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hyperrogue/reg3.cpp
Zeno Rogue 59a9605b13 arb::relative_matrix
2020-01-16 17:13:37 +01:00

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// Hyperbolic Rogue -- regular honeycombs
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file reg3.cpp
* \brief regular honeycombs
*
* works with spherical and hyperbolic ones -- Euclidean cubic tiling implemented in euclid.cpp
* includes non-quotient spaces as well as field quotient and elliptic spaces
* hyperbolic honeycombs rely on bt:: to deal with floating point errors (just like archimedean)
*/
#include "hyper.h"
namespace hr {
#if MAXMDIM >= 4
namespace binary {
void build_tmatrix();
void virtualRebaseSimple(heptagon*& base, transmatrix& at);
int celldistance3(heptagon *c1, heptagon *c2);
hyperpoint deparabolic3(hyperpoint h);
}
EX namespace reg3 {
#if HDR
inline short& altdist(heptagon *h) { return h->emeraldval; }
#endif
map<int, int> close_distances;
EX int loop;
EX int face;
EX vector<hyperpoint> cellshape;
EX vector<hyperpoint> vertices_only;
EX transmatrix spins[12], adjmoves[12];
EX ld adjcheck;
EX ld strafedist;
EX bool dirs_adjacent[16][16];
/** for adjacent directions a,b, next_dir[a][b] is the next direction adjacent to a, in (counter?)clockwise order from b */
EX int next_dir[16][16];
template<class T> ld binsearch(ld dmin, ld dmax, const T& f) {
for(int i=0; i<200; i++) {
ld d = (dmin + dmax) / 2;
if(f(d)) dmax = d;
else dmin = d;
}
return dmin;
}
EX void generate() {
if(S7 == 4) face = 3;
if(S7 == 6) face = 4;
if(S7 == 12) face = 5;
if(S7 == 8) face = 3;
/* icosahedron not implemented */
loop = ginf[geometry].tiling_name[5] - '0';
DEBB(DF_GEOM, ("face = ", face, " loop = ", loop, " S7 = ", S7));
/* dual_angle : the angle between two face centers in the dual cell */
ld dual_angle = binsearch(0, M_PI, [&] (ld d) {
hyperpoint h0 = cpush(0, 1) * C0;
hyperpoint h1 = cspin(0, 1, d) * h0;
hyperpoint h2 = cspin(1, 2, 2*M_PI/loop) * h1;
return hdist(h0, h1) > hdist(h1, h2);
});
/* angle_between_faces : the distance between two face centers of cells */
ld angle_between_faces = binsearch(0, M_PI, [&] (ld d) {
hyperpoint h0 = cpush(0, 1) * C0;
hyperpoint h1 = cspin(0, 1, d) * h0;
hyperpoint h2 = cspin(1, 2, 2*M_PI/face) * h1;
return hdist(h0, h1) > hdist(h1, h2);
});
if(S7 == 8) {
angle_between_faces = min(angle_between_faces, M_PI - angle_between_faces);
/* 24-cell is a special case because it is the only one with '4' in the middle of the Schlaefli symbol. */
/* The computations above assume 3 */
hyperpoint h1 = hpxy3(.5,.5,.5);
hyperpoint h2 = hpxy3(.5,.5,-.5);
dual_angle = hdist(h1, h2);
}
DEBB(DF_GEOM, ("angle between faces = ", angle_between_faces));
DEBB(DF_GEOM, ("dual angle = ", dual_angle));
ld inp_length = binsearch(0, 1.55, [&] (ld d) {
hyperpoint h = xpush(-d) * spin(2*M_PI/face) * xpush0(d);
ld alpha = M_PI - atan2(-h[1], h[0]);
return (alpha < dual_angle / 2) ? hyperbolic : sphere;
});
DEBB(DF_GEOM, ("inp length = ", inp_length));
ld edge_length = hdist(xpush0(inp_length), spin(2*M_PI/face) * xpush0(inp_length));
if(S7 == 8) edge_length = hdist(normalize(hpxyz3(1,1,0,0)), normalize(hpxyz3(1,0,1,0)));
DEBB(DF_GEOM, ("edge length = ", edge_length));
/* frontal face direction */
hyperpoint h0 = xtangent(1);
/* three faces adjacent to frontal face direction */
hyperpoint h1 = cspin(0, 1, angle_between_faces) * h0;
hyperpoint h2 = cspin(1, 2, 2*M_PI/face) * h1;
hyperpoint h3 = cspin(1, 2, -2*M_PI/face) * h1;
/* directions of vertices [h0,h1,h2] and [h0,h1,h3] */
hyperpoint dir_v2 = S7 == 8 ? (h1 + h2) : (h0 + h1 + h2);
hyperpoint dir_v3 = S7 == 8 ? (h1 + h3) : (h0 + h1 + h3);
DEBB(DF_GEOM, ("dir_v2 = ", dir_v2));
