A MATLAB Application for Visualizing the Effect of a Single 3D Rotation on a Tetrahedron about the Cartesian Coordinate Axes
Faculty of Science, Universiti Teknologi Malaysia
About the Project
Understanding three-dimensional (3D) rotation is fundamental in mathematics, engineering, geodesy, and many other fields. However, interpreting the changes in the position and orientation of a 3D object using mathematical equations alone can be challenging. This project presents a MATLAB-based graphical user interface (GUI) for visualizing the effect of a single 3D rotation on a tetrahedron, the simplest three-dimensional polyhedron. The application accepts the coordinates of the tetrahedron's four vertices as input, allows users to specify a rotation angle about one of the Cartesian coordinate axes, computes the new vertex coordinates using the appropriate rotation matrix, and animates the rotation from the original to the final position. Since a tetrahedron is uniquely defined by its vertices and their connectivity, rotating the four vertices is sufficient to determine its new position and orientation. This innovation extends our previous work involving tetrahedra by introducing an interactive visualization of 3D rotation. The GUI transforms the classroom concepts of vectors and linear transformations into an intuitive learning experience, enabling users to clearly observe the effects of rotation and enhancing their understanding of 3D geometric transformations. Owing to its educational value and ease of use, the proposed GUI has commercialization potential through integration into higher education textbooks, teaching materials, and digital learning resources, with further applications in surveying and mapping education and robotics training.