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hyperrogue/goldberg.cpp

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// Hyperbolic Rogue -- Goldberg-Coxeter construction
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file goldberg.cpp
* \brief Goldberg-Coxeter construction
*
* This is generally not used for standard pure and bitruncated tilings, even though they are technically Goldberg too.
*/
#include "hyper.h"
namespace hr {
#if HDR
struct hrmap;
extern hrmap *currentmap;
#endif
EX namespace gp {
#if HDR
struct loc : pair<int, int> {
loc() {}
loc(int x, int y) : pair<int,int> (x,y) {}
loc operator+(loc e2) {
return loc(first+e2.first, second+e2.second);
}
loc operator-(loc e2) {
return loc(first-e2.first, second-e2.second);
}
loc operator*(loc e2) {
return loc(first*e2.first-second*e2.second,
first*e2.second + e2.first*second + (S3 == 3 ? second*e2.second : 0));
}
loc operator*(int i) {
return loc(first*i, second*i);
}
int operator %(int i) {
return gmod(first, i) + gmod(second, i);
}
loc operator /(int i) {
return loc(first/i, second/i);
}
loc conj() {
if(S3 == 4) return loc(first, -second);
return loc(first+second, -second);
}
};
struct local_info {
int last_dir;
loc relative;
int first_dir;
int total_dir;
};
#endif
EX local_info current_li;
EX cell *li_for;
EX loc eudir(int d) {
if(S3 == 3) {
d %= 6; if (d < 0) d += 6;
switch(d) {
case 0: return loc(1, 0);
case 1: return loc(0, 1);
case 2: return loc(-1, 1);
case 3: return loc(-1, 0);
case 4: return loc(0, -1);
case 5: return loc(1, -1);
default: return loc(0, 0);
}
}
else switch(d&3) {
case 0: return loc(1, 0);
case 1: return loc(0, 1);
case 2: return loc(-1, 0);
case 3: return loc(0, -1);
default: return loc(0, 0);
}
}
EX int length(loc p) {
return euc::dist(p.first, p.second);
}
#if CAP_GP
EX loc param = loc(1, 0);
EX hyperpoint next;
struct goldberg_mapping_t {
cellwalker cw;
signed char rdir;
signed char mindir;
loc start;
transmatrix adjm;
};
EX int fixg6(int x) { return gmod(x, SG6); }
const int GOLDBERG_LIMIT_HALF = GOLDBERG_LIMIT/2;
const int GOLDBERG_MASK_HALF = GOLDBERG_MASK/2;
EX int get_code(const local_info& li) {
return
((li.relative.first & GOLDBERG_MASK_HALF) << 0) +
((li.relative.second & GOLDBERG_MASK_HALF) << (GOLDBERG_BITS-1)) +
((fixg6(li.total_dir)) << (2*GOLDBERG_BITS-2)) +
((li.last_dir & 15) << (2*GOLDBERG_BITS+2));
}
EX local_info get_local_info(cell *c) {
if(INVERSE) {
c = get_mapped(c);
return UIU(get_local_info(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<int> 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;
}
EX int last_dir(cell *c) {
return get_local_info(c).last_dir;
}
EX loc get_coord(cell *c) {
return get_local_info(c).relative;
}
EX int pseudohept_val(cell *c) {
loc v = get_coord(c);
return gmod(v.first - v.second, 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[GOLDBERG_LIMIT][GOLDBERG_LIMIT];
void clear_mapping() {
for(int y=0; y<GOLDBERG_LIMIT; y++) for(int x=0; x<GOLDBERG_LIMIT; 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&GOLDBERG_MASK][c.first&GOLDBERG_MASK];
}
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);
}
if(do_adjm) wc1.adjm = wc.adjm * get_adj(wcw.at, wcw.spin);
}
return false;
}
if(peek(wcw)) {
set_localwalk(wc1, dir1, wcw + wstep);
