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450 lines
13 KiB
C++
450 lines
13 KiB
C++
// show the fundamental domain for quotient spaces
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// Copyright (C) 2018-2025 Zeno and Tehora Rogue, see 'hyper.cpp' for details
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#include "hyper.h"
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namespace hr {
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EX namespace fundamental {
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transmatrix current_position, last_view;
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void analyze_view_pre() {
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current_position = current_position * last_view * inverse(View);
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}
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void analyze_view_post() {
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last_view = View;
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}
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struct settings {
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int funmode;
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bool single_edges;
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bool fill_faces;
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ld widthfactor;
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color_t color_other;
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color_t color_main;
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int lq;
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color_t color_mirage;
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color_t color_mirror;
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ld label_dist;
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ld label_scale;
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int alpha;
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void show_options();
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} sett;
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cell *starter;
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struct shapedata {
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map<cell*, set<int>> same;
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map<cell*, shiftmatrix> gm;
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int corners, corners0;
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vector<hyperpoint> abs_cornerpos;
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vector<cell*> cells;
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vector<cellwalker> cornerlist;
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map<cellwalker, int> corner_id;
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cell *current_starter;
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vector<int> connections;
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vector<bool> mirrored;
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bool is_connected(cellwalker cw);
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void be_connected(cellwalker cw);
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int group_count(cellwalker cw);
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void auto_corners();
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void find_corners();
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shiftpoint cwcorner(cellwalker cw);
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void compute_shape();
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void render();
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} sd;
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bool shapedata::is_connected(cellwalker cw) {
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return same[cw.at].count(cw.spin);
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}
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void shapedata::be_connected(cellwalker cw) {
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same[cw.at].insert(cw.spin);
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cw += wstep;
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same[cw.at].insert(cw.spin);
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}
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shiftpoint shapedata::cwcorner(cellwalker cw) {
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shiftmatrix T = gm[cw.at];
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if(sett.funmode == 2 && BITRUNCATED) {
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while(cw.at->type != S7) {
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cw++;
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T = T * currentmap->adj(cw.at, cw.spin);
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cw += wstep;
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}
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return T * C0;
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}
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return gm[cw.at] * get_corner_position(cw.at, cw.spin+(cw.mirrored?0:1), 3);
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}
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void shapedata::auto_corners() {
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cellwalker cw;
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corners = 0;
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for(int k=0; k<isize(cells); k++) {
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cell *c = cells[k];
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for(int i=0; i<c->type; i++) {
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cellwalker cw0(c, i);
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if(sett.single_edges) {
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if(!is_connected(cw0)) corners++, cw = cw0;
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}
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else {
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if(group_count(cw0) >= 3) corners++, cw = cw0;
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}
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}
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}
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if(!corners) return;
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cornerlist.clear();
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corner_id.clear();
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for(int ci=0; ci<corners; ci++) {
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corner_id[cw] = cornerlist.size();
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cornerlist.push_back(cw);
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while(true) {
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cw++;
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while(is_connected(cw)) {
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cw += wstep;
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cw++;
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}
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if(sett.single_edges || group_count(cw) >= 3) break;
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}
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}
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corners0 = corners;
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corners = isize(cornerlist);
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cornerlist.push_back(cw);
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if(corners0 != corners) println(hlog, "corners=", tie(corners0, corners));
