The Camera - Essentials of Interactive Computer Graphics - page 368

ure 14.6 shows that as we adjust θ ,

V up 2 =( sin θ , cos θ , 0 )

0 ◦ , the up vector

rotates on the z = − 25 plane. In this way, when θ =

90 ◦ corresponds to a rotation
of 90 degrees from the WC y -axis such that the rendered image has
up direction aligned with the WC x -direction.

is aligned with the WC y -axis, and θ =

0 ◦ , changing slider z will
alter the rendered image. As we learn about the mathematical details behind
the up vector in Section 14.3, this will become clear.

One last point we should notice is that when θ =

2. Camera positions. Here we can adjust any of the slider bars to observe
the effects of changing camera positions. We can observe the effects of in-
valid up vector specification by resetting the camera parameters and then
increasing the camera z -position toward 0. Pay attention to the red and
blue axes: as the camera position z -value approaches 0, notice that the blue
and red axes flip direction as z changes sign and becomes positive. This
sudden change of the rendered image is a result of an undefined camera
specification. ,andas

the z -component of the camera position approaches 0, the viewing direc-
tion approaches the negative y direction. This means that the up vector
will become parallel to the view direction when the camera's z -component
becomes zero. As described, the up vector should never be parallel to
the view direction, and thus this correspond to an invalid camera defini-
tion. Because it can be difficult to adjust the slider bar to get exactly
zero, the “CameraZ0” button is provided to set the camera z -component
to zero. Click on the button to see that the graphics API is not able to ren-
der any object when the camera definition is invalid. Adjusting the camera
z -position slider bar slightly in either direction will give us a valid rendered
image.

Recall that the default up vector is set to ( 0 , 1 , 0 )

3. Look-at positions. Change the look-at position to see the effect in the

rendered image.

14.2 The Visible Volume

In the real world, all objects participate in the photographic process because all
objects reflect/emit light energy toward the camera. The physical laws of optics