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https://github.com/zenorogue/hyperrogue.git
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596 lines
17 KiB
C++
596 lines
17 KiB
C++
// Hyperbolic Rogue
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// advanced geometry
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// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details
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namespace hr {
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transmatrix &ggmatrix(cell *c);
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void fixelliptic(transmatrix& at) {
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if(elliptic && at[2][2] < 0) {
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for(int i=0; i<3; i++) for(int j=0; j<3; j++)
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at[i][j] = -at[i][j];
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}
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}
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void fixelliptic(hyperpoint& h) {
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if(elliptic && h[2] < 0)
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for(int i=0; i<3; i++) h[i] = -h[i];
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}
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transmatrix master_relative(cell *c, bool get_inverse) {
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if(IRREGULAR) {
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int id = irr::cellindex[c];
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ld alpha = 2 * M_PI / S7 * irr::periodmap[c->master].base.spin;
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return get_inverse ? irr::cells[id].rpusher * spin(-alpha-master_to_c7_angle()): spin(alpha + master_to_c7_angle()) * irr::cells[id].pusher;
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}
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else if(GOLDBERG) {
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if(c == c->master->c7) {
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return spin((get_inverse?-1:1) * master_to_c7_angle());
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}
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else {
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auto li = gp::get_local_info(c);
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transmatrix T = spin(master_to_c7_angle()) * gp::Tf[li.last_dir][li.relative.first&31][li.relative.second&31][gp::fixg6(li.total_dir)];
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if(get_inverse) T = inverse(T);
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return T;
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}
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}
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else if(BITRUNCATED && !euclid) {
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for(int d=0; d<S7; d++) if(c->master->c7->move(d) == c)
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return (get_inverse?invhexmove:hexmove)[d];
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return Id;
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}
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else
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return pispin * Id;
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}
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transmatrix calc_relative_matrix(cell *c2, cell *c1, int direction_hint) {
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return calc_relative_matrix(c2, c1, ddspin(c1, direction_hint) * xpush0(1e-2));
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}
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// target, source, direction from source to target
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namespace gp { extern gp::local_info draw_li; }
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transmatrix calc_relative_matrix(cell *c2, cell *c1, const hyperpoint& point_hint) {
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if(sphere_narcm) {
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if(!gmatrix0.count(c2) || !gmatrix0.count(c1)) {
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printf("building gmatrix0 (size=%d)\n", isize(gmatrix0));
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auto bak = gp::draw_li;
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swap(gmatrix, gmatrix0);
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just_gmatrix = true;
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drawStandard();
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just_gmatrix = false;
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swap(gmatrix, gmatrix0);
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gp::draw_li = bak;
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}
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if(gmatrix0.count(c2) && gmatrix0.count(c1)) {
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transmatrix T = inverse(gmatrix0[c1]) * gmatrix0[c2];
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if(elliptic && T[2][2] < 0)
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T = centralsym * T;
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return T;
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}
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else {
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printf("error: gmatrix0 not known\n");
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return Id;
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}
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}
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if(binarytiling) return binary::relative_matrix(c2->master, c1->master);
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if(archimedean) return arcm::relative_matrix(c2->master, c1->master);
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if(euwrap) {
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transmatrix t = Id;
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// if(whateveri) printf("[%p,%d] ", c2, celldistance(c2, c1));
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int d = celldistance(c2, c1);
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while(d) {
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forCellIdEx(cc, i, c1) {
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int d1 = celldistance(cc, c2);
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if(d1 < d) {
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t = t * cellrelmatrix(c1, i);
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c1 = cc;
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d = d1;
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goto again;
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}
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}
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printf("ERROR not reached\n");
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break;
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again: ;
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}
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return t;
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}
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if(euclid)
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return eumove(cell_to_vec(c2) - cell_to_vec(c1));
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heptagon *h1 = c1->master;
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transmatrix gm = master_relative(c1, true);
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heptagon *h2 = c2->master;
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transmatrix where = master_relative(c2);
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// always add to last!