DEBB(DF_GEOM, ("dir_v3 = ", dir_v3));
dir_v2 = tangent_length(dir_v2, 1);
dir_v3 = tangent_length(dir_v3, 1);
DEBB(DF_GEOM, ("S7 = ", S7));
DEBB(DF_GEOM, ("dir_v2 = ", dir_v2));
DEBB(DF_GEOM, ("dir_v3 = ", dir_v3));
/* the distance from cell center to cell vertex */
ld vertex_distance;
if(cgflags & qIDEAL) {
vertex_distance = 13;
}
else {
vertex_distance = binsearch(0, M_PI, [&] (ld d) {
// sometimes breaks in elliptic
dynamicval<eGeometry> g(geometry, elliptic ? gCell120 : geometry);
hyperpoint v2 = direct_exp(dir_v2 * d, iTable);
hyperpoint v3 = direct_exp(dir_v3 * d, iTable);
return hdist(v2, v3) >= edge_length;
});
}
DEBB(DF_GEOM, ("vertex_distance = ", vertex_distance));
/* actual vertex */
hyperpoint v2 = direct_exp(dir_v2 * vertex_distance, iTable);
hyperpoint mid = Hypc;
for(int i=0; i<face; i++) mid += cspin(1, 2, 2*i*M_PI/face) * v2;
mid = normalize(mid);
ld between_centers = 2 * hdist0(mid);
DEBB(DF_GEOM, ("between_centers = ", between_centers));
if(S7 == 12 || S7 == 8) {
spins[0] = Id;
spins[1] = cspin(0, 1, angle_between_faces) * cspin(1, 2, M_PI);
for(int a=2; a<face+1; a++) spins[a] = cspin(1, 2, 2*M_PI*(a-1)/face) * spins[1];
for(int a=S7/2; a<S7; a++) spins[a] = cspin(0, 1, M_PI) * spins[a-S7/2];
if(S7 == 8) swap(spins[6], spins[7]);
if(S7 == 12) swap(spins[8], spins[11]);
if(S7 == 12) swap(spins[9], spins[10]);
}
if(S7 == 6) {
spins[0] = Id;
spins[1] = cspin(0, 1, angle_between_faces) * cspin(1, 2, M_PI);
spins[2] = cspin(1, 2, M_PI/2) * spins[1];
for(int a=S7/2; a<S7; a++) spins[a] = spins[a-S7/2] * cspin(0, 1, M_PI);
}
if(S7 == 4) {
spins[0] = Id;
spins[1] = cspin(0, 1, angle_between_faces) * cspin(1, 2, M_PI);
for(int a=2; a<face+1; a++) spins[a] = cspin(1, 2, 2*M_PI*(a-1)/face) * spins[1];
}
cellshape.clear();
for(int a=0; a<S7; a++)
for(int b=0; b<face; b++)
cellshape.push_back(spins[a] * cspin(1, 2, 2*M_PI*b/face) * v2);
adjmoves[0] = cpush(0, between_centers) * cspin(0, 2, M_PI);
for(int i=1; i<S7; i++) adjmoves[i] = spins[i] * adjmoves[0];
for(int a=0; a<S7; a++)
DEBB(DF_GEOM, ("center of ", a, " is ", tC0(adjmoves[a])));
DEBB(DF_GEOM, ("doublemove = ", tC0(adjmoves[0] * adjmoves[0])));
adjcheck = hdist(tC0(adjmoves[0]), tC0(adjmoves[1])) * 1.0001;
int numedges = 0;
for(int a=0; a<S7; a++) for(int b=0; b<S7; b++) {
dirs_adjacent[a][b] = a != b && hdist(tC0(adjmoves[a]), tC0(adjmoves[b])) < adjcheck;
if(dirs_adjacent[a][b]) numedges++;
}
DEBB(DF_GEOM, ("numedges = ", numedges));
if(loop == 4) strafedist = adjcheck;
else strafedist = hdist(adjmoves[0] * C0, adjmoves[1] * C0);
vertices_only.clear();
for(hyperpoint h: cellshape) {
bool found = false;
for(hyperpoint h2: vertices_only) if(hdist(h, h2) < 1e-6) found = true;
if(!found) vertices_only.push_back(h);
}
for(int a=0; a<12; a++)
for(int b=0; b<12; b++)
if(reg3::dirs_adjacent[a][b])
for(int c=0; c<12; c++)
if(reg3::dirs_adjacent[a][c] && reg3::dirs_adjacent[b][c]) {
transmatrix t = build_matrix(tC0(reg3::adjmoves[a]), tC0(reg3::adjmoves[b]), tC0(reg3::adjmoves[c]), C0);
if(det(t) > 1e-3) reg3::next_dir[a][b] = c;
}
}
void binary_rebase(heptagon *h, const transmatrix& V) {
}
void test();
#if HDR
struct hrmap_quotient3 : hrmap {
vector<heptagon*> allh;
vector<vector<transmatrix>> tmatrices;
vector<cell*> acells;
transmatrix adj(heptagon *h, int d) override { return tmatrices[h->fieldval][d]; }
heptagon *getOrigin() override { return allh[0]; }
void draw() override;
transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override;
void initialize(int cell_count);
vector<cell*>& allcells() override { return acells; }
vector<hyperpoint> get_vertices(cell* c) override { return vertices_only; }
};
#endif
void hrmap_quotient3::initialize(int cell_count) {
allh.resize(cell_count);
acells.clear();
