Contour curves and isophotes on rational ruled surfaces

Ruled surfaces, i.e., surfaces generated by a one-parametric set of lines, are widely used in the field of applied geometry. An isophote on a surface is a curve consisting of those surface points whose normals form a constant angle with a fixed vector. Choosing the angle equal to pi/2 we obtain a special instance of the isophote - the so called contour curve. While contours on rational ruled surfaces are rational curves, this is no longer true for the isophotes. Hence we will provide a formula for their genus. Moreover we will show that the only surfaces with a rational generic contour are just the rational ruled surfaces and a particular class of cubic surfaces. In addition we will deal with a reconstruction of ruled surfaces from their silhouettes. (C) 2018 Elsevier B.V. All rights reserved.