namespace hr { namespace gp { loc operator+(loc e1, loc e2) { return make_pair(e1.first+e2.first, e1.second+e2.second); } loc operator-(loc e1, loc e2) { return make_pair(e1.first-e2.first, e1.second-e2.second); } loc operator*(loc e1, loc e2) { return make_pair(e1.first*e2.first-e1.second*e2.second, e1.first*e2.second + e2.first*e1.second + (S3 == 3 ? e1.second*e2.second : 0)); } loc operator*(loc e1, int i) { return loc(e1.first*i, e1.second*i); } loc eudir(int d) { if(S3 == 3) { d %= 6; if (d < 0) d += 6; switch(d) { case 0: return make_pair(1, 0); case 1: return make_pair(0, 1); case 2: return make_pair(-1, 1); case 3: return make_pair(-1, 0); case 4: return make_pair(0, -1); case 5: return make_pair(1, -1); default: return make_pair(0, 0); } } else switch(d&3) { case 0: return make_pair(1, 0); case 1: return make_pair(0, 1); case 2: return make_pair(-1, 0); case 3: return make_pair(0, -1); default: return make_pair(0, 0); } } int length(loc p) { return eudist(p.first, p.second); } #if CAP_GP loc param(1, 0); hyperpoint next; struct goldberg_mapping_t { cellwalker cw; signed char rdir; signed char mindir; loc start; }; int fixg6(int x) { return (x + MODFIXER) % SG6; } int get_code(const local_info& li) { return ((li.relative.first & 15) << 0) + ((li.relative.second & 15) << 4) + ((fixg6(li.total_dir)) << 8) + ((li.last_dir & 15) << 12); } local_info get_local_info(cell *c) { local_info li; if(c == c->master->c7) { li.relative = loc(0,0); li.first_dir = -1; li.last_dir = -1; li.total_dir = -1; } else { vector dirs; while(c != c->master->c7) { dirs.push_back(c->c.spin(0)); c = c->move(0); } li.first_dir = dirs[0]; li.last_dir = dirs.back(); loc at(0,0); int dir = 0; at = at + eudir(dir); dirs.pop_back(); while(dirs.size()) { dir += dirs.back() + SG3; dirs.pop_back(); at = at + eudir(dir); } li.relative = at; li.total_dir = dir + SG3; } return li; } int last_dir(cell *c) { return get_local_info(c).last_dir; } loc get_coord(cell *c) { return get_local_info(c).relative; } int pseudohept_val(cell *c) { loc v = get_coord(c); return (v.first - v.second + MODFIXER)%3; } // mapping of the local equilateral triangle // goldberg_map[y][x].cw is the cellwalker in this triangle at position (x,y) // facing local direction 0 goldberg_mapping_t goldberg_map[32][32]; void clear_mapping() { for(int y=0; y<32; y++) for(int x=0; x<32; x++) { goldberg_map[y][x].cw.at = NULL; goldberg_map[y][x].rdir = -1; goldberg_map[y][x].mindir = 0; } } goldberg_mapping_t& get_mapping(loc c) { return goldberg_map[c.second&31][c.first&31]; } int spawn; cell*& peek(cellwalker cw) { return cw.at->move(cw.spin); } cellwalker get_localwalk(const goldberg_mapping_t& wc, int dir) { if(dir < wc.mindir) dir += SG6; if(dir >= wc.mindir + SG6) dir -= SG6; return wc.cw + dir; } void set_localwalk(goldberg_mapping_t& wc, int dir, const cellwalker& cw) { if(dir < wc.mindir) dir += SG6; if(dir >= wc.mindir + SG6) dir -= SG6; wc.cw = cw - dir; } bool pull(loc at, int dir) { auto& wc = get_mapping(at); auto at1 = at + eudir(dir); int dir1 = fixg6(dir+SG3); cellwalker wcw = get_localwalk(wc, dir); auto& wc1= get_mapping(at1); if(wc1.cw.at) { if(peek(wcw)) { auto wcw1 = get_localwalk(wc1, dir1); if(wcw + wstep != wcw1) { DEBB(DF_GP, (at1, " : ", (wcw+wstep), " / ", wcw1, " (pull error from ", at, " :: ", wcw, ")") ); exit(1); } } return false; } if(peek(wcw)) { set_localwalk(wc1, dir1, wcw + wstep); DEBB(DF_GP, (at1, " :", wcw+wstep, " (pulled from ", at, " :: ", wcw, ")")); return true; } return false; } void conn1(loc at, int dir, int dir1) { auto& wc = get_mapping(at); auto wcw = get_localwalk(wc, dir); auto& wc1 = get_mapping(at + eudir(dir)); DEBB0(DF_GP, (format(" md:%02d s:%d", wc.mindir, wc.cw.spin)); ) DEBB0(DF_GP, (" connection ", at, "/", dir, " ", wc.cw+dir, "=", wcw, " ~ ", at+eudir(dir), "/", dir1); ) if(!wc1.cw.at) { wc1.start = wc.start; if(peek(wcw)) { DEBB0(DF_GP, ("(pulled) "); ) set_localwalk(wc1, dir1, wcw + wstep); } else { peek(wcw) = newCell(SG6, wc.cw.at->master); wcw.at->c.setspin(wcw.spin, 0, false); set_localwalk(wc1, dir1, wcw + wstep); spawn++; DEBB0(DF_GP, ("(created) "); ) } } DEBB0(DF_GP, (wc1.cw+dir1, " ")); auto wcw1 = get_localwalk(wc1, dir1); if(peek(wcw)) { if(wcw+wstep != wcw1) { DEBB(DF_GP, ("FAIL: ", wcw, " / ", wcw1); exit(1); ) } else { DEBB(DF_GP, ("(was there)")); } } else { DEBB(DF_GP, ("ok")); peek(wcw) = wcw1.at; wcw.at->c.setspin(wcw.spin, wcw1.spin, wcw.mirrored != wcw1.mirrored); if(wcw+wstep != wcw1) { DEBB(DF_GP | DF_ERROR, ("assertion failed")); exit(1); } } } void conn(loc at, int dir) { conn1(at, fixg6(dir), fixg6(dir+SG3)); conn1(at + eudir(dir), fixg6(dir+SG3), fixg6(dir)); } goldberg_mapping_t& set_heptspin(loc at, heptspin hs) { auto& ac0 = get_mapping(at); ac0.cw = cellwalker(hs.at->c7, hs.spin, hs.mirrored); ac0.start = at; DEBB(DF_GP, (at, " : ", ac0.cw)); return ac0; } void extend_map(cell *c, int d) { DEBB(DF_GP, ("EXTEND ",c, " ", d)); if(c->master->c7 != c) { while(c->master->c7 != c) { DEBB(DF_GP, (c, " direction 0 corresponds to ", c->move(0), " direction ", c->c.spin(0)); ) d = c->c.spin(0); c = c->move(0); } // c move 0 equals c' move spin(0) extend_map(c, d); extend_map(c, fixdir(d-1, c)); extend_map(c, fixdir(d+1, c)); if(S3 == 4 && !c->move(d)) for(int i=0; imaster, i)->c7, j); return; } if(S3 == 4 && param.first <= param.second) { d--; if(d<0) d += S7; } clear_mapping(); // we generate a local map from an Euclidean grid to the // hyperbolic grid we build. // we fill the equilateral triangle with the following vertices: loc vc[4]; vc[0] = loc(0,0); vc[1] = param; if(S3 == 3) vc[2] = param * loc(0,1); else vc[2] = param * loc(1,1), vc[3] = param * loc(0,1); heptspin hs(c->master, d, false); auto& ac0 = set_heptspin(vc[0], hs); ac0.mindir = -1; auto& ac1 = set_heptspin(vc[1], hs + wstep - SG3); ac1.mindir = 0; auto& ac2 = set_heptspin(vc[S3-1], S3 == 3 ? hs + 1 + wstep - 4 : hs + 1 + wstep + 1); ac2.mindir = S3 == 3 ? 1 : -2; if(S3 == 4) { set_heptspin(vc[2], hs + wstep - 1 + wstep + 1).mindir = -3; } if(S3 == 4 && param == loc(1,1)) { conn(loc(0,0), 1); conn(loc(0,1), 0); conn(loc(0,1), 1); conn(loc(0,1), 2); conn(loc(0,1), 3); return; } if(nonorientable && param.first == param.second) { int x = param.first; if(ac1.cw.mirrored != hs.mirrored) ac1.cw--; if(ac2.cw.mirrored != hs.mirrored) ac2.cw--; for(int d=0; d<3; d++) for(int k=0; k<3; k++) for(int i=0; i= 2 && (S3 == 3 ? rel.first >= 2 - rel.second : true)) { build(start, 0, true); build(end, SG3, false); rel.first -= 2; } while(rel.second >= 2) { build(start, 1, true); build(end, 1+SG3, false); rel.second -= 2; } while(rel.second <= -2 && S3 == 3) { build(start, 5, true); build(end, 2, false); rel.second += 2; rel.first -= 2; } if(S3 == 3) while((rel.first>0 && rel.second > 0) | (rel.first > 1 && rel.second < 0)) { build(start, 0, true); build(end, 3, false); rel.first -= 2; } if(S3 == 4 && rel == loc(1,1)) { if(param == loc(3,1) || param == loc(5,1)) { build(start, 1, true); build(end, 2, false); rel.first--; rel.second--; } else { build(start, 0, true); build(end, 3, false); rel.first--; rel.second--; } } for(int