Surfaces of congruent sections of pendulum type on cylinders with generatrix superellipses

Abstract

In 1972, I.I. Kotov proposed to separate the surfaces of congruent sections into a separate class and to include the surfaces of plane-and-parallel translation, surfaces of revolution, carved surfaces of Monge, cyclic surfaces with a generatrix circle of constant radius, rotative, spiroidal, and helical surfaces in it. The aim of the research is to obtain generalized parametric equations of surfaces of congruent sections of the pendulum type on right cylinders with plane-and-parallel translation of movable rigid superellipses. Analytical geometry methods are used. Computer systems MathCad and AutoCAD are applied to visualize surfaces. The results consist in the derivation of parametric equations of the studied surfaces in a general form convenient for the use of computer modeling methods. The technique is demonstrated on five examples with congruent mobile superellipses. The possibility of using obtained surface shapes in parametric architecture, free-form architecture, and in shaping of the surfaces of some technical products is noted.

Keywords

• surfaces
• congruent sections
• superellipse
• plane-parallel transfer
• curves
• astroid
• surface assignment