Construction of minimal surfaces using trigonometric Pythagorean hodograph curves

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Abstract

Minimal surfaces have zero mean curvature. These surfaces have the smallest possible area for a given boundary curve, and are widely used in engineering, biological design, and architecture. In this study, we present a method to construct minimal surfaces using trigonometric Pythagorean hodograph (PH) curves. First, we generate PH trigonometric curves, and subsequently apply the Weierstrass representation to derive the corresponding minimal surface. The constructed PH curve serves as a boundary isoparametric curve of the surface. We analyze key geometric properties such as symmetry, surface area and mean curvature. Representative examples are provided to demonstrate the effectiveness of the proposed method.

Keywords

Curvature analysis

Holomorphic functions

Iso-parametric curves

mean curvature

surface area

Weierstrass representation

Funding

None.

Conflict of interest

The authors declare no conflict of interest.

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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing