On Curves and Surfaces in Illumination Geometry

G. Weiss ; H. Martini

Journal for geometry and graphics, Tome 4 (2000) no. 2, pp. 169-18

Résumé

A point like light source in Rd induces a certain illumination intensity at hypersurface elements of Rd. Manifolds of such elements with the same intensity of illumination are called isophotic. A uniformly radiating light source causes isophotic strips along sinusoidal spirals. In the present paper this investigation is extended in two directions. First all isophotic C2-hypersurfaces are found, and also manifolds of hypersurface elements which are isophotic with respect to two and more central illuminations are discussed. It suggests itself to treat such illumination problems also in non-Euclidean spaces. The second part of the paper deals with the generating curves of isophotic strips. They belong to the well-known families of Clairaut curves and sinusoidal spirals. Their known relations to each other and to other curve families (such as Ribaucour curves and roses) are extended by some perhaps new aspects.