namespace hr { namespace arcm { #define SDEBUG(x) if(debug_geometry) { doindent(); x; fflush(stdout); } static const int sfPH = 1; static const int sfLINE = 2; static const int sfCHESS = 4; static const int sfTHREE = 8; static const int sfSEMILINE = 16; struct archimedean_tiling { int coloring; string symbol; vector faces; vector adj; vector invert; vector nflags; bool have_ph, have_line, have_symmetry; int real_faces; int real_face_type; int repetition; int N; ld euclidean_angle_sum; vector flags; vector>> adjacent; vector>> triangles; void make_match(int a, int i, int b, int j); void prepare(); void compute_geometry(); void parse(); void parse(string s) { symbol = s; parse(); } ld edgelength; vector inradius, circumradius, alphas; int matches[30][30]; int periods[30]; int tilegroup[30], groupoffset[30], tilegroups; int errors; string errormsg; pair& get_adj(heptagon *h, int cid); pair& get_adj(heptspin hs) { return get_adj(hs.at, hs.spin); } pair& get_triangle(heptagon *h, int cid); pair& get_triangle(heptspin hs) { return get_triangle(hs.at, hs.spin); } pair& get_triangle(const pair& p, int delta = 0); pair& get_adj(const pair& p, int delta = 0); int support_threecolor(); int support_threecolor_bitruncated(); int support_football(); bool support_chessboard(); void regroup(); string world_size(); eGeometryClass get_class(); ld scale(); }; archimedean_tiling current; // id of vertex in the archimedean tiling // odd numbers = reflected tiles // 0, 2, ..., 2(N-1) = as in the symbol // 2N = bitruncated tile short& id_of(heptagon *h) { return h->zebraval; } // which index in id_of's neighbor list does h->move[0] have short& parent_index_of(heptagon *h) { return h->emeraldval; } // total number of neighbors int neighbors_of(heptagon *h) { return isize(current.triangles[id_of(h)]); } int gcd(int x, int y) { return x ? gcd(y%x, x) : y < 0 ? -y : y; } void archimedean_tiling::make_match(int a, int i, int b, int j) { if(isize(adjacent[a]) != isize(adjacent[b])) { SDEBUG(printf("(error here)")); errormsg = XLAT("polygons match incorrectly"); errors++; } if(matches[a][b] == -1) matches[a][b] = j - i, matches[b][a] = i - j; else periods[a] = periods[b] = gcd(matches[a][b] - (j-i), periods[a]); } void archimedean_tiling::prepare() { euclidean_angle_sum = 0; for(int f: faces) euclidean_angle_sum += (f-2.) / f; for(int i: faces) if(i > MAX_EDGE) { errormsg = XLAT("currently no more than %1 edges", its(MAX_EDGE)); errors++; return; } if(isize(faces) > MAX_EDGE/2) { errormsg = XLAT("currently no more than %1 faces in vertex", its(MAX_EDGE)); errors++; return; } if(isize(faces) < 2) { errormsg = XLAT("not enough faces"); errors++; return; } for(int i: faces) if(i < 2) { errormsg = XLAT("not enough edges"); errors++; return; } real_faces = 0, real_face_type = 0; for(int i=0; i 2) real_faces++, real_face_type += faces[i]; real_face_type /= 2; if(real_faces) { for(int i=1; i [%d %d]\n", at, inv);) } } for(int i=0; i= isize(adjacent[ai])) aj = 0; } SDEBUG( printf("-> [%d %d]\n", ai, aj); ) make_match(i, j, ai, aj); } } for(int i=0; i<2*N; i++) { for(int j=0; j 2.000001) return gcHyperbolic; else return gcEuclid; } void archimedean_tiling::compute_geometry() { ginf[gArchimedean].cclass = get_class(); SDEBUG( printf("euclidean_angle_sum = %f\n", float(euclidean_angle_sum)); ) dynamicval dv(geometry, gArchimedean); /* compute the geometry */ inradius.resize(N); circumradius.resize(N); alphas.resize(N); ld elmin = 0, elmax = hyperbolic ? 