Graphics Reference
In-Depth Information
reason it was not used much for mechanical CAD or CAM (computer-aided manu-
facture) initially except for gross models to help with certain calculations such as col-
lision checking and getting a rough estimate of volume. This has changed now that
computers with gigabytes of memory have become a reality and voxel-based repre-
sentation schemes for volumes have become very popular in certain parts of computer
graphics. A more detailed discussion of this subject follows in the next section. Section
5.8.2 will describe the standard approach to cutting down on the amount of data one
has to store.
5.3.8
Volume Modeling
Here are four terms and their definitions that usually appear in the same context:
Volumetric data
:
The aggregate of voxels tessellating a volume.
Volume modeling
:
The synthesis, analysis, and manipulation of sampled, com-
puted, and synthetic objects contained within a volumetric
data set.
Volume visualization
:
A visualization method concerned with the representation,
manipulation, and rendering of volumetric data.
Volume graphics
:
The subfield of computer graphics that employs a volume
buffer for scene representation and is concerned with synthe-
sizing, manipulating, and rendering such scenes. Volume
graphics is the three-dimensional counterpart of raster
graphics.
The definitions are taken from [KaCY93] and are an adequate representation of how
these terms are usually used. The subject matter that is addressed by these terms is
what this section is about. It really only dates back to the early 1980s and started in
the context of tomography.
Although our main interest in this topic is on modeling geometric objects, volume
modeling covers a much broader subject in that the “volumes” may have arisen in
other ways. Volume modeling in its most general sense deals with scalar-valued func-
tions defined on three-dimensional space. In that sense, it is not really a modeling
scheme per se but has close connections with modeling. In the special case where the
function takes on only two values, 0 and 1, we can, in fact, interpret the function as
defining a space-based decomposition scheme generalizing the voxel-based spatial
occupancy enumeration scheme. The voxel case is the uniform case, but the data set
may have different geometries such as being composed of rectangular or curved cells.
Cells might be different distances apart. On the other hand, the function could come
from some arbitrary mathematical model. For example, one might want to display
the temperature of a heated solid visually, perhaps by displaying the surfaces of con-
stant temperature. We can think of volume modeling as modeling data that is acquired
from appropriate instruments and then sampled to get the voxelization. The data
could also be an “object” that is defined in terms of point samples.
Volume rendering
refers to the process of displaying such models. We shall have more to say about
volume rendering in Section 10.4.