DEBB(DF_GP, (at1, " :", wcw+wstep, " (pulled from ", at, " :: ", wcw, ")"));
if(do_adjm) wc1.adjm = wc.adjm * get_adj(wcw.at, wcw.spin);
return true;
}
return false;
}
EX bool do_adjm;
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);
if(do_adjm) wc1.adjm = wc.adjm * get_adj(wcw.at, wcw.spin);
}
else {
peek(wcw) = newCell(SG6, wc.cw.at->master);
wcw.at->c.setspin(wcw.spin, 0, false);
set_localwalk(wc1, dir1, wcw + wstep);
if(do_adjm) wc1.adjm = wc.adjm;
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, " connected to ", wcw+wstep, " not to ", 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);
}
}
if(do_adjm) {
get_adj(wcw.at, wcw.spin) = inverse(wc.adjm) * wc1.adjm;
get_adj(wcw1.at, wcw1.spin) = inverse(wc1.adjm) * wc.adjm;
}
}
void conn(loc at, int dir) {
conn1(at, fixg6(dir), fixg6(dir+SG3));
conn1(at + eudir(dir), fixg6(dir+SG3), fixg6(dir));
}
EX map<pair<cell*, int>, transmatrix> gp_adj;
EX transmatrix& get_adj(cell *c, int i) { return gp_adj[make_pair(c,i)]; }
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;
}
EX void extend_map(cell *c, int d) {
DEBB(DF_GP, ("EXTEND ",c, " ", d));
indenter ind(2);
if(c->master->c7 != c) {
auto c1 = c;
auto d1 = d;
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, c->c.fix(d-1));
extend_map(c, c->c.fix(d+1));
if(S3 == 4 && !c1->move(d1)) {
for(int i=0; i<S7; i++)
for(int j=0; j<S7; j++)
extend_map(createStep(c->master, i)->c7, j);
}
if(S3 == 4 && !c1->move(d1)) {
for(int i=0; i<S7; i++)
for(int i1=0; i1<S7; i1++)
for(int j=0; j<S7; j++)
extend_map(createStep(createStep(c->master, i), i1)->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;
}
do_adjm = quotient || sphere;
if(do_adjm) {
auto m = (hrmap_standard*)currentmap;
get_mapping(vc[0]).adjm = Id;
get_mapping(vc[1]).adjm = m->adj(c->master, d);
get_mapping(vc[S3-1]).adjm = m->adj(c->master, (d+1)%c->master->type);
if(S3 == 4) {
heptspin hs1 = hs + wstep - 1;
get_mapping(vc[2]).adjm = m->adj(c->master, d) * m->adj(hs1.at, hs1.spin);
}
}
auto fix_mirrors = [&] {
if(ac1.cw.mirrored != hs.mirrored) ac1.cw--;
if(ac2.cw.mirrored != hs.mirrored) ac2.cw--;
if(S3 == 4) {
auto& ac3 = get_mapping(vc[2]);
if(ac3.cw.mirrored != hs.mirrored) ac3.cw--;
}
};
if(S3 == 4 && param == loc(1,1)) {
fix_mirrors();
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(S3 == 4 && param.first == param.second && nonorientable) {
fix_mirrors();
int size = param.first;
// go along the boundary of the 'diamond'
for(int dir=0; dir<4; dir++) {
int dir_orth = (dir+1) & 3;
loc at = vc[dir];
for(int i=0; i<size; i++) {
if(!pull(at, dir)) break;
at = at + eudir(dir);
if(!pull(at, dir_orth)) break;
at = at + eudir(dir_orth);
}
}
// build the skeleton
for(int dir=0; dir<4; dir++) {
int dir_orth = (dir+1) & 3;
for(int i=0; i<size; i++) {
conn(vc[dir] + eudir(dir_orth) * i, dir_orth);
}
}
// fill everything
for(int y=0; y<2*size; y++) {
int xdist = min(y, 2*size-y);
for(int x=0; x<xdist; x++)
for(int d=0; d<4; d++) {
conn(loc(x, y), d);
conn(loc(-x, y), d);
}
}
return;
}
if(nonorientable && param.first == param.second) {
int x = param.first;
fix_mirrors();
for(int d=0; d<3; d++) for(int k=0; k<3; k++)
for(int i=0; i<x; i++) {
int dd = (2*d+k);
loc cx = vc[d] + eudir(dd) * i;
if(!pull(cx, dd)) break;
}
for(int i=0; i<=2*x; i++)
for(int d=0; d<3; d++) {
