OpenGL Programming Guide

Chapter 3Viewing

Projection Transformations

Orthographic Projection

With an orthographic projection, the viewing volume is a rectangular parallelepiped, or more informally, a box (see Figure 3-13 ). Unlike perspective projection, the size of the viewing volume doesn't change from one end to the other, so distance from the camera doesn't affect how large an object appears. This type of projection is used for applications such as creating architectural blueprints and computer-aided design, where it's crucial to maintain the actual sizes of objects and angles between them as they're projected.

Figure 3-13 : The Orthographic Viewing Volume

The command glOrtho() creates an orthographic parallel viewing volume. As with glFrustum(), you specify the corners of the near clipping plane and the distance to the far clipping plane. void glOrtho(GLdouble left, GLdouble right, GLdouble bottom,
GLdouble top, GLdouble near, GLdouble far);

Creates a matrix for an orthographic parallel viewing volume and multiplies the current matrix by it. The near clipping plane is a rectangle with the lower left corner at (left, bottom, -near) and the upper right corner at (right, top, -near). The far clipping plane is a rectangle with corners at (left, bottom, -far) and (right, top, -far). Both near and far can be positive or negative.

With no other transformations, the direction of projection is parallel to the z-axis, and the viewpoint faces toward the negative z-axis. Note that this means that the values passed in for far and near are used as negative z values if these planes are in front of the viewpoint, and positive if they're behind the viewpoint.

For the special case of projecting a two-dimensional image onto a two-dimensional screen, use the Utility Library routine gluOrtho2D(). This routine is identical to the three-dimensional version, glOrtho(), except that all the z coordinates for objects in the scene are assumed to lie between -1.0 and 1.0. If you're drawing two-dimensional objects using the two-dimensional vertex commands, all the z coordinates are zero; thus, none of the objects are clipped because of their z values. void gluOrtho2D(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top);

Creates a matrix for projecting two-dimensional coordinates onto the screen and multiplies the current projection matrix by it. The clipping plane is a rectangle with the lower left corner at (left, bottom) and the upper right corner at (right, top).

OpenGL Programming Guide