mirror of
https://github.com/zenorogue/hyperrogue.git
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Triangle vizualization now includes the network
This commit is contained in:
Zeno Rogue
parent
f4130ec730
commit
d68ff2eeda
@ -12,10 +12,13 @@
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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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// network of triangles:
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// ./hyper -geo Nil -canvas x -tri-net
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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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bool net = false;
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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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@ -35,123 +38,130 @@ 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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struct triangledata {
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hyperpoint at;
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bool computed;
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int tcolor;
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int id;
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// each color group (i.e., each face direction) is a different hpcshape
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triangledata(hyperpoint h) : at(h), computed(false) { tcolor = 0; id = 0; }
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};
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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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struct trianglemaker {
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hyperpoint ds[4];
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map<cell*, vector<triangledata> > tds;
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array<hpcshape, 6> ptriangle;
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array<hpcshape, 6> pcube;
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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 ds[4], uds[4], dmoves[6];
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hyperpoint start = point31(0, 0, 0);
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ld scale;
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void init() {
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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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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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double lastz;
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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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// compute the shift between the cubes
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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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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, "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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// 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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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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// 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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}
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return res;
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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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// 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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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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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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@ -160,31 +170,10 @@ void make_shape() {
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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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scale = 1;
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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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for(int si=0; si<6; si++) {
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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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@ -192,88 +181,290 @@ void make_shape() {
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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 cube_at = [&] (hyperpoint online) {
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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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auto sidesquare1 = [&] (hyperpoint a00, hyperpoint a01, hyperpoint a10, hyperpoint a11) {
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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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if(scale) shf = shf * scale - start * (scale-1);
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cgi.hpcpush(nisot::translate(online) * (shf));
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});
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};
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if(si == 0) sidesquare1(verts[0], verts[2], verts[4], verts[6]);
