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rogueviz:: impossible triangle viz
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Zeno Rogue
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299
rogueviz/triangle.cpp
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299
rogueviz/triangle.cpp
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#include "../hyper.h"
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// Impossible Triangle visualization
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// used in: https://www.youtube.com/watch?v=YmFDd49WsrY
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// settings:
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// ./mymake rogueviz/triangle
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// ./hyper -geo Nil -canvas x -tstep 8 -nilperiod 3 3 3
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// also used in: https://youtu.be/RPL4-Ydviug
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// ./hyper -geo Nil -nilwidth .9 -canvas x -tstep 1 -nilperiod 1 10 1 -triset 32 31 992
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namespace hr {
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// each color group (i.e., each face direction) is a different hpcshape
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hpcshape ptriangle[6];
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EX hyperpoint lerp(hyperpoint a0, hyperpoint a1, ld x) {
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return a0 + (a1-a0) * x;
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}
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hyperpoint operator+(hyperpoint x) { return x; }
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// do not change this
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int shape = 1;
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// how many cubes to subdivide edges to
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int how = 4;
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// how many cubes to draw (should be smaller than how because they are not really cubes and thus they get into each other)
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int how1 = how - 1;
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// precision: number of substeps to simulate (best if divisible by how and how1)
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int isteps = 4 * 1024;
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/* make the impossible triangle shape */
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void make_shape() {
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static bool done = false;
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if(done) return;
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done = true;
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// four main axes of the regular tetrahedron, rotated so that ds[3] points to (0,0,1)
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ld rest = sqrt(8/9.);
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ld rex = sqrt(1 - 1/9. - pow(rest/2., 2));
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hyperpoint ds[4];
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ds[0] = point3(rex, -rest/2, -1/3.);
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ds[1] = point3(0, rest, -1/3.);
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ds[2] = point3(-rex, -rest/2, -1/3.);
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ds[3] = point3(0, 0, +1);
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hyperpoint start = point31(0, 0, 0);
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double lastz;
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double lasta;
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double ca;
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// compute how to scale this in Nil so that everything fits
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for(ld a = 1e-5;; a+=1e-5) {
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hyperpoint at = start;
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for(int d=0; d<3; d++) {
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for(int i=0; i<isteps; i++) {
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at = nisot::translate(at) * (start + ds[d] * a);
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}
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}
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println(hlog, "at = ", at, " for a = ", a, " sq = ", at[2] / a / a);
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if(at[2] > 0) {
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ld z = at[2];
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ca = lerp(lasta, a, ilerp(lastz, z, 0));
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break;
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}
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lastz = at[2]; lasta =a;
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}
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println(hlog, "ca = ", ca);
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ld scale = .2;
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// compute the shift between the cubes
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array<hyperpoint, 4> uds;
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for(int d=0; d<3; d++) {
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hyperpoint at = start;
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for(int i=0; i<isteps/how; i++) {
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at = nisot::translate(at) * (start + ds[d] * ca);
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}
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uds[d] = (at - start) / 2.;
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}
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println(hlog, "uds = ", uds);
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for(int a=0; a<3; a++) println(hlog, sqhypot_d(3, inverse_exp(start + ds[a] * ca, iTable, false)));
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for(int a=0; a<3; a++) println(hlog, sqhypot_d(3, inverse_exp(uds[a], iTable, false)));
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// compute cube vertices
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hyperpoint verts[8];
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for(int a=0; a<8; a++) {
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verts[a] = start;
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for(int k=0; k<3; k++)
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verts[a] += (a&(1<<k)) ? uds[k] : -uds[k];
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}
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// since Nil does not really have cubes, we need to move the vertices a bit so that it looks nicer
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// ugliness of the current vertices
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auto errf = [&] {
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ld res = 0;
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for(int s=0; s<8; s++)
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for(int t=0; t<3; t++) {
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if((s & (1<<t)) == 0) {
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int s1 = s | (1<<t);
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ld dix = sqhypot_d(3, inverse(nisot::translate(nisot::translate(start + 2*uds[t]) * verts[s])) * verts[s1]);
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// println(hlog, tie(s, t), "di = ", dix);
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res += dix * dix;
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}
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}
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return res;
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};
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// minimize the ugliness
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ld curerr = errf();
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println(hlog, "curerr = ", curerr);
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int att = 0;
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if(1) while(true) {
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int id = rand() % 8;
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int j = rand() % 3;
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ld eps = (rand() % 100 - rand() % 100) / 100000.;
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verts[id][j] += eps;
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ld nerr = errf();
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if(nerr < curerr) {
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curerr = nerr;
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println(hlog, "curerr = ", curerr, " # ", att);
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att = 0;
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}
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else {
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verts[id][j] -= eps;
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}
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att++;
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if(att > 50000) break;
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}
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for(int s=0; s<8; s++)
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for(int t=0; t<3; t++) {