loc cx = vc[d] + eudir(1+2*d) * i;
if(i < 2*x) conn(cx, 1+2*d);
int jmax = x-i, drev = 2*d;
if(jmax < 0) drev += 3, jmax = -jmax;
for(int j=0; j<jmax; j++) {
loc cy = cx + eudir(drev) * j;
conn(cy, drev);
conn(cy, drev+1);
conn(cy, drev+2);
}
}
return;
}
// then we set the edges of our big equilateral triangle (in a symmetric way)
for(int i=0; i<S3; i++) {
loc start = vc[i];
loc end = vc[(i+1)%S3];
DEBB(DF_GP, ("from ", start, " to ", end); )
loc rel = param;
auto build = [&] (loc& at, int dx, bool forward) {
int dx1 = dx + SG2*i;
DEBB(DF_GP, (at, " .. ", make_pair(at + eudir(dx1), fixg6(dx1+SG3))));
conn(at, dx1);
if(forward) get_mapping(at).rdir = fixg6(dx1);
else get_mapping(at+eudir(dx1)).rdir = fixg6(dx1+SG3);
at = at + eudir(dx1);
};
while(rel.first >= 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; k<SG6; k++)
if(start + eudir(k+SG2*i) == end)
build(start, k, true);
if(start != end) { DEBB(DF_GP | DF_ERROR, ("assertion failed: start ", start, " == end ", end)); exit(1); }
}
// now we can fill the interior of our big equilateral triangle
loc at = vc[0];
int maxstep = 3000;
while(true) {
maxstep--; if(maxstep < 0) { DEBB(DF_GP | DF_ERROR, ("maxstep exceeded")); exit(1); }
auto& wc = get_mapping(at);
int dx = wc.rdir;
auto at1 = at + eudir(dx);
auto& wc1 = get_mapping(at1);
DEBB(DF_GP, (make_pair(at, dx), " ", make_pair(at1, wc1.rdir)));
int df = wc1.rdir - dx;
if(df < 0) df += SG6;
if(df == SG3) break;
if(S3 == 3) switch(df) {
case 0:
case 4:
case 5:
at = at1;
continue;
case 2: {
conn(at, dx+1);
wc.rdir = (dx+1) % 6;
break;
}
case 1: {
auto at2 = at + eudir(dx+1);
auto& wc2 = get_mapping(at2);
if(wc2.cw.at) { at = at1; continue; }
wc.rdir = (dx+1) % 6;
conn(at, (dx+1) % 6);
conn(at1, (dx+2) % 6);
conn(at2, (dx+0) % 6);
wc1.rdir = -1;
wc2.rdir = dx;
break;
}
default:
println(hlog, "case unhandled ", df);
exit(1);
}
else switch(df) {
case 0:
case 3:
at = at1;
continue;
case 1:
auto at2 = at + eudir(dx+1);
auto& wc2 = get_mapping(at2);
if(wc2.cw.at) {
auto at3 = at1 + eudir(wc1.rdir);
auto& wc3 = get_mapping(at3);
auto at4 = at3 + eudir(wc3.rdir);
if(at4 == at2) {
wc.rdir = (dx+1)%4;
wc1.rdir = -1;
wc3.rdir = -1;
conn(at, (dx+1)%4);
}
else {
at = at1;
}
}
else {
wc.rdir = (dx+1)%4;
wc1.rdir = -1;
wc2.rdir = dx%4;
int bdir = -1;
int bdist = 100;
for(int d=0; d<4; d++) {
auto &wcm = get_mapping(at2 + eudir(d));
if(wcm.cw.at && length(wcm.start - at2) < bdist)
bdist = length(wcm.start - at2), bdir = d;
}
if(bdir != -1) conn(at2 + eudir(bdir), bdir ^ 2);
conn(at, (dx+1)%4);
conn(at2, dx%4);
at = param * loc(1,0) + at * loc(0, 1);
}
break;
}
}
DEBB(DF_GP, ("DONE"))
}
EX hyperpoint loctoh_ort(loc at) {
return point3(at.first, at.second, 1);
}
hyperpoint corner_coords6[7] = {
point3(2, -1, 0),
point3(1, 1, 0),
point3(-1, 2, 0),
point3(-2, 1, 0),
point3(-1, -1, 0),
point3(1, -2, 0),
point3(0, 0, 0) // center, not a corner
};
hyperpoint corner_coords4[7] = {
point3(1.5, -1.5, 0),
// point3(1, 0, 0),
point3(1.5, 1.5, 0),
// point3(0, 1, 0),
point3(-1.5, 1.5, 0),
// point3(-1, 0, 0),
point3(-1.5, -1.5, 0),
// point3(0, -1, 0),
point3(0, 0, 0),
point3(0, 0, 0),
point3(0, 0, 0)
};
#define corner_coords (S3==3 ? corner_coords6 : corner_coords4)
hyperpoint cornmul(const transmatrix& corners, const hyperpoint& c) {
