PSCG: A MATLAB Application for Visualizing and Computing Properties of a Few Nonnegative Curves with a Maximum Point

About the Project

Nonnegative curves with a maximum point, such as parabolas, semicircles and Gaussian curves, have various applications in fundamental science, engineering and geometric modelling of structures. However, visualising these curves and determining their geometric properties based on the radius, r, and height, h, require careful mathematical formulation, which may be challenging for users without a strong mathematical background. Therefore, this project aims to develop an interactive MATLAB application for visualising three selected curves, namely the parabola, semicircle or its portion, and Gaussian curve, and computing their corresponding geometric properties based on r and h. The novelty of this application lies in its extension of our previous MyIPO-copyrighted innovation, CRLY2024J05921, which focused on a 3D paraboloid, and its connection to our previous publications. Its main inventiveness is the integration of three mathematical curves into a single interactive platform, allowing users to visualise and compare their shapes and geometric properties. The application enhances the real-world applications of STEM, particularly through the comparison of parabolic and semicircular curves in structural engineering. Furthermore, it supports the mathematical description and modelling of architectural heritage, particularly the historical charcoal kilns in Langkawi. Insights gained from laser scanning a functional charcoal kiln in Gelang Patah, Johor, provide a basis for using the application to model possible dome structures of the historical kiln, thereby contributing to heritage research and preservation. The application also supports the United Nations Sustainable Development Goals, particularly SDG 4 (Quality Education) and SDG 9 (Industry, Innovation and Infrastructure). With its educational and practical applications, the application has commercialisation potential in higher education and TVET institutions, as well as potential applications in engineering research and development, architectural heritage interpretation and educational tourism. Overall, this innovation provides an interactive mathematical platform that bridges fundamental mathematical concepts with practical applications in science, engineering and heritage preservation.