VISUALIZATION OF 3D GRAY-TONE IMAGES - Fundamentals of Three-Dimensional Digital Image Processing - page 219

Remark 7.8. The projection of a curved surface and a curve is discussed as
follows:
(1) If they are defined by using mathematical expressions, those expressions
are transformed mathematically into expressions for corresponding 2D
curves and 2D figures.
(2) If curved surfaces or curves in a 3D space are represented by piecewise
linear expressions, the methods explained here can be applied.
7.5 The concept of visualization based on ray casting -
(2) manipulation of density values
The methods to determine where an arbitrary point (or voxel) in a 3D space
should be mapped onto a 2D image plane was explained in the previous sec-
tion. The next step to consider is what density value should be given to a point
projected on a 2D image plane by methods presented in previous sections. The
following methods have been developed for this problem:
(1) Suitable light and dark shades are added when rendering surfaces in a 3D
space so that the shape of a surface may be perceived easily. This process
is called shading .
(2) Appropriate values reflecting density values of corresponding points (or
voxels) in 3D spaces are given to each point on a 2D image plane. By
doing this, we aim to visualize information of the spacial distribution of
density values in a 3D space on a 2D image plane.
(3) We can effectively use colors in the second method as described above.
Colors are usually represented by three numerical values corresponding to
the three color components, red (R), green (G), and blue (B). We call this
the triplet color code . A few different definitions have been proposed for
the physical meanings of the color code.
These three methods are important topics in computer graphics. Here we
only explain the minimum needed for visualizing a 3D gray-tone image. Let us
note that our objective here is to provide images that assist us to understand
the contents of 3D images. We do not intend to generate images with a high
reality level.
7.6 Rendering surfaces based on ray casting - surface
rendering
The existence of a surface in a 3D space is not perceived until each point on
a surface is given density values (or it is shaded suitably) in such a way that
it is compatible with the shape and other properties of a surface.