Visualization and Poperties of Scaling a Tetrahedron about Its Vertices or Centre Using MATLAB

About the Project

Understanding the scaling (either enlarging or shrinking) of 3D object is essential for many applications, from architecture to science and engineering. In this project, the scaling of a tetrahedron is investigated, as it provides a fundamental example of 3D object transformation, being the simplest three-dimensional polyhedron. An object may be scaled down (shrunk) when its original size is impractical for visualization, testing, or physical modelling, while maintaining its geometric proportions. On the other hand, enlargement is useful when a small component needs to be made easier to inspect, measure, manufacture, or test. Due to its wide range of applications, concepts related to scaling, such as ratio and proportion, are taught in Malaysian schools as early as primary school. However, visualizing the enlargement and shrinking of a 3D object can be challenging, especially when different scaling centers are considered. In this case, the scaling center allows an object to be resized while maintaining the position of a critical reference point, such as a connection, joint, or attachment point. Moreover, changes in physical properties such as surface area, volume, edge lengths and centre after scaling may not be easy to see. Therefore, the objective of this study is to develop an interactive visualization that demonstrates how a tetrahedron shrinks or enlarges through scaling about any of its four vertices or its centroid, and shows the corresponding changes in its surface area, volume, edge lengths, and centre. In this project, a MATLAB application has been developed with interactive features to visualize the enlargement or shrinking of a tetrahedron by scaling about its vertices or centre, as well as to compute the changes in some of its properties after scaling.