Contour curves and isophotes on rational ruled surfaces
Abstract
The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some fixed vector. Choosing an angle equal to we obtain a special instance of a~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 rational ruled surfaces and a one particular class of cubic surfaces. In addition we will deal with the reconstruction of ruled surfaces from their contours and silhouettes.
Cite
@article{arxiv.1609.07900,
title = {Contour curves and isophotes on rational ruled surfaces},
author = {Jan Vršek},
journal= {arXiv preprint arXiv:1609.07900},
year = {2016}
}