Technical Background - Computer Animation: Algorithms and Techniques - page 38

y

y

x

x

z

Object
Space

World Space

z

y

Lines of sight
emanating from
observer

y

Eye at
negative
infinity

z

z

x

x

Eye
Space

Parallel lines of sight

Image Space

y

x

Screen Space

FIGURE 2.4
Display pipeline showing transformation between spaces.

2.1.2 Homogeneous coordinates and the transformation matrix
Computer graphics often uses a homogeneous representation of a point in space. This means that a
three-dimensional point is represented by a four-element vector. 1 The coordinates of the represented
point are determined by dividing the fourth component into the first three (Eq. 2.3) .
x
w ;

y
w ;

z
w

½x; y; z; w (2.3)

1 Note the potential source of confusion in the use of the term vector to mean (1) a direction in space or (2) a 1

n or n 1