A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be visualized as shining a (point) light source (located at infinity) through a translucent sheet of paper and making an image of whatever is drawn on it on a second sheet of paper. The branch of geometry dealing with the properties and invariants of geometric figures under projection is called projective geometry.

The projection of a vector  onto a vector  is given by

where  is the dot product, and the length of this projection is

General projections are considered by Foley and VanDam (1983).

The average projected area over all orientations of any ellipsoid is 1/4 the total surface area. This theorem also holds for any convex solid.

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