Mathematics of Projections

Specifying Arbitrary 3D Views

Projection plane (view plane) specified by
VRP: View Reference Point
VPN: View Plane Normal
VUP: View Up Vector
View Volume (visible part of world) specified by
Window on View plane
PRP: Projection Reference Point
CW: Center of Window
COP: Center of Projection (Perspective Proj.) (derived)
DOP: Direction of Projection (Parallel Proj.) (derived)
PRP and CW are used to determine COP and DOP
perspective: COP = PRP
parallel: DOP = PRP - CW
Coordinate Systems
WC: World Coordinates - normal, 3-space (x, y, z)
VRC: Viewing Reference Coordinates - defined by VRP, VPN, and VUP above, and called (u, n), Think of the synthetic camera paradigm