if(sphere && S3 == 3) {
ld cmin = c[0] * c[1] * c[2] * (6 - S7);
return corners * point3(c[0] + cmin, c[1] + cmin, c[2] + cmin);
}
else return corners * c;
}
hyperpoint atz(const transmatrix& T, const transmatrix& corners, loc at, int cornerid = 6, ld cf = 3) {
int sp = 0;
again:
auto corner = corners * (loctoh_ort(at) + (corner_coords[cornerid] / cf));
if(corner[1] < -1e-6 || corner[2] < -1e-6) {
at = at * eudir(1);
if(cornerid < SG6) cornerid = (1 + cornerid) % SG6;
sp++;
goto again;
}
if(sp>SG3) sp -= SG6;
return normalize(spin(2*M_PI*sp/S7) * cornmul(T, corner));
}
transmatrix dir_matrix(int i) {
auto ddspin = [] (int d) -> transmatrix {
return spin(M_PI - d * 2 * M_PI / S7 - cgi.hexshift);
};
return spin(-cgi.gpdata->alpha) * build_matrix(
C0,
ddspin(i) * xpush0(cgi.tessf),
ddspin(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
));
cgi.gpdata->Tf.resize(S7);
for(int i=0; i<S7; i++) {
transmatrix T = dir_matrix(i);
for(int x=-GOLDBERG_LIMIT_HALF; x<GOLDBERG_LIMIT_HALF; x++)
for(int y=-GOLDBERG_LIMIT_HALF; y<GOLDBERG_LIMIT_HALF; y++)
for(int d=0; d<(S3==3?6:4); d++) {
loc at = loc(x, y);
hyperpoint h = atz(T, cgi.gpdata->corners, at, 6);
hyperpoint hl = atz(T, cgi.gpdata->corners, at + eudir(d), 6);
cgi.gpdata->Tf[i][x&GOLDBERG_MASK][y&GOLDBERG_MASK][d] = rgpushxto0(h) * rspintox(gpushxto0(h) * hl) * spin(M_PI);
}
}
}
EX hyperpoint get_corner_position(const local_info& li, int cid, ld cf IS(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&GOLDBERG_MASK][li.relative.second&GOLDBERG_MASK][fixg6(li.total_dir)];
return inverse(cellmatrix) * atz(dir_matrix(i), cgi.gpdata->corners, li.relative, fixg6(cid + li.total_dir), cf);
}
}
EX hyperpoint get_corner_position(cell *c, int cid, ld cf IS(3)) {
return get_corner_position(get_local_info(c), cid, cf);
}
map<pair<int, int>, loc> center_locs;
EX void compute_geometry(bool inv) {
center_locs.clear();
if(GOLDBERG_INV || inv) {
if(!cgi.gpdata) cgi.gpdata = make_shared<geometry_information::gpdata_t>();
gp::clear_plainshapes();
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);
if(!GOLDBERG) scale = 1;
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;
EX bool rotate_and_check_limits(loc& v) {
int& x = v.first, &y = v.second;
while(x < 0 || y < 0 || (x == 0 && y > 0))
v = v * loc(0, 1);
return 2*(x+y) < (1<<GOLDBERG_BITS);
}
EX bool check_limits(loc v) {
return rotate_and_check_limits(v);
}
loc internal_representation(loc v) {
int& x = v.first, &y = v.second;
while(!rotate_and_check_limits(v)) {
if(x > y) x--; else y--;
}
if(S3 == 3 && y > x) v = v * loc(1, -1);
return v;
}
EX 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;
}
EX eVariation variation_for(loc xy) {
if(xy.first == 1 && xy.second == 0)
return eVariation::pure;
if(xy.first == 1 && xy.second == 1 && S3 == 3)
return eVariation::bitruncated;
return eVariation::goldberg;
}
EX 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;
stop_game();
param = xy;
if(xy.first == 1 && xy.second == 0) {
set_variation(eVariation::pure);
}
else if(xy.first == 1 && xy.second == 1 && S3 == 3) {
set_variation(eVariation::bitruncated);
}
else
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"), PURE || (GOLDBERG && univ_param() == loc(1,0)), 'a');
dialog::lastItem().value = "GP(1,0)";