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if(si == 1) sidesquare1(verts[1], verts[3], verts[5], verts[7]);
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if(si == 2) sidesquare1(verts[0], verts[1], verts[4], verts[5]);
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if(si == 3) sidesquare1(verts[2], verts[3], verts[6], verts[7]);
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if(si == 4) sidesquare1(verts[0], verts[1], verts[2], verts[3]);
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if(si == 5) sidesquare1(verts[4], verts[5], verts[6], verts[7]);
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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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scale = 2;
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cgi.bshape(pcube[si], PPR::WALL);
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cube_at(start);
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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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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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scale = 1;
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cgi.bshape(ptriangle[si], PPR::WALL);
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hyperpoint at = start;
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vector<hyperpoint> atx = {start};
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cube_at(start);
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for(int dx: {0, 1, 2}) {
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int d = dx;
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if(net) at = start;
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else cube_at(at);
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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 * (dx >= 3 ? -1 : 1));
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}
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path[isteps] = at;
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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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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 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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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=1; a<how1; a++) {
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ld c = a * 1. / how1;
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cube_at(path[int(c * isteps + .1)]);
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}
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dmoves[d] = at;
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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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tds[cwt.at].emplace_back(start);
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dmoves[3] = inverse(nisot::translate(dmoves[0])) * C0;
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dmoves[4] = inverse(nisot::translate(dmoves[1])) * C0;
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dmoves[5] = inverse(nisot::translate(dmoves[2])) * C0;
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}
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void compute(triangledata &td, cell *c) {
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if(td.computed) return;
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td.computed = true;
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if(!net) return;
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hyperpoint at;
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for(int d=0; d<6; d++) {
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hyperpoint at = nisot::translate(td.at) * dmoves[d];
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cell *c0 = c;
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virtualRebase(c0, at);
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bool newat = true;
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for(auto& td: tds[c0]) {
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||||
ld d = sqhypot_d(3, at - td.at);
|
||||
if(d < .01) {
|
||||
if(d>1e-5) println(hlog, "d = ", d);
|
||||
newat = false;
|
||||
}
|
||||
}
|
||||
|
||||
if(shape == 1) for(int a=0; a<how1; a++) {
|
||||
ld c = a * 1. / how1;
|
||||
|
||||
/*
|
||||
if(si == d*2) sidesquare(v, w, u, c);
|
||||
if(si == d*2+1) sidesquare(w, v, -u, c);
|
||||
if(si == d1*2) sidesquare(w, u, v, c);
|
||||
if(si == d1*2+1) sidesquare(u, w, -v, c);
|
||||
if(si == d2*2) sidesquare(u, v, w, c);
|
||||
if(si == d2*2+1) sidesquare(v, u, -w, c);
|
||||
*/
|
||||
|
||||
if(si == 0) sidesquare1(verts[0], verts[2], verts[4], verts[6], c);
|
||||
if(si == 1) sidesquare1(verts[1], verts[3], verts[5], verts[7], c);
|
||||
if(si == 2) sidesquare1(verts[0], verts[1], verts[4], verts[5], c);
|
||||
if(si == 3) sidesquare1(verts[2], verts[3], verts[6], verts[7], c);
|
||||
if(si == 4) sidesquare1(verts[0], verts[1], verts[2], verts[3], c);
|
||||
if(si == 5) sidesquare1(verts[4], verts[5], verts[6], verts[7], c);
|
||||
|
||||
if(newat) {
|
||||
triangledata ntd = at;
|
||||
ntd.id = td.id + 1;
|
||||
tds[c0].push_back(ntd);
|
||||
tds[c0].back().tcolor = (td.tcolor + (d < 3 ? 1 : 2)) % 3;
|
||||
}
|
||||
}
|
||||
|
||||
cgi.last->flags |= POLY_TRIANGLES;
|
||||
cgi.last->tinf = &floor_texture_vertices[0];
|
||||
cgi.last->texture_offset = 0;
|
||||
cgi.finishshape();
|
||||
cgi.extra_vertices();
|
||||
}
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
trianglemaker *mkr;