10 : sphere ? M_PI : 1; if(real_faces == 2) { /* standard methods fail for dihedra, but the answer is easy */ edgelength = 2 * M_PI / faces[0]; for(int i=0; i edgelength) crmax = circumradius[i]; else crmin = circumradius[i]; } if(el < edgelength - 1e-3) alpha_total += 100; // could not make an edge that long hyperpoint h = xpush(edgelength/2) * xspinpush0(M_PI/2, inradius[i]); ld a = atan2(-h[1], h[0]); if(a < 0) a += 2 * M_PI; alphas[i] = a; // printf(" H = %s alp = %f\n", display(h), (float) atan2(-h[1], h[0])); alpha_total += alphas[i]; } // printf("el = %f alpha = %f\n", float(edgelength), float(alpha_total)); if(sphere ^ (alpha_total > M_PI)) elmin = edgelength; else elmax = edgelength; if(euclid) break; } SDEBUG( printf("computed edgelength = %f\n", float(edgelength)); ) triangles.clear(); triangles.resize(2*N+2); for(int i=0; i > > altmap; map> archimedean_gmatrix; hrmap *current_altmap; heptagon *build_child(heptspin p, pair adj); struct hrmap_archimedean : hrmap { heptagon *origin; heptagon *getOrigin() { return origin; } hrmap_archimedean() { int id = DUAL ? current.N * 2 : 0;; int N0 = isize(current.adjacent[id]); origin = tailored_alloc (N0); origin->s = hsOrigin; origin->emeraldval = 0; origin->zebraval = 0; origin->fiftyval = 0; origin->fieldval = 0; origin->rval0 = origin->rval1 = 0; origin->cdata = NULL; origin->alt = NULL; origin->distance = 0; parent_index_of(origin) = DUAL ? 1 : 0; id_of(origin) = id; origin->c7 = newCell(N0/DUALMUL, origin); heptagon *alt = NULL; if(hyperbolic) { dynamicval g(geometry, gNormal); alt = tailored_alloc (S7); alt->s = hsOrigin; alt->emeraldval = 0; alt->zebraval = 0; alt->distance = 0; alt->c7 = NULL; alt->alt = alt; alt->cdata = NULL; current_altmap = newAltMap(alt); } transmatrix T = xpush(.01241) * spin(1.4117) * xpush(0.1241) * Id; archimedean_gmatrix[origin] = make_pair(alt, T); altmap[alt].emplace_back(origin, T); if(current.real_faces == 0 && DUAL) { heptspin hs(origin, 0); heptagon *hnew = build_child(hs, current.get_adj(hs)); for(int s=1; s<2*current.N; s++) origin->c.connect(s, hnew, s, false); } else if(current.real_faces == 0) { create_adjacent(origin, 0); heptagon *o0 = origin->move(0); create_adjacent(origin, 1); heptagon *o1 = origin->move(1); for(int s=1; s<2*current.N; s+=2) o0->c.connect(s, o1, 2*current.N-s, false); for(int s=2; s<2*current.N; s+=2) { heptspin hs(o0, s); heptagon *hnew = build_child(hs, current.get_adj(hs)); // no need to specify archimedean_gmatrix and altmap hnew->c.connect(1, heptspin(o1, 2*current.N-s)); } o1->c.connect(1, o0, 2*current.N-1, false); } else if(origin->degree() == 2) { create_adjacent(origin, 0); create_adjacent(origin, 1); origin->move(0)->c.connect(1, origin->move(1), 2*current.N-1, false); origin->move(1)->c.connect(1, origin->move(0), 2*current.N-1, false); } base_distlimit = 0; celllister