In 2006, Andy Sloane introduced a fascinating project: a program that renders a spinning donut using ASCII characters in the terminal. The goal is to delve into the mathematical principles underpinning the spinning donut and provide insights into its Python implementation using Pygame.
To understand the math you can go to Andy Sloane website: https://www.a1k0n.net/2011/07/20/donut-math.html
Mathematical Foundation: A donut, or torus, is formed by revolving a circle around an axis at a distance greater than its radius. Understanding the parametric equation for circles helps construct the framework for the spinning donut.
Python Implementation: Pygame, a versatile Python library, enables the visualization of the donut by rendering characters at precise locations on the screen. Cartesian coordinates are converted to Pygame's system, allowing the rendering of a rotating pastry.
Rotation and 3D Perspective Rendering: Rotation around the x- and z-axes breathes life into the donut, facilitated by rotation matrices. Realistic 3D perspective rendering involves projecting points onto a 2D plane, enhancing visual fidelity.
Illumination and Luminance: Simulated illumination enhances realism by considering the luminance of each point on the donut's surface. Calculating the dot product between the surface normal and a light vector determines brightness, adding depth to the scene.
Grid-based Rendering and Visual Presentation: Grid-based rendering assigns ASCII characters based on luminance levels, enhancing clarity and visual appeal.
In conclusion, the Spinning Donut project merges mathematics and programming to create an engaging visual experience. Understanding the underlying mathematics and implementing efficient rendering techniques unlock the potential for artistic expression and technical mastery. It serves as a gateway to the fascinating world of mathematics and computer graphics, inviting exploration and creativity.