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3d:: all the regular honeycombs
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Zeno Rogue
267
sphere.cpp
267
sphere.cpp
@@ -164,271 +164,4 @@ heptagon *getDodecahedron(int i) {
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return s->dodecahedron[i];
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}
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namespace sphere3 {
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vector<hyperpoint> vertices120;
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array<transmatrix, 120> vmatrix120;
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vector<int> adj0;
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array<array<int, 4>, 120> js;
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array<hyperpoint, 60> dodefaces;
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int opposite[120];
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hyperpoint zero4;
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int root;
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ld norm(hyperpoint a, hyperpoint b) {
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ld res = 0;
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for(int i=0; i<4; i++) res += pow(a[i]-b[i], 2);
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return res;
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}
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void gen600() {
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dynamicval<eGeometry> gp(geometry, gCell120);
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vertices120.clear();
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root = 23;
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/// coordinates taken from Wikipedia
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for(int a=0; a<16; a++) {
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hyperpoint v = zero4;
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for(int i=0; i<4; i++) v[i] = ((a >> i) & 1) ? .5 : -.5;
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vertices120.push_back(v);
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}
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for(int i=0; i<4; i++) for(int q: {-1, 1}) {
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hyperpoint v = zero4;
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v[i]=q;
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vertices120.push_back(v);
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}
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ld phi = (1 + sqrt(5)) / 2;
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array<ld, 4> coo = make_array<ld>(1, phi, 1/phi, 0);
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// all permutations
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array<int, 4> tab;
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for(int i=0; i<4; i++) tab[i] = i;
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do {
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// check the permutation's sign
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auto tabs = tab;
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int inv = 0;
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for(int i=0; i<4; i++) while(tabs[i] != i) {
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swap(tabs[i], tabs[tabs[i]]);
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inv++;
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}
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if(inv&1) goto again;
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// 8 vertices for each permutation
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for(int sg=0; sg<8; sg++) {
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hyperpoint v;
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for(int i=0; i<4; i++)
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v[i] = (((sg >> tab[i])&1) ? 1 : -1) * coo[tab[i]]/2;
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vertices120.push_back(v);
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}
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again: ;
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}
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while(std::next_permutation(tab.begin(), tab.end()));
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if(isize(vertices120) != 120) {
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printf("error: wrong number of vertices\n");
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exit(1);
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}
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// we add edges between vertices which are close to each other
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// ((specifically in distance 1/phi/phi)
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bool inedge[120][120];
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for(int i=0; i<120; i++)
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for(int j=0; j<120; j++) {
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ld d = hdist(vertices120[i], vertices120[j]);
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inedge[i][j] = (i != j) && d < sqrt(.4);
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}
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vector<hyperpoint> cellvertices;
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for(int i=0; i<120; i++)
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for(int j=0; j<120; j++) if(inedge[i][j])
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for(int k=0; k<120; k++) if(inedge[i][k] && inedge[k][j])
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for(int l=0; l<120; l++) if(inedge[i][l] && inedge[j][l] && inedge[k][l]) {
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array<int, 4> ijkl = make_array(i, j, k, l);
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transmatrix T;
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for(int z=0; z<4; z++) set_column(T, z, vertices120[ijkl[z]]);
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if(det(T) > 0) js[i] = ijkl;
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}
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/* transmatrix src;
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for(int z=0; z<4; z++) set_column(src, z, vertices120[js[0][z]]); */
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for(int i=0; i<120; i++)
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for(int z=0; z<4; z++) set_column(vmatrix120[i], z, vertices120[js[i][z]]);
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for(int i=0; i<120; i++) {
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println(hlog, i, ": ", js[i], " -> ", vmatrix120[i]);
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println(hlog, vmatrix120[i] * hyperpoint(1,0,0,0), " should be ", vertices120[i]);
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}
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adj0.clear();
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for(int i=0; i<120; i++) if(inedge[root][i]) adj0.push_back(i);
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using namespace hyperpoint_vec;
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for(int i=0; i<6; i++) for(int j=i+1; j<12; j++) if(zero_d(3, vertices120[adj0[i]] + vertices120[adj0[j]]))
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swap(adj0[j], adj0[i+6]);
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for(int i=0; i<120; i++) for(int j=0; j<120; j++)
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if(hdist(vertices120[i], vertices120[j]) > 3)
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opposite[i] = j;
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using namespace hyperpoint_vec;
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int id = 0;
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for(int i=0; i<12; i++) {
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int ot = adj0[i];
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vector<int> pentagon;
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for(int j: adj0) if(inedge[ot][j]) pentagon.push_back(j);
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println(hlog, i, ": ", pentagon);
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int illegal = -1;
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int at = pentagon[0];
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for(int d=0; d<5; d++) {