cl(origin->c7, 1000, 200, NULL); base_distlimit = cl.dists.back(); if(sphere) base_distlimit = 15; } ~hrmap_archimedean() { clearfrom(origin); altmap.clear(); archimedean_gmatrix.clear(); if(current_altmap) { dynamicval g(geometry, gNormal); delete current_altmap; current_altmap = NULL; } } void verify() { } }; hrmap *new_map() { return new hrmap_archimedean; } transmatrix adjcell_matrix(heptagon *h, int d); heptagon *build_child(heptspin p, pair adj) { indenter ind; auto h = buildHeptagon1(tailored_alloc (isize(current.adjacent[adj.first])), p.at, p.spin, hstate(1), 0); SDEBUG( printf("NEW %p.%d ~ %p.0\n", p.at, p.spin, h); ) id_of(h) = adj.first; parent_index_of(h) = adj.second; int nei = neighbors_of(h); h->c7 = newCell(nei/DUALMUL, h); h->distance = p.at->distance + 1; if(adj.first < 2*current.N && !DUAL) { int s = 0; heptspin hs(p); while(id_of(hs.at->move(0)) >= 2 * current.N) { s += hs.spin / 2 - 1; hs = hs - hs.spin + wstep - 1; } h->fieldval = hs.at->move(0)->fieldval + s + hs.spin/2; } else h->fieldval = -100; h->fiftyval = isize(archimedean_gmatrix); if(p.at->s == hsOrigin) h->rval1 = 1 + (p.spin % 2); else { if(p.spin % 2 == 0) h->rval1 = p.at->move(0)->rval1; else h->rval1 = 3 - p.at->move(0)->rval1 - p.at->rval1; } h->rval0 = hrand(256); heptspin hs(h, 0); return h; } bool skip_digons(heptspin hs, int step) { return isize(current.adjacent[current.get_adj(hs).first]) == 2 || isize(current.adjacent[current.get_adj(hs+step).first]) == 2; } void connect_digons_too(heptspin h1, heptspin h2) { if(skip_digons(h1, -1)) { h1--, h2++; heptagon *hnew = build_child(h1, current.get_adj(h1)); // no need to specify archimedean_gmatrix and altmap hnew->c.connect(1, h2); h1--, h2++; SDEBUG( printf("OL2 %p.%d ~ %p.%d\n", h1.at, h1.spin, h2.at, h2.spin); ) h1.at->c.connect(h1.spin, h2); } } void connectHeptagons(heptspin hi, heptspin hs) { SDEBUG( printf("OLD %p.%d ~ %p.%d\n", hi.at, hi.spin, hs.at, hs.spin); ) if(hi.at->move(hi.spin) == hs.at && hi.at->c.spin(hi.spin) == hs.spin) { SDEBUG( printf("WARNING: already connected\n"); ) return; } if(hi.peek()) { SDEBUG( printf("ERROR: already connected left\n"); ) exit(1); } if(hs.peek()) { SDEBUG( printf("ERROR: already connected right\n"); ) exit(1); } hi.at->c.connect(hi.spin, hs); auto p = current.get_adj(hi); if(current.tilegroup[p.first] != current.tilegroup[id_of(hs.at)]) { printf("should merge %d %d\n", p.first, id_of(hs.at)); current.make_match(p.first, p.second, id_of(hs.at), hs.spin + parent_index_of(hs.at)); current.regroup(); } // heptagon *hnew = build_child(h, d, get_adj(h, d).first, get_adj(h, d).second); } void create_adjacent(heptagon *h, int d) { SDEBUG( printf("%p.%d ~ ?\n", h, d); ) heptspin hi(h, d); while(skip_digons(hi, 1)) hi++; auto& t1 = current.get_triangle(hi); // * spin(-tri[id][pi+i].first) * xpush(t.second) * pispin * spin(tri[id'][p'+d'].first) auto& p = archimedean_gmatrix[h]; heptagon *alt = p.first; transmatrix T = p.second * spin(-t1.first) * xpush(t1.second); if(hyperbolic) { dynamicval g(geometry, gNormal); virtualRebaseSimple(alt, T); } if(euclid) alt = encodeId(pair_to_vec(int(T[0][2]), int(T[1][2]))); SDEBUG( printf("look