tmatrices.resize(cell_count);
for(int a=0; a<cell_count; a++) {
allh[a] = tailored_alloc<heptagon> (S7);
allh[a]->c7 = newCell(S7, allh[a]);
allh[a]->fieldval = a;
allh[a]->zebraval = 0;
allh[a]->alt = NULL;
acells.push_back(allh[a]->c7);
}
}
void hrmap_quotient3::draw() {
sphereflip = Id;
// for(int i=0; i<S6; i++) queuepoly(ggmatrix(cwt.at), shWall3D[i], 0xFF0000FF);
dq::visited_by_matrix.clear();
dq::enqueue_by_matrix(centerover->master, cview());
while(!dq::drawqueue.empty()) {
auto& p = dq::drawqueue.front();
heptagon *h = get<0>(p);
transmatrix V = get<1>(p);
dynamicval<ld> b(band_shift, get<2>(p));
bandfixer bf(V);
dq::drawqueue.pop();
cell *c = h->c7;
if(!do_draw(c, V)) continue;
drawcell(c, V);
if(in_wallopt() && isWall3(c) && isize(dq::drawqueue) > 1000) continue;
for(int d=0; d<S7; d++)
dq::enqueue_by_matrix(h->move(d), V * tmatrices[h->fieldval][d]);
}
}
transmatrix hrmap_quotient3::relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) {
if(h1 == h2) return Id;
int d = hr::celldistance(h2->c7, h1->c7);
for(int a=0; a<S7; a++) if(hr::celldistance(h1->move(a)->c7, h2->c7) < d)
return adj(h1, a) * relative_matrix(h2, h1->move(a), hint);
println(hlog, "error in hrmap_quotient3:::relative_matrix");
return Id;
}
int encode_coord(const crystal::coord& co) {
int c = 0;
for(int i=0; i<4; i++) c |= ((co[i]>>1) & 3) << (2*i);
return c;
}
EX crystal::coord decode_coord(int a) {
crystal::coord co;
for(int i=0; i<4; i++) co[i] = (a & 3) * 2, a >>= 2;
return co;
}
struct hrmap_from_crystal : hrmap_quotient3 {
hrmap_from_crystal() {
generate();
initialize(256);
if(1) {
auto m = crystal::new_map();
dynamicval<hrmap*> cm(currentmap, m);
for(int a=0; a<256; a++) {
auto co = decode_coord(a);
heptagon *h1 = get_heptagon_at(co);
for(int d=0; d<8; d++) {
int b = encode_coord(crystal::get_coord(h1->cmove(d)));
allh[a]->c.connect(d, allh[b], h1->c.spin(d), false);
tmatrices[a].push_back(crystal::get_adj(h1, d));
}
}
delete m;
}
}
};
struct hrmap_field3 : reg3::hrmap_quotient3 {
hrmap_field3() {
auto& f = currfp;
auto lgr = f.local_group;
int N = isize(f.matrices) / lgr;
initialize(N);
vector<int> moveid(S7), movedir(lgr);
for(int s=0; s<lgr; s++)
for(int i=0; i<S7; i++) if(eqmatrix(f.fullv[s] * reg3::adjmoves[0], reg3::adjmoves[i]))
moveid[i] = s;
for(int s=0; s<lgr; s++)
for(int i=0; i<S7; i++) if(hdist(tC0(inverse(f.fullv[s]) * reg3::adjmoves[0]), tC0(reg3::adjmoves[i])) < 1e-4)
movedir[s] = i;
for(int a=0; a<N; a++) {
tmatrices[a].resize(S7);
for(int b=0; b<S7; b++) {
int k = lgr*a;
k = f.gmul(f.gmul(k, moveid[b]), lgr);
for(int l=0; l<lgr; l++) if(f.gmul(k, l) % lgr == 0) {
tmatrices[a][b] = reg3::adjmoves[b] * f.fullv[l];
allh[a]->c.connect(b, allh[k/lgr], movedir[l], false);
}
}
}
create_patterns();
}
set<cellwalker> plane;
void make_plane(cellwalker cw) {
if(plane.count(cw)) return;
plane.insert(cw);
for(int i=0; i<S7; i++)
if(reg3::dirs_adjacent[i][cw.spin])
make_plane(reg3::strafe(cw, i));
}
void create_patterns() {
auto& f = currfp;
// change the geometry to make sure that the correct celldistance is used
dynamicval<eGeometry> g(geometry, gFieldQuotient);
// also, strafe needs currentmap
dynamicval<hrmap*> c(currentmap, this);
if(S7 == 12) {
// Emerald in 534
cell *a = gamestart();
cell *b = a;
for(cell *c: allcells())
if(hr::celldistance(a, c) == 5) {
b = c;
break;
}
for(cell *c: allcells())
if(hr::celldistance(a, c) > hr::celldistance(b, c))
c->master->zebraval |= 1;
// Vineyard in 534
b = (cellwalker(a, 0) + wstep + rev + wstep).at;
for(cell *c: allcells())
if(hr::celldistance(a, c) == hr::celldistance(b, c))
c->master->zebraval |= 2;
}
if(S7 == 6) {
// Emerald in 534
cell *a = gamestart();
for(cell *c: allcells())
if(hr::celldistance(a, c) > 3)