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abs_cornerpos.clear();
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for(auto c: cornerlist) {
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auto co = inverse_shift(gm[starter], cwcorner(c));
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if(isize(abs_cornerpos) && (hdist(co, abs_cornerpos[0]) < 1e-3 || hdist(co, abs_cornerpos.back()) < 1e-3)) continue;
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abs_cornerpos.push_back(co);
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}
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corners = isize(abs_cornerpos); abs_cornerpos.push_back(abs_cornerpos[0]);
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}
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void shapedata::find_corners() {
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abs_cornerpos.clear();
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auto build = [&] (int sides, ld a, ld a1, ld shift) {
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transmatrix T = Id;
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if(variation == eVariation::untruncated)
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T = T * rgpushxto0(get_corner_position(starter, 0, 3));
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for(int i=0; i<=sides; i++) {
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abs_cornerpos.push_back(T * xspinpush0(-i * TAU/sides + shift, (i&1) ? a : a1));
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}
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corners = sides;
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};
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if(sett.funmode == 3) switch(geometry) {
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case gKleinQuartic: {
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ld a = edge_of_triangle_with_angles(90._deg, M_PI/14, M_PI*2/14);
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return build(14, a, a, 0);
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}
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case gSchmutzM2: {
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ld a = edge_of_triangle_with_angles(90._deg, M_PI/12, M_PI/6);
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ld a1 = edge_of_triangle_with_angles(45._deg, M_PI/12, 60._deg);
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return build(24, a1, a, 0);
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}
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case gSchmutzM3: {
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ld a = edge_of_triangle_with_angles(60._deg, M_PI/12, M_PI/12);
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ld a1 = edge_of_triangle_with_angles(M_PI/12, 60._deg, M_PI/12);
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return build(24, a, a1, 0);
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}
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case gBolza: {
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ld a = edge_of_triangle_with_angles(90._deg, M_PI/8, M_PI/8);
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return build(8, a, a, 22.5_deg);
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}
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case gBolza2: {
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ld a = edge_of_triangle_with_angles(90._deg, M_PI/8, M_PI/8);
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hyperpoint h1 = xspinpush0(0, a);
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hyperpoint h2 = xspinpush0(45._deg, a);
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hyperpoint hm = mid(h1, h2);
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ld a1 = hdist0(hm) * 2;
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return build(16, a, a1, 0);
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}
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default: break;
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}
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return auto_corners();
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}
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transmatrix rel(cellwalker cw) {
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return currentmap->adj(cw.at, cw.spin);
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}
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shiftmatrix labelpos(shiftpoint h1, shiftpoint h2) {
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shiftpoint h = mid(h1, h2);
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shiftmatrix T = rgpushxto0(h);
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hyperpoint hx = inverse_shift(T, h2);
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ld alpha = atan2(-hx[1], hx[0]);
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return T * xspinpush(alpha + 90._deg, sett.label_dist);
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}
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int shapedata::group_count(cellwalker cw) {
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if(is_connected(cw)) return 0;
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auto cw1 = cw;
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int groups = 0;
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do {
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if(!is_connected(cw1)) groups++;
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cw1 = cw1 + wstep - 1;
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}
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while(cw1 != cw);
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return groups;
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}
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map<unsigned, color_t> bucket_color;
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color_t *current_domain = nullptr;
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void shapedata::compute_shape() {
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if(current_starter == starter) return;
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current_starter = starter;
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same.clear();
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gm.clear();
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gm[starter] = ggmatrix(starter);
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cells = {starter};
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int tree_edges = 0;
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int face_edges = 0;
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bool first_zebra_phase = geometry == gZebraQuotient && sett.funmode == 3 && PURE;
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bool second_zebra_phase = false;
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again:
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for(int k=0; k<isize(cells); k++) {
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cell *c = cells[k];
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for(int i=0; i<c->type; i++) {
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cellwalker cw(c, i);
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cell *c2 = cw.cpeek();
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if(gm.count(c2)) continue;
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if(first_zebra_phase && (zebra40(c) % 4) != (zebra40(c2) % 4))
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continue;
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if(second_zebra_phase) {
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int j = 0;
