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hyperrogue/euclid.cpp

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// Hyperbolic Rogue -- Euclidean geometry
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file euclid.cpp
* \brief Euclidean geometry, including 2D, 3D, and quotient spaces
*/
#include "hyper.h"
namespace hr {
EX namespace euc {
#if HDR
struct coord : array<int, 3> {
coord() {}
coord(int x, int y, int z) { self[0] = x; self[1] = y; self[2] = z; }
coord& operator += (coord b) { for(int i: {0,1,2}) self[i] += b[i]; return self; }
coord& operator -= (coord b) { for(int i: {0,1,2}) self[i] -= b[i]; return self; }
coord operator + (coord b) const { coord a = self; return a += b; }
coord operator - (coord b) const { coord a = self; return a -= b; }
coord operator -() const { return coord(-self[0], -self[1], -self[2]); }
coord& operator +() { return self; }
const coord& operator +() const { return self; }
coord operator *(int x) const { return coord(x*self[0], x*self[1], x*self[2]); }
friend coord operator *(int x, const coord& y) { return coord(x*y[0], x*y[1], x*y[2]); }
};
typedef array<coord, 3> intmatrix;
#endif
EX const coord euzero = coord(0,0,0);
EX const coord eutester = coord(3,7,0);
EX intmatrix euzeroall = make_array<coord>(euzero, euzero, euzero);
static const intmatrix main_axes = make_array<coord>(coord(1,0,0), coord(0,1,0), coord(0,0,1));
EX vector<coord> get_shifttable() {
static const coord D0 = main_axes[0];
static const coord D1 = main_axes[1];
static const coord D2 = main_axes[2];
vector<coord> shifttable;
/* for portal spaces... */
auto g = geometry;
if(S7 == 6 && WDIM == 3) g = gCubeTiling;
switch(g) {
case gCubeTiling:
shifttable = { +D0, +D1, +D2 };
break;
case gRhombic3:
shifttable = { D0+D1, D0+D2, D1+D2, D1-D2, D0-D2, D0-D1 };
break;
case gBitrunc3:
shifttable = { 2*D0, 2*D1, 2*D2, D0+D1+D2, D0+D1-D2, D0-D1-D2, D0-D1+D2 };
break;
case gEuclid:
shifttable = { D0, D1, D1-D0, -D0, -D1, D0-D1 };
break;
case gEuclidSquare:
shifttable = { D0, D1, -D0, -D1 };
break;
default:
printf("euc::get_shifttable() called in geometry that is not euclid3");
exit(1);
}
// reverse everything
int s = isize(shifttable);
for(int i=0; i<s; i++) shifttable.push_back(-shifttable[i]);
return shifttable;
}
EX coord basic_canonicalize(coord x);
#if HDR
struct torus_config {
/** periods entered by the user */
intmatrix user_axes;
/** OR'ed flags: 1 -- flip X in 3D, 2 -- flip Y in 3D, 4 -- flip X/Y in 3D, 8 -- Klein bottle in 2D, 16 -- third turn in 3D, 32 -- Hantzsche-Wendt in 3D */
int twisted;
torus_config() {}
torus_config(intmatrix user_axes, int twisted) : user_axes(user_axes), twisted(twisted) {}
};
struct torus_config_full : torus_config {
/** optimal representation of the periods */
intmatrix optimal_axes;
/** regular axes (?) */
intmatrix regular_axes;
/** in 2D: the period vector which is reflected */
gp::loc twisted_vec;
/** in 2D: a vector orthogonal to twisted_vec */
gp::loc ortho_vec;
/** determinant */
int det;
/** the number of infinite dimensions */
int infinite_dims;
/** ? */
intmatrix inverse_axes;
/** for canonicalization on tori */
map<coord, int> hash;
vector<coord> seq;
int index;
void reset() { index = 0; hash.clear(); seq.clear(); }
/** add to the tori canonicalization list */
void add(coord val);
/** get the representative on the tori canonicalization list */
coord get(coord x);
/** find the equivalence class of coo */
coord compute_cat(coord coo);
/** canonicalize coord x; in case of twisting, adjust d, M, and mirr accordingly */
