On the Design and Invariants of a Ruled Surface

TL;DR

This paper introduces a novel method for designing ruled surfaces using dual unit spherical Bézier-like curves, exploring their invariants and providing illustrative examples within geometric design and kinematics.

Contribution

It presents a new approach to ruled surface design via dual Bézier-like curves and investigates their integral invariants, combining geometric design with kinematic concepts.

Findings

A new method for creating ruled surfaces using dual Bézier-like curves.

Identification of integral invariants for closed ruled surfaces.

Illustrative examples demonstrating the design process and invariants.

Abstract

This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with respect the control points by a new method. So, with the aid of Study [1] transference principle, a dual unit spherical B\'ezier-like curve corresponds to a ruled surface. Furthermore, closed ruled surfaces are determined via control points and integral invariants of these surfaces are investigated. The results are illustrated by examples.