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for(; j<c->type; j++) if(zebra40(c->move(j)) == 4 + zebra40(c) % 12) break;
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int v = gmod(i-j+2, 7); if(v < 5) continue;
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}
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gm[c2] = gm[c] * rel(cw);
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be_connected(cw);
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tree_edges++;
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cells.push_back(c2);
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}
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}
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if(first_zebra_phase) {
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first_zebra_phase = false;
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second_zebra_phase = true;
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goto again;
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}
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while(sett.fill_faces) {
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int f = face_edges;
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for(int k=0; k<isize(cells); k++) {
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cell *c = cells[k];
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for(int i=0; i<c->type; i++) {
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cellwalker cw(c, i);
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if(group_count(cw) == 1) {
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face_edges++;
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be_connected(cw);
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}
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}
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}
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if(f == face_edges) break;
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}
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find_corners();
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connections.clear(); connections.resize(corners, -1);
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mirrored.clear(); mirrored.resize(corners, false);
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}
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void shapedata::render() {
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if(!sd.corners) return;
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set<unsigned> buckets_used;
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for(int i=0; i<corners; i++) curvepoint_pretty(sd.abs_cornerpos[i], sd.abs_cornerpos[i+1], sett.lq);
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curvepoint_first();
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auto pos = current_position * last_view * inverse(View);
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map<unsigned, int> midedge_id;
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auto T = ggmatrix(starter);
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unsigned central_bucket = bucketer(unshift(T*C0));
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for(int i=0; i<corners; i++)
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midedge_id[bucketer(unshift(T*mid(abs_cornerpos[i], abs_cornerpos[i+1])))] = i;
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int next_connection_id = 0;
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dynamicval<ld> lw(vid.linewidth, vid.linewidth * sett.widthfactor);
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for(auto c: cells)
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for(const shiftmatrix& V : hr::span_at(current_display->all_drawn_copies, c)) {
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auto V1 = V * inverse_shift(gm[c], gm[starter]);
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auto bu = bucketer(pos * unshift(V1*C0));
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if(buckets_used.count(bu)) continue;
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buckets_used.insert(bu);
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if(sett.alpha && !bucket_color.count(bu)) {
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if(bucket_color.empty()) bucket_color[bu] = sett.alpha;
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else bucket_color[bu] = (hrand(0x1000000) << 8) | sett.alpha;
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}
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if(c == cwt.at && sett.alpha && !current_domain) current_domain = &bucket_color[bu];
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queuecurve_reuse(V1, sett.color_other, sett.alpha ? bucket_color[bu] : 0, PPR::LINE);
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if(bu != central_bucket) {
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for(int i=0; i<corners; i++) {
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unsigned val = bucketer(unshift(V1*mid(abs_cornerpos[i], abs_cornerpos[i+1])));
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auto p = at_or_null(midedge_id, val);
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if(p && connections[*p] == -1) {
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connections[*p] = connections[i] = next_connection_id++;
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mirrored[*p] = mirrored[i] = det(V1.T) * det(T.T) < 0;
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}
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}
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}
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}
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queuecurve(T, sett.color_main, 0, PPR::LINE);
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string conlabels = "123456789ABCDEFGHIJKLMNOPQRSTUVWYXZabcdefghijklmnopqrstuvwxyz$%@&+#";
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for(int ci=0; ci<corners; ci++) {
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int mc = mirrored[ci] ? sett.color_mirror : sett.color_mirage;
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int id = connections[ci];
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if(id == -1) continue;
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id++;
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string lab = s0;
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while(id) {
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lab += conlabels[(id-1) % isize(conlabels)];
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id /= isize(conlabels);
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}
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queuestr(labelpos(T * abs_cornerpos[ci], T * abs_cornerpos[ci+1]), sett.label_scale/cgi.scalefactor, lab, mc);
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}
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}
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void fundamental_marker() {
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current_domain = nullptr;
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if(!sett.funmode || !quotient || !closed_manifold || WDIM != 2) return;
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sd.compute_shape();
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sd.render();
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}
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void clear_data() {
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sd = {};
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bucket_color.clear();
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}
