Dimensional Analysis through Perspective, by James R. Williamson & Michael H. Brill
ASPRS, 1990

Object-Space Reference Frame

Z-axis

Positive direction oriented vertically upward.

X-axis

Positive direction oriented toward the right and away from the camera station.

Y-axis

Positive direction oriented toward the left and away from the camera station.

Camera coordinates in Object-Space

Xc and Yc are always negative with the above choice for X and Y.

Zc is either positive (view from above) or negative (view from below the XY plane or "ground level").

Camera Reference Frame

(See Figures 2-1 or 10-1)

The x-y coordinates range from -1 to 1 in both x (Left --> Right) and y (Bottom --> Up) directions.

z-axis

Optical axis (inverted Principal Ray).

Positive direction from the Principal Point (PP) to the Camera Station (CS) or lens nodal position. The distance between PP and CS is the effective focal length  f  (at time of exposure or drawing).

x-axis

Horizontal axis of the image plane.

Is better kept approximately parallel to the bottom edge of the scene frame to have positive measurements.

y-axis

Vertical axis of the image plane.

Rotation of Object-Space to Image-space Coordinates

Azimuth (a)

The angular displacement of the Principal Plane. It is measured as the angle (a) between Y axis (Object-space) and the Principal Plane. Varies from +0 to +90 degrees.

It is a clockwise rotation about the Z axis (Object-space), i.e., about the vertical direction in the scene (akin "yaw").

Tilt (t)

Angle (t) between the Principal Ray and the Vertical or Plumb line defining the Nadir point. Varies from +0 to +180 degrees. If the tilt is greater than +90 degrees, than the camera is pointing upward (worm's eye viewpoint); otherwise it is point downward (bird's eye viewpoint).

It corresponds to a rotation around a line parallel to the true horizon line (akin "pitch").

Swing (s)

Angle (s) between the positive image y-axis and the trace of the projection of the Principal Plane below the image x-axis. It varies from +90 to +270 degrees. If the image x-axis is parallel to the horizon line (between the X and Y Vanishing Points), than the swing angle is +180 degrees.

It is a clockwise rotation about the image z-axis (or Principal Ray) (akin "roll").