1.2.1 The Perspective Transform
• A set of basic viewing parameters may be defined (variations are also common),
- The point the Eye is looking at, and from which direction
- The focal distance to the viewing plane
- The size of the viewing plane being focused on
- Which direction is up for the eye
• As seen above the viewing parameters can all be combined using simple matrix multiplication which will convert a point in 3D space to a point on the screen.
• The process of drawing an object is merely applying this transformation to each point in the 3D model, then using the resulting (x, y) point on the 2D screen. (Note: If this transformation is done properly then z = depth in the view plane.)
• The point mapped to the computer screen can then be converted to a single pixel using a simple scaling calculation. (Note: It is not shown, but if a point is off the screen, then it cannot be drawn.)
• Visual display can be done using,
- CRT monitors with Frame Buffer memory to store the image.
- plotters which draw one line at a time
- printers using special and proprietary graphics languages
• For the sake of simplicity, the remaining graphics methods ignore some trivial operations such as screen coordinates, line clipping at edge of screen, etc.
• The ‘z’ value after the perspective transform gives a relative depth of a point. This can be used later for depth sorting, or to set light intensity to cue the user to view depth.