Viewing in 3D

Setting up the Viewing Parameters is undoubtedly the most complicated part of any 3D graphics system. When primitives are output to a workstation they (conceptually) pass through a series of processes called the Viewing Pipeline before they finally reach the display surface. This pipeline is briefly described below in order that the reader is aware of the complete process (see ). The transformations will then be covered in more detail.

1. The primitives are transformed by the Normalization Transformation from World Coordinates (WC3) to Normalized Device Coordinates (NDC3), which are always in the range [0.0, 1.0]. This transformation is composed of a translation and change of scale, but no rotation. GKS-3D allows for the existence of many World Coordinates systems, and their corresponding Normalization Transformations are numbered from 0 upwards. Normalization Transformation 0 always corresponds to the identity matrix. Normalization in 3D is exactly analogous to the 2D case described in section on Page .
2. Primitives which are stored in segments are also processed by the Segment Transformation before proceeding to the next stage. In the 3D case this requires a 3 x 4 matrix which is described below. The segment transformation maps NDC3 to NDC3, and includes scaling, rotation, and translation.
3. Having assembled the components in a unique NDC3 space, primitives may next be clipped to a box to remove extraneous information. This is called the Normalization Clip, and may be switched on or off using the Normalization Clip Flag.
4. The primitives are now 'viewed' from some arbitrary direction. The View Orientation Transformation performs a rotation only to take Normalized Device Coordinates to View Reference Coordinates (VRC3). The application is free to calculate the corresponding matrix itself, or to use a utility routine which is described below.
5. The View Mapping (Projection) Transformation next takes View Reference Coordinates to Normalized Projection Coordinates (NPC3) in order to provide parallel or perspective projection of the image. As for the View Orientation Transformation, the application is free to calculate the required matrix using its own algorithm, or to call a utility function.

    

    

   
   Figure: The GKS-3D Viewing Pipeline
   

6. At this point the View Clip takes place. It is positioned at this stage in the pipeline so that the clip box may be defined as a rectangular parallelepiped with its sides parallel to the axes of the NPC3 system, and thus the clipping algorithm is more efficient. The View Clip is controlled by three Clip Flags which allow clipping to be turned on or off separately for the front plane, back plane, and window.
7. Finally, the Workstation Transformation takes Normalized Projection Coordinates to Display Coordinates (DC3) in order to position the projected image in the device coordinate space. It preserves the aspect ratio, and includes a clipping operation which cannot be disabled. As their clip faces are parallel, the View Clip and Workstation Clip are usually combined internally for efficiency. DC3 coordinates may be in metres or raster units. The Workstation Window limits are [0,1]x[0,1]x[0,1].

A good implementation of the graphics pipeline will attempt to combine as many as possible of the stages in the pipeline using matrix concatenation in order to reduce the amount of computation necessary.

• The Normalization Transformation
• The View Orientation Transformation
• The View Mapping (Projection) Transformation
• Setting the 3D View Representation
• Workstation Transformation
• But I don't see anything!