Graphics Reference
In-Depth Information
Figure 4.5.
Vanishing point.
original line, will project to lines that intersect in a point. If c = 0, then one can check
that nothing special happens and parallel lines project into parallel lines.
In the context of the world-to-view plane transformation with respect to a given
camera, what we have shown is that lines in the world project into lines in the view
plane. Furthermore, the projection of some lines gives rise to certain special points
in the view plane. Specifically, let L be a line in the world and let equation (4.6) be a
parameterization for L in camera coordinates. We use the notation in the discussion
above.
Definition. If the point in the view plane of the camera that corresponds to the point
on the right hand side of equation (4.8) exists, then it is called the vanishing point for
the line L with respect to the given camera or view.
Clearly, if a line has a vanishing point, then this point is well-defined and unique.
Any line parallel to such a line will have the same vanishing point. Figure 4.5 shows
a projected cube and its vertices. Notice how the lines through the pairs of vertices A
and E , B and F , C and G , and D and H meet in the vanishing point P . If we assume
that the view direction of the camera is perpendicular to the front face of the cube,
then the lines through vertices such as A , B , and E , F , or A , C , and B , D , are paral-
lel. (This is the c = 0 case.)
Perspective views are divided into three types depending on the number of
vanishing points of the standard unit cube (meaning the number of vanishing points
of lines parallel to the edges of the cube).
One-point Perspective View. Here we have one vanishing point, which means
that the view plane must be parallel to a face of the cube. Figure 4.5 shows such a
perspective view.
Two-point Perspective View. Here we have two vanishing points and is the case
where the view plane is parallel to an edge of the cube but not to a face. See Figure
4.6 and the vanishing points P 1 and P 2 .
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