omnicognate3 days ago
This is awesome.
Am I understanding correctly? I don't have the necessary background for the paper, but it sounds like in 3D space they capture the x and y coordinate of each point (so like an orthographic projection, not the screen coordinates) but for the z coordinate instead of storing actual values for each point they store the difference between the z coordinates of the endpoints of each edge.
That sounds like the object would still only be viewable from one direction, but when doing things like the heat diffusion you can consider each triangle to be at whatever depth makes sense for it to be touching the triangle you're reaching it from. So the same bit of geometry could be at different depths depending how you get there when movimg along the surface (a bit like a Riemann surface, I suppose). Is that right?
osullivj3 days ago
So my imperfect understanding is they formalised Escher's shading tricks. And so systematised making the impossible look possible. Which is what magicians do by gaming our perceptual firmware. Which is the reverse of what we do when debugging a nasty corner case. The observed behaviours seem impossible, until our perception of possible causes realigns.
mallowdram3 days ago
Are they tricks, or are they topological, non-Euclidean integrations? My guess is as the occipital is not 3-D, but dual input 2-D that splinters into thousands of topological units, that our 2.5-D (it's not 3-D in the slightest) vision slammed together on the primate face for parallax response times is uniquely suited for plastic revolutions in dimensions beyond 2-D, not just 3-D.
mallowdram3 days ago
This is extraordinary, thanks!
uecker3 days ago
This is super nice!