Graphics Reference
In-Depth Information
in video games, where the player character's movement is often constrained by
natural obstacles but the designer wishes to efficiently represent a larger world
than the navigable portion of the scene.
Most of the descriptions of matter that we've surveyed are surface representations.
These are extremely efficient because they are mostly “empty”; they need not
explicitly represent the space inside objects.
Volumetric modeling methods represent solid shapes rather than surfaces.
Doing so enables richer simulation, both for dynamics and for illumination in
the presence of translucency.
Finite element models
are general divisions of solid objects into polyhedral
chunks. These are very popular for detailed engineering simulation to model the
internal forces within objects, heat and pressure propagation, and fluid flow. They
are less popular for pure-rendering applications because they offer few advantages
in that context over surface meshes.
A regular finite element subdivision into tetrahedrons or cubes offers addi-
tional advantages for modeling and simulation applications. Regularizing shapes
allows constant-time random spatial access and stabilizes propagation. The
tetrahedral division is good for simulation because the tetrahedron is the three-
dimensional simplex—it is the simplest polyhedron, and is therefore a good prim-
itive to model effects like fracture. The cube division naturally lends itself to a
regular grid, making for straightforward representations, and is also easy to build
hierarchies from. This representation is known as a
voxel
model. It is very com-
mon for fluid flow simulation and medical or geoscientific imaging, where the
underlying source data are often captured on a regular grid.
Voxels have gone in and out of favor for rendering, especially in entertainment.
Figure 14.21 shows a contemporary game, Minecraft, which models the world
with large voxels to intentionally inspire a building-block aesthetic. The game
takes advantage of the efficiency of local graphlike operations on voxels to model
all illumination and physical dynamics as cellular finite automata. Because the
voxel representation requires only storage of the type of material in each cell (the
position is implicit in the 3D array), the game is able to efficiently represent huge
worlds with a single byte per cubic meter of storage—and large homogeneous
regions are amenable to further compression. In comparison, modeling the same
world even as a triangle list of cubes would require 12 triangles
×
3 vertices/tri-
angle
4 bytes/float = 432 bytes per cubic meter, and would be
less amenable to compression.
Note that the scene in Figure 14.21 appears to have detail at finer resolution
than the 1m
3
-voxel grid. For example, fences and reeds are represented by thin
objects within a single grid cell. This is because that rendering system uses the
voxels for simulation, but for rendering it replaces each with a proxy object that
may be more detailed than a simple cube. This is an extreme form of
geometry
×
3 floats/vertex
×
