1.6 Perspective Transformation

Perspective transformation produces perspective by viewing the 3-D space from an arbitrary eye point. In the DCL library, it refers to the transformation from a 3-D VC to 2-D RC.

Generally, parallel lines in 3-D space projected onto a 2-D plane are not parallel. If the eye point is placed at the line of infinity, parallel lines will be projected as parallel lines, but graphics projected in such a manner seem unnatural.

To perform perspective transformation, the  "eye point" and the "center of focus" must be set. The eye point is the position from which the 3-D space is viewed, and can be thought of as the position of the camera lens. The center of focus, on the other hand, is not the focus on the film inside the camera, but is the point being viewed from the eye point. The line connecting the eye point and the center of focus is the "line of sight" .

With the perspective transformation, a point in a 3-D graphic is projected onto a point on a plane where the line connecting the point in 3-D space and the eye point intersects with the "plane of projection". In the DCL, the plane of projection is the plane passing through the center of focus and perpendicular to the line of sight.

In the case of 2-D coordinate systems, perspective transformation can be made by allocating the 2-D VC to a plane in a 3-D VC. The plane onto which the 2-D plane can be allocated is one which is perpendicular to either the X-, Y-, or the Z-axis, and cannot be allocated to an oblique plane. (To view the plane from an oblique angle, move the eye point.)