viewing

Viewing
We now investigate the multitude of ways in which we can describe our virtual camera. Along the way, we examine related topics, such as the relationship between classical viewing techniques and computer viewing and how projection is implemented using projective transformations.
?There are three parts to our approach. First, we look at the types of views that we can create and why we need more than one type of view. Then we examine how an application program can specify a particular view within OpenGL.
CLASSICAL AND COMPUTER VIEWING
?The basic elements in both cases (classical and computer viewing) are the same. We have objects, a viewer, projectors, and a projection plane (Figure 5.1). The projectors meet at the center of projection (COP). The COP corresponds to the center of the lens in the camera or in the eye, and in a computer graphics system, it is the origin of the camera frame for perspective views. The projection surface is a plane, and the projectors are straight lines.
Both classical and computer graphics allow the viewer to be an infinite distance from the objects. Note that as we move the COP to infinity, the projectors become parallel and the COP can be replaced by a direction of projection (DOP), as shown in Figure 5.2. Note also that as the COP moves to infinity, we can leave the projection plane fixed and the size of the image remains about the same, even though the COP is infinitely far from the objects.
Views with a finite COP are called perspective views; views with a COP at infinity are called parallel views. For parallel views, the origin of the camera frame usually lies in the projection plane.
?Although computer-graphics systems have two fundamental types of viewing (parallel and perspective).

Classical Viewing
?When an architect draws an image of a building, she knows which side she wishes to display and thus where she should place the viewer in relationship to the building. Each classical view is determined by a specific relationship between the objects and the viewer. In classical viewing, there is the underlying notion of a principal face. The types of objects viewed in real-world applications, such as architecture, tend to be composed of a number of planar faces, each of which can be thought of as a principal face. For a rectangular object, such as a building, there are natural notions of the front, back, top, bottom, right, and left faces.
Orthographic Projections
?Our first classical view is the orthographic projection shown in Figure 5.4. In all orthographic (or orthogonal) views, the projectors are perpendicular to the projection plane. In a multiview orthographic projection, we make multiple projections, in each case with the projection plane parallel to one of the principal faces of the object. Usually, we use three views—such as the front, top, and right—to display the object