c->master->zebraval |= 1;
// Vineyard in 435
make_plane(cellwalker(gamestart(), 0));
println(hlog, "plane size = ", isize(plane));
set<int> plane_indices;
for(auto cw: plane) plane_indices.insert(cw.at->master->fieldval);
set<int> nwi;
for(int i=0; i<currfp_n(); i++) {
bool ok = true;
for(auto o: plane_indices) {
int j = currfp_gmul(i, o * f.local_group) / f.local_group;
if(plane_indices.count(j)) ok = false;
forCellEx(c1, allcells()[j]) if(plane_indices.count(c1->master->fieldval)) ok = false;
}
if(ok) nwi.insert(i);
}
int gpow = 0;
for(int i: nwi) {
int pw = 1;
int at = i;
while(true) {
at = currfp_gmul(at, i);
if(!nwi.count(at)) break;
pw++;
}
if(pw == 4) gpow = i;
}
int u = 0;
for(int a=0; a<5; a++) {
for(int o: plane_indices) {
int j = currfp_gmul(u, o * f.local_group) / f.local_group;
allcells()[j]->master->zebraval |= 2;
}
u = currfp_gmul(u, gpow);
}
}
}
};
/** homology cover of the Seifert-Weber space */
namespace seifert_weber {
using crystal::coord;
vector<coord> periods;
int flip(int x) { return (x+6) % 12; }
void build_reps() {
reg3::generate();
// start_game();
for(int a=0; a<12; a++)
for(int b=0; b<12; b++)
if(reg3::dirs_adjacent[a][b])
for(int c=0; c<12; c++)
if(reg3::dirs_adjacent[a][c] && reg3::dirs_adjacent[b][c]) {
transmatrix t = build_matrix(tC0(reg3::adjmoves[a]), tC0(reg3::adjmoves[b]), tC0(reg3::adjmoves[c]), C0);
if(det(t) > 0) next_dir[a][b] = c;
}
set<coord> boundaries;
for(int a=0; a<12; a++)
for(int b=0; b<12; b++) if(reg3::dirs_adjacent[a][b]) {
coord res = crystal::c0;
int sa = a, sb = b;
do {
// printf("%d ", sa);
if(sa < 6) res[sa]++; else res[sa-6]--;
sa = flip(sa);
sb = flip(sb);
swap(sa, sb);
sb = next_dir[sa][sb];
// sb = next_dirsa][sb];
}
while(a != sa || b != sb);
// printf("\n");
if(res > crystal::c0)
boundaries.insert(res);
}
periods.clear();
for(int index = 5; index >= 0; index--) {
for(auto k: boundaries) println(hlog, k);
println(hlog, "simplifying...");
for(auto by: boundaries) if(among(by[index], 1, -1)) {
println(hlog, "simplifying by ", by);
periods.push_back(by);
set<coord> nb;
for(auto v: boundaries)
if(v == by) ;
else if(v[index] % by[index] == 0)
nb.insert(v - by * (v[index] / by[index]));
else println(hlog, "error");
boundaries = move(nb);
break;
}
}
}
int get_rep(coord a) {
a = a - periods[0] * (a[5] / periods[0][5]);
a = a - periods[1] * (a[4] / periods[1][4]);
a = a - periods[2] * (a[3] / periods[2][3]);
for(int i=0; i<3; i++) a[i] = gmod(a[i], 5);
return a[2] * 25 + a[1] * 5 + a[0];
}
coord decode(int id) {
coord res = crystal::c0;
for(int a=0; a<3; a++) res[a] = id % 5, id /= 5;
return res;
}
struct hrmap_singlecell : hrmap_quotient3 {
hrmap_singlecell(ld angle) {
generate();
initialize(1);
tmatrices[0].resize(S7);
for(int b=0; b<S7; b++) {
allh[0]->c.connect(b, allh[0], (b+S7/2) % S7, false);
transmatrix T = reg3::adjmoves[b];
hyperpoint p = tC0(T);
tmatrices[0][b] = rspintox(p) * xpush(hdist0(p)) * cspin(2, 1, angle) * spintox(p);
}
}
};
struct hrmap_seifert_cover : hrmap_quotient3 {
hrmap_seifert_cover() {
if(periods.empty()) build_reps();
initialize(125);
for(int a=0; a<125; a++) {
tmatrices[a].resize(12);
for(int b=0; b<12; b++) {
coord x = decode(a);
if(b < 6) x[b]++;
else x[b-6]--;
int a1 = get_rep(x);
allh[a]->c.connect(b, allh[a1], flip(b), false);
transmatrix T = reg3::adjmoves[b];
hyperpoint p = tC0(T);
tmatrices[a][b] = rspintox(p) * xpush(hdist0(p)) * cspin(2, 1, 108 * degree) * spintox(p);
}
}
}
};
}
struct hrmap_reg3 : hrmap {
heptagon *origin;
hrmap *binary_map;
hrmap_quotient3 *quotient_map;
unordered_map<heptagon*, pair<heptagon*, transmatrix>> reg_gmatrix;
unordered_map<heptagon*, vector<pair<heptagon*, transmatrix> > > altmap;
vector<cell*> spherecells;
