The Camera - Essentials of Interactive Computer Graphics - page 381

the view vector. We can compute the adjusted up vector:

V u = V v × V w .

With normalization, we define EC orthonormal basis. The

camera space, or camera coor-
dinate, orthonormal basis and
the EC orthonormal basis are
used interchangeably.

⎧
⎨

V w =(

x w , y w , z w ) ,

V u =(

EC orthonormal basis: x u , y u , z u ) , (14.3)

⎩

V v =(

x v , y v , z v ) .

These three unit vectors are perpendicular to each other, and the directions of
these three vectors agree with the axes of the right-handed coordinate system.
For example, if we consider V w to be in the x -direction, then V u is in the y -axis
direction, and V v is in the z -axis direction.

y View

Vector ( V v )

( V u )

(- V w )

z

x

Eye
Position (p e )

14.5.2 Eye Coordinate (EC) Space

The eye coordinate (EC) space is defined with reference to the EC orthonormal
basis. As illustrated in Figure 14.17, the EC is a right-handed coordinate system
such that

Figure 14.17. The eye

coordinate space .

• Origin. The eye position p e is the origin.
• Axes directions. The view vector V v points in the negative z -direction, the
adjusted up vector V u is in the y -direction, and the V w vector points in the
x -direction.

In the EC space with the eye located at the origin looking toward the negative
z -axis, the z -components tell us the distance to the eye:

• Visible volume. If the near and far planes are n and f units from the cam-
era, then the near plane is located at z

= − n , and the far plane at z = − f .

We know that only objects with z -component within the range

− f ≤ object . z ≤− n

are inside the visible volume. All other objects are outside of the visible
volume and cannot participate in the rendering process.

• Object depth ordering. Objects' relative ordering from the camera can be
easily determined from their z -component: the larger the value, the closer
the object is to the camera. The Z-buffer algorithm takes advantage of this
characteristic to resolve object occlusion when projecting 3D objects to the
2D image plane.