k=0; kSG3) sp -= SG6; return normalize(spin(2*M_PI*sp/S7) * cornmul(T, corner)); } transmatrix dir_matrix(int i) { cell cc; cc.type = S7; return spin(-cgi.gpdata->alpha) * build_matrix( C0, ddspin(&cc, i) * xpush0(cgi.tessf), ddspin(&cc, i+1) * xpush0(cgi.tessf), C03 ); } void prepare_matrices() { cgi.gpdata->corners = inverse(build_matrix( loctoh_ort(loc(0,0)), loctoh_ort(param), loctoh_ort(param * loc(0,1)), C03 )); for(int i=0; icorners, at, 6); hyperpoint hl = atz(T, cgi.gpdata->corners, at + eudir(d), 6); cgi.gpdata->Tf[i][x&31][y&31][d] = rgpushxto0(h) * rspintox(gpushxto0(h) * hl) * spin(M_PI); } } } hyperpoint get_corner_position(const local_info& li, int cid, ld cf = 3) { int i = li.last_dir; if(i == -1) return atz(dir_matrix(cid), cgi.gpdata->corners, li.relative, 0, cf); else { auto& cellmatrix = cgi.gpdata->Tf[i][li.relative.first&31][li.relative.second&31][fixg6(li.total_dir)]; return inverse(cellmatrix) * atz(dir_matrix(i), cgi.gpdata->corners, li.relative, fixg6(cid + li.total_dir), cf); } } hyperpoint get_corner_position(cell *c, int cid, ld cf = 3) { return get_corner_position(get_local_info(c), cid, cf); } map, loc> center_locs; void compute_geometry() { center_locs.clear(); if(GOLDBERG) { if(!cgi.gpdata) cgi.gpdata = make_shared(); int x = param.first; int y = param.second; if(S3 == 3) cgi.gpdata->area = ((2*x+y) * (2*x+y) + y*y*3) / 4; else cgi.gpdata->area = x * x + y * y; next = point3(x+y/2., -y * sqrt(3) / 2, 0); ld scale = 1 / hypot_d(2, next); cgi.crossf *= scale; cgi.hepvdist *= scale; cgi.hexhexdist *= scale; cgi.hexvdist *= scale; cgi.rhexf *= scale; // spin = spintox(next); // ispin = rspintox(next); cgi.gpdata->alpha = -atan2(next[1], next[0]) * 6 / S7; if(S3 == 3) cgi.base_distlimit = (cgi.base_distlimit + log(scale) / log(2.618)) / scale; else cgi.base_distlimit = 3 * max(param.first, param.second) + 2 * min(param.first, param.second); if(S7 == 12) cgi.base_distlimit = 2 * param.first + 2 * param.second + 1; if(cgi.base_distlimit > SEE_ALL) cgi.base_distlimit = SEE_ALL; prepare_matrices(); DEBB(DF_GEOM | DF_POLY, ("scale = ", scale)); } } loc config; loc internal_representation(loc v) { int& x = v.first, &y = v.second; while(x < 0 || y < 0 || (x == 0 && y > 0)) v = v * loc(0, 1); if(x > 8) x = 8; if(y > 8) y = 8; if(S3 == 3 && y > x) v = v * loc(1, -1); return v; } loc human_representation(loc v) { int& x = v.first, &y = v.second; if(S3 == 3) while(x < 0 || y < 0 || (x == 0 && y > 0)) v = v * loc(0, 1); return v; } void whirl_set(loc xy) { xy = internal_representation(xy); if(xy.second && xy.second != xy.first && nonorientable) { addMessage(XLAT("This does not work in non-orientable geometries")); xy.second = 0; } config = human_representation(xy); auto g = screens; if(xy.first == 0 && xy.second == 0) xy.first = 1; if(xy.first == 1 && xy.second == 0) { stop_game(); set_variation(eVariation::pure); } else if(xy.first == 1 && xy.second == 1 && S3 == 3) { stop_game(); set_variation(eVariation::bitruncated); } else { param = xy; stop_game(); set_variation(eVariation::goldberg); } start_game(); screens = g; } string helptext() { return XLAT( "Goldberg polyhedra are obtained by adding extra hexagons to a dodecahedron. " "GP(x,y) means that, to get to a nearest non-hex from any non-hex, you should move x " "cells in any direction, turn right 60 degrees, and move y cells. " "HyperRogue generalizes this to any tesselation with 3 faces per vertex. " "By default HyperRogue uses bitruncation, which corresponds to GP(1,1)." ); } void show() { cmode = sm::SIDE | sm::MAYDARK; gamescreen(0); dialog::init(XLAT("variations")); int min_quality_chess = 0; int min_quality = 0; #if CAP_TEXTURE if((texture::config.tstate == texture::tsActive) && (S7 % 2 == 1)) { if(texture::cgroup == cpFootball || texture::cgroup == cpThree) min_quality = 1; } if((texture::config.tstate == texture::tsActive) && (S7 % 2 == 1) && (S3 == 4)) { if(texture::cgroup == cpChess) min_quality = 1; } #endif if(min_quality == 0 && min_quality_chess == 0) { dialog::addBoolItem(XLAT("pure"), param == loc(1,0) && !IRREGULAR, 'a'); dialog::lastItem().value = "GP(1,0)"; } if(min_quality_chess == 0) dialog::addBoolItem(XLAT("bitruncated"), param == loc(1,1) && BITRUNCATED, 'b'); dialog::lastItem().value = S3 == 3 ? "GP(1,1)" : XLAT(BITRUNCATED ? "ON" : "OFF"); if(min_quality == 0 || min_quality_chess) { dialog::addBoolItem(XLAT(S3 == 3 ? "chamfered" : "expanded"), param == loc(2,0), 'c'); dialog::lastItem().value = "GP(2,0)"; } if(S3 == 3) { dialog::addBoolItem(XLAT("2x bitruncated"), param == loc(3,0), 'd'); dialog::lastItem().value = "GP(3,0)"; } else { dialog::addBoolItem(XLAT("rectified"), param == loc(1,1) && GOLDBERG, 'd'); dialog::lastItem().value = "GP(1,1)"; } dialog::addBreak(100); dialog::addSelItem("x", its(config.first), 'x'); dialog::addSelItem("y", its(config.second), 'y'); if(config.second && config.second != config.first && nonorientable) { dialog::addInfo(XLAT("This does not work in non-orientable geometries")); } else if((config.first-config.second)%3 && min_quality) dialog::addInfo(XLAT("This pattern needs x-y divisible by 3")); else if((config.first-config.second)%2 && min_quality_chess) dialog::addInfo(XLAT("This pattern needs x-y divisible by 2")); else dialog::addBoolItem(XLAT("select"), param == internal_representation(config) && !IRREGULAR, 'f'); if(irr::supports(geometry)) { dialog::addBoolItem(XLAT("irregular"), IRREGULAR, 'i'); dialog::add_action(dialog::add_confirmation([=] () { if(min_quality && !irr::bitruncations_requested) irr::bitruncations_requested++; if(!IRREGULAR) irr::visual_creator(); })); } dialog::addBreak(100); dialog::addHelp(); dialog::addBack(); dialog::display(); keyhandler = [] (int sym, int uni) { dialog::handleNavigation(sym, uni); if(uni == 'a') dialog::do_if_confirmed([] { whirl_set(loc(1, 0)); }); else if(uni == 'b') dialog::do_if_confirmed([] { if(S3 == 4) { if(!BITRUNCATED) { stop_game(); set_variation(eVariation::bitruncated); start_game(); } } else whirl_set(loc(1, 1)); }); else if(uni == 'c') dialog::do_if_confirmed([] { whirl_set(loc(2, 0)); }); else if(uni == 'd') dialog::do_if_confirmed([] { whirl_set(S3 == 3 ? loc(3, 0) : loc(1,1)); }); else if(uni == 'f') dialog::do_if_confirmed([] { whirl_set(config); }); else if(uni == 'x') dialog::editNumber(config.first, 0, 8, 1, 1, "x", helptext()); else if(uni == 'y') dialog::editNumber(config.second, 0, 8, 1, 1, "y", helptext()); else if(uni == 'z') swap(config.first, config.second); else if(uni == '?' || sym == SDLK_F1 || uni == 'h' || uni == '2') gotoHelp(helptext()); else if(doexiton(sym, uni)) popScreen(); }; } loc univ_param() { if(GOLDBERG) return param; else if(PURE) return loc(1,0); else return loc(1,1); } void configure() { auto l = univ_param(); param = l; config = human_representation(l); pushScreen(gp::show); } void be_in_triangle(local_info& li) { int sp = 0; auto& at = li.relative; again: auto corner = cgi.gpdata->corners * loctoh_ort(at); if(corner[1] < -1e-6 || corner[2] < -1e-6) { at = at * eudir(1); sp++; goto again; } if(sp>SG3) sp -= SG6; li.last_dir = fix7(li.last_dir - sp); } // from