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for(int s: pentagon) if(inedge[at][s] && s != illegal) {
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hyperpoint m = vertices120[root] + vertices120[ot] + vertices120[at] + vertices120[s];
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m = mid(m, m);
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println(hlog, id, ": ", m);
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dodefaces[id++] = m;
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illegal = at;
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at = s;
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break;
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}
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}
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}
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printf("id = %d\n", id);
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}
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bool goodside(int i) {
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if(!elliptic) return true;
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hyperpoint& h = vertices120[i];
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for(int k=3; k>=0; k--) {
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if(h[k] > 1e-3) return true;
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if(h[k] < -1e-3) return false;
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}
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return false;
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}
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struct hrmap_spherical3 : hrmap {
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heptagon* cells[120];
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hrmap_spherical3() {
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gen600();
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for(int i=0; i<120; i++) {
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if(!goodside(i)) {
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cells[i] = NULL;
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continue;
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}
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cells[i] = tailored_alloc<heptagon> (12);
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heptagon& h = *(cells[i]);
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h.s = hsOrigin;
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h.emeraldval = i;
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h.zebraval = i;
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h.fiftyval = i;
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h.rval0 = h.rval1 = 0;
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h.alt = NULL;
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h.cdata = NULL;
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h.c.fullclear();
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h.fieldval = i;
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h.c7 = newCell(12, &h);
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}
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for(int i=0; i<120; i++) if(cells[i]) {
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for(int k=0; k<12; k++) {
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hyperpoint which = vmatrix120[i] * inverse(vmatrix120[root]) * vertices120[adj0[k]];
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for(int s=0; s<120; s++) if(hdist(which, vertices120[s]) < 1e-6) {
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int s1 = s;
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if(!cells[s1]) continue;
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cells[i]->move(k) = cells[s1];
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println(hlog, i,".",k, " -> ", s1, " ; ", js[i], " distance = ", hdist(vertices120[i], vertices120[s]));
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}
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}
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}
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for(int i=0; i<120; i++)
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for(int k=0; k<12; k++)
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for(int l=0; l<12; l++)
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if(cells[i] && cells[i]->move(k)->move(l) == cells[i])
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cells[i]->c.setspin(k, l, false);
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}
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heptagon *getOrigin() { return cells[root]; }
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~hrmap_spherical3() {
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for(int i=0; i<120; i++) if(cells[i]) tailored_delete(cells[i]);
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}
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};
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transmatrix gmatr(heptagon *h) {
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return vmatrix120[h->zebraval] * inverse(vmatrix120[root]);
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}
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transmatrix relative_matrix(heptagon *h2, heptagon *h1) {
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return inverse(gmatr(h1)) * gmatr(h2);
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}
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bool pseudohept(cell *c) {
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return c->master->zebraval < 16;
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}
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void draw() {
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sphereflip = Id;
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auto m = (hrmap_spherical3*) currentmap;
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for(int i=0; i<120; i++) if(m->cells[i])
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drawcell(m->cells[i]->c7, View * relative_matrix(m->cells[i], viewctr.at), 0, false);
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}
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void makewax(int x) {
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int waxcenter = 63;
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auto m = (hrmap_spherical3*) currentmap;
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for(int i=0; i<120; i++) if(m->cells[i]) m->cells[i]->c7->wall = waNone;
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m->cells[waxcenter]->c7->wall = waDune;
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int cols[16] = {0x202020, 0x2020A0, 0x20A020, 0x20A0A0, 0xA02020, 0xA020A0, 0xA0A020, 0xA0A0A0,
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0x606060, 0x6060FF, 0x60FF60, 0x60FFFF, 0xFF6060, 0xFF60FF, 0xFFFF60, 0xFFFFFF };
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if(x) for(int i=0; i<12; i++) {
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m->cells[waxcenter]->c7->move(i)->wall = waWaxWall;
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m->cells[waxcenter]->c7->move(i)->landparam = cols[i];
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}
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}
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#if CAP_COMMANDLINE
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int readArgs() {
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using namespace arg;
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if(argis("-wax1")) {
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PHASE(3);
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start_game();
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makewax(1);
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}
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else if(argis("-wax0")) {
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PHASE(3);
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start_game();
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makewax(0);
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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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auto hook =
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addHook(hooks_args, 100, readArgs);
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#endif
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}
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}
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