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//bool hsol = false;
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//transmatrix sol;
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set<heptagon*> visited;
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map<ld, vector<pair<heptagon*, transmatrix>>> hbdist;
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int steps = 0;
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while(h1 != h2) {
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steps++; if(steps > 10000) {
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println(hlog, "not found"); return Id;
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}
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if(bounded) {
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transmatrix T;
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ld bestdist = 1e9;
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for(int d=0; d<S7; d++) if(h2->move(d)) {
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int sp = h2->c.spin(d);
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transmatrix S = heptmove[sp] * spin(2*M_PI*d/S7);
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if(h2->c.mirror(d)) S = heptmove[sp] * Mirror * spin(2*M_PI*d/S7);
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if(h2->move(d) == h1) {
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transmatrix T1 = gm * S * where;
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auto curdist = hdist(tC0(T1), point_hint);
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if(curdist < bestdist) T = T1, bestdist = curdist;
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}
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if(geometry != gMinimal) for(int e=0; e<S7; e++) if(h2->move(d)->move(e) == h1) {
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int sp2 = h2->move(d)->c.spin(e);
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transmatrix T1 = gm * heptmove[sp2] * spin(2*M_PI*e/S7) * S * where;
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auto curdist = hdist(tC0(T1), point_hint);
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if(curdist < bestdist) T = T1, bestdist = curdist;
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}
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}
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if(bestdist < 1e8) return T;
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}
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for(int d=0; d<S7; d++) if(h2->move(d) == h1) {
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int sp = h2->c.spin(d);
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return gm * heptmove[sp] * spin(2*M_PI*d/S7) * where;
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}
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if(among(geometry, gFieldQuotient, gBring, gMacbeath)) {
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int bestdist = 1000000, bestd = 0;
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for(int d=0; d<S7; d++) {
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int dist = celldistance(h2->cmove(d)->c7, c1);
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if(dist < bestdist) bestdist = dist, bestd = d;
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}
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int sp = h2->c.spin(bestd);
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where = heptmove[sp] * spin(2*M_PI*bestd/S7) * where;
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h2 = h2->move(bestd);
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}
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else if(geometry == gCrystal) {
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for(int d3=0; d3<S7; d3++) {
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auto h3 = h2->cmove(d3);
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if(visited.count(h3)) continue;
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visited.insert(h3);
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int sp3 = h2->c.spin(d3);
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transmatrix where3 = heptmove[sp3] * spin(2*M_PI*d3/S7) * where;
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ld dist = crystal::space_distance(h3->c7, c1);
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hbdist[dist].emplace_back(h3, where3);
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}
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auto &bestv = hbdist.begin()->second;
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tie(h2, where) = bestv.back();
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bestv.pop_back();
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if(bestv.empty()) hbdist.erase(hbdist.begin());
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}
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else if(h1->distance < h2->distance) {
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int sp = h2->c.spin(0);
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h2 = h2->move(0);
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where = heptmove[sp] * where;
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}
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else {
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int sp = h1->c.spin(0);
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h1 = h1->move(0);
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gm = gm * invheptmove[sp];
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}
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}
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/*if(hsol) {
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transmatrix sol2 = gm * where;
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for(int i=0; i<3; i++) for(int j=0; j<3; j++)
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if(fabs(sol2[i][j]-sol[i][j] > 1e-3)) {
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printf("ERROR\n");
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display(sol);
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display(sol2);
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exit(1);
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}
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} */
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return gm * where;
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}
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transmatrix &ggmatrix(cell *c) {
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transmatrix& t = gmatrix[c];
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if(t[2][2] == 0) {
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if(euwrap && centerover.at)
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t = calc_relative_matrix(c, centerover.at, C0);
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else if(euclid) {
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if(!centerover.at) centerover = cwt;
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t = View * eumove(cell_to_vec(c) - cellwalker_to_vec(centerover));
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}
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else
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t = actualV(viewctr, cview()) * calc_relative_matrix(c, viewctr.at->c7, C0);
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}
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return t;
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}
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transmatrix calc_relative_matrix_help(cell *c, heptagon *h1) {
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transmatrix gm = Id;
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heptagon *h2 = c->master;
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transmatrix where = Id;
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if(GOLDBERG && c != c->master->c7) {
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auto li = gp::get_local_info(c);
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where = gp::Tf[li.last_dir][li.relative.first&31][li.relative.second&31][fix6(li.total_dir)];
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}
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else if(BITRUNCATED) for(int d=0; d<S7; d++) if(h2->c7->move(d) == c)
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where = hexmove[d];
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// always add to last!
