We know that the picture is stored in the computer memory using any convenient Cartesian co-ordinate system, referred to as World Co-Ordinate System (WCS). However, when picture is displayed on the display device it is measured in Physical Device Co-Ordinate System (PDCS) corresponding to the display device. Therefore, displaying an image of a picture involves mapping the co-ordinates of the Points and lines that form the picture into the appropriate physical device co-ordinate where the image is to be displayed. This mapping of co-ordinates is achieved with the use of co-ordinate transformation known as viewing transformation.
The viewing transformation which maps picture co-ordinates in the WCS to display co-ordinates in PDCS is performed by the following transformations.
• Converting world co-ordinates to viewing co-ordinates.
• Normalizing viewing co-ordinates.
• Converting normalized viewing co-ordinates to device co-ordinates.
The steps involved in viewing transformation:-
- Construct the scene in world co-ordinate using the output primitives and attributes.
- Obtain a particular orientation for the window by setting a two-dimensional viewing co-ordinate system in the world co-ordinate plane and define a window in the viewing co-ordinate system.
- Use viewing co-ordinates reference frame to provide a method for setting up arbitrary orientations for rectangular windows.
- Once the viewing reference frame is established, transform descriptions in world co-ordinates to viewing co-ordinates.
- Define a view port in normalized co-ordinates and map the viewing co-ordinates description of the scene to normalized co-ordinates.
- Clip all the parts of the picture which lie outside the viewport.