for: %p / %s\n", alt, display(T * C0)); ) for(auto& p: altmap[alt]) if(intval(p.second * C0, T * C0) < 1e-4) { SDEBUG( printf("cell found: %p\n", p.first); ) for(int d2=0; d2degree(); d2++) { heptspin hs(p.first, d2); auto& t2 = current.get_triangle(p.first, d2); transmatrix T1 = T * spin(M_PI + t2.first); SDEBUG( printf("compare: %s", display(T1 * xpush0(1))); ) SDEBUG( printf(":: %s\n", display(p.second * xpush0(1))); ) if(intval(T1 * xpush0(1), p.second * xpush0(1)) < 1e-4) { while(skip_digons(hs, -1)) hs--; connectHeptagons(hi, hs); connect_digons_too(hi, hs); return; } } SDEBUG( printf("but rotation not found\n")); } auto& t2 = current.get_triangle(current.get_adj(hi)); transmatrix T1 = T * spin(M_PI + t2.first); fixmatrix(T1); heptagon *hnew = build_child(hi, current.get_adj(hi)); altmap[alt].emplace_back(hnew, T1); archimedean_gmatrix[hnew] = make_pair(alt, T1); connect_digons_too(hi, heptspin(hnew, 0)); } set visited; queue> drawqueue; void enqueue(heptagon *h, const transmatrix& T) { if(visited.count(h)) { return; } visited.insert(h); drawqueue.emplace(h, T); } pair& archimedean_tiling::get_triangle(heptagon *h, int cid) { return triangles[id_of(h)][(parent_index_of(h) + cid + MODFIXER) % neighbors_of(h)]; } pair& archimedean_tiling::get_adj(heptagon *h, int cid) { return adjacent[id_of(h)][(parent_index_of(h) + cid + MODFIXER) % neighbors_of(h)]; } pair& archimedean_tiling::get_adj(const pair& p, int delta) { return adjacent[p.first][(p.second + delta + MODFIXER) % isize(adjacent[p.first])]; } pair& archimedean_tiling::get_triangle(const pair& p, int delta) { return triangles[p.first][(p.second + delta + MODFIXER) % isize(adjacent[p.first])]; } transmatrix adjcell_matrix(heptagon *h, int d) { auto& t1 = current.get_triangle(h, d); heptagon *h2 = h->move(d); int d2 = h->c.spin(d); auto& t2 = current.get_triangle(h2, d2); return spin(-t1.first) * xpush(t1.second) * spin(M_PI + t2.first); } void draw() { visited.clear(); enqueue(viewctr.at, cview()); int idx = 0; while(!drawqueue.empty()) { auto p = drawqueue.front(); drawqueue.pop(); heptagon *h = p.first; transmatrix V = p.second; int id = id_of(h); int S = isize(current.triangles[id]); if(id < 2*current.N ? !DUAL : !PURE) { if(!dodrawcell(h->c7)) continue; drawcell(h->c7, V, 0, false); } for(int i=0; icmove(i); if(PURE && id >= 2*current.N && h->move(i) && id_of(h->move(i)) >= 2*current.N) continue; enqueue(h->move(i), V * adjcell_matrix(h, i)); } idx++; } } transmatrix relative_matrix(heptagon *h2, heptagon *h1) { if(gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7)) return inverse(gmatrix0[h1->c7]) * gmatrix0[h2->c7]; transmatrix gm = Id, where = Id; while(h1 != h2) { for(int i=0; imove(i) == h2) { return gm * adjcell_matrix(h1, i) * where; } } if(h1->distance > h2->distance) { gm = gm * adjcell_matrix(h1, 0); h1 = h1->move(0); } else { where = inverse(adjcell_matrix(h2, 0)) * where; h2 = h2->move(0); } } return gm * where; } int fix(heptagon *h, int spin) { int type = isize(current.adjacent[id_of(h)]); spin %= type; if(spin < 0) spin += type; return spin; } void archimedean_tiling::parse() { int at = 0; auto peek = [&] () { if(at == isize(symbol)) return char(0); else return symbol[at]; }; auto isnumber = [&] () { char p = peek(); return p >= '0' && p <= '9'; }; auto read_number = [&] () { int result = 0; while(isnumber()) result = 10 * result + peek() - '0', at++; return result; }; faces.clear(); nflags.clear(); have_line = false; have_ph = false; int nflags0; auto nfback = [this, &nflags0] () -> int& { if(nflags.empty()) return nflags0; else return nflags.back(); }; while(true) { if(peek() == ')' || (peek() == '(' && isize(faces)) || peek() == 0) break; else if((peek() == 'L') && faces.size()) { if(!nflags.empty()) nfback() |= sfLINE; have_line = true, at++; } else if((peek() == 'l') && faces.size()) { if(!nflags.empty()) nfback() |= sfSEMILINE; have_line = true, at++; } else if((peek() == 'H' || peek() == 'h') && faces.size()) { if(!nflags.empty()) nfback() |= sfPH; have_ph = true, at++; } else if(isnumber()) faces.push_back(read_number()), nflags.push_back(0); else if(peek() == '^' && !faces.empty()) { at++; int rep = read_number(); if(rep == 0) nflags.pop_back(), faces.pop_back(); for(int i=1; i 1 ? 1 : 0; return 2; } int archimedean_tiling::support_threecolor_bitruncated() { for(int i: faces) if(i % 2) return 0; return 2; } int archimedean_tiling::support_football() { return have_ph ? 1 : (isize(faces) == 3 && invert[0] && invert[1] && invert[2] && faces[1] % 2 == 0 && faces[2] % 2 == 0) ? 2 : 0; } bool archimedean_tiling::support_chessboard() { return N % 2 == 0; } bool pseudohept(cell *c) { if(DUAL) return !(c->master->rval0 & 3); int id = id_of(c->master); if(PURE) return current.flags[id] & arcm::sfPH; if(BITRUNCATED) return id < current.N * 2; return false; } bool chessvalue(cell *c) { if(DUAL) return c->master->rval1 - 1; return c->master->fieldval & 1; } bool linespattern(cell *c) { return current.flags[id_of(c->master)] & arcm::sfLINE; } int threecolor(cell *c) { if(current.have_ph) return !arcm::pseudohept(c); else if(PURE) return current.tilegroup[id_of(c->master)]; else { int id = id_of(c->master); if(current.support_threecolor() == 2) return id < current.N * 2 ? (id&1) : 2; return current.tilegroup[id]; } } int cEucRegular = 0x008000; int cEucSemiregular = 0x40C040; int cPlatonic = 0x000080; int cArchimedean = 0x4040C0; int cPrism = 0x40A0A0; int cAntiPrism = 0x80A0A0; int cHyperRegular = 0x800000; int cHyperSemi = 0xC04040; int cWeird = 0xA000A0; vector > samples = { /* Euclidean */ {"(3,3,3,3,3,3)", cEucRegular}, {"(4,4,4,4)", cEucRegular}, {"(6,6,6)", cEucRegular}, {"(8,8,4)", cEucSemiregular}, {"(4,6,12)", cEucSemiregular}, {"(6,4,3,4)", cEucSemiregular}, {"(3,6,3,6)", cEucSemiregular}, {"(3,12,12)", cEucSemiregular}, {"(4,4,3L,3L,3L) [3,4]", cEucSemiregular}, {"(3,3,3,3,6) (1,2)(0,4)(3)", cEucSemiregular}, {"(3,3,4,3,4) (0,4)(1)(2,3)", cEucSemiregular}, /* Platonic */ {"(3,3,3)", cPlatonic}, {"(3,3,3,3)", cPlatonic}, {"(3,3,3,3,3)", cPlatonic}, {"(4,4,4)", cPlatonic}, {"(5,5,5)", cPlatonic}, /* Archimedean solids */ {"(3,6,6)", cArchimedean}, {"(3,4,3,4)", cArchimedean}, {"(3,8,8)", cArchimedean}, {"(4,6,6)", cArchimedean}, {"(3,4,4,4)", cArchimedean}, {"(4,6,8)", cArchimedean}, {"(3,3,3,3,4) (1,2)(0,4)(3)", cArchimedean}, {"(3,5,3,5)", cArchimedean}, {"(3,10,10)", cArchimedean}, {"(5,6,6)", cArchimedean}, {"(3,4,5,4)", cArchimedean}, {"(4,6,10)", cArchimedean}, {"(3,3,3,3,5) (1,2)(0,4)(3)", cArchimedean}, /* prisms */ {"(3,4,4)", cPrism}, {"(5,4,4)", cPrism}, {"(6,4,4)", cPrism}, {"(7,4,4)", cPrism}, /* sample antiprisms */ {"(3,3,3,4)(1)(2)", cAntiPrism}, {"(3,3,3,5)(1)(2)", cAntiPrism}, {"(3,3,3,6)(1)(2)", cAntiPrism}, {"(3,3,3,7)(1)(2)", cAntiPrism}, /* hyperbolic ones */ {"(3)^7", cHyperRegular}, {"(4)^5", cHyperRegular}, {"(4)^6", cHyperRegular}, {"(5,5,5,5)", cHyperRegular}, {"(7,7,7)", cHyperRegular}, {"(8,8,8)", cHyperRegular}, {"(7,6^2)", cHyperSemi}, {"(4,6,14)", cHyperSemi}, {"(3,4,7,4)", cHyperSemi}, {"(6,6,4L,4L)", cHyperSemi}, {"(8,8,4L,4L)", cHyperSemi}, {"(3,3,3,3,7) (1,2)(0,4)(3)", cHyperSemi}, {"(3H,6,6,6) (1,0)[2](3)", cHyperSemi}, {"(3,6,6,6) (0 1)(2)(3)", cHyperSemi}, {"(3,4,4L,4L,4)", cHyperSemi}, // buggy {"(3l,4l,4,4,4) (0 1)[2 3](4)", cHyperSemi}, {"(3,4,4,4,4) (0 1)(2)(3)(4)", cHyperSemi}, {"(3,4,4L,4L,4L,4)", cHyperSemi}, {"(6,6,3L,3L,3L) (0 2)(1)(3)(4)", cHyperSemi}, {"(5,3,5,3,3) (0 1)(2 3)(4)", cHyperSemi}, {"(4,3,3,3,3,3) (0 1)(2 3)(4 5)", cHyperSemi}, {"(3l,5l,5,5,5,5) (0 1)[2 3](4)(5)", cHyperSemi}, {"(3,5,5,5,5,5) (0 1)(2 4)(3 5)", cHyperSemi}, {"(3l,5l,5,5,5,5) (0 1)(2 4)[3 5]", cHyperSemi}, {"(3l,5l,5,5,5,5) (0 1)[2 4](3)(5)", cHyperSemi}, {"(3,5,5,5,5,5) (0 1)(2)(3)(4)(5)", cHyperSemi}, /* interesting symmetry variants */ {"(3,3,3,3,3,3) (0,1)(2,3)(4,5)", cEucRegular}, {"(3,3H,3,3,3L,3L,3L) (0 4)(1 2)(3)(5)(6)", cHyperRegular}, {"(3,3H,3,3,3L,3L,3L) (0 4)(1 2)(3)[5 6]", cHyperRegular}, {"(3,3H,3,3L,3,3L,3L) [0 4](1 2)[3 5](6)", cHyperRegular}, /* with digons */ {"(2,3,3,3,3,3) (2,3)(4,5)", cWeird}, {"(6,6)", cWeird}, {"(2,2)", cWeird}, {"(2,2,2,2,2,2)", cWeird}, {"(6,6,2)", cWeird}, {"(6,2,6,2)", cWeird}, }; int lastsample = 0; vector tilings; int spos = 0; int editpos = 0; archimedean_tiling edited; bool symbol_editing; void next_variation() { set_variation( PURE ? eVariation::dual : DUAL ? eVariation::bitruncated : eVariation::pure); need_reset_geometry = true; start_game(); } void enable(archimedean_tiling& arct) { stop_game(); if(!archimedean) set_variation(eVariation::pure); set_geometry(gArchimedean); patterns::whichPattern = patterns::PAT_NONE; current = arct; #if CAP_TEXTURE if(texture::config.tstate == texture::tsActive && texture::cgroup == cpThree) { patterns::whichPattern = patterns::PAT_COLORING; if(geosupport_threecolor() < 2) { if(arct.support_threecolor() == 2) set_variation(eVariation::pure); else if(arct.support_threecolor_bitruncated() == 2) set_variation(eVariation::bitruncated); } } if(texture::config.tstate == texture::tsActive && texture::cgroup == cpFootball) { patterns::whichPattern = patterns::PAT_TYPES, patterns::subpattern_flags = patterns::SPF_FOOTBALL; if(geosupport_football() < 2) set_variation(eVariation::bitruncated); } if(texture::config.tstate == texture::tsActive && texture::cgroup == cpChess) { patterns::whichPattern = patterns::PAT_CHESS; if(!geosupport_chessboard()) { if(arct.support_chessboard()) set_variation(eVariation::pure); else