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void settings::show_options() {
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dialog::init(XLAT("display fundamental domains"), 0xFFFFFFFF, 150, 0);
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add_edit(funmode);
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add_edit(single_edges);
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add_edit(fill_faces);
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add_edit(alpha);
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dialog::addBreak(50);
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add_edit(widthfactor);
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add_edit(color_main);
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add_edit(color_other);
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add_edit(lq);
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dialog::addBreak(50);
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add_edit(label_dist);
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add_edit(label_scale);
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add_edit(color_mirage);
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add_edit(color_mirror);
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}
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EX void showMenu() {
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cmode = sm::SIDE | sm::MAYDARK;
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gamescreen();
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sett.show_options();
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dialog::addBreak(100);
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dialog::addSelItem("set the central tile to current position", its(celldistance(starter, cwt.at)), 's');
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dialog::add_action([] () {
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starter = cwt.at;
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});
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if(sett.alpha) {
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dialog::addItem("reshuffle all fill colors", 'r');
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dialog::add_action([] { bucket_color.clear(); });
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if(current_domain) {
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dialog::addColorItem("current central domain", *current_domain, 'y');
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dialog::add_action([] () {
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dialog::openColorDialog(*current_domain, NULL);
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dialog::get_di().dialogflags |= sm::MAYDARK | sm::SIDE;
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});
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}
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}
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dialog::addBack();
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dialog::display();
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}
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int enable_fundamental() {
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addHook(hooks_post_initgame, 100, [] {
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starter = cwt.at; current_position = Id; last_view = View;
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});
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addHook(hooks_frame, 100, fundamental_marker);
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addHook(hooks_clearmemory, 100, clear_data);
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addHook(hooks_o_key, 80, [] (o_funcs& v) {
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if(sett.funmode) v.push_back(named_dialog("fundamental", showMenu));
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});
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addHook(hooks_preoptimize, 75, analyze_view_pre);
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addHook(hooks_postoptimize, 75, analyze_view_post);
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addHook(hooks_configfile, 100, [] {
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param_enum(sett.funmode, "funmode", 0)
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->editable({{"disabled", "do not construct or draw the fundamental domains"}, {"corners", "find the shape automatically"}, {"centers", "may produce less corners"}, {"special", "nice domains for specific quotient shapes"}}, "fundamental domain method", 'm')
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->set_reaction(clear_data);
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param_color(sett.color_main, "fundamental_color_main", true, 0xFFFFFFFF)
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->editable("boundary of the central domain", "", 'c');
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param_color(sett.color_other, "fundamental_color_other", true, 0xFFFFFF40)
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->editable("boundary of the other domains", "", 'o');
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param_color(sett.color_mirage, "fundamental_color_mirage", false, winf[waCloud].color)
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->editable("gluing label color", "", 'd');
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param_color(sett.color_mirror, "fundamental_color_mirror", false, winf[waMirror].color)
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->editable("mirrored gluing label color", "", 'b');
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param_b(sett.single_edges, "fundamental_single_edges", false)
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->editable("fundamental: single edges", '1')
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->set_reaction(clear_data);
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param_b(sett.fill_faces, "fundamental_fill_faces", true)
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->editable("fundamental: fill faces", '2')
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->set_reaction(clear_data);
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param_f(sett.label_dist, "fundamental_label_dist", .3)
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->editable(0, 10, .05, "gluing label distance", "", 'd');
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param_f(sett.widthfactor, "fundamental_width", 5)
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->editable(0, 5, 1, "domain boundary width factor", "", 'w');
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param_f(sett.label_scale, "fundamental_label_scale", 1)
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->editable(0, 10, 0.2, "gluing label scale", "", 's');
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param_i(sett.lq, "fundamental_lq", 3)
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->editable(0, 5, 1, "domain line quality", "", 'w');
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param_i(sett.alpha, "fundamental_alpha", 32)
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->editable(0, 5, 8, "opacity of domain fill colors", "", 'a');
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});
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return 0;
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}
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auto fundamentalhook = enable_fundamental();
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}
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}
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