Generalized Developable Cubic Trigonometric Bézier Surfaces

Author:

Ammad MuhammadORCID,Misro Md YushalifyORCID,Abbas MuhammadORCID,Majeed AbdulORCID

Abstract

This paper introduces a new approach for the fabrication of generalized developable cubic trigonometric Bézier (GDCT-Bézier) surfaces with shape parameters to address the fundamental issue of local surface shape adjustment. The GDCT-Bézier surfaces are made by means of GDCT-Bézier-basis-function-based control planes and alter their shape by modifying the shape parameter value. The GDCT-Bézier surfaces are designed by maintaining the classic Bézier surface characteristics when the shape parameters take on different values. In addition, the terms are defined for creating a geodesic interpolating surface for the GDCT-Bézier surface. The conditions appropriate and suitable for G1, Farin–Boehm G2, and G2 Beta continuity in two adjacent GDCT-Bézier surfaces are also created. Finally, a few important aspects of the newly formed surfaces and the influence of the shape parameters are discussed. The modeling example shows that the proposed approach succeeds and can also significantly improve the capability of solving problems in design engineering.

Funder

Universiti Sains Malaysia

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference50 articles.

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