Calculus Visualizations

Calculus Visualizations is a tool for visualizing calculus concepts such as solids of revolution and solids of cross sections.

Overview

The project is built with Godot 4.3. It ships two interactive 3D scenes: the disk/washer method for solids of revolution, and solids with known cross sections. Functions are entered as Godot expressions and evaluated at runtime, so the geometry updates live as you change parameters.

The Web build runs on the Compatibility (WebGL2) renderer, since that is the only renderer available for Godot web exports.

Web Version

The tool runs in the browser at yunusey.github.io/CalculusVisualizations. The desktop build behaves identically and runs faster locally.

Building

Builds are reproducible through Nix (see flake.nix):

• nix build .#web produces the WebAssembly/HTML export.
• nix build .#linux and nix build .#linux-portable produce Linux binaries (the portable variant keeps the upstream dynamic linker for generic distros).
• nix run launches the Linux build.
• nix develop opens a shell with Godot and the export templates already wired up.

Without Nix, clone the repository and open it in Godot 4.3:

git clone https://github.com/yunusey/CalculusVisualizations.git

Continuous Integration

.github/workflows/godot-ci.yml builds the Web and Linux exports with Nix on every push to main and deploys the Web build to GitHub Pages. It uses DeterminateSystems' nix-installer-action and magic-nix-cache-action, actions/upload-artifact for the build outputs, and actions/upload-pages-artifact with actions/deploy-pages for publishing.

User Guide

• To move around, use the WASD keys. The camera always rotates around the origin.

• To zoom in and out, use Mouse Wheel Up and Mouse Wheel Down. The value is clamped when you zoom in or out too far, so you do not lose track.

• Press H to toggle the menu if it takes up too much space.

• Press F to toggle full-screen mode.

• Equations use Godot expressions, not standard mathematical notation (for example, x^2 does not work). Some examples:

  • $x^2$ = x * x = pow(x, 2)
  • $ln(x)$ = log(x)
  • $\sqrt{x}$ = sqrt(x)
  • $3x$ = 3 * x

Parameters

Disk & Washer Method

• # Rectangles: Changes the number of rectangles for a more or less precise version of the shape.
• Shape Rot.: Changes the rotation of the entire shape.
• Disk Rot.: Changes the rotation of the disk.
• Shape Trans.: Changes the transparency of the entire shape (useful to show the disk in the shape).
• Disk Trans.: Changes the transparency of the disk.
• Coloring: Distinct makes the disk red and the rest of the shape blue (so that you can distinct the disk from the rest of the shape). Gradient gives nice coloring to the rectangles for better visuals.
• $f(x)$: Changes the upper function.
• $g(x)$: Changes the lower function (by default, it is 0 so that you can visualize the disk method).
• $a$ and $b$: Represents the domain of the functions: $[a, b]$.

Shape Cross-Sections

• Shapes: Change the shape of the cross-sections (available options are Squares, Equilateral Triangles, Isosceles Right Triangles, and Semi Circles).
• # Shapes: Changes the number of disks/cross-sections in the shape.
• Shape Trans.: Changes the transparency of the entire shape (useful to show the disk in the shape).
• Disk Trans.: Changes the transparency of the disk.
• Coloring: Distinct makes the disk red and the rest of the shape blue (so that you can distinct the disk from the rest of the shape). Gradient gives nice coloring to the rectangles for better visuals.
• $f(x)$: Changes the function.
• $a$ and $b$: Represents the domain of the function: $[a, b]$.

References & Thanks

• Godot Game Engine for everything.
• DeterminateSystems' nix-installer-action for installing Nix in CI.