void canonicalize(coord& x, coord& d, transmatrix& M, bool& mirr);
};
#endif
EX torus_config eu_input, eu_edit;
EX torus_config_full eu;
struct hrmap_euclidean : hrmap_standard {
vector<coord> shifttable;
vector<transmatrix> tmatrix;
map<coord, heptagon*> spacemap;
map<heptagon*, coord> ispacemap;
cell *camelot_center;
map<gp::loc, struct cdata> eucdata;
void compute_tmatrix() {
shifttable = get_shifttable();
tmatrix.resize(S7);
for(int i=0; i<S7; i++)
tmatrix[i] = eumove(shifttable[i]);
}
void on_dim_change() override {
compute_tmatrix();
}
vector<cell*> toruscells;
vector<cell*>& allcells() override {
if(bounded) {
if(isize(toruscells) == 0) {
celllister cl(getOrigin()->c7, 1000, 1000000, NULL);
toruscells = cl.lst;
}
return toruscells;
}
return hrmap::allcells();
}
hrmap_euclidean() {
compute_tmatrix();
camelot_center = NULL;
build_torus3(geometry);
#if CAP_IRR
if(!valid_irr_torus()) {
addMessage(XLAT("Error: period mismatch"));
eu_input = irr::base_config;
build_torus3(geometry);
}
#endif
}
heptagon *getOrigin() override {
return get_at(euzero);
}
heptagon *get_at(coord at) {
if(spacemap.count(at))
return spacemap[at];
else {
auto h = tailored_alloc<heptagon> (S7);
if(!IRREGULAR)
h->c7 = newCell(S7, h);
#if CAP_IRR
else {
coord m0 = shifttable[0];
transmatrix dummy;
bool mirr;
auto ati = at;
irr::base_config.canonicalize(ati, m0, dummy, mirr);
indenter id(2);
for(int spin=0; spin<S7; spin++) if(shifttable[spin] == m0) {
irr::link_to_base(h, heptspin(((hrmap_euclidean*)irr::base)->get_at(ati), spin, mirr));
break;
}
}
#endif
h->distance = 0;
h->cdata = NULL;
h->alt = NULL;
if(S7 != 14)
h->zebraval = gmod(at[0] + at[1] * 2 + at[2] * 4, 5);
else
h->zebraval = at[0] & 1;
spacemap[at] = h;
ispacemap[h] = at;
return h;
}
}
heptagon *create_step(heptagon *parent, int d) override {
int d1 = (d+S7/2)%S7;
bool mirr = false;
transmatrix I;
auto v = ispacemap[parent] + shifttable[d];
auto st = shifttable[d1];
eu.canonicalize(v, st, I, mirr);
if(eu.twisted)
for(int i=0; i<S7; i++) if(shifttable[i] == st) d1 = i;
heptagon *h = get_at(v);
h->c.connect(d1, parent, d, mirr);
return h;
}
transmatrix adj(heptagon *h, int i) override {
if(!eu.twisted) return tmatrix[i];
transmatrix res = tmatrix[i];
coord id = ispacemap[h];
id += shifttable[i];
auto dummy = euzero;
bool dm = false;
eu.canonicalize(id, dummy, res, dm);
return res;
}
transmatrix adj(cell *c, int i) override {
if(WDIM == 3) return adj(c->master, i);
else return hrmap_standard::adj(c, i);
}
void draw_at(cell *at, const shiftmatrix& where) override {
dq::clear_all();
dq::enqueue_by_matrix(at->master, where * master_relative(centerover, true));
while(!dq::drawqueue.empty()) {
auto& p = dq::drawqueue.front();
heptagon *h = p.first;
shiftmatrix V = p.second;
dq::drawqueue.pop();
cell *c = h->c7;
bool draw = drawcell_subs(c, V * spin(master_to_c7_angle()));
if(in_wallopt() && isWall3(c) && isize(dq::drawqueue) > 1000 && !hybrid::pmap) continue;
if(draw) for(int i=0; i<S7; i++)
dq::enqueue_by_matrix(h->move(i), optimized_shift(V * adj(h, i)));
}
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
if(eu.twisted) {
if(h1 == h2) return Id;
for(int s=0; s<S7; s++) if(h2 == h1->move(s)) return adj(h1, s);
coord c1 = ispacemap[h1];
coord c2 = ispacemap[h2];
transmatrix T = eumove(c2 - c1);
transmatrix I = Id;
coord cs = c1;
for(int s=0; s<4; s++) {
for(int a=-1; a<=1; a++)
for(int b=-1; b<=1; b++) {
if(b && WDIM == 2) continue;
transmatrix T1 = I * eumove((c2 - cs) + a*eu.user_axes[0] + b*eu.user_axes[1]);
