Automatic modeling of surfaces with identical slopes

The visualization problem of the formation process of surfaces with the same slope (generator angle) is considered. Among them, there are surfaces with different guides, such as a parabola, a circular cosine wave, a spherical evolvent. The possibility of helicoidal surface formation is also considered, since their generators have the same angle of inclination in all positions to the horizontal plane. The principles and techniques of surface formation in the AutoCAD environment are described using the functional language AutoLisp. The tasks of visualizing the formation of surfaces with the same slope with the guide parabola and the general cosine, as well as Monge surfaces and different types of helicoids are solved by means of authors’ programs coded in AutoLisp language, tools and the color palette of the AutoCAD program. The generator in all presented cases is a straight line with the same inclination angle α to the guide line (surfaces with parabola, circle cosine and evolvent) or to the horizontal plane xy (helicoids). © 2019, Springer International Publishing AG, part of Springer Nature.