A geometric model of formation of surfaces comprising an interconnected triple of emitter, reflector and receiver is presented in the paper. The model is based on cyclographic mapping of a spatial curve to the plane. In such map any given point (x, y, z) of the curve corresponds to a cycle with center (x, y) and radius equal to z applicate. The entire curve corresponds to a directed envelope of cycles consisting, in the general case, of two branches.
It is shown that the triad of curves consisting of two branches of the envelope and the orthogonal projection of the original curve within the plane (xy) corresponds to a triad of developable surfaces. The triad of curves in the plane (xy) and the original curve together form a triad of ruled surfaces. Both triads have an optical property. Any ray of light emerging from the point of the emitter surface along the normal to it and falling on the surface of the reflector afterwards is directed along the normal vector to the surface of the receiver.
The direct and inverse problems of formation of the triad of surfaces are solved. In the first case, a one-parameter set of triads of surfaces is defined from a given spatial curve. In the second case, a single triad of surfaces is defined from a pair of curves "emitter-receiver" defined on the plane (xy). Numerical examples of solutions of the direct and inverse problems are considered and the corresponding visualizations are given.
The results of the work can be used in the design of reflector antennas in radar systems and systems for converting solar energy into electric and thermal energy.