some point X, (0,0) is in distance dmain, param is in distance d0, and param*z is in distance d1 // what is the distance of at from X? int solve_triangle(int dmain, int d0, int d1, loc at) { loc centerloc(0, 0); auto rel = make_pair(d0-dmain, d1-dmain); if(center_locs.count(rel)) centerloc = center_locs[rel]; else { bool found = false; for(int y=-20; y<=20; y++) for(int x=-20; x<=20; x++) { loc c(x, y); int cc = length(c); int c0 = length(c - param); int c1 = length(c - param*loc(0,1)); if(c0-cc == d0-dmain && c1-cc == d1-dmain) found = true, centerloc = c; } if(!found && !quotient) { println(hlog, "Warning: centerloc not found: ", make_tuple(dmain, d0, d1)); } center_locs[rel] = centerloc; } return dmain + length(centerloc-at) - length(centerloc); } int solve_quad(int dmain, int d0, int d1, int dx, loc at) { loc centerloc(0, 0); auto rel = make_pair(d0-dmain, (d1-dmain) + 1000 * (dx-dmain) + 1000000); if(center_locs.count(rel)) centerloc = center_locs[rel]; else { bool found = false; for(int y=-20; y<=20; y++) for(int x=-20; x<=20; x++) { loc c(x, y); int cc = length(c); int c0 = length(c - param); int c1 = length(c - param*loc(0,1)); int c2 = length(c - param*loc(1,1)); if(c0-cc == d0-dmain && c1-cc == d1-dmain && c2-cc == dx-dmain) found = true, centerloc = c; } if(!found && !quotient) { println(hlog, "Warning: centerloc not found: ", make_tuple(dmain, d0, d1, dx)); } center_locs[rel] = centerloc; } return dmain + length(centerloc-at) - length(centerloc); } hyperpoint get_master_coordinates(cell *c) { auto li = get_local_info(c); be_in_triangle(li); return cgi.gpdata->corners * loctoh_ort(li.relative); } int compute_dist(cell *c, int master_function(cell*)) { auto li = get_local_info(c); be_in_triangle(li); cell *cm = c->master->c7; int i = li.last_dir; auto at = li.relative; auto dmain = master_function(cm); auto d0 = master_function(createStep(cm->master, i)->c7); auto d1 = master_function(createStep(cm->master, fixdir(i+1, cm))->c7); if(S3 == 4) { heptspin hs(cm->master, i); hs += wstep; hs+=-1; hs += wstep; auto d2 = master_function(hs.at->c7); return solve_quad(dmain, d0, d1, d2, at); } return solve_triangle(dmain, d0, d1, at); } int dist_2() { return length(univ_param()); } int dist_3() { return length(univ_param() * loc(1,1)); } int dist_1() { return dist_3() - dist_2(); } #else int dist_1() { return 1; } int dist_2() { return BITRUNCATED ? 2 : 1; } int dist_3() { return BITRUNCATED ? 3 : 2; } #endif array get_masters(cell *c) { if(0); #if CAP_GP else if(GOLDBERG) { auto li = get_local_info(c); be_in_triangle(li); auto cm = c->master; int i = li.last_dir; return make_array(cm, createStep(cm, i), createStep(cm, fix7(i+1))); } #endif #if CAP_IRR else if(IRREGULAR) return irr::get_masters(c); #endif else return make_array(c->move(0)->master, c->move(2)->master, c->move(4)->master); } string operation_name() { if(0); #if CAP_IRR else if(IRREGULAR) return XLAT("irregular"); #endif else if(DUAL) return XLAT("dual"); else if(PURE) return XLAT("pure"); else if(BITRUNCATED) return XLAT("bitruncated"); #if CAP_GP else if(param == loc(1, 0)) return XLAT("pure"); else if(param == loc(1, 1) && S3 == 3) return XLAT("bitruncated"); else if(param == loc(1, 1) && S3 == 4) return XLAT("rectified"); else if(param == loc(2, 0)) return S3 == 3 ? XLAT("chamfered") : XLAT("expanded"); else if(param == loc(3, 0) && S3 == 3) return XLAT("2x bitruncated"); else { auto p = human_representation(param); return "GP(" + its(p.first) + "," + its(p.second) + ")"; } #else else return "UNSUPPORTED"; #endif } }}