vector<cell*>& allcells() override {
if(sphere) return spherecells;
return hrmap::allcells();
}
hrmap_reg3() {
generate();
origin = tailored_alloc<heptagon> (S7);
heptagon& h = *origin;
h.s = hsOrigin;
h.cdata = NULL;
h.alt = NULL;
h.distance = 0;
h.fieldval = 0;
h.c7 = newCell(S7, origin);
if(sphere) spherecells.push_back(h.c7);
worst_error1 = 0, worst_error2 = 0;
dynamicval<hrmap*> cr(currentmap, this);
heptagon *alt = NULL;
transmatrix T = Id;
binary_map = nullptr;
quotient_map = nullptr;
#if CAP_FIELD
if(geometry == gSpace344) {
quotient_map = new hrmap_from_crystal;
h.zebraval = quotient_map->allh[0]->zebraval;
}
else if(geometry == gSpace535) {
quotient_map = new seifert_weber::hrmap_seifert_cover;
h.zebraval = quotient_map->allh[0]->zebraval;
}
else if(hyperbolic) {
quotient_map = new hrmap_field3;
h.zebraval = quotient_map->allh[0]->zebraval;
}
#endif
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gBinary3);
bt::build_tmatrix();
alt = tailored_alloc<heptagon> (S7);
alt->s = hsOrigin;
alt->emeraldval = 0;
alt->zebraval = 0;
alt->distance = 0;
alt->alt = alt;
alt->cdata = NULL;
alt->c7 = NULL;
binary_map = bt::new_alt_map(alt);
T = xpush(.01241) * spin(1.4117) * xpush(0.1241) * cspin(0, 2, 1.1249) * xpush(0.07) * Id;
}
reg_gmatrix[origin] = make_pair(alt, T);
altmap[alt].emplace_back(origin, T);
celllister cl(origin->c7, 4, 100000, NULL);
for(cell *c: cl.lst) {
hyperpoint h = tC0(relative_matrix(c->master, origin, C0));
close_distances[bucketer(h)] = cl.getdist(c);
}
}
ld worst_error1, worst_error2;
heptagon *getOrigin() override {
return origin;
}
void fix_distances(heptagon *h, heptagon *h2) {
vector<heptagon*> to_fix;
auto fix_pair = [&] (heptagon *h, heptagon *h2) {
if(!h2) return;
if(h->distance > h2->distance+1) {
h->distance = h2->distance + 1;
to_fix.push_back(h);
}
else if(h2->distance > h->distance+1) {
h2->distance = h->distance + 1;
to_fix.push_back(h2);
}
if(h->alt && h->alt == h2->alt) {
if(altdist(h) > altdist(h2) + 1) {
altdist(h) = altdist(h2) + 1;
to_fix.push_back(h);
}
else if (altdist(h2) > altdist(h) + 1) {
altdist(h2) = altdist(h) + 1;
to_fix.push_back(h2);
}
}
};
if(!h2) to_fix = {h};
else fix_pair(h, h2);
for(int i=0; i<isize(to_fix); i++) {
h = to_fix[i];
for(int j=0; j<S7; j++) fix_pair(h, h->move(j));
}
}
#define DEB 0
heptagon *counterpart(heptagon *h) {
return quotient_map->allh[h->fieldval];
}
heptagon *create_step(heptagon *parent, int d) override {
auto& p1 = reg_gmatrix[parent];
if(DEB) println(hlog, "creating step ", parent, ":", d, ", at ", p1.first, tC0(p1.second));
heptagon *alt = p1.first;
#if CAP_FIELD
transmatrix T = p1.second * (quotient_map ? quotient_map->tmatrices[parent->fieldval][d] : adjmoves[d]);
#else
transmatrix T = p1.second * adjmoves[d];
#endif
transmatrix T1 = T;
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gBinary3);
dynamicval<hrmap*> cm(currentmap, binary_map);
binary_map->virtualRebase(alt, T);
}
fixmatrix(T);
auto hT = tC0(T);
if(DEB) println(hlog, "searching at ", alt, ":", hT);
if(DEB) for(auto& p2: altmap[alt]) println(hlog, "for ", tC0(p2.second), " intval is ", intval(tC0(p2.second), hT));
ld err;
for(auto& p2: altmap[alt]) if((err = intval(tC0(p2.second), hT)) < 1e-3) {
if(err > worst_error1) println(hlog, format("worst_error1 = %lg", double(worst_error1 = err)));
// println(hlog, "YES found in ", isize(altmap[alt]));
if(DEB) println(hlog, "-> found ", p2.first);
int fb = 0;
hyperpoint old = T * (inverse(T1) * tC0(p1.second));
#if CAP_FIELD
if(quotient_map) {
p2.first->c.connect(counterpart(parent)->c.spin(d), parent, d, false);
fix_distances(p2.first, parent);
return p2.first;
}
#endif
for(int d2=0; d2<S7; d2++) {
hyperpoint back = p2.second * tC0(adjmoves[d2]);