dialog::add_action_confirmed([] { whirl_set(loc(1, 0)); });
}
if(min_quality_chess == 0) {
dialog::addBoolItem(XLAT("bitruncated"), BITRUNCATED, 'b');
dialog::add_action_confirmed([] {
if(S3 == 4) {
if(!BITRUNCATED) {
stop_game();
set_variation(eVariation::bitruncated);
start_game();
}
}
else
whirl_set(loc(1, 1));
});
}
dialog::lastItem().value = S3 == 3 ? "GP(1,1)" : ONOFF(BITRUNCATED);
if(min_quality == 0 || min_quality_chess) {
dialog::addBoolItem(S3 == 3 ? XLAT("chamfered") : XLAT("expanded"), univ_param() == loc(2,0) && GOLDBERG, 'c');
dialog::lastItem().value = "GP(2,0)";
dialog::add_action_confirmed([] {
whirl_set(loc(2, 0));
});
}
if(S3 == 3) {
dialog::addBoolItem(XLAT("2x bitruncated"), GOLDBERG && univ_param() == loc(3,0), 'd');
dialog::lastItem().value = "GP(3,0)";
dialog::add_action_confirmed([] {
whirl_set(loc(3, 0));
});
}
else {
dialog::addBoolItem(XLAT("rectified"), param == loc(1,1) && GOLDBERG, 'd');
dialog::lastItem().value = "GP(1,1)";
dialog::add_action_confirmed([] {
whirl_set(loc(1, 1));
});
}
dialog::addBreak(100);
dialog::addSelItem("x", its(config.first), 'x');
dialog::add_action([] { dialog::editNumber(config.first, 0, 8, 1, 1, "x", helptext()); });
dialog::addSelItem("y", its(config.second), 'y');
dialog::add_action([] { dialog::editNumber(config.second, 0, 8, 1, 1, "y", helptext()); });
if(!check_limits(config))
dialog::addInfo(XLAT("Outside of the supported limits"));
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 && !INVERSE, 'f');
dialog::lastItem().value = "GP(x,y)";
}
dialog::add_action_confirmed([] { whirl_set(config); });
dialog::addBreak(100);
#if CAP_IRR
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(euclid && (!bounded || nonorientable)) {
println(hlog, XLAT("To create Euclidean irregular tesselations, first enable a torus"));
return;
}
if(!IRREGULAR) irr::visual_creator();
}));
}
#endif
dialog::addBreak(100);
int style = 0;
auto v0 = variation_for(param);
bool bad_bi = BITRUNCATED && a4;
if(!bad_bi) {
dynamicval<eVariation> v(variation, v0);
if(geosupport_football() == 2) style = 3;
if(geosupport_chessboard()) style = 2;
}
if(style == 2) {
dialog::addBoolItem(XLAT("inverse rectify"), UNRECTIFIED, 'r');
dialog::add_action_confirmed([v0] {
param = univ_param();
if(UNRECTIFIED) set_variation(v0);
else set_variation(eVariation::unrectified);
start_game();
config = human_representation(univ_param());
});
}
else if(style == 3) {
dialog::addBoolItem(XLAT("inverse truncate"), UNTRUNCATED, 't');
dialog::add_action_confirmed([v0] {
param = univ_param();
if(UNTRUNCATED) set_variation(v0);
else set_variation(eVariation::untruncated);
start_game();
});
dialog::addBoolItem(XLAT("warped version"), WARPED, 'w');
dialog::add_action_confirmed([v0] {
param = univ_param();
if(WARPED) set_variation(v0);
else set_variation(eVariation::warped);
start_game();
});
}
dialog::addBreak(100);
dialog::addItem(XLAT("swap x and y"), 'z');
dialog::add_action([] { swap(config.first, config.second); });
bool have_dual = !bad_bi && !IRREGULAR && !WARPED;
if(S3 == 3 && UNTRUNCATED && (univ_param()*loc(1,1)) % 3) have_dual = false;
if(S3 == 4 && UNRECTIFIED && (univ_param()*loc(1,1)) % 2) have_dual = false;
if(have_dual) {
dialog::addItem(XLAT("dual of current"), 'D');
dialog::add_action([] {