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while(h1 != h2) {
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for(int d=0; d<S7; d++) if(h1->move(d) == h2) printf("(adj) ");
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if(h1->distance < h2->distance) {
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int sp = h2->c.spin(0);
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printf("A%d ", sp);
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h2 = h2->move(0);
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where = heptmove[sp] * where;
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}
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else {
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int sp = h1->c.spin(0);
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printf("B%d ", sp);
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h1 = h1->move(0);
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gm = gm * invheptmove[sp];
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}
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}
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println(hlog, "OK");
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println(hlog, gm * where);
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return gm * where;
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}
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template<class T, class U>
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void virtualRebase(cell*& base, T& at, bool tohex, const U& check) {
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if(euclid || sphere) {
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again:
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if(euwrap) for(int i=0; i<6; i++) {
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// fix cylinder and square grid
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auto newat = eumovedir(3+i) * at;
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if(hdist0(check(newat)) < hdist0(check(at))) {
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at = newat;
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base = createMov(base, i);
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goto again;
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}
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}
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else forCellCM(c2, base) {
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auto newat = inverse(ggmatrix(c2)) * ggmatrix(base) * at;
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if(hypot(check(newat)[0], check(newat)[1])
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< hypot(check(at)[0], check(at)[1])) {
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at = newat;
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base = c2;
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goto again;
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}
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}
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fixelliptic(at);
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return;
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}
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at = master_relative(base) * at;
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base = base->master->c7;
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while(true) {
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double currz = check(at)[2];
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heptagon *h = base->master;
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cell *newbase = NULL;
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transmatrix bestV;
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if(!binarytiling) for(int d=0; d<S7; d++) {
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heptspin hs(h, d, false);
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heptspin hs2 = hs + wstep;
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transmatrix V2 = spin(-hs2.spin*2*M_PI/S7) * invheptmove[d];
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double newz = check(V2 * at) [2];
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if(newz < currz) {
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currz = newz;
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bestV = V2;
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newbase = hs2.at->c7;
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}
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}
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if(newbase) {
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base = newbase;
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at = bestV * at;
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}
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else {
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if(tohex && BITRUNCATED) for(int d=0; d<S7; d++) {
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cell *c = createMov(base, d);
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transmatrix V2 = spin(-base->c.spin(d)*2*M_PI/S6) * invhexmove[d];
