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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 introductory scene to the game welcomes the player as well as explains to them how to navigate the text based tutorial. The player has attempted to fill in the cylinder blueprint to construct a cylinder as a ruled surface.

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 player has pushed the hint button multiple times, resulting in a sequence of animated orange rulings that trace out the motion needed to construct a cylinder as a ruled surface. The player holds up the hyperbolic paraboloid blueprint and their constructed hyperbolic paraboloid, comparing the two surfaces. The two surfaces look similar and an orange visual hint on the blueprint matches up with the rulings in the player's construction.

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


This project is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0).


  • 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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