First time playing with cube maps. Instead of using them to paint the sky, I'm using them to paint the cube/sphere. Idea is to use this grid map for a game. It's a finite map, but you never reach the end of it.pic.twitter.com/LbixTIXnin
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Sometimes I make some visualizations for debugging (they helped a lot tonight). Turning them all on at the same time was amusing :-)pic.twitter.com/6GqD7bC41T
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Another thing I should keep in mind: adding labels is often more useful than just showing colors and then trying to decipher them in my head ;-)pic.twitter.com/6elpMqDX3G
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I had extended the colors of the four equatorial faces to the polar regions, and it turned out to be quite handy when debugging the 96 movement rules. There are 3 cases: 1. Polar to equatorial 2. Equatorial to equatorial 3. Equatorial to polar Next step is to build a map! :)pic.twitter.com/eW67xzMgm4
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Well, I didn't build a map, but instead tried out movement. I want a flat grid tile map for the player. This is what movement would look like on the flat world. As long as you stay away from the 8 corners, it looks like the earth is flat.pic.twitter.com/ZpIwAybMfp
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Replying to @redblobgames
Neat! Kinda reminds me of https://www.youtube.com/watch?v=kEB11PQ9Eo8 ….
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Replying to @qualmist @redblobgames
The fact that any "map" of the sphere needs to have vertices where angles act weirdly (e.g. you can return to where you start by going only 270° around the vertex) is a consequence of "Descartes' thm". It says "angular defects" need to add up to 720°. https://en.wikipedia.org/wiki/Angular_defect …
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Replying to @qualmist @redblobgames
Interesting! I've never seen this attributed to Descartes before, since I learned it as a consequence of the Gauss-Bonnet theorem. One thing that Gauss-Bonnet gives you beyond the sum rule is the interpretation of the defects as points of concentrated "intrinsic" curvature...
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which you could imagine spreading about more smoothly and once you get to thinking about spatially-varying curvature or more generally other local geometric invariants of a space, you're not so far from a lot more beautiful geometry and physics.
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Replying to @blockspins @redblobgames
Agreed! This "Descartes' theorem" is kinda an elementary, discretized approach to Gauss-Bonet. (It only relies on plane geometry, plus V - E + F = 2.) Unrelatedly, someone in this discussion needs to use the word "holonomy".
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