An approach for designing a surface pencil through a given geodesic curve

TL;DR

This paper introduces a new method for constructing surfaces that interpolate a given curve as a geodesic, analyzing conditions for ruled surfaces and developability, with practical examples illustrating the approach.

Contribution

The paper presents a novel technique for designing surfaces with a specified geodesic curve, including conditions for ruled surfaces and developability, advancing geometric design methods.

Findings

Method successfully constructs surfaces passing through a given geodesic curve

Conditions for ruled surface formation are derived

Examples demonstrate the effectiveness of the proposed approach

Abstract

Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface interpolating a given curve as the geodesic curve of it. Also, we analyze the conditions when the resulting surface is a ruled surface. In addition, developablity along the common geodesic of the members of surface family are discussed. Finally, we illustrate this method by presenting some examples.