if((err = intval(back, old)) < 1e-3) {
if(err > worst_error2) println(hlog, format("worst_error2 = %lg", double(worst_error2 = err)));
if(p2.first->move(d2)) println(hlog, "error: repeated edge");
p2.first->c.connect(d2, parent, d, false);
fix_distances(p2.first, parent);
fb++;
}
}
if(fb != 1) {
println(hlog, "found fb = ", fb);
println(hlog, old);
for(int d2=0; d2<S7; d2++) {
println(hlog, p2.second * tC0(adjmoves[d2]), " in distance ", intval(p2.second * tC0(adjmoves[d2]), old));
}
parent->c.connect(d, parent, d, false);
return parent;
}
return p2.first;
}
if(DEB) println(hlog, "-> not found");
int d2 = 0, fv = isize(reg_gmatrix);
#if CAP_FIELD
if(quotient_map) {
auto cp = counterpart(parent);
d2 = cp->c.spin(d);
fv = cp->c.move(d)->fieldval;
}
#endif
heptagon *created = tailored_alloc<heptagon> (S7);
created->c7 = newCell(S7, created);
if(sphere) spherecells.push_back(created->c7);
created->alt = NULL;
created->cdata = NULL;
#if CAP_FIELD
if(quotient_map) {
created->zebraval = quotient_map->allh[fv]->zebraval;
}
else
#endif
created->zebraval = hrand(10);
created->fieldval = fv;
created->distance = parent->distance + 1;
fixmatrix(T);
reg_gmatrix[created] = make_pair(alt, T);
altmap[alt].emplace_back(created, T);
created->c.connect(d2, parent, d, false);
return created;
}
~hrmap_reg3() {
if(binary_map) {
dynamicval<eGeometry> g(geometry, gBinary3);
delete binary_map;
}
if(quotient_map) delete quotient_map;
clearfrom(origin);
}
map<heptagon*, int> reducers;
void link_alt(const cellwalker& hs) override {
auto h = hs.at->master;
altdist(h) = 0;
if(h->alt->s != hsOrigin) reducers[h] = hs.spin;
}
void generateAlts(heptagon* h, int levs, bool link_cdata) override {
if(reducers.count(h)) {
heptspin hs(h, reducers[h]);
reducers.erase(h);
hs += wstep;
hs += rev;
altdist(hs.at) = altdist(h) - 1;
hs.at->alt = h->alt;
reducers[hs.at] = hs.spin;
fix_distances(hs.at, NULL);
}
for(int i=0; i<S7; i++) {
auto h2 = h->cmove(i);
if(h2->alt == NULL) {
h2->alt = h->alt;
altdist(h2) = altdist(h) + 1;
fix_distances(h2, NULL);
}
}
}
void draw() override {
sphereflip = Id;
// for(int i=0; i<S6; i++) queuepoly(ggmatrix(cwt.at), shWall3D[i], 0xFF0000FF);
dq::visited.clear();
dq::enqueue(centerover->master, cview());
while(!dq::drawqueue.empty()) {
auto& p = dq::drawqueue.front();
heptagon *h = get<0>(p);
transmatrix V = get<1>(p);
dynamicval<ld> b(band_shift, get<2>(p));
bandfixer bf(V);
dq::drawqueue.pop();
cell *c = h->c7;
if(!do_draw(c, V)) continue;
drawcell(c, V);
if(in_wallopt() && isWall3(c) && isize(dq::drawqueue) > 1000) continue;
for(int i=0; i<S7; i++) if(h->move(i)) {
dq::enqueue(h->move(i), V * adj(h, i));
}
}
}
transmatrix adj(heptagon *h, int d) override {
#if CAP_FIELD
if(quotient_map) return quotient_map->adj(h, d);
else
#endif
return relative_matrix(h->cmove(d), h, C0);
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
auto p1 = reg_gmatrix[h1];
auto p2 = reg_gmatrix[h2];
transmatrix T = Id;
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gBinary3);
dynamicval<hrmap*> cm(currentmap, binary_map);
T = binary_map->relative_matrix(p2.first, p1.first, hint);
}
T = inverse(p1.second) * T * p2.second;
if(elliptic && T[LDIM][LDIM] < 0) T = centralsym * T;
return T;
}
vector<hyperpoint> get_vertices(cell* c) override {
return vertices_only;
}
};
EX hrmap* new_map() {
if(geometry == gSeifertCover) return new seifert_weber::hrmap_seifert_cover;
if(geometry == gSeifertWeber) return new seifert_weber::hrmap_singlecell(108*degree);
if(geometry == gHomologySphere) return new seifert_weber::hrmap_singlecell(36*degree);
if(quotient && !sphere) return new hrmap_field3;
return new hrmap_reg3;
}
hrmap_reg3* regmap() {
return ((hrmap_reg3*) currentmap);
}
