PaSCap : An Interactive MATLAB GUI for Visualizing and Computing a few Parameters of Paraboloid or Spherical-Cap Domes

Abstract

This paper presents PaSCap, an interactive MATLAB-based graphical user interface (GUI) designed to visualize and calculate key geometric parameters of paraboloid and spherical cap domes. The GUI integrates mathematical modeling with dynamic 3D visualization, allowing users to adjust input variables, observe real-time geometric changes, and obtain accurate values for volume, surface area, and related parameters. PaSCap is intended to support students, educators, and researchers in mathematics, engineering, and architecture by providing an intuitive environment that links equations to visual outputs, thereby enhancing conceptual understanding. Its automated computations and comparative visualizations enable users to explore similarities and differences between the two dome types while gaining deeper insight into their structural and geometric properties. Overall, PaSCap demonstrates how interactive computational tools can simplify complex geometry, enrich teaching and learning experiences, and assist in preliminary analysis and design tasks.