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Poincare Disk / Hyperbolic Geometry Test

UIuiopscratch327•Created July 19, 2020
Poincare Disk / Hyperbolic Geometry Test
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Instructions

WASD/Arrow Keys to Move (IN HYPERBOLIC SPACE) This is just a demonstration of hyperbolic geometry using the Poincare Disk Model. I might make this a "raycaster" with the first 3d hyperbolic scratch game or something. It is just really tedious and strange to my brain to convert lines to circles and SOO MUCH GEOMETRY....

Description

Hyperbolic spaces are cool in that they are non-euclidean. Parallel lines diverge, 5 right angles can make a regular pentagon, but angles remain constant. This was coded by first having all the points lie on the poincare half-plane model (with the y logarithmic to save space) and then everything can be transformed with a scale or a translation along the x axis (in euclidean coordinates). With that in mind, anyone can offset all coordinates by scaling and translating, then convert it to the disk model, and then rotate it to whatever view.... I couldn't find this done on scratch so I did it myself.

Project Details

Project ID412613080
CreatedJuly 19, 2020
Last ModifiedApril 19, 2022
SharedJuly 30, 2020
Visibilityvisible
CommentsAllowed