The View Orientation Transformation

The View Orientation Transformation algorithm provided by a utility function in the GKS-3D standard performs a rotation in three dimensions in order to take Normalized Device Coordinates to View Reference Coordinates (VRC3), where the axes are labeled U, V and N (see ). The definition of the UVN system requires the application to specify:

1. The View Reference Point (VRP), which is a point on or near the object to be viewed, and is the origin of the VRC3 system.
2. The View Plane Normal (VPN), which points from the View Reference Point towards the eye point. The VPN is the third axis of the VRC3 system, and the plane perpendicular to the View Plane Normal through the View Reference Point is called the View Reference Plane.
3. The View Up Vector (VUV), which defines the direction to be considered as 'UP' within the View Plane. It is the second axis of the VRC3 system. Clearly, the View Plane Normal and the View Up Vector must not be defined to be collinear.

Thus, in the View Reference system, the axis N is along the View Plane Normal, the axis V is the projection of the View Up Vector onto the View Reference Plane, and the axis U is constructed to form the third axis of a right-handed coordinate system. The default transformation sets the identity matrix. The limits of the VRC3 system are [0,1]x[0,1]x[0,1].

The GKS-3D View Reference System. The View Reference Point, defined in World Coordinates, should be situated near the object to be viewed. The View Plane Normal is directed at the eye point.