Properties of Three Shadows on a Plane

Toshio Moriya, Fumiko Beniyama, Kosei Matsumoto, Tsuyoshi Minakawa, Kei Utsugi, and Haruo Takeda
Hitachi, Ltd.
Advanced Research Laboratory, Systems Development Laboratory
215-0013 Kawasaki




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 a explicit feature can emerge.  We also show the geometrical meaning of this property by invoking other properties.