Properties of three shadows on a plane

Abstract

We describe the geometrical properties of solid's shadows projected onto a flat plane by point-light sources. Even though the shape and position of each element are arbitrary and unknown, we indicate that there exists a certain constraint between three shadows on the plane; i.e., three cross points determined by pairs of tangential lines must sit on a straight line. This property is considered to be a derivation of epipolar geometry. However, the situation we treat is a special one in which an explicit feature can emerge. We also show the geometrical meaning of this property by invoking other properties.