Matthew Arcus @MatthewArcus
Cambridge, UK Joined February 2012-
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@tessellationfan They look like k-uniform tilings, with the duals superimposed (see Grunbaum & Shephard 2.2).
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@tessellationfan Aha, thanks for the link. Not the friendliest website, as you say. Grabbed some of the images & stretched the contrast, which makes things a little easier.
@neozhaoliang I had a play with WebXR & Shadertoy shaders a while ago, if you are interested. I haven't done anything on it for a while, but it seems to still work with browser VR emulation: matthewarcus.github.io/xrshader/
@manujarvinen @tdhooper If there's any of my code involved, no problem!
@technolapin @iquilezles My code is doing the same thing, but reducing to a 2x3 problem by mapping three points to the reference triangle so only three coefficients are needed and we can just use cross product to get the 3 minors.
@iquilezles Shader here: shadertoy.com/view/XXGcD1
@iquilezles Conic through 5 points: mat3 conic(vec3 p, vec3 q, vec3 r, vec3 s, vec3 t) { mat3 a = mat3(cross(q,r),cross(r,p),cross(p,q)); s *= a; t *= a; vec4 m = vec4(cross(s*s.yzx,t*t.yzx),0); mat3 x = mat3(m.wxz,m.xwy,m.zyw); return a*x*transpose(a); } x.com/shawn_halayka/…
@iquilezles Do you have a similar function called getEllipse? Thank you for your time and guidance.
@shawn_halayka @iquilezles Well, my code is intended to be GLSL, but for C++, looks like glm doesn't like *= for matrices, but s = s*a seems to work (note order, this is same as s = transpose(a)*s). Swizzling might cause problems too, but you can use eg. yzx(s) instead of s.yzx etc.).
@neozhaoliang Nice. My C++ code takes about 2 minutes, but I'm impressed that the slowdown from using Python isn't more.
@panlepan Nice. That seems to be the only way to make 2025 as the sum of two squares (so in fact it's the sum of a 4th power and a 6th power).
@gs_bangalore Okan's circle gives another nice octagon: x.com/OkanAtalay1970…
@MatthewArcus @gs_bangalore I hope this helps. Notice the central angle of 90 degrees and the inscribed angle of 45 degrees, both having the same arc of the circle.
@OkanAtalay1970 @gs_bangalore Aha! Thanks for the explanation, very nice...
@OkanAtalay1970 @gs_bangalore Nice, but I can't see how to show that these two lengths are equal (I'm a bit out of practise with these puzzles, so I'm probably missing something obvious):
@gs_bangalore Here's a nice octagon:
@panlepan Nice. Can you do something with 2025 = 1³+2³+3³+4³+5³+6³+7³+8³+9³ ( = (1+2+3+4+5+6+7+8+9)²) ?
Euclid in Syriac, from the new exhibition at @theUL. x.com/theUL/status/1…
Endless Stories, opens on 28 Sep at Cambridge University Library. It showcases the extraordinary manuscripts collected by 17th-century visionary, Thomas Van Erpe. The exhibition includes works in Arabic, Hebrew, Persian, and Malay. Book your free ticket: lib.cam.ac.uk/endlessstories
@stevejtrettel So it would seem - I only realized this after looking at this excellent volumetric Hopf shader by "tmst'": shadertoy.com/view/ttVXWt
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