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https://github.com/yunusey/calculusvisualizations

Visualizations that can be helpful for Calculus students.
https://github.com/yunusey/calculusvisualizations

3d calculus-1 godot godot-engine godot4-3 visualization

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Visualizations that can be helpful for Calculus students.

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# Calculus Visualizations



_[Calculus Visualizations](https://github.com/yunusey/CalculusVisualizations) is a tool for visualizing calculus concepts such as solids of revolution and solids of cross sections._



## Before Beginning

Probably you are wondering why the project is named something as awkward as **Calculus Visualizations**. Well, I want to remind you one of my favorite quotes:



> There are only two hard things in Computer Science: cache invalidation and naming things.

> ~ Phil Karlton



Yeah, I couldn't think of a better name...

## Why?

I love [Godot](https://godotengine.org). I needed to create a project that needed to visualize AP Calculus BC concepts for future students at my high school, so I did this!



## Installation

You can check the web version of the tool [here](https://calculus-visualizations.netlify.app/). There is nothing added in the desktop version, but of course, it will work faster locally. I didn't set up GitHub Actions for building the project for desktop, but you can easily open the project locally in Godot following these instructions:



1. Clone the repository or [download the project as ZIP](https://github.com/yunusey/CalculusVisualizations/archive/refs/heads/main.zip) if you don't know how to use GitHub.

```bash

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

```

2. Import the project to Godot.



## User Guide



* To move around, you should use `WASD` keys. The camera always rotates *around the origin*.



* To zoom in and out, you should use `Mouse Wheel Up` and `Mouse Wheel Down`. The value gets clamped down when you zoom in too much or zoom out too much (again, so that you don't lose track).



* If the menu takes too much space and you want to get rid of that, you can use `H` key to toggle the menu.



* To toggle full-screen mode, you should use `F` key.



* When you are entering equations, the standard mathematical format may not work as intended (e.g. `x^2` doesn't work). You should use [Godot's expressions](https://docs.godotengine.org/en/stable/tutorials/scripting/evaluating_expressions.html). Here are several examples you may want to consider:

    - $x^2$ = `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](https://godotengine.org) for *everything*.

- [MikulasZelinka's Godot Web Export Template](https://github.com/MikulasZelinka/godot-web-export-template) for automatic web builds.

- [Netlify](https://www.netlify.com/) for free hosting.