how to: code donut-shaped C code that generates a 3D spinning donut

When I thought of coding tutorial, I know I must a post on donut-shaped C code that generates a 3D spinning donut. It’s just so legendary that you have to know it.

Although I’m good at math in highschool, I haven’t touched math for the last 3 years. In this post, instead of bombing with code, I will help you understand the process and the match behind this masterpiece.

donut-shaped C code that generates a 3D spinning donut

anh’s note from reading Math Behind Donut Shape C Code by whoisslimshady and Donut Math: Make a 3D spinning torus with C by Shreyos Ghosh:

Mathematical Background:

• 3D Projection:
  • Projecting 3D coordinates onto a 2D plane by scaling a coordinate by a screen distance constant, denoted as 𝐾1K1​.
• Rotation Matrix:
  • Rotating a point in 3D space involves matrix multiplications. In this case, rotation around the y-axis is utilized.

Drawing the Torus:

• Torus Construction:
  • A torus is formed by revolving a circle of radius 𝑅2R2​ around a line generated by a bigger circle of radius 𝑅1R1​.
• Point Rotation:
  • Each point on the circle with radius 𝑅2R2​ is rotated by an angle 𝜙ϕ, and the circle is rotated by an angle 𝜃θ.
• Rotation Matrices:
  • Utilizing rotation matrices, points are rotated around the y-axis and additional axes if required.

3D Projection and Illumination:

• Depth Adjustment:
  • To move the torus in front of the viewer, a constant 𝐾′K′ is added to the Z-coordinate.
• Projection Formulas:
  • The 3D coordinates are projected onto the 2D screen with adjustments based on constants 𝐾1K1​ and 𝐾′K′.
• Illuminance Calculation:
  • Illuminance is determined by the dot product of the surface normal and the chosen lighting direction.

Coding the Donut:

• Headers Used:
  • The necessary libraries like <stdio.h> and <math.h> are included.
• Variables Initialization:
  • Various constants and variables for screen resolution, rotation angles, and buffer size are declared.
• Custom Functions:
  • render_frame() calculates pixel positions and illuminance.
  • display() outputs the rendered frame to the console.

Final Code Execution:

• Loop Execution:
  • The code repeatedly generates and displays frames, updating rotation angles for animation.
• ASCII Art Implementation:
  • Pixels are represented by ASCII characters based on illuminance levels, producing a donut-like shape.

Understanding the Code:

• Framebuffer Approach:
  • The code utilizes a framebuffer and a Z-buffer to render ASCII art of the donut.
• Pixel Plotting:
  • Pixels along the torus surface are plotted at fixed-angle increments, simulating a solid shape.
• Projection Simplification:
  • 3D projection onto the 2D screen involves scaling coordinates and depth buffering to manage overlapping points.
• Surface Normal Calculation:
  • The direction perpendicular to the torus surface at each point is computed for illumination purposes.
• Lighting Direction:
  • A lighting direction is chosen to determine the shade of each pixel, affecting its appearance.

any fun codes suggestion?

Same, after writing this post, I didn’t understand a thing. But I hope you have fun feeling cool reading this! I only know donut in coding C, so please lemme know if there is any fun code math out there in the comment section.