Image Processing Reference
In-Depth Information
"
"
%
%
$
#!
$
#!
"
(
a
)
(
b
)
Fig. 7.7.
Viewport transformation and view volume (clipping on 3D space): (
a
)
Perspective projection; (
b
) parallel projection.
7.4.2 Displaying lines
A line (or a line segment) is determined automatically by fixing both of its
end points. Thus there is no problem in the projection of a line segment
except for in a few specific cases. For example, a part of a line segment in a
3D space may not be seen on a 2D image plane due to occlusion caused by
other objects. This is an important problem that is widely known as a
hidden
line problem
in computer graphics. We do not explain details of the hidden
line problem here because they are discussed in many ordinary text books on
graphics [Foley84, Watt98].
7.4.3 Displaying surfaces
A piece of a surface (= part of a plane in the finite area) is defined as an area
surrounded by line segments (= edges) connecting vertexes. Therefore, the
projection of a surface is obtained again by projecting vertexes (by the pro-
jection of points). However, additional considerations are required concerning
at least two problems.
One problem is the question of which side of a borderline (usually a closed
sequence of line segments or a polygon) is the surface that we are going to
define. One possible assumption is that we regard the left-hand side of a border
as the inside when we trace vertexes according to the order given beforehand,
and that we consider the inside as the surface we want to define. The other is
which surface is nearest to the viewpoint when more than one surface exist is
the current 3D space.
The portion of a surface hidden by other surfaces must not be rendered on
a 2D image plane. This is also called a
hidden surface problem
and has been
studied extensively in computer graphics. Details can be found in computer
graphics text books [Foley84, Watt98].
Displaying a surface is important also in the visualization of a 3D image
of a voxel type, because the polygon model described in Section 7.2 is also
employed frequently in practical applications.
Search WWH ::
Custom Search