if(arct.support_threecolor_bitruncated() == 2) set_variation(eVariation::dual); } } #endif need_reset_geometry = true; start_game(); } void show() { if(lastsample < isize(samples)) { string s = samples[lastsample].first; int col = samples[lastsample].second; lastsample++; archimedean_tiling tested; tested.parse(s); if(tested.errors) { printf("WARNING: %d errors on %s '%s'\n", tested.errors, s.c_str(), tested.errormsg.c_str()); } else { tested.coloring = col; tilings.push_back(move(tested)); /* sort(tilings.begin(), tilings.end(), [] (archimedean_tiling& s1, archimedean_tiling& s2) { if(s1.euclidean_angle_sum < s2.euclidean_angle_sum - 1e-6) return true; if(s2.euclidean_angle_sum < s1.euclidean_angle_sum - 1e-6) return false; return s1.symbol < s2.symbol; }); */ } } cmode = sm::SIDE | sm::MAYDARK; gamescreen(0); dialog::init(XLAT("Archimedean tilings")); if(symbol_editing) { string cs = edited.symbol; if(editpos < 0) editpos = 0; if(editpos > isize(cs)) editpos = isize(cs); cs.insert(editpos, "°"); dialog::addSelItem("edit", cs, '/'); dialog::add_action([] () { symbol_editing = false; if(!edited.errors) enable(edited); }); dialog::addBreak(100); if(edited.errors) dialog::addInfo(edited.errormsg, 0xFF0000); else dialog::addInfo(XLAT("OK"), 0x00FF00); dialog::addBreak(100); dialog::addSelItem(XLAT("full angle"), fts(edited.euclidean_angle_sum * 180) + "°", 0); dialog::addSelItem(XLAT("size of the world"), edited.world_size(), 0); edited.compute_geometry(); dialog::addSelItem(XLAT("edge length"), fts(edited.edgelength) + (edited.get_class() == gcEuclid ? XLAT(" (arbitrary)") : ""), 0); current.compute_geometry(); dialog::addBreak(100); } else { string cs = archimedean ? current.symbol : XLAT("OFF"); dialog::addSelItem("edit", cs, '/'); dialog::add_action([] () { symbol_editing = true; edited = current; editpos = isize(current.symbol); edited.parse(); }); dialog::addBreak(100); int nextpos = spos; int shown = 0; while(nextpos < isize(tilings) && shown < 10) { auto &ps = tilings[nextpos++]; bool valid = true; string suffix = ""; #if CAP_TEXTURE if(texture::config.tstate == texture::tsActive && texture::cgroup == cpThree) { valid = false; if(ps.support_threecolor() == 2) valid = true, suffix += bitruncnames[int(eVariation::pure)]; if(ps.support_threecolor_bitruncated() == 2) valid = true, suffix += bitruncnames[int(eVariation::bitruncated)]; } if(texture::config.tstate == texture::tsActive && texture::cgroup == cpFootball) { if(ps.support_football() == 2) suffix += bitruncnames[int(eVariation::pure)]; suffix += bitruncnames[int(eVariation::bitruncated)]; } if(texture::config.tstate == texture::tsActive && texture::cgroup == cpChess && !ps.support_chessboard()) { valid = false; if(ps.support_chessboard()) valid = true, suffix += bitruncnames[int(eVariation::pure)]; if(ps.support_threecolor_bitruncated() == 2) valid = true, suffix += bitruncnames[int(eVariation::dual)]; } #endif if(!valid) continue; dialog::addSelItem(ps.symbol, fts(ps.euclidean_angle_sum * 180) + "°" + suffix, 'a' + shown); dialog::lastItem().color = ps.coloring; dialog::add_action([&] () { enable(ps); }); shown++; } dialog::addItem(XLAT("next