|
||||
|
||||
// Magic Cube (aka Rubik Cube) colors
|
||||
|
||||
color_t magiccolors[6] = { 0xFFFF00FF, 0xFFFFFFFF, 0x0000FFFF, 0x00FF00FF, 0xFF0000FF, 0xFF8000FF};
|
||||
|
||||
bool draw_ptriangle(cell *c, const transmatrix& V) {
|
||||
make_shape();
|
||||
#define CTO (isize(cnts))
|
||||
|
||||
vector<int> cnts;
|
||||
vector<ld> coef;
|
||||
int valid_from;
|
||||
int tested_to;
|
||||
int coefficients_known;
|
||||
|
||||
bool verify(int id) {
|
||||
if(id < isize(coef)) return false;
|
||||
ld res = 0;
|
||||
for(int t=0; t<isize(coef); t++)
|
||||
res += coef[t] * cnts[id-t-1];
|
||||
return abs(res - cnts[id]) < .5;
|
||||
}
|
||||
|
||||
|
||||
int valid(int v, int step) {
|
||||
if(step < 0) return 0;
|
||||
if(step+v+v+5 >= CTO) return 0;
|
||||
ld matrix[100][128];
|
||||
for(int i=0; i<v; i++)
|
||||
for(int j=0; j<v+1; j++)
|
||||
matrix[i][j] = cnts[step+i+j];
|
||||
|
||||
if(c == cwt.at) {
|
||||
for(int side=0; side<6; side++) {
|
||||
auto &s = queuepoly(V, ptriangle[side], magiccolors[side]);
|
||||
ensure_vertex_number(*s.tinf, s.cnt);
|
||||
for(int k=0; k<v; k++) {
|
||||
int nextrow = k;
|
||||
while(nextrow < v && std::abs(matrix[nextrow][k]) < 1e-6)
|
||||
nextrow++;
|
||||
if(nextrow == v) return 1;
|
||||
if(nextrow != k) {
|
||||
// printf("swap %d %d\n", k, nextrow);
|
||||
for(int l=0; l<=v; l++) swap(matrix[k][l], matrix[nextrow][l]);
|
||||
// display();
|
||||
}
|
||||
}
|
||||
ld divv = 1. / matrix[k][k];
|
||||
for(int k1=k; k1<=v; k1++) matrix[k][k1] *= divv;
|
||||
// printf("divide %d\n", k);
|
||||
// display();
|
||||
for(int k1=k+1; k1<v; k1++) if(matrix[k1][k] != 0) {
|
||||
ld coef = -matrix[k1][k];
|
||||
for(int k2=k; k2<=v; k2++) matrix[k1][k2] += matrix[k][k2] * coef;
|
||||
}
|
||||
// printf("zeros below %d\n", k);
|
||||
// display();
|
||||
}
|
||||
|
||||
for(int k=v-1; k>=0; k--)
|
||||
for(int l=k-1; l>=0; l--)
|
||||
if(matrix[l][k]) matrix[l][v] -= matrix[l][k] * matrix[k][v];
|
||||
|
||||
coef.resize(v);
|
||||
for(int i=0; i<v; i++) coef[i] = matrix[v-1-i][v];
|
||||
|
||||
println(hlog, "coef = ", coef);
|
||||
for(int t=step+v; t<step+v+v+5; t++) {
|
||||
println(hlog, "verify(", t, ") = ", verify(t));
|
||||
if(!verify(t)) return 2;
|
||||
}
|
||||
println(hlog, "got here");
|
||||
tested_to = step+v+v+5;
|
||||
while(tested_to < CTO) {
|
||||
if(!verify(tested_to)) return 2;
|
||||
tested_to++;
|
||||
}
|
||||
|
||||
valid_from = step+v;
|
||||
return 3;
|
||||
}
|
||||
|
||||
void find_coefficients() {
|
||||
if(coefficients_known) return;
|
||||
for(int v=1; v<25; v++)
|
||||
for(int step=0; step<1000; step++) {
|
||||
int val = valid(v, step);
|
||||
if(val == 0) break;
|
||||
println(hlog, "v=", v, "step=", step, " val=", val);
|
||||
if(val == 3) { coefficients_known = 2; return; }
|
||||
}
|
||||
coefficients_known = 1;
|
||||
}
|
||||
|
||||
void growthrate() {
|
||||
/*
|
||||
for(int a=0; a<CTO; a++) {
|
||||
int cnt = 0;
|
||||
map<cell*, int> howmany;
|
||||
for(auto& p: mkr->tds) cnt += (howmany[p.first] = isize(p.second));
|
||||
for(auto& p: howmany) for(int i=0; i<p.second; i++) {
|
||||
// println(hlog, p.first, mkr->tds[p.first][i].at, mkr->tds[p.first][i].computed);
|
||||
mkr->compute(mkr->tds[p.first][i], p.first);
|
||||
}
|
||||
println(hlog, "cnt = ", cnt, " / ", cnt / pow(1+a, 4));
|
||||
cnts[a] = cnt;
|
||||
if(a >= 4) println(hlog, "D4 = ", cnts[a-4] - 4 * cnts[a-3] + 6 * cnts[a-2] - 4 * cnts[a-1] + cnts[a]);
|
||||
println(hlog, "cnts = ", cnts);
|
||||
}*/
|
||||
|
||||
cnts = {1,7,31,113,299,681,1363,2501,4181,6570,9874,14256,20027,27601,37171,48815,62993,79912,100181,123868,151680,184339,222347,265733,314523,369424,431221,500952,578350,665794,763300,871250,988488,1116635,1256293,1409165,1575969,1758327,1958977,2174877};
|
||||
find_coefficients();
|
||||
|
||||
println(hlog, "coefficients_known = ", coefficients_known);
|
||||
if(coefficients_known == 2) {
|
||||
string fmt = "a(d+" + its(isize(coef)) + ") = ";
|
||||
bool first = true;
|
||||
for(int i=0; i<isize(coef); i++) if(coef[i]) {
|
||||
if(first && coef[i] == 1) ;
|
||||
else if(first) fmt += its(coef[i]);
|
||||
else if(coef[i] == 1) fmt += " + ";
|
||||
else if(coef[i] == -1) fmt += " - ";
|
||||
else if(coef[i] > 1) fmt += " + " + its(coef[i]);
|
||||
else if(coef[i] < -1) fmt += " - " + its(-coef[i]);
|
||||
fmt += "a(d";
|
||||
if(i != isize(coef) - 1)
|
||||
fmt += "+" + its(isize(coef) - 1 - i);
|
||||
fmt += ")";
|
||||
first = false;
|
||||
}
|
||||
fmt += " (d>" + its(valid_from-1) + ")";
|
||||
println(hlog, fmt);
|
||||
}
|
||||
}
|
||||
|
||||
color_t tcolors[3] = { 0xFF0000FF, 0x00FF00FF, 0x0000FFFF };
|
||||
|
||||
|
||||
bool draw_ptriangle(cell *c, const transmatrix& V) {
|
||||
|
||||
if(!mkr) { mkr = new trianglemaker; mkr->init();
|
||||
growthrate();
|
||||
}
|
||||
|
||||
for(auto& td: mkr->tds[c]) {
|
||||
mkr->compute(td, c);
|
||||
for(int side=0; side<6; side++) {
|
||||
auto &s = queuepoly(V * nisot::translate(td.at), mkr->ptriangle[side], magiccolors[side]);
|
||||
ensure_vertex_number(*s.tinf, s.cnt);
|
||||
|
||||
/* auto& s1 = queuepoly(V * nisot::translate(td.at), mkr->pcube[side], gradient(tcolors[td.tcolor], magiccolors[side], 0, .2, 1));
|
||||
ensure_vertex_number(*s1.tinf, s1.cnt); */
|
||||
}
|
||||
}
|
||||
|
||||
return false;
|
||||
}
|
||||
@ -290,6 +481,9 @@ auto hchook = addHook(hooks_drawcell, 100, draw_ptriangle)
|
||||
shift(); how1 = argi();
|
||||
shift(); isteps = argi();
|
||||
}
|
||||
else if(argis("-tri-net")) {
|
||||
net = true;
|
||||
}
|
||||
else return 1;
|
||||
return 0;
|
||||
});
|
||||
|
||||
Loading…
Reference in New Issue
Block a user