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double newz = check(V2 *at) [2];
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if(newz < currz) {
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currz = newz;
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bestV = V2;
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newbase = c;
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}
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}
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if(newbase) {
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base = newbase;
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at = bestV * at;
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}
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else at = master_relative(base, true) * at;
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if(binarytiling || (tohex && (GOLDBERG || IRREGULAR))) {
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while(true) {
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newbase = NULL;
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forCellCM(c2, base) {
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transmatrix V2 = calc_relative_matrix(base, c2, C0);
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double newz = check(V2 * at) [2];
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if(newz < currz) {
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currz = newz;
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bestV = V2;
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newbase = c2;
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}
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}
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if(!newbase) break;
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base = newbase;
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at = bestV * at;
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}
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}
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break;
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}
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}
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}
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void virtualRebase(cell*& base, transmatrix& at, bool tohex) {
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virtualRebase(base, at, tohex, tC0);
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}
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void virtualRebase(cell*& base, hyperpoint& h, bool tohex) {
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// we perform fixing in check, so that it works with larger range
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virtualRebase(base, h, tohex, [] (const hyperpoint& h) { return hyperbolic ? hpxy(h[0], h[1]) :h; });
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}
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// works only in geometries similar to the standard one, and only on heptagons
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void virtualRebaseSimple(heptagon*& base, transmatrix& at) {
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while(true) {
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double currz = at[2][2];
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heptagon *h = base;
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heptagon *newbase = NULL;
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transmatrix bestV;
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for(int d=0; d<S7; d++) {
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heptspin hs(h, d, false);
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heptspin hs2 = hs + wstep;
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transmatrix V2 = spin(-hs2.spin*2*M_PI/S7) * invheptmove[d] * at;
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double newz = V2[2][2];
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if(newz < currz) {
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currz = newz;
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bestV = V2;
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newbase = hs2.at;
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}
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}
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if(newbase) {
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base = newbase;
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at = bestV;
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continue;
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}
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return;
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}
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}
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double cellgfxdist(cell *c, int i) {
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if(euclid) {
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if(c->type == 8 && (i&1)) return eurad * sqrt(2);
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return eurad;
