Update projects.md

Author: ryan-stees

geolab/projects.md

@@ -65,7 +65,7 @@ permalink: /geolab/projects/
 + Computer Visualization
     - Mentors: Gennady Uraltsev
     - Mentees: Lincoln Curtis, Diego Dimattina, Michelle Giulajan, Yejun Kim, Liran Li, Katherine Moore, Mandy Unterhalter, Zerui Wang
-    - Description: This project explores the perception of a world with a geometry unlike our own, with a special focus on vision. We examine the standard computer graphics infrastructure and discuss challenges associated with visualizing non-Euclidean geometries. We reference various media that depict non-Euclidean worlds; the project aims to understand the mechanics of these models beyond their visually striking effects: <a href="https://stevejtrettel.site/talk/optics/">Optics, Mirages, and Curved Space - Steve Trettel</a>; <a href="https://www.shadertoy.com/view/wtXBRH">Living on Surface of 4D Sphere - Gijs Bellaard</a>; <a href=https://codeparade.itch.io/hyperbolica">Hyperbolica - A whimsical Non-Euclidean adventure</a>; <a href=https://zenorogue.itch.io/hyperrogue">HyperRogue - A rougelike on the hyperbolic plane</a>; <a href="https://4dtoys.com/">4D Toys. An interactive toy for 4D children.</a>; <a href="https://www.youtube.com/watch?v=5xN4DxdiFrs">Rotation Tesseract (4D cube)</a>. First, we constructed platonic solids and discussed how a two-dimensional being on these surfaces would interpret geometric concepts and vision. We considered how a two-dimensional being would perceive and communicate concepts such as ‘straight line’ and ‘angle. A significant part of the project was understanding the concept of “dimension”. We used the surface of a 4D cube as a model of a non-Euclidean three-dimensional space.” Discussions revolved around how a three-dimensional being would experience living on the surface of a 4D cube. We reformulated the basics of vision, including three-point perspective through the language of linear algebra and projective geometry. This knowledge was applied to understand how the standard computer graphics pipeline works. The project also involved learning the basics of programming with Python notebooks, as well as 3D modeling with the A-frame web library. The team successfully projected a 4D cube wireframe to 3D space and applied 3D standard visualization. Ultimately, the project resulted in a 3D Virtual Reality depiction of a non-Euclidean world, created by integrating combinatorial logic coded by students with a standard Euclidean graphics pipeline. This exploration provided insights into visualizing dimensions beyond our own and the potential for computer-generated visualizations of complex geometries.
+    - Description: This project explores the perception of a world with a geometry unlike our own, with a special focus on vision. We examine the standard computer graphics infrastructure and discuss challenges associated with visualizing non-Euclidean geometries. We reference various media that depict non-Euclidean worlds; the project aims to understand the mechanics of these models beyond their visually striking effects: <a href="https://stevejtrettel.site/talk/optics/">Optics, Mirages, and Curved Space - Steve Trettel</a>; <a href="https://www.shadertoy.com/view/wtXBRH">Living on Surface of 4D Sphere - Gijs Bellaard</a>; <a href="https://codeparade.itch.io/hyperbolica">Hyperbolica - A whimsical Non-Euclidean adventure</a>; <a href="https://zenorogue.itch.io/hyperrogue">HyperRogue - A rougelike on the hyperbolic plane</a>; <a href="https://4dtoys.com/">4D Toys. An interactive toy for 4D children.</a>; <a href="https://www.youtube.com/watch?v=5xN4DxdiFrs">Rotation Tesseract (4D cube)</a>. First, we constructed platonic solids and discussed how a two-dimensional being on these surfaces would interpret geometric concepts and vision. We considered how a two-dimensional being would perceive and communicate concepts such as ‘straight line’ and ‘angle. A significant part of the project was understanding the concept of “dimension”. We used the surface of a 4D cube as a model of a non-Euclidean three-dimensional space.” Discussions revolved around how a three-dimensional being would experience living on the surface of a 4D cube. We reformulated the basics of vision, including three-point perspective through the language of linear algebra and projective geometry. This knowledge was applied to understand how the standard computer graphics pipeline works. The project also involved learning the basics of programming with Python notebooks, as well as 3D modeling with the A-frame web library. The team successfully projected a 4D cube wireframe to 3D space and applied 3D standard visualization. Ultimately, the project resulted in a 3D Virtual Reality depiction of a non-Euclidean world, created by integrating combinatorial logic coded by students with a standard Euclidean graphics pipeline. This exploration provided insights into visualizing dimensions beyond our own and the potential for computer-generated visualizations of complex geometries.
 
 + 3D Printing
     - Mentors: David Chasteen-Boyd, Alec Traaseth