Generalized Perspective Projection

Perspective projection is a well-understood aspect of 3D graphics. It is not something that 3D programmers spend much time thinking about. Most OpenGL applications simply select a field of view, specify near and far clipping plane distances, and call gluPerspective or glFrustum. These functions suffice in the vast majority of cases. But there are a few assumptions implicit in these. gluPerspective assumes that the user is positioned directly in front of the screen, facing perpendicular to it, and looking at the center of it. glFrustum generalizes the position of the view point, but still assumes a perspective rooted at the origin and a screen lying in the XY plane. The configuration of the user and his screen seldom satisfy these criteria, but perspective projection remains believable in spite of this. Leonardo’s The Last Supper uses perspective, but still appears to be a painting of a room full of people regardless of the position from which you view it. Likewise, one can still enjoy a movie even when sitting off to the side of the theater.