The Camera - Essentials of Interactive Computer Graphics - page 376

It is interesting that decreasing the FOV value creates a zoom-in effect. This
is because as FOV decreases, so do the image plane and the width and height of
the viewing frustum. A smaller viewing frustum sees smaller cross-sections of the
scene, and the squares in the scene will occupy a more significant proportion of
the image plane. When this image plane is mapped onto the application window,
the small cross-sections of the screen end up being enlarged into the application
window, thus the zoom-in effect. In contrast, increasing the FOV will create a
zoom-out effect. Notice that unlike the orthographic projected image, it is difficult
to measure relative sizes of objects on a perspective projected image. In this case,
we can tell one square is closer to the camera than the other, but it is difficult to
determine the relative sizes of these squares.

14.2.3 Discussion

Theoretically, just as in the real world, all objects can participate in the rendering
process, whereas the simulation computation will ensure that only those within
the view will occupy pixels in the final image. The visible volume optimizes
this process by eliminating objects outside of the volume from being rendered.
Notice that visible volumes (both the simple rectangular volume and the viewing
frustum) are defined by distances measured with respect to the camera position.
The far plane distance f must be greater than the near plane distance n ,otherwise
an invalid visible volume is specified and the output is undefined. The near plane
distance must always be greater than 0. A 0 or negative near plane distance will
result in an undefined image.
It is important to tightly bound the depth of the visible volume with optimized
near and far planes. That is, the near plane should be as far away from the camera
as the closest visible object, while the far plane should be as close to the cam-
era as possible. Referring to Figures 14.10 and 14.7, we should maximize n and
minimize f to create a visible volume with minimum depth range ( f

−

n ). For
example, in our scene with the two squares, initially we set the near plane dis-
tance to n 18 is reasonable

for viewing the two squares. We have also seen that as we manipulate the cam-
era position, the near/far plane distance settings run the risk of clipping away the
squares. The reason to optimize the depth range is that in order to resolve fron-
t/back visibility, we must uniquely identify objects' positions in depth. The depth
visibility hardware implementation relies on a fixed number of bits to resolve the
near/far plane depth range. For example, the hardware may dedicate 16 bits to
resolve the near/far depth range. We know that 16 bits can represent

= 18 and far plane to f = 36. This depth range of 36 −

2 16 = 65536