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if((s & (1<<t)) == 0) {
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int s1 = s | (1<<t);
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ld dix = sqhypot_d(3, inverse(nisot::translate(nisot::translate(start + 2*uds[t]) * verts[s])) * verts[s1]);
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println(hlog, tie(s, t), "di = ", dix);
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}
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}
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scale = 1.;
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// build all the faces
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for(int si=0; si<6; si++) {
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cgi.bshape(ptriangle[si], PPR::WALL);
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hyperpoint at = start;
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for(int d=0; d<3; d++) {
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int d1 = (d+1) % 3;
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int d2 = (d+2) % 3;
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hyperpoint path[isteps+1];
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for(int i=0; i<isteps; i++) {
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path[i] = at;
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at = nisot::translate(at) * (start + ds[d] * ca);
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}
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path[isteps] = at;
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auto &u = uds[d];
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auto &v = uds[d1];
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auto &w = uds[d2];
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auto textured_square = [&] (auto f) {
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texture_order([&] (ld ix, ld iy) { f(.5 + ix/2 + iy/2, .5 + ix/2 - iy/2); });
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texture_order([&] (ld ix, ld iy) { f(.5 - ix/2 - iy/2, .5 - ix/2 + iy/2); });
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texture_order([&] (ld ix, ld iy) { f(.5 + ix/2 - iy/2, .5 - ix/2 - iy/2); });
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texture_order([&] (ld ix, ld iy) { f(.5 - ix/2 + iy/2, .5 + ix/2 + iy/2); });
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};
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auto sidewall = [&] (hyperpoint wide, hyperpoint shift) {
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textured_square( [&] (ld ix, ld iy) {
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hyperpoint online = path[int(ix * isteps + .1)];
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hyperpoint shf = lerp(u, -u, ix) + lerp(-wide, wide, iy) + shift;
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shf *= scale;
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cgi.hpcpush(nisot::translate(online) * (start + shf));
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});
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};
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auto sidesquare = [&] (hyperpoint wx, hyperpoint wy, hyperpoint shift, ld p) {
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textured_square( [&] (ld ix, ld iy) {
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hyperpoint online = path[int(p * isteps + .1)];
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hyperpoint shf = lerp(wx, -wx, ix) + lerp(wy, -wy, iy) + shift;
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shf *= scale;
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cgi.hpcpush(nisot::translate(online) * (start + shf));
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});
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};
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auto sidesquare1 = [&] (hyperpoint a00, hyperpoint a01, hyperpoint a10, hyperpoint a11, ld p) {
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hyperpoint online = path[int(p * isteps + .1)];
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textured_square( [&] (ld ix, ld iy) {
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hyperpoint shf = lerp(lerp(a00, a01, ix), lerp(a10, a11, ix), iy);
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shf *= scale;
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cgi.hpcpush(nisot::translate(online) * (shf));
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});
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};
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if(shape == 0) {
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if(si == d2*2) sidewall(v, w);
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if(si == d1*2) sidewall(w, v);
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if(si == d2*2+1) sidewall(v, -w);
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if(si == d1*2+1) sidewall(w, -v);
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if(si == d2*2) sidesquare(u, v, w, 0);
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if(si == d1*2) sidesquare(w, u, v, 0);
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if(si == d1*2+1) sidesquare(u, w, -v, 0);
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if(si == d*2+1) sidesquare(w, v, -u, 0);
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}
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if(shape == 1) for(int a=0; a<how1; a++) {
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ld c = a * 1. / how1;
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/*
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if(si == d*2) sidesquare(v, w, u, c);
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if(si == d*2+1) sidesquare(w, v, -u, c);
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if(si == d1*2) sidesquare(w, u, v, c);
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if(si == d1*2+1) sidesquare(u, w, -v, c);
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if(si == d2*2) sidesquare(u, v, w, c);
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if(si == d2*2+1) sidesquare(v, u, -w, c);
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*/
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if(si == 0) sidesquare1(verts[0], verts[2], verts[4], verts[6], c);
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if(si == 1) sidesquare1(verts[1], verts[3], verts[5], verts[7], c);
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if(si == 2) sidesquare1(verts[0], verts[1], verts[4], verts[5], c);
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if(si == 3) sidesquare1(verts[2], verts[3], verts[6], verts[7], c);
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if(si == 4) sidesquare1(verts[0], verts[1], verts[2], verts[3], c);
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if(si == 5) sidesquare1(verts[4], verts[5], verts[6], verts[7], c);
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}
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}
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cgi.last->flags |= POLY_TRIANGLES;
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cgi.last->tinf = &floor_texture_vertices[0];
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cgi.last->texture_offset = 0;
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cgi.finishshape();
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cgi.extra_vertices();
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}
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}
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// Magic Cube (aka Rubik Cube) colors
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color_t magiccolors[6] = { 0xFFFF00FF, 0xFFFFFFFF, 0x0000FFFF, 0x00FF00FF, 0xFF0000FF, 0xFF8000FF};
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bool draw_ptriangle(cell *c, const transmatrix& V) {
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make_shape();
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if(c == cwt.at) {
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for(int side=0; side<6; side++) {
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auto &s = queuepoly(V, ptriangle[side], magiccolors[side]);
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ensure_vertex_number(*s.tinf, s.cnt);
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}
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}
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return false;
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}
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auto hchook = addHook(hooks_drawcell, 100, draw_ptriangle)
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+ addHook(hooks_args, 100, [] {
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using namespace arg;
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if(0) ;
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else if(argis("-triset")) {
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shift(); how = argi();
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shift(); how1 = argi();
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shift(); isteps = argi();
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}
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else return 1;
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return 0;
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});
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}
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