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}
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if(NONSTDVAR || archimedean) return hdist0(tC0(calc_relative_matrix(c->move(i), c, i)));
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return !BITRUNCATED ? tessf : (c->type == 6 && (i&1)) ? hexhexdist : crossf;
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}
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transmatrix cellrelmatrix(cell *c, int i) {
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if(NONSTDVAR || archimedean) return calc_relative_matrix(c->move(i), c, i);
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double d = cellgfxdist(c, i);
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transmatrix T = ddspin(c, i) * xpush(d);
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if(c->c.mirror(i)) T = T * Mirror;
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T = T * iddspin(c->move(i), c->c.spin(i), M_PI);
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return T;
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}
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double randd() { return (rand() + .5) / (RAND_MAX + 1.); }
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hyperpoint randomPointIn(int t) {
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if(NONSTDVAR || archimedean) {
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// Let these geometries be less confusing.
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// Also easier to implement ;)
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return xspinpush0(2 * M_PI * randd(), asinh(randd() / 20));
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}
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while(true) {
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hyperpoint h = xspinpush0(2*M_PI*(randd()-.5)/t, asinh(randd()));
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double d =
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PURE ? tessf : t == 6 ? hexhexdist : crossf;
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if(hdist0(h) < hdist0(xpush(-d) * h))
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return spin(2*M_PI/t * (rand() % t)) * h;
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}
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}
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hyperpoint get_horopoint(ld y, ld x) {
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return xpush(-y) * binary::parabolic(x) * C0;
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}
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hyperpoint get_corner_position(cell *c, int cid, ld cf) {
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if(GOLDBERG) return gp::get_corner_position(c, cid, cf);
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if(IRREGULAR) {
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auto& vs = irr::cells[irr::cellindex[c]];
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return mid_at_actual(vs.vertices[cid], 3/cf);
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}
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if(binarytiling) {
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ld yx = log(2) / 2;
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ld yy = yx;
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ld xx = 1 / sqrt(2)/2;
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hyperpoint vertices[7];
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vertices[0] = get_horopoint(-yy, xx);
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vertices[1] = get_horopoint(yy, 2*xx);
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vertices[2] = get_horopoint(yy, xx);
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vertices[3] = get_horopoint(yy, -xx);
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vertices[4] = get_horopoint(yy, -2*xx);
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vertices[5] = get_horopoint(-yy, -xx);
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vertices[6] = get_horopoint(-yy, 0);
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return mid_at_actual(vertices[cid], 3/cf);
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}
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if(archimedean) {
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auto &ac = arcm::current;
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if(PURE) {
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if(arcm::id_of(c->master) >= ac.N*2) return C0;
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auto& t = ac.get_triangle(c->master, cid-1);
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return xspinpush0(-t.first, t.second * 3 / cf * (ac.real_faces == 0 ? 0.999 : 1));
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}
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if(BITRUNCATED) {
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auto& t0 = ac.get_triangle(c->master, cid-1);
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auto& t1 = ac.get_triangle(c->master, cid);
