Description:
For this project, I created an interactive visualization to explore a mathematical problem involving the tiling of rhombuses. The core concept lies in the idea that 3 rhombuses can be grouped to form a hexagon, and that these hexagons can be interpreted as a 3D isometric arrangement of cubes depending on their rotation. Rotating a hexagon by 60-degrees creates a cube where there wasn't one before, and rotating 60-degrees once more removes it. The program allows the user to select rhombuses and rotate them, while updating a real-time display of the 3D representation of cubes. This assists the user in bridging the gap between two-dimensional and three-dimensional representations, helping users understand complex coordinate transformations.
Built with OpenGL, the project emphasizes challenges in converting coordinates into a 3rd dimension, detecting clicks, and applying dynamic rotations. It provides an interactive, digestible way to visualize how tiled 2D rhombuses may represent cubes in a 3D space.
Abstract:
This project focuses on visualizing a mathematical concept involving rhombus tiling and rotation. It presents the fact that three rhombuses can be grouped together to form a hexagon and that by rotating these groups, a 2D tiling can be interpreted as a 3D isometric arrangement of cubes. By letting users interact with a 2D tiling and reflecting their actions in real-time 3D, the program shows how simple shapes transform into cubes.