auto p = univ_param();
if(S3 == 3 && !UNTRUNCATED) {
println(hlog, "set param to ", p * loc(1,1));
whirl_set(p * loc(1, 1));
set_variation(eVariation::untruncated);
start_game();
config = human_representation(univ_param());
}
else if(S3 == 4 && !UNRECTIFIED) {
whirl_set(p * loc(1, 1));
set_variation(eVariation::unrectified);
start_game();
config = human_representation(univ_param());
}
else if(S3 == 3 && UNTRUNCATED) {
println(hlog, "whirl_set to ", (p * loc(1,1)) / 3);
whirl_set((p * loc(1,1)) / 3);
config = human_representation(univ_param());
}
else if(S3 == 4 && UNRECTIFIED) {
whirl_set((p * loc(1,1)) / 2);
config = human_representation(univ_param());
}
});
}
dialog::addBreak(100);
dialog::addHelp();
dialog::add_action([] { gotoHelp(helptext()); });
dialog::addBack();
dialog::display();
}
EX loc univ_param() {
if(GOLDBERG_INV) return param;
else if(PURE) return loc(1,0);
else return loc(1,1);
}
EX void configure() {
auto l = univ_param();
param = l;
config = human_representation(l);
pushScreen(gp::show);
}
EX 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 = gmod(li.last_dir - sp, S7);
}
// 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?
EX 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);
}
EX hyperpoint get_master_coordinates(cell *c) {
auto li = get_local_info(c);
be_in_triangle(li);
return cgi.gpdata->corners * loctoh_ort(li.relative);
}
EX int compute_dist(cell *c, int master_function(cell*)) {
if(!GOLDBERG) return master_function(c);
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, cm->c.fix(i+1))->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);
}
EX int dist_2() {
return length(univ_param());
}
EX int dist_3() {
return length(univ_param() * loc(1,1));
}
EX int dist_1() {
return dist_3() - dist_2();
}
#else
EX int dist_1() { return 1; }
EX int dist_2() { return BITRUNCATED ? 2 : 1; }
EX int dist_3() { return BITRUNCATED ? 3 : 2; }
#endif
EX array<heptagon*, 3> get_masters(cell *c) {
if(0);
#if CAP_GP
else if(INVERSE) {
c = get_mapped(c);
return UIU(get_masters(c));
}
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, cm->cmove(i), cm->cmodmove(i+1));
}
#endif
#if CAP_IRR
else if(IRREGULAR)
return irr::get_masters(c);
#endif
else
return make_array(c->cmove(0)->master, c->cmove(2)->master, c->cmove(4)->master);
}
EX 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(GOLDBERG && param == loc(1, 0))
return XLAT("pure");
else if(GOLDBERG && param == loc(1, 1) && S3 == 3)
return XLAT("bitruncated");
else if(GOLDBERG && param == loc(1, 1) && S3 == 4)
return XLAT("rectified");
else if(UNRECTIFIED && param == loc(1, 1) && S3 == 4)
return XLAT("dual");
else if(UNTRUNCATED && param == loc(1, 1) && S3 == 3)
return XLAT("dual");
else if(GOLDBERG && param == loc(2, 0))
return S3 == 3 ? XLAT("chamfered") : XLAT("expanded");
else if(GOLDBERG && param == loc(3, 0) && S3 == 3)
return XLAT("2x bitruncated");
else if(variation == eVariation::subcubes)
return XLAT("subcubed") + "(" + its(reg3::subcube_count) + ")";
else if(variation == eVariation::dual_subcubes)
return XLAT("dual-subcubed") + "(" + its(reg3::subcube_count) + ")";
else if(variation == eVariation::bch)
return XLAT("bitruncated-subcubed") + "(" + its(reg3::subcube_count) + ")";
else if(variation == eVariation::coxeter)
