Integrating Vector Computation and Numerical Methods for Complex Surface Design in Engineering via MATLAB

Abstract

The teaching and practical use of vector calculus in engineering often face challenges rooted in mathematical abstraction and the limited availability of tools capable of supporting three-dimensional geometric analysis. These constraints hinder precision when designing complex structural surfaces. Addressing this gap, the present study proposes the development and implementation of an interactive computational tool—built in MATLAB App Designer that integrates vector-based formulations with numerical methods to parameterize, visualize, and compute the surface area of three-dimensional geometries, with a particular focus on sizing geomembranes for circular aquaculture ponds. The research methodology comprised theoretical, numerical, and experimental components. Exact vector parameterizations were formulated, symbolic integration and discretization algorithms were implemented, and the resulting computations were assessed through error estimation and convergence analysis. The findings demonstrate a close match between analytical and numerical solutions, with relative errors below 0.1%, stable computational behavior under moderate discretization settings, and distortion-free threedimensional visualizations. Overall, the study shows that combining exact vector modeling with adaptive numerical techniques and interactive visualization provides an efficient and low-cost framework for surface-area computation and structural design. This approach offers a practical alternative to conventional CAD platforms and delivers meaningful benefits for both engineering education and industrial applications within sustainable production systems.OPEN ACCESS Received: 10/11/2025 Accepted: 14/01/2026 Published: 16/04/2026

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