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hyperpoint h0 = xspinpush0(-t0.first, t0.second * 3 / cf * (ac.real_faces == 0 ? 0.999 : 1));
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hyperpoint h1 = xspinpush0(-t1.first, t1.second * 3 / cf * (ac.real_faces == 0 ? 0.999 : 1));
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return mid3(C0, h0, h1);
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}
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if(DUAL) {
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auto& t0 = ac.get_triangle(c->master, 2*cid-1);
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return xspinpush0(-t0.first, t0.second * 3 / cf * (ac.real_faces == 0 ? 0.999 : 1));
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}
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}
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if(PURE) {
|
|
return ddspin(c,cid,M_PI/S7) * xpush0(hcrossf * 3 / cf);
|
|
}
|
|
if(BITRUNCATED) {
|
|
if(!ishept(c))
|
|
return ddspin(c,cid,M_PI/S6) * xpush0(hexvdist * 3 / cf);
|
|
else
|
|
return ddspin(c,cid,M_PI/S7) * xpush0(rhexf * 3 / cf);
|
|
}
|
|
return C0;
|
|
}
|
|
|
|
hyperpoint nearcorner(cell *c, int i) {
|
|
if(GOLDBERG) {
|
|
cellwalker cw(c, i);
|
|
cw += wstep;
|
|
transmatrix cwm = calc_relative_matrix(cw.at, c, i);
|
|
if(elliptic && cwm[2][2] < 0) cwm = centralsym * cwm;
|
|
return cwm * C0;
|
|
}
|
|
if(IRREGULAR) {
|
|
auto& vs = irr::cells[irr::cellindex[c]];
|
|
hyperpoint nc = vs.jpoints[vs.neid[i]];
|
|
return mid_at(C0, nc, .94);
|
|
}
|
|
if(archimedean) {
|
|
if(PURE) {
|
|
auto &ac = arcm::current;
|
|
auto& t = ac.get_triangle(c->master, i-1);
|
|
int id = arcm::id_of(c->master);
|
|
int id1 = ac.get_adj(ac.get_adj(c->master, i-1), -2).first;
|
|
return xspinpush0(-t.first - M_PI / c->type, ac.inradius[id/2] + ac.inradius[id1/2] + (ac.real_faces == 0 ? 2 * M_PI / (ac.N == 2 ? 2.1 : ac.N) : 0));
|
|
}
|
|
if(BITRUNCATED) {
|
|
auto &ac = arcm::current;
|
|
auto& t = ac.get_triangle(c->master, i);
|
|
return xspinpush0(-t.first, t.second);
|
|
}
|
|
if(DUAL) {
|
|
auto &ac = arcm::current;
|
|
auto& t = ac.get_triangle(c->master, i * 2);
|
|
return xspinpush0(-t.first, t.second);
|
|
}
|
|
}
|
|
if(binarytiling) {
|
|
ld yx = log(2) / 2;
|
|
ld yy = yx;
|
|
// ld xx = 1 / sqrt(2)/2;
|
|
hyperpoint neis[7];
|
|
neis[0] = get_horopoint(0, 1);
|
|
neis[1] = get_horopoint(yy*2, 1);
|
|
neis[2] = get_horopoint(yy*2, 0);
|
|
neis[3] = get_horopoint(yy*2, -1);
|
|
neis[4] = get_horopoint(0, -1);
|
|
if(c->type == 7)
|
|
neis[5] = get_horopoint(-yy*2, -.5),
|
|
neis[6] = get_horopoint(-yy*2, +.5);
|
|
else
|
|
neis[5] = get_horopoint(-yy*2, 0);
|
|
return neis[i];
|
|
}
|
|
double d = cellgfxdist(c, i);
|
|
return ddspin(c, i) * xpush0(d);
|
|
}
|
|
|
|
hyperpoint farcorner(cell *c, int i, int which) {
|
|
if(GOLDBERG) {
|
|
cellwalker cw(c, i);
|
|
int hint = cw.spin;
|
|
cw += wstep;
|
|
transmatrix cwm = calc_relative_matrix(cw.at, c, hint);
|
|
if(elliptic && cwm[2][2] < 0) cwm = centralsym * cwm;
|
|
// hyperpoint nfar = cwm*C0;
|
|
auto li1 = gp::get_local_info(cw.at);
|
|
if(which == 0)
|
|
return cwm * get_corner_position(li1, (cw+2).spin);
|
|
if(which == 1)
|
|
return cwm * get_corner_position(li1, (cw-1).spin);
|
|
}
|
|
if(IRREGULAR) {
|
|
auto& vs = irr::cells[irr::cellindex[c]];
|
|
int neid = vs.neid[i];
|
|
int spin = vs.spin[i];
|
|
auto &vs2 = irr::cells[neid];
|
|
int cor2 = isize(vs2.vertices);
|
|
transmatrix rel = vs.rpusher * vs.relmatrices[vs2.owner] * vs2.pusher;
|
|
|
|
if(which == 0) return rel * vs2.vertices[(spin+2)%cor2];
|
|
if(which == 1) return rel * vs2.vertices[(spin+cor2-1)%cor2];
|
|
}
|
|
if(binarytiling)
|
|
return nearcorner(c, (i+which) % c->type); // lazy
|
|
if(archimedean) {
|
|
if(PURE) {
|
|
auto &ac = arcm::current;
|
|
auto& t = ac.get_triangle(c->master, i-1);
|
|
int id = arcm::id_of(c->master);
|
|
auto id1 = ac.get_adj(ac.get_adj(c->master, i-1), -2).first;
|
|
int n1 = isize(ac.adjacent[id1]);
|
|
return spin(-t.first - M_PI / c->type) * xpush(ac.inradius[id/2] + ac.inradius[id1/2]) * xspinpush0(M_PI + M_PI/n1*(which?3:-3), ac.circumradius[id1/2]);
|
|
}
|
|
if(BITRUNCATED || DUAL) {
|
|
int mul = DUALMUL;
|
|
auto &ac = arcm::current;
|
|
auto adj = ac.get_adj(c->master, i * mul);
|
|
heptagon h; cell cx; cx.master = &h;
|
|
arcm::id_of(&h) = adj.first;
|
|
arcm::parent_index_of(&h) = adj.second;
|
|
|
|
auto& t1 = arcm::current.get_triangle(c->master, i);
|
|
|
|
auto& t2 = arcm::current.get_triangle(adj);
|
|
|
|
return spin(-t1.first) * xpush(t1.second) * spin(M_PI + t2.first) * get_corner_position(&cx, which ? -mul : 2*mul);
|
|
}
|
|
}
|
|
|
|
return cellrelmatrix(c, i) * get_corner_position(c->move(i), (cellwalker(c, i) + wstep + (which?-1:2)).spin);
|
|
}
|
|
|
|
hyperpoint midcorner(cell *c, int i, ld v) {
|
|
auto hcor = farcorner(c, i, 0);
|
|
auto tcor = get_corner_position(c, i, 3);
|
|
return mid_at(tcor, hcor, v);
|
|
}
|
|
|
|
hyperpoint get_warp_corner(cell *c, int cid) {
|
|
// midcorner(c, cid, .5) but sometimes easier versions exist
|
|
if(GOLDBERG) return gp::get_corner_position(c, cid, 2);
|
|
if(IRREGULAR || archimedean) return midcorner(c, cid, .5);
|
|
return ddspin(c,cid,M_PI/S7) * xpush0(tessf/2);
|
|
}
|
|
|
|
}
|
|
|