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goldberg.cpp
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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;
signed char rdir1;
};
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_map[y][x].rdir1 = -1;
}
}
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, (hr::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;
if(geom3::flipped) gp_swapped.emplace(wcw.at, wcw.spin);
if(geom3::flipped) gp_swapped.emplace(wcw1.at, wcw1.spin);
}
}
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 set<pair<cell*, int>> gp_swapped;
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)
// rdir describes a loop on the boundary of that triangle, and rdir1 is the same loop in reverse direction
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 dx0 = fixg6(dx + SG2*i);
auto at1 = at + eudir(dx0);
auto dx1 = fixg6(dx0 + SG3);
DEBB(DF_GP, (at, " .. ", make_pair(at1, dx1)));
conn(at, dx0);
if(forward) { get_mapping(at).rdir = dx0; get_mapping(at1).rdir1 = dx1; }
else { get_mapping(at).rdir1 = dx0; get_mapping(at1).rdir = dx1; }
at = at + eudir(dx0);
};
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)) {
build(start, 1, true);
build(end, 2, 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
vector<loc> all_locations;
set<loc> visited;
auto visit = [&] (loc x) {
if(visited.count(x)) return;
visited.insert(x);
all_locations.push_back(x);
};
for(int i=0; i<S3; i++) visit(vc[i]);
for(int i=0; i<isize(all_locations); i++) {
auto at = all_locations[i];
auto& m = get_mapping(at);
for(int j=0; j<SG6; j++) {
if(m.rdir >= 0) {
if(m.rdir1 > m.rdir && !(j >= m.rdir && j <= m.rdir1)) continue;
if(m.rdir1 < m.rdir && !(j >= m.rdir || j <= m.rdir1)) continue;
}
auto at1 = at + eudir(j);
conn(at, j);
visit(at1);
}
}
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;
}
EX bool gp_style = true; /** disable for the old implementation which did not support fake */
/** for h in corner cordinates, rotate until it is in the correct triangle, and return the number of rotations needed */
int rotate_to_correct(hyperpoint& h) {
int sp = 0;
while(h[1] < -1e-6 || h[2] < -1e-6) {
h = cgi.gpdata->rotator * h;
sp++;
}
if(sp>SG3) sp -= SG6;
return sp;
}
hyperpoint atz(const transmatrix& T, const transmatrix& corners, loc at, int cornerid = 6, ld cf = 3) {
auto corner = corners * (loctoh_ort(at) + (corner_coords[cornerid] / cf));
int sp = rotate_to_correct(corner);
if(gp_style && corner[0] < -1e-6) {
auto ac = corner; ac[1] = 1 - corner[1]; ac[2] = 1 - corner[2]; ac[0] = -ac[0];
hyperpoint ctr = normalize(cornmul(T, hyperpoint(0, 0.5, 0.5, 0)));
int sp2 = rotate_to_correct(ac);
return spin(TAU*sp/S7) *
rgpushxto0(ctr) * rgpushxto0(ctr) * spin(M_PI + TAU*sp2/S7) *
normalize(cornmul(T, ac));
}
return normalize(spin(TAU*sp/S7) * cornmul(T, corner));
}
EX transmatrix dir_matrix(int i) {
// println(hlog, "0.8424 = 1.8705 = ", cgi.hcrossf);
auto ddspin = [] (int d) -> transmatrix {
return spin(M_PI - d * TAU / S7 - cgi.hexshift);
};
auto gxpush0 = geom3::flipped ? xpush0 : lxpush0;
return spin(-cgi.gpdata->alpha) * build_matrix(
geom3::flipped ? C02 : tile_center(),
gp_style ? (ddspin(i) * spin(-M_PI/S7) * gxpush0(cgi.hcrossf)) : ddspin(i) * gxpush0(cgi.tessf),
gp_style ? (ddspin(i) * spin(M_PI/S7) * gxpush0(cgi.hcrossf)) : ddspin(i+1) * gxpush0(cgi.tessf),
C03
);
}
EX void prepare_matrices(bool inv) {
if(!(GOLDBERG_INV || inv)) return;
if(embedded_plane) geom3::light_flip(true);
cgi.gpdata->corners_for_triangle = inverse(build_matrix(
loctoh_ort(loc(0,0)),
loctoh_ort(param),
loctoh_ort(param * loc(0,1)),
C03
));
cgi.gpdata->corners = (!gp_style) ? cgi.gpdata->corners_for_triangle : inverse(build_matrix(
loctoh_ort(loc(0,0)),
S3 == 4 ? (loctoh_ort(param * loc(1,1)) + C02)/2 : (loctoh_ort(loc(0,0)) + loctoh_ort(param) + loctoh_ort(param * loc(0,1))) / 3,
S3 == 4 ? (loctoh_ort(param * loc(1,-1)) + C02)/2 : (loctoh_ort(loc(0,0)) + loctoh_ort(param) + loctoh_ort(param * loc(0,1) * loc(0,1) * loc(0,1) * loc(0,1) * loc(0,1))) / 3,
C03
));
for(int i=0; i<MDIM; i++) {
auto ac = Hypc; ac[i] = 1;
auto xac = inverse(cgi.gpdata->corners) * ac;
xac = xac[0] * loctoh_ort(eudir(1)) + xac[1] * loctoh_ort(eudir(2)); xac[2] = 1; xac[3] = 0;
ac = cgi.gpdata->corners * xac;
set_column(cgi.gpdata->rotator, i, ac);
}
cgi.gpdata->Tf.resize(S7);
/* should work directly without flipping but it does not... flipping for now */
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);
auto& res = cgi.gpdata->Tf[i][x&GOLDBERG_MASK][y&GOLDBERG_MASK][d];
res = rgpushxto0(h) * rspintox(gpushxto0(h) * hl) * spin180();
}
}
if(geom3::flipped) {
geom3::light_flip(false);
for(int i=0; i<S7; 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++) {
auto& T = cgi.gpdata->Tf[i][x&GOLDBERG_MASK][y&GOLDBERG_MASK][d];
T = cgi.emb->base_to_actual(T);
}
} }
}
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;
if(special_fake()) scale = 1;
cgi.crossf *= 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;
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;
}
EX bool check_whirl_set(loc xy) {
if(!check_limits(xy)) {
addMessage(XLAT("Outside of the supported limits"));
return false;
}
whirl_set(xy);
return true;
}
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();
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);
int max_goldberg = (1<<GOLDBERG_BITS)/2 - 1;
dialog::addSelItem("x", its(config.first), 'x');
dialog::add_action([max_goldberg] { dialog::editNumber(config.first, 0, max_goldberg, 1, 1, "x", helptext()); });
dialog::addSelItem("y", its(config.second), 'y');
dialog::add_action([max_goldberg] { dialog::editNumber(config.second, 0, max_goldberg, 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 && (!closed_manifold || 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));
if(!check_whirl_set(p * loc(1, 1))) return;
set_variation(eVariation::untruncated);
start_game();
config = human_representation(univ_param());
}
else if(S3 == 4 && !UNRECTIFIED) {
if(!check_whirl_set(p * loc(1, 1))) return;
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);
if(!check_whirl_set((p * loc(1,1)) / 3)) return;
config = human_representation(univ_param());
}
else if(S3 == 4 && UNRECTIFIED) {
if(!check_whirl_set((p * loc(1,1)) / 2)) return;
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;