Abstract
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 π/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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
