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VR experience developed to illustrate the mathematical concept of ruled surfaces and their physical construction out of strings and wire.

# GCIEL/VMM-Ruled-Surfaces-Experience

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# VMM-Ruled-Surfaces-Experience

An alpha-level prototype virtual reality experience developed to illustrate ruled surfaces and their physical construction out of strings and wire. Developed during a Mentored Advanced Project entitled Virtual Mathematical Models at Grinnell College during the summer of 2019 with Professor Christopher French.

The ruled surfaces investigated in this experience are grounded in models made by German mathematicians in the late 19th century. They key concept illustrated is that of how a ruled surface can be constructed out of a continuous sweeping of lines. This is a sandbox experience where players are challenged to figure out how to construct a ruled surface out of lines. Players are tasked to use the positions of their hands in space to draw out lines, called rulings, that construct four possible ruled surfaces. The player can reach out and grab to manipulate the virtual drawing.

The experience interactively explains what a ruled surface is to the player by showing them how to construct a cylinder. Each challenge is visualized as a blue transparent blueprint that players have to fill in with their rulings. The experience also draws animated hints that show how one can move their hands to create the challenges. Players must decide for themselves whether or not they have solved how to construct a given challenge.

Here are links to recordings of a walkthrough of the interface tutorial and a player completing different ruled surfaces.

The main Unity scene file is Ruled Surfaces Experience/Assets/Scenes/Ruled Surfaces Demo and the important code that I developed is in the Ruled Surfaces Experience/Assets/Scripts folder. Here are the poster and paper that I wrote for the VMM MAP summer project.

## Built With

• Unity - The game engine and development environment used.
• SteamVR SDK - Unity plugin used to target HTC Vive and Oculus Rift VR headsets (using version 1.2.3).
• Blender - Used to create 3D models and textures.

## Authors and Contributors

• Tal Rastopchin - Initial work on virtual reality experience - GitHub

## Acknowledgments

• This project was funded by Grinnell College.
• The project was supervised by Christopher French.
• My MAP coworkers Charun Upara and William Song.

VR experience developed to illustrate the mathematical concept of ruled surfaces and their physical construction out of strings and wire.

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