3 dimensional visualization can be approached in two different ways: Volume graphics and Surface graphics [29]. The two methods has the 2D counter parts in vector graphics and raster graphics. The voxel based graphics is more computational expensive and require more storage than surface graphics.
In volume graphics a three dimensional matrix is storing all voxel values. A method for obtaining the 2D projection of the volume is through ray tracing, which comes in two variants [34]: object space methods, where the volume is resampled along the rays, and image space methods, where the volume first is transformed to be axis aligned before the ray tracing.
The ray in the ray tracing collects voxel values along its line to build up the 2D projection pixel intensity and color. The transformation from voxel values to intensity need not to be linearly: it is more often a soft threshold function (figure 5.1).
Figure 5.1: One of the threshold function of the volren program.
Along with the threee parameters, level, window and brightness comes a
fourth: the transparency. It do not directly translate into a intensity
value, but rather indexes into a color tabel.
Surface graphics shows an isosurface in the volume. The representation of the surface can be parametric or quadratic, but this is seldom seen. Most 3D surface graphics systems used the polygon as the graphical primitive.
The usual method of constructing the polygons from a volume is the \ matching cubes of Lorensen [44]. This method constructs subvoxel polygons by looking at the value of vertices from the little cube span by 8 neighboring voxels. An other method is the cubrille approach, where every voxels with a higher value than the isosurface is boxed with a cube --- cuberilles [25]. Joining cuberilles can be melted together to form a bigger cuberille. This approach leads an octree, with a spatial spectrum representation.
The advantage of surface graphics over volume graphics is the smaller memory and processing requirements, and the more immediate concept of objects . The disadvantage is the static isosurface and the missing interior [29]. The static isosurface can be overcomed by interactive --- data flow --- system such as AVS and IRIS Explorer.