactive Virtual Materials.”

In
Proceedings of Graphics Interface 2004
, pp. 239-246. Waterloo, Ontario:

Canadian Human-Computer Communications Society, 2004.

[Muller and Teschner 03] M. Muller and M. Teschner. “Volumetric Meshes for

Real-Time Medical Simulations.” In
Bildverarbeitung fur die Medizin 2003
,

CEUR Workshop Proceedings, 80, pp. 279-283. Aachen, Germany: CEUR-

WS.org, 2003.

[Press et al. 07] William H. Press, Saul A. Teukolsky, William T. Vetterling, and

Brian P. Flannery.
Numerical Recipes: The Art of Sientific Computing
.New

York: Cambridge University Press, 2007.