You gotta think outside the hypercube
5 days ago
- #visualization
- #mathematics
- #geometry
- Introduction to the tesseract and its visualizations in media.
- Mathematical modeling of a hypercube starting from a square.
- Extension of the model to three dimensions (cube) and then to four dimensions (tesseract).
- Explanation of rotations in 2D, 3D, and 4D spaces.
- Different projection methods for rendering 4D objects in 2D: Cavalier, Cabinet, Isometric, Rectilinear one-point perspective, Fisheye perspective, and Mixed isometric + vanishing point.
- Visual examples and comparisons of tesseract renderings using various projection techniques.
- Discussion on the challenges and distortions in projecting 4D objects onto 2D screens.
- Link to MATLAB code for generating animation frames of the tesseract.