EX int celldistance(cell *c1, cell *c2) {
if(c1 == c2) return 0;
if(c1 == currentmap->gamestart()) return c2->master->distance;
if(c2 == currentmap->gamestart()) return c1->master->distance;
auto r = regmap();
hyperpoint h = tC0(r->relative_matrix(c1->master, c2->master, C0));
int b = bucketer(h);
if(close_distances.count(b)) return close_distances[b];
dynamicval<eGeometry> g(geometry, gBinary3);
return 20 + bt::celldistance3(r->reg_gmatrix[c1->master].first, r->reg_gmatrix[c2->master].first);
}
EX bool pseudohept(cell *c) {
auto m = regmap();
if(cgflags & qSINGLE) return true;
if(sphere) {
hyperpoint h = tC0(m->relative_matrix(c->master, regmap()->origin, C0));
if(S7 == 12) {
hyperpoint h1 = cspin(0, 1, atan2(16, 69) + M_PI/4) * h;
for(int i=0; i<4; i++) if(abs(abs(h1[i]) - .5) > .01) return false;
return true;
}
if(S7 == 8)
return h[3] >= .99 || h[3] <= -.99 || abs(h[3]) < .01;
if(loop == 3 && face == 3 && S7 == 4)
return c == m->gamestart();
if(loop == 4 && face == 3)
return abs(h[3]) > .9;
if(loop == 3 && face == 4)
return abs(h[3]) > .9;
if(loop == 5 && face == 3)
return abs(h[3]) > .99 || abs(h[0]) > .99 || abs(h[1]) > .99 || abs(h[2]) > .99;
}
// chessboard pattern in 534
if(geometry == gSpace534)
return c->master->distance & 1;
if(geometry == gField534)
return hr::celldistance(c, currentmap->gamestart()) & 1;
if(geometry == gCrystal344 || geometry == gCrystal534 || geometry == gSeifertCover)
return false;
if(quotient) return false; /* added */
if(hyperbolic) {
heptagon *h = m->reg_gmatrix[c->master].first;
return (h->zebraval == 1) && (h->distance & 1);
}
return false;
}
EX void generate_cellrotations() {
auto &cr = cgi.cellrotations;
if(isize(cr)) return;
for(int a=0; a<S7; a++)
for(int b=0; b<S7; b++)
for(int c=0; c<S7; c++) {
using reg3::adjmoves;
transmatrix T = build_matrix(adjmoves[a]*C0, adjmoves[b]*C0, adjmoves[c]*C0, C0);
if(abs(det(T)) < 0.001) continue;
transmatrix U = build_matrix(adjmoves[0]*C0, adjmoves[1]*C0, adjmoves[2]*C0, C0);
transmatrix S = U * inverse(T);
if(abs(det(S) - 1) > 0.01) continue;
vector<int> perm(S7);
for(int x=0; x<S7; x++) perm[x] = -1;
for(int x=0; x<S7; x++)
for(int y=0; y<S7; y++)
if(hdist(S * adjmoves[x] * C0, adjmoves[y] * C0) < .1) perm[x] = y;
bool bad = false;
for(int x=0; x<S7; x++) if(perm[x] == -1) bad = true;
if(bad) continue;
cr.emplace_back(S, perm);
}
}
#endif
#if 0
/* More precise, but very slow distance. Not used/optimized for now */
ld adistance(cell *c) {
hyperpoint h = tC0(regmap()->reg_gmatrix[c->master].second);
h = bt::deparabolic3(h);
return regmap()->reg_gmatrix[c->master].first->distance * log(2) - h[0];
}
unordered_map<pair<cell*, cell*>, int> memo;
bool cdd;
int celldistance(cell *c1, cell *c2) {
if(memo.count(make_pair(c1, c2))) return memo[make_pair(c1, c2)];
if(c1 == c2) return 0;
vector<cell*> v[2];
v[0].push_back(c1);
v[1].push_back(c2);
int steps = 0;
map<cell*, int> visited;
visited[c1] = 1;
visited[c2] = 2;
while(true) {
if(cdd) {
println(hlog, "state ", steps, "/",isize(v[0]), "/", isize(v[1]));
println(hlog, " A: ", v[0]);
println(hlog, " B: ", v[1]);
}
for(int i: {0,1}) {
vector<cell*> new_v;
for(cell *c: v[i]) forCellCM(cn, c) if(adistance(cn) < adistance(c)) {
auto &vi = visited[cn];
if((vi&3) == 0) {
vi = 4 * (steps+1);
vi |= (1<<i);
new_v.push_back(cn);
}
else if((vi&3) == 2-i) {
vector<pair<cell*, int>> ca1, ca2;
int b1 = 4*steps-4;
int b2 = ((vi>>2)<<2) - 4;
for(auto p: visited) {
if(cdd) println(hlog, p);
int ps = p.second & 3;
if(ps == 1+i && p.second >= b1)
ca1.emplace_back(p.first, p.second/4);
if(ps == 2-i && p.second >= b2 && p.second <= b2+8)
ca2.emplace_back(p.first, p.second/4);
}
int bound = 1<<16;
for(auto p1: ca1) for(auto p2: ca2) {
hyperpoint h = tC0(relative_matrix(p1.first->master, p2.first->master));
int b = bucketer(h);
if(close_distances.count(b)) {
int d = close_distances[b] + p1.second + p2.second;
if(cdd) println(hlog, "candidate: close=", close_distances[b], p1, p2, "; h = ", h);
if(d < bound) bound = d;
}
else if(cdd) println(hlog, "bucket missing");
}
return memo[make_pair(c1, c2)] = bound;
return bound;
}
}
v[i] = std::move(new_v);
}
steps++;
}
}
cellwalker target;
int tsteps;
int dist_alt(cell *c) {
if(!target.at) {
target = cellwalker(currentmap->gamestart(), 0);
tsteps = 0;
for(int i=0; i<30; i++) target += wstep, target += rev, tsteps++;
}
if(specialland == laCamelot) return reg3::celldistance(c, target.at);
else {
int d = reg3::celldistance(c, target.at) - tsteps;
if(d < 10) target += wstep, target += rev, tsteps++;
return d;
}
}
#endif
// Construct a cellwalker in direction j from cw.at, such that its direction is as close
// as possible to cw.spin. Assume that j and cw.spin are adjacent
#if MAXMDIM >= 4
EX cellwalker strafe(cellwalker cw, int j) {
hyperpoint hfront = tC0(adjmoves[cw.spin]);
transmatrix T = currentmap->adj(cw.at, j);
for(int i=0; i<S7; i++) if(i != cw.at->c.spin(j))
if(hdist(hfront, T * tC0(adjmoves[i])) < strafedist + .01)
return cellwalker(cw.at->move(j), i);
println(hlog, "incorrect strafe");
exit(1);
}
EX vector<pair<string, string> > rels;
EX int xp_order, r_order, rx_order;
EX transmatrix full_X, full_R, full_P;
geometry_information *for_cgi;
EX int matrix_order(const transmatrix A) {
transmatrix T = A;
int res = 1;
while(!eqmatrix(T, Id)) {
res++; T = T * A;
}
return res;
}
EX void construct_relations() {
if(for_cgi == &cgi) return;
for_cgi = &cgi;
rels.clear();
reg3::generate();
reg3::generate_cellrotations();
vector<transmatrix> all;
vector<string> formulas;
formulas.push_back("");
all.push_back(Id);
hyperpoint v = reg3::cellshape[0];
auto add = [&] (transmatrix T) {
for(int i=0; i<isize(all); i++) if(eqmatrix(all[i], T)) return i;
int S = isize(all);
all.push_back(T);
return S;
};
auto cons = [&] (int i0, int i1, int i2) {
using reg3::adjmoves;
transmatrix T = build_matrix(adjmoves[ 0]*C0, adjmoves[ 1]*C0, adjmoves[ 2]*C0, C0);
transmatrix U = build_matrix(adjmoves[i0]*C0, adjmoves[i1]*C0, adjmoves[i2]*C0, C0);
return U * inverse(T);
};
full_P = reg3::adjmoves[0];
full_R = S7 == 8 ? cons(1, 7, 0) : cons(1, 2, 0);
full_X = S7 == 8 ? cons(1, 0, 6) : S7 == 6 ? cons(1, 0, 5) : cons(1, 0, reg3::face);
println(hlog, reg3::cellshape);
println(hlog, "cellshape = ", isize(reg3::cellshape));
bool ok = true;
int last_i = -1;
for(hyperpoint h: reg3::cellshape) {
int i = 0, j = 0;
for(hyperpoint u: reg3::cellshape) if(hdist(h, full_X*u) < 1e-4) i++;
for(hyperpoint u: reg3::cellshape) if(hdist(h, full_R*u) < 1e-4) j++;
if(last_i == -1) last_i = i;
if(i != j || i != last_i) ok = false;
}
if(!ok) { println(hlog, "something wrong"); exit(1); }
add(Id);
auto work = [&] (transmatrix T, int p, char c) {
if(hdist0(tC0(T)) > 5) return;
for(hyperpoint h: reg3::cellshape) if(hdist(T * h, v) < 1e-4) goto ok;
return;
ok:
int id = add(T);
// println(hlog, p, " x ", (s0+c), " = ", id);
if(id >= isize(formulas)) formulas.push_back(formulas[p] + c);
else if(id == 0) println(hlog, "reached identity: ", formulas[p]+c);
else if(formulas[p][0] != formulas[id][0])
rels.emplace_back(formulas[p] + c, formulas[id]);
};
for(int i=0; i<isize(all); i++) {
transmatrix T = all[i];
work(T * full_R, i, 'R');
work(T * full_X, i, 'X');
work(T * full_P, i, 'P');
}
xp_order = matrix_order(full_X * full_P);
r_order = matrix_order(full_R);
rx_order = matrix_order(full_R * full_X);
println(hlog, "orders = ", tie(rx_order, r_order, xp_order));
}
EX }
#endif
}
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