page"), '-'); if(shown == 0) nextpos = 0; dialog::add_action([nextpos] () { if(nextpos >= isize(tilings)) spos = 0; else spos = nextpos; }); dialog::addItem(XLAT("previous page"), '='); dialog::add_action([] () { spos -= 10; if(spos < 0) spos = 0; }); auto setcanvas = [] (char c) { return [c] () { stop_game(); firstland = specialland = laCanvas; patterns::whichCanvas = c; start_game(); }; }; if(archimedean) { dialog::addSelItem(XLAT("size of the world"), current.world_size(), 0); dialog::addSelItem(XLAT("edge length"), current.get_class() == gcEuclid ? (fts(current.edgelength) + XLAT(" (arbitrary)")) : fts6(current.edgelength), 0); dialog::addItem(XLAT("color by symmetries"), 't'); dialog::add_action(setcanvas('A')); } else { dialog::addBreak(100); dialog::addBreak(100); dialog::addBreak(100); } if(true) { dialog::addItem(XLAT("color by sides"), 'u'); dialog::add_action(setcanvas('B')); } if(geosupport_threecolor() == 2) { dialog::addItem(XLAT("three colors"), 'w'); dialog::add_action(setcanvas('T')); } else if(geosupport_football() == 2) { dialog::addItem(XLAT("football"), 'w'); dialog::add_action(setcanvas('F')); } else if(geosupport_chessboard()) { dialog::addItem(XLAT("chessboard"), 'w'); dialog::add_action(setcanvas('c')); } else dialog::addBreak(100); if(archimedean) { dialog::addSelItem(XLAT("variations"), gp::operation_name(), 'v'); dialog::add_action(next_variation); } else dialog::addBreak(100); } dialog::addHelp(); dialog::addBack(); dialog::display(); keyhandler = [] (int sym, int uni) { if(symbol_editing && sym == SDLK_RETURN) sym = uni = '/'; if(sym == SDLK_LEFT) editpos--; if(sym == SDLK_RIGHT) editpos++; dialog::handleNavigation(sym, uni); if(symbol_editing && uni == 8) { if(editpos == 0) return; edited.symbol.replace(editpos-1, 1, ""); editpos--; edited.parse(edited.symbol); return; } if(symbol_editing && uni >= 32 && uni < 128) { edited.symbol.insert(editpos, 1, uni); editpos++; edited.parse(edited.symbol); return; } if(doexiton(sym, uni)) popScreen(); }; } string archimedean_tiling::world_size() { if(get_class() == gcEuclid) return "∞"; int nom = 2 - N, denom = 2; for(int f: faces) { int g = gcd(denom, f); nom = (nom * f + denom) / g; denom = denom / g * f; } int anom = 0, adenom = 1; if(BITRUNCATED || DUAL) anom = 1, adenom = 1; if(!DUAL) for(int f: faces) { int g = gcd(adenom, f); anom = (anom * f + adenom) / g; adenom = adenom / g * f; } anom *= 2 * denom, adenom *= nom; int g = gcd(anom, adenom); anom /= g; adenom /= g; if(adenom < 0) anom = -anom, adenom = -adenom; string s; bool hyp = (anom < 0); if(hyp) anom = -anom; if(adenom > 1) s += its(anom) + "/" + its(adenom); else s += its(anom); if(hyp) s += " exp(∞)"; return s; } int degree(heptagon *h) { return isize(current.adjacent[id_of(h)]); } bool is_vertex(heptagon *h) { return id_of(h) >= 2 * current.N; } int valence() { if(PURE) return arcm::current.N; if(BITRUNCATED) return 3; // in DUAL, usually valence would depend on the vertex. // 3 is the most interesting, as it allows us to kill hedgehog warriors int total = 0; for(int i: current.faces) { if(i == 3) return 3; total += i; } return total / isize(current.faces); } } }