Vector Fields

About

Simply enter a vector field to view it in Augmented Reality. I created this app for the final project of my Multivariable Calculus class since I had been working with AR for a project completely unrelated to school where some of the basic parts like the arrows themselves could be reused, and I figured something like this could be fun, especially since the project guidelines allowed us to do pretty much anything as long as some calculus was involved.

Acknowledgments

This is heavily based on this cool Desmos 3D graph by Elliot Wymore that allows you to input each component of a vector field and see it graphed. That was largely my reference for this project. One thing to note though is that in Desmos, the z-axis is up, but in SceneKit, it is the y-axis, which does not really change many things.

Usage

When the app is launched, there will be a popup asking you to input a vector field. Enter one in the text box in the top center of the app. As long as it is valid, it will be graphed. You should receive a warning popup if that is not the case. Please enter the vector field as one string, with each of the three components separated by commas, and no parentheses, then hit Done. Each component can be a function of x, y, z, or even constant. You can input almost anything, including square roots, absolute values, powers, and logarithms, but you might need to type them in as pseudo-Swift so it can be parsed properly. This does mean that to multiply two or more terms, you need to type in a * between each one, etc. Also, the length of each arrow corresponds to the magnitude of the vector at that point, and lastly, people occlusion is enabled. The latest feature is the ability to move the world origin (and therefore the grid origin) to the location of an ArUco marker. Currently, only the 6x6_1000-0 marker can be used, but look at AddMarkers.md to see how to add more. As soon as the marker is detected, the grid and any vectors present will move.

Challenges

• Orienting the vector correctly: solved using the look(at:up:localFront:), where up and localFront are both the j vector, instead of using the atan2 function, which was my inital method.
• Passing in custom values to the vector field: solved using NSExpression to evaluate each component, where the variables are replaced with their actual values using replacingOccurrences(of:with:).

Installation

1. Clone this repository or download it as a zip folder and uncompress it.
2. Open up the .xcodeproj file, which should automatically launch Xcode.
3. You might need to change the signing of the app from the current one.
4. Click the Run button near the top left of Xcode to build and install.

Prerequisites

Hopefully this goes without saying, but you need Xcode, which is only available on Macs.

Notes

You can run this app on the Xcode simulator or connect a physical device.
The device must be either an iPhone or iPad running iOS 16.0 or newer.
If using a simulator, you can only view the vector field along the x-axis.

SDKs

• ARKit - Integrate hardware sensing features to produce augmented reality apps and games.
• SceneKit - Create 3D games and add 3D content to apps using high-level scene descriptions.
• UIKit - Construct and manage a graphical, event-driven user interface for your iOS, iPadOS, or tvOS app.
• Swift - A powerful and intuitive programming language for all Apple platforms.

Bugs

I have not tested this app super rigorously, so I would not be surprised if there were more than the known ones. If you find any, feel free to open up a new issue or even better, create a pull request fixing it.

Known

• Vector fields that seem like they should work may crash the app. Workaround: just restart the app and enter the vector field again, but make sure the syntax looks correct and add parenthesis as needed.

Resolved

• Trigonometric functions are not supported because they are forbidden from NSExpression. Partially fixed by replacing only sin and cos with the first 10 terms of their Taylor Series, as suggested by my amazing math teacher. This is sometimes a little bit finicky.

Change Log

• v1.0 - initial release
• v1.1 - some sin/cos support
• v1.2 - better error handling
• v1.3 - improved regex matching
• v1.4 - change world origin
• v1.5 - support iOS 18 icons

To-Do List

• Add ability to change world origin
• Add sliders to control arrow attributes

Contributors

Sachin Agrawal: I'm a self-taught programmer who knows many languages and I'm into app, game, and web development. For more information, check out my website or Github profile. If you would like to contact me, my email is github@sachin.email.

License

This package is licensed under the MIT License.