return XLAT("subdivided") + "(" + its(reg3::coxeter_param) + ")";
else {
auto p = human_representation(param);
string s = "GP(" + its(p.first) + "," + its(p.second) + ")";
if(UNRECTIFIED) return XLAT("unrectified") + " " + s;
if(WARPED) return XLAT("warped") + " " + s;
if(UNTRUNCATED) return XLAT("untruncated") + " " + s;
return s;
}
#else
else return "UNSUPPORTED";
#endif
}
/* inverse map */
EX hrmap *pmap;
// EX geometry_information *underlying_cgip;
struct hrmap_inverse : hrmap {
hrmap *underlying_map;
map<cell*, cell*> mapping;
map<cell*, int> shift;
template<class T> auto in_underlying(const T& t) -> decltype(t()) {
dynamicval<hrmap*> gpm(pmap, this);
dynamicval<eVariation> gva(variation, variation_for(param));
dynamicval<hrmap*> gu(currentmap, underlying_map);
// dynamicval<geometry_information*> gc(cgip, underlying_cgip);
return t();
}
cell* get_mapped(cell *underlying_cell, int set_shift) {
if(mapping.count(underlying_cell))
return mapping[underlying_cell];
int d = underlying_cell->type;
if(UNTRUNCATED) d /= 2;
if(WARPED && set_shift < 2) d /= 2;
cell *c = newCell(d, underlying_cell->master);
mapping[underlying_cell] = c;
if(!UNRECTIFIED) shift[c] = set_shift;
mapping[c] = underlying_cell;
return c;
}
transmatrix relative_matrixh(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
return in_underlying([&] { return currentmap->relative_matrix(h2, h1, hint); });
}
transmatrix relative_matrixc(cell *c2, cell *c1, const hyperpoint& hint) override {
c1 = mapping[c1];
c2 = mapping[c2];
return in_underlying([&] { return currentmap->relative_matrix(c2, c1, hint); });
}
~hrmap_inverse() {
in_underlying([this] { delete underlying_map; });
}
heptagon *getOrigin() override { return in_underlying([this] { return underlying_map->getOrigin(); }); }
cell *gs;
cell* gamestart() override {
return gs;
}
hrmap_inverse() {
if(0) {
println(hlog, "making ucgi");
dynamicval<eVariation> gva(variation, variation_for(param));
check_cgi();
cgi.require_basics();
// underlying_cgip = cgip;
println(hlog, "done ucgi");
}
bool warped = WARPED;
in_underlying([&,this] {
initcells();
underlying_map = currentmap;
gs = currentmap->gamestart();
if(!warped) gs = gs->cmove(0);
});
if(UNTRUNCATED) gs = get_mapped(gs, 1);
else gs = get_mapped(gs, 2);
for(hrmap*& m: allmaps) if(m == underlying_map) m = NULL;
}
cell *create_move(cell *parent, int d) {
if(UNRECTIFIED) {
cellwalker cw(mapping[parent], d);
bool b = cw.mirrored;
in_underlying([&] {
cw += wstep;
cw --;
cw += wstep;
cw --;
if(cw.mirrored != b) cw++;
});
cw.at = get_mapped(cw.at, 0);
parent->c.connect(d, cw.at, cw.spin, cw.mirrored);
return cw.at;
}
if(UNTRUNCATED) {
cellwalker cw(mapping[parent], 2*d+shift[parent]);
in_underlying([&] {
cw += wstep;
});
cw.at = get_mapped(cw.at, cw.spin & 1);
parent->c.connect(d, cw.at, cw.spin / 2, cw.mirrored);
return cw.at;
}
if(WARPED) {
int sh = shift[parent];
if(sh == 2) {
cellwalker cw(mapping[parent], d);
in_underlying([&] { cw += wstep; });
cw.at = get_mapped(cw.at, cw.spin & 1);
parent->c.connect(d, cw.at, cw.spin / 2, cw.mirrored);
return cw.at;
}
else {
cellwalker cw(mapping[parent], 2*d+sh);
in_underlying([&] {
cw += wstep;
});
cw.at = get_mapped(cw.at, 2);
parent->c.connect(d, cw.at, cw.spin, cw.mirrored);
return cw.at;
}
}
throw hr_exception("unimplemented");
