Every point on the line that passes through the point P and the light source is of the form

P + t T

The shadow is on this line and it is of the form (x, y, 0), so we look at the equation

P + t T = (x, y, 0)

which give us three equations similar to the three equations we obtained earlier by looking at the equation

S+ t (P - S) = (x, y, 0)

We can solve the third equation for t and then substitute this value for t into the first two equations to find the shadow (x, y, 0) of the object at P.

Copyright c 1995 by Frank Wattenberg, Department of Mathematics, Montana State University, Bozeman, MT 59717