The Modeling Transformation
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You use the modeling transformation to position and orient the model. For example, you can rotate, translate, or scale the model - or perform some combination of these operations. Rotating and translating are performed using the commands already mentioned - glRotatef() and glTranslatef(). In this example, however, the modeling transformation is invoked with glScalef(). The arguments for this command specify how scaling should occur along the three axes. If all the arguments are 1.0, this command has no effect; in Example 3-1 , the cube is drawn twice as large in the y direction. Thus, if one corner of the cube had originally been at (3.0, 3.0, 3.0), that corner would wind up being drawn at (3.0, 6.0, 3.0). The effect of this modeling transformation is to transform the cube so that it isn't a cube but a rectangular box.

Note that instead of pulling the camera back away from the cube (with a viewing transformation) so that it could be viewed, you could have moved the cube away from the camera (with a modeling transformation). This duality in the nature of viewing and modeling transformations is why you need to think about the effect of both types of transformations simultaneously. It doesn't make sense to try to separate the effects, but sometimes it's easier to think about them one way rather than the other. This is also why modeling and viewing transformations are combined into the modelview matrix before the transformations are applied. "Viewing and Modeling Transformations," explains in more detail how to think about modeling and viewing transformations and how to specify them so that you get the result you want.

Also note that the modeling and viewing transformations are included in the display() routine, along with the call that's used to draw the cube, auxWireCube(). This way, display() can be used repeatedly to draw the contents of the window if, for example, the window is moved or uncovered, and you've ensured that each time, the cube is drawn in the desired way, with the appropriate transformations. The potential repeated use of display() underscores the need to load the identity matrix before performing the viewing and modeling transformations, especially when other transformations might be performed between calls to display().

The Projection Transformation
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Specifying the projection transformation is like choosing a lens for a camera. You can think of this transformation as determining what the field of view or viewing volume is and therefore what objects are inside it and to some extent how they look. This is equivalent to choosing among wide-angle, normal, and telephoto lenses, for example. With a wide-angle lens, you can include a wider scene in the final photograph than with a telephoto lens, but a telephoto lens allows you to photograph objects as though they're closer to you than they actually are. In computer graphics, you don't have to pay $10,000 for a 2000-millimeter telephoto lens; once you've bought your graphics workstation, all you need to do is use a smaller number for your field of view.

In addition to the field-of-view considerations, the projection transformation determines how objects are projected onto the screen, as its name suggests. Two basic types of projections are provided for you by OpenGL, along with several corresponding commands for describing the relevant parameters in different ways. One type is the perspective projection, which matches how you see things in daily life. Perspective makes objects that are farther away appear smaller; for example, it makes railroad tracks appear to converge in the distance. If you're trying to make realistic pictures, you'll want to choose perspective projection, which is specified with the glFrustum() command in this code example.

The other type of projection is orthographic, which maps objects directly onto the screen without affecting their relative size. Orthographic projection is used in architectural and computer-aided design applications where the final image needs to reflect the measurements of objects rather than how they might look. Architects create perspective drawings to show how particular buildings or interior spaces look when viewed from various vantage points; the need for orthographic projection arises when blueprint plans or elevations are generated, which are used in the construction of buildings. "Projection Transformations," discusses the ways to specify both kinds of projection transformations in more detail.

Before glFrustum() can be called to set the projection transformation, some preparation needs to happen. As shown in the myReshape() routine in Example 3-1 , the command called glMatrixMode() is used first, with the argument GL_PROJECTION. This indicates that the current matrix specifies the projection transformation; the following transformation calls then affect the projection matrix. As you can see, a few lines later glMatrixMode() is called again, this time with GL_MODELVIEW as the argument. This indicates that succeeding transformations now affect the modelview matrix instead of the projection matrix. See "Manipulating the Matrix Stacks," for more information about how to control the projection and modelview matrices.

Note that glLoadIdentity() is used to initialize the current projection matrix so that only the specified projection transformation has an effect. Now glFrustum() can be called, with arguments that define the parameters of the projection transformation. In this example, both the projection transformation and the viewport transformation are contained in the myReshape() routine, which is called when the window is first created and whenever the window is moved or reshaped. This makes sense, since both projecting and applying the viewport relate directly to the screen, and specifically to the size of the window on the screen.