}
transmatrix adj(cell *c, int d) override {
transmatrix T;
if(UNRECTIFIED) {
cellwalker cw(mapping[c], d);
in_underlying([&] {
T = currentmap->adj(cw.at, cw.spin);
cw += wstep;
cw --;
T = T * currentmap->adj(cw.at, cw.spin);
});
}
if(UNTRUNCATED) {
cellwalker cw(mapping[c], 2*d+shift[c]);
in_underlying([&] { T = currentmap->adj(cw.at, cw.spin); });
}
if(WARPED) {
int sh = shift[c];
if(sh == 2) {
auto c1 = mapping[c];
in_underlying([&] { T = currentmap->adj(c1, d); });
}
else {
cellwalker cw(mapping[c], 2*d+shift[c]);
in_underlying([&] { T = currentmap->adj(cw.at, cw.spin); });
}
}
return T;
}
void draw_at(cell *at, const shiftmatrix& where) override {
dq::clear_all();
auto enqueue = (quotient ? dq::enqueue_by_matrix_c : dq::enqueue_c);
enqueue(at, where);
while(!dq::drawqueue_c.empty()) {
auto& p = dq::drawqueue_c.front();
cell *c = p.first;
shiftmatrix V = p.second;
auto c1 = get_mapped(c, 0);
in_underlying([&] {
if(GOLDBERG) {
gp::current_li = gp::get_local_info(c1);
}
else {
gp::current_li.relative.first = shvid(c1);
gp::current_li.relative.second = shift[c];
}
});
dq::drawqueue_c.pop();
if(!do_draw(c, V)) continue;
drawcell(c, V);
for(int i=0; i<c->type; i++) if(c->cmove(i))
enqueue(c->move(i), optimized_shift(V * adj(c, i)));
}
}
void find_cell_connection(cell *c, int d) override {
inverse_move(c, d);
}
int shvid(cell *c) override {
return gp::get_plainshape_id(c);
}
hyperpoint get_corner(cell *c, int cid, ld cf) override {
if(UNTRUNCATED) {
cell *c1 = gp::get_mapped(c);
cellwalker cw(c1, cid*2);
if(!gp::untruncated_shift(c)) cw--;
hyperpoint h = UIU(nearcorner(c1, cw.spin));
return mid_at_actual(h, 3/cf);
}
if(UNRECTIFIED) {
cell *c1 = gp::get_mapped(c);
hyperpoint h = UIU(nearcorner(c1, cid));
return mid_at_actual(h, 3/cf);
}
if(WARPED) {
int sh = gp::untruncated_shift(c);
cell *c1 = gp::get_mapped(c);
if(sh == 2) {
cellwalker cw(c, cid);
hyperpoint h1 = UIU(tC0(currentmap->adj(c1, cid)));
cw--;
hyperpoint h2 = UIU(tC0(currentmap->adj(c1, cw.spin)));
hyperpoint h = mid(h1, h2);
return mid_at_actual(h, 3/cf);
}
else {
cellwalker cw(c1, cid*2);
if(!gp::untruncated_shift(c)) cw--;
hyperpoint h = UIU(nearcorner(c1, cw.spin));
h = mid(h, C0);
return mid_at_actual(h, 3/cf);
}
}
return C0;
}
};
EX hrmap* new_inverse() { return new hrmap_inverse; }
hrmap_inverse* inv_map() { return (hrmap_inverse*)currentmap; }
EX hrmap* get_underlying_map() { return inv_map()->underlying_map; }
EX cell* get_mapped(cell *c) { return inv_map()->get_mapped(c, 0); }
EX int untruncated_shift(cell *c) { return inv_map()->shift[c]; }
EX void delete_mapped(cell *c) {
if(!pmap) return;
auto i = (hrmap_inverse*) pmap;
if(i->mapping.count(c))
destroy_cell(i->mapping[c]);
}
EX cell *inverse_move(cell *c, int d) { return inv_map()->create_move(c, d); }
#if HDR
template<class T> auto in_underlying_geometry(const T& f) -> decltype(f()) {
if(!INVERSE) return f();
dynamicval<hrmap*> gpm(pmap, currentmap);
dynamicval<eVariation> gva(variation, variation_for(param));
dynamicval<hrmap*> gu(currentmap, get_underlying_map());
// dynamicval<geometry_information*> gc(cgip, underlying_cgip);
return f();
}
#define UIU(x) hr::gp::in_underlying_geometry([&] { return (x); })
#endif
}}
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