Game Engine Architecture

436 10. The Rendering Engine

10.1.4.4. Projection and Homogeneous Clip Space

Both perspective and orthographic projections transform points in view space

into a coordinate space called homogeneous clip space. This three-dimensional

space is really just a warped version of view space. The purpose of clip space

is to convert the camera-space view volume into a canonical view volume that

is independent both of the kind of projection used to convert the 3D scene into

2D screen space, and of the resolution and aspect ratio of the screen onto which

the scene is going to be rendered.

In clip space, the canonical view volume is a rectangular prism extending

from –1 to +1 along the x- and y-axes. Along the z-axis, the view volume ex-

tends either from –1 to +1 (OpenGL) or from 0 to 1 (DirectX). We call this coor-

Figure 10.33. An orthographic view volume.

Far

yV Plane

Near

Plane

xV

zV

(r, b, n)

(r, b, f)

(r, t, f)

(l, t, f)

(l, b, n)

(l, t, n)

(l, b, f)

(r, t, n)

PlaneFar

yH

PlaneNear

xH

zH

(1, –1, –1)

( 1, – 1, 1 )

(1 , 1, 1)

(–1 , 1, 1)

(–1, –1, –1)

( –1, 1, – 1)

Figure 10.34. The canonical view volume in homogeneous clip space.