A MATLAB application to visualize and describe a paraboloid shaped object

The paraboloid is one of the most important three dimensional (3D) geometries in many real-life applications. In the fields of engineering and technology, paraboloid shaped antennas are used for communications, while paraboloid solar dishes are designed to generate solar energy. The shape of a parabola is also investigated when studying the mechanics of a fluid inside a rotating bottle, as the fluid may form a parabolic surface due to the rotation. Besides, in architecture, parabola is used to build arches or domes of buildings. For some buildings, such as charcoal kilns, instead of using a straight flat roof, a paraboloid-shaped dome is placed on top to ensure faster heat circulation inside the building, resulting in better charcoal production. Due to these motivations, this project proposes an application that is able to easily visualize and describe a paraboloid-shaped object using MATLAB software. When using this application, users only need to specify the radius and the height of the object in order to display the 3D graph of a paraboloid with circular base that represents the object. The application will also present a two dimensional (2D) visualization of the paraboloid from either the top (the base of the paraboloid) or the front (the body of the paraboloid shaped object). For further characterization of the object, the surface area and the volume are also given by the application. We believe our proposed application has an advantage in visualizing and characterizing paraboloids, as it provides graphs, surface area, and volume within a single user-friendly interface that can be utilized in related applications in the future