Doing the Math ...

• Every point on the base (red) is on the plane

• Interior angles of the base are 90°

• All other interior angles are 90°

• All sides are of the same length

• The vertical sides are parallel planes

• The cube is a convex hull

• Only points in the red region are transformed by the map projection

• Every point on the base (red) is on the

ORS

• Since the projection is conformal, interior angles of the base are 90°

• All other angles are generally not 90°

• In general, none of the sides are equal

• The vertical lines are not parallel, and are not even coplanar

• The 3D volume is no longer convex

Transforming a Cube from an Augmented Conformal Projection-based SRF to celestiodetic coordinates: