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hyperrogue/reg3.cpp

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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 binary:: 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 bucketer(ld x) {
return int(x * 10 + 100000.5) - 100000;
}
EX int bucketer(hyperpoint h) {
return bucketer(h[0]) + 1000 * bucketer(h[1]) + 1000000 * bucketer(h[2]);
}
EX int loop;
EX int face;
EX vector<hyperpoint> cellshape;
vector<hyperpoint> vertices_only;
EX transmatrix spins[12], adjmoves[12];
EX ld adjcheck;
EX ld strafedist;
EX bool dirs_adjacent[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';
println(hlog, "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);
}
println(hlog, "angle between faces = ", angle_between_faces);
println(hlog, "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;
});
println(hlog, "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)));
println(hlog, "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);
println(hlog, "dir_v2 = ", dir_v2);
println(hlog, "dir_v3 = ", dir_v3);
dir_v2 = tangent_length(dir_v2, 1);
dir_v3 = tangent_length(dir_v3, 1);
println(hlog, "S7 = ", S7);
println(hlog, "dir_v2 = ", dir_v2);
println(hlog, "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;
});
}
println(hlog, "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);
println(hlog, "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++)
println(hlog, "center of ", a, " is ", tC0(adjmoves[a]));
println(hlog, "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++;
}
println(hlog, "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);
}
}
void binary_rebase(heptagon *h, const transmatrix& V) {
}
void test();
struct hrmap_quotient3 : hrmap {
vector<heptagon*> allh;
vector<vector<transmatrix>> tmatrices;
};
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();
allh.resize(256);
tmatrices.resize(256);
for(int a=0; a<256; 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;
}
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 : hrmap_quotient3 {
vector<cell*> acells;
int mgmul(std::initializer_list<int> v) {
int a = 0;
for(int b: v) a = a ? currfp_gmul(a, b) : b;
return a;
}
vector<transmatrix> fullmatrices;
int P, R, X;
transmatrix full_P, full_R, full_X;
vector<int> field_adjmoves;
vector<int> cyclers;
int perm_group;
vector<int> cell_to_code;
vector<int> code_to_cell;
void seek(set<int>& seen_matrices, set<int>& seen_codes, const transmatrix& at, int ccode, const hyperpoint checker) {
if(hdist0(tC0(at)) > 4) return;
int b = reg3::bucketer(tC0(at));
if(seen_matrices.count(b)) return;
seen_matrices.insert(b);
for(int a=0; a<perm_group; a++) {
transmatrix T = at * fullmatrices[a];
if(hdist(T * checker, checker) < 1e-2) {
int co = mgmul({ccode, a});
seen_codes.insert(co);
fullmatrices[co] = T;
}
}
for(int a=0; a<perm_group; a++) seek(seen_matrices, seen_codes, at * fullmatrices[a] * full_P, mgmul({ccode, a, P}), checker);
}
hrmap_field3() {
eGeometry g = geometry;
geometry = gSpace435;
reg3::generate();
R = currfp_get_R();
P = currfp_get_P();
X = currfp_get_X();
full_P = reg3::adjmoves[0] * cspin(0, 2, M_PI) * cspin(0, 1, M_PI);
full_R = spin(-2 * M_PI / 4);
full_X = cspin(1, 2, M_PI / 2);
println(hlog, "full_P = ", full_P, " / ", R);
println(hlog, "full_R = ", full_R, " / ", P);
println(hlog, "full_X = ", full_X, " / ", X);
int N = currfp_n();
perm_group = 24;
fullmatrices.resize(N);
fullmatrices[0] = Id;
vector<bool> known(perm_group, false);
known[0] = true;
for(int a=0; a<perm_group; a++)
for(int i=0; i<perm_group; i++) if(known[i]) {
int iR = currfp_gmul(i, R);
fullmatrices[iR] = fullmatrices[i] * full_R;
known[iR] = true;
int iX = currfp_gmul(i, X);
fullmatrices[iX] = fullmatrices[i] * full_X;
known[iX] = true;
}
for(int i=0; i<perm_group; i++) if(known[i]) {
println(hlog, i, ". ", fullmatrices[i]);
}
// find cav such that:
// cav * Id * C0 = corner0
// cav * adjmoves[0] * C0 = corner1
// cav * adjmoves[1] * C0 = corner3
// cav * adjmoves[2] * C0 = cornerx
hyperpoint corner0 = reg3::cellshape[0];
hyperpoint corner1 = reg3::cellshape[1];
hyperpoint corner3 = reg3::cellshape[3];
hyperpoint cornerx;
for(hyperpoint h: reg3::cellshape) println(hlog, "some corner ", h);
for(hyperpoint h: reg3::cellshape)
if(hdist(h, corner1) > .1 && hdist(h, corner3) > .1 && abs(hdist(h, corner0)-hdist(corner0, corner1)) < .1)
cornerx = h;
println(hlog, "corner0 = ", corner0);
println(hlog, "corner1 = ", corner1);
println(hlog, "corner3 = ", corner3);
println(hlog, "cornerx = ", cornerx);
transmatrix adj = Id, iadj = Id;
geometry = g;
reg3::generate();
cyclers.clear();
println(hlog, "S7 = ", S7);
if(S7 == 12) {
transmatrix resmatrix;
set_column(resmatrix, 0, corner0);
set_column(resmatrix, 1, corner1);
set_column(resmatrix, 2, corner3);
set_column(resmatrix, 3, cornerx);
transmatrix transformer;
set_column(transformer, 0, C0);
set_column(transformer, 1, tC0(reg3::adjmoves[0]));
set_column(transformer, 2, tC0(reg3::adjmoves[1]));
set_column(transformer, 3, tC0(reg3::adjmoves[2]));
transmatrix cav = resmatrix * inverse(transformer);
println(hlog, "cav = ", cav);
println(hlog, "cav * C0 = ", cav * C0);
set<int> seen_matrices;
set<int> seen_codes;
seek(seen_matrices, seen_codes, Id, 0, corner0);
for(int x: seen_codes) cyclers.push_back(x);
perm_group = isize(cyclers);
adj = cav;
iadj = inverse(cav);
}
else {
for(int i=0; i<perm_group; i++) cyclers.push_back(i);
}
field_adjmoves.resize(S7);
for(int i=0; i<S7; i++) field_adjmoves[i] = -1;
for(int i=0; i<S7; i++)
for(int a: cyclers)
for(int b: cyclers) {
transmatrix T = iadj * fullmatrices[a] * full_P * fullmatrices[b] * adj;
if(eqmatrix(T, reg3::adjmoves[i])) {
int code = mgmul({a,P,b});
field_adjmoves[i] = code;
println(hlog, i, " = ", make_tuple(a,P,b), " = ", code, " T = ", T);
}
}
println(hlog, "field_adjmoves = ", field_adjmoves);
println(hlog, "finding code_to_cell/cell_to_code...");
cell_to_code.clear();
code_to_cell.resize(N);
for(int i=0; i<N; i++) code_to_cell[i] = -1;
for(int i=0; i<N; i++) if(code_to_cell[i] == -1) {
for(int j: cyclers) code_to_cell[currfp_gmul(i, j)] = isize(cell_to_code);
cell_to_code.push_back(i);
}
println(hlog, "building allh...");
int cells = N / perm_group;
allh.resize(cells);
for(int i=0; i<cells; i++) {
allh[i] = tailored_alloc<heptagon> (S7);
allh[i]->c7 = newCell(S7, allh[i]);
allh[i]->fieldval = i;
allh[i]->zebraval = 0;
allh[i]->alt = NULL;
acells.push_back(allh[i]->c7);
}
println(hlog, "finding tmatrices...");
tmatrices.resize(cells);
for(int i=0; i<cells; i++) {
for(int d=0; d<S7; d++) {
int found = 0;
int tmul = currfp_gmul(cell_to_code[i], field_adjmoves[d]);
for(int s: cyclers) {
int tmul2 = currfp_gmul(tmul, s);
if(cell_to_code[code_to_cell[tmul2]] == tmul2) {
allh[i]->move(d) = allh[code_to_cell[tmul2]];
allh[i]->c7->move(d) = allh[i]->move(d)->c7;
tmatrices[i].push_back(reg3::adjmoves[d] * iadj * fullmatrices[s] * adj);
found++;
}
}
if(found != 1) println(hlog, "bad found: ", i, "/", d, "/", found);
// println(hlog, "tmatrix(",i,",",d,") = ", tmatrices[i][d]);
}
}
println(hlog, "setting spin...");
for(int i=0; i<cells; i++)
for(int d=0; d<S7; d++)
for(int e=0; e<S7; e++)
if(allh[i]->move(d)->move(e) == allh[i]) {
allh[i]->c.setspin(d, e, false);
allh[i]->c7->c.setspin(d, e, 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() {
// change the geometry to make sure that the correct celldistance is used
dynamicval<eGeometry> g(geometry, S7 == 12 ? gField534 : gField435);
// 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 = code_to_cell[currfp_gmul(i, cell_to_code[o])];
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 = code_to_cell[currfp_gmul(u, cell_to_code[o])];
allcells()[j]->master->zebraval |= 2;
}
u = currfp_gmul(u, gpow);
}
}
}
void draw() override {
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(viewctr.at, 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(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 relative_matrix(heptagon *h2, heptagon *h1) override {
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 tmatrices[h1->fieldval][a] * relative_matrix(h2, h1->move(a));
println(hlog, "error in hrmap_field3:::relative_matrix");
return Id;
}
heptagon *getOrigin() override { return allh[0]; }
vector<cell*>& allcells() override { return acells; }
vector<hyperpoint> get_vertices(cell* c) override {
return vertices_only;
}
};
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;
}
if(hyperbolic && !(cgflags & qIDEAL)) {
quotient_map = new hrmap_field3;
h.zebraval = quotient_map->allh[0]->zebraval;
}
#endif
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gBinary3);
binary::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 = binary::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));
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::virtualRebaseSimple(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(viewctr.at, 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(wallopt && isWall3(c) && isize(dq::drawqueue) > 1000) continue;
for(int i=0; i<S7; i++) if(h->move(i)) {
#if CAP_FIELD
if(quotient_map) dq::enqueue(h->move(i), V * quotient_map->tmatrices[h->fieldval][i]);
else
#endif
dq::enqueue(h->move(i), V * relative_matrix(h->move(i), h));
}
}
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1) 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);
}
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(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));
int b = bucketer(h);
if(close_distances.count(b)) return close_distances[b];
dynamicval<eGeometry> g(geometry, gBinary3);
return 20 + binary::celldistance3(r->reg_gmatrix[c1->master].first, r->reg_gmatrix[c2->master].first);
}
EX bool pseudohept(cell *c) {
auto m = regmap();
if(sphere) {
hyperpoint h = tC0(m->relative_matrix(c->master, regmap()->origin));
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)
return false;
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 = binary::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->relative_matrix(cw.at->cmove(j)->master, cw.at->master);
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 }
#endif
}
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