if(hdist(tC0(T1), hint) < hdist(tC0(T), hint))
T = T1;
}
auto co = eu.user_axes[WDIM-1];
cs += co;
I = I * eumove(co);
auto dummy = euzero;
bool dm = false;
eu.canonicalize(cs, dummy, I, dm);
}
return T;
}
auto d = ispacemap[h2] - ispacemap[h1];
d = basic_canonicalize(d);
return eumove(d);
}
vector<hyperpoint> get_vertices(cell* c) override {
vector<hyperpoint> res;
if(S7 < 14)
for(ld a: {-.5,.5}) for(ld b: {-.5,.5}) for(ld c: {-.5, .5}) res.push_back(hpxy3(a,b,c));
if(S7 == 12) {
res.push_back(hpxy3(1,0,0));
res.push_back(hpxy3(-1,0,0));
res.push_back(hpxy3(0,1,0));
res.push_back(hpxy3(0,-1,0));
res.push_back(hpxy3(0,0,1));
res.push_back(hpxy3(0,0,-1));
}
if(S7 == 14) {
for(ld a: {-1.,-.5,0.,.5,1.})
for(ld b: {-1.,-.5,0.,.5,1.})
for(ld c: {-1.,-.5,0.,.5,1.})
if(a == 0 || b == 0 || c == 0)
if(a == .5 || a == -.5 || b == .5 || b == -.5 || c == .5 || c == -.5)
if(a == 1 || a == -1 || b == 1 || b == -1 || c == 1 || c == -1)
res.push_back(hpxy3(a,b,c));
}
return res;
}
};
hrmap_euclidean* cubemap() {
if(fake::in()) return FPIU(cubemap());
return ((hrmap_euclidean*) currentmap);
}
hrmap_euclidean* eucmap() {
return cubemap();
}
EX vector<coord>& get_current_shifttable() { return cubemap()->shifttable; }
EX map<coord, heptagon*>& get_spacemap() { return cubemap()->spacemap; }
EX map<heptagon*, coord>& get_ispacemap() { return cubemap()->ispacemap; }
EX cell *& get_camelot_center() { return cubemap()->camelot_center; }
EX heptagon* get_at(coord co) { return cubemap()->get_at(co); }
EX hrmap* new_map() {
return new hrmap_euclidean;
}
EX transmatrix move_matrix(heptagon *h, int i) {
return cubemap()->adj(h, i);
}
EX bool pseudohept(cell *c) {
if(cgflags & qPORTALSPACE) return false;
coord co = cubemap()->ispacemap[c->master];
if(S7 == 12) {
for(int i=0; i<3; i++) if((co[i] & 1)) return false;
}
else {
for(int i=0; i<3; i++) if(!(co[i] & 1)) return false;
}
return true;
}
EX int dist_alt(cell *c) {
if(WDIM == 2) {
auto v = full_coords2(c);
return euclidAlt(v.first, v.second);
}
if(specialland == laCamelot) return dist_relative(c) + roundTableRadius(c);
auto v = cubemap()->ispacemap[c->master];
if(S7 == 6) return v[2];
else if(S7 == 12) return (v[0] + v[1] + v[2]) / 2;
else return v[2]/2;
}
EX bool get_emerald(cell *c) {
auto v = cubemap()->ispacemap[c->master];
int s0 = 0, s1 = 0;
for(int i=0; i<3; i++) {
v[i] = gmod(v[i], 6);
int d = min(v[i], 6-v[i]);;
s0 += min(v[i], 6-v[i]);
s1 += 3-d;
}
if(s0 == s1) println(hlog, "equality");
return s0 > s1;
}
bool cellvalid(coord v) {
if(S7 == 6) return true;
if(S7 == 12) return (v[0] + v[1] + v[2]) % 2 == 0;
if(S7 == 14) return v[0] % 2 == v[1] % 2 && v[0] % 2 == v[2] % 2;
return false;
}
EX int celldistance(coord v) {
if(S7 == 6)
return abs(v[0]) + abs(v[1]) + abs(v[2]);
else {
for(int i=0; i<3; i++) v[i] = abs(v[i]);
sort(v.begin(), v.end());
int dist = 0;
if(S7 == 12) {
int d = v[1] - v[0]; v[1] -= d; v[2] -= d;
dist += d;
int m = min((v[2] - v[0]), v[0]);
dist += 2 * m;
v[0] -= m; v[1] -= m; v[2] -= m * 2;
if(v[0])
dist += (v[0] + v[1] + v[2]) / 2;
else
dist += v[2];
}
else {
dist = v[0] + (v[1] - v[0]) / 2 + (v[2] - v[0]) / 2;
}
return dist;
}
}
EX int celldistance(cell *c1, cell *c2) {
auto cm = cubemap();
if(GDIM == 2)
return dist(full_coords2(c1), full_coords2(c2));
return celldistance(basic_canonicalize(cm->ispacemap[c1->master] - cm->ispacemap[c2->master]));
}
EX void set_land(cell *c) {
if(cgflags & qPORTALSPACE) return;
setland(c, specialland);
auto m = cubemap();
auto co = m->ispacemap[c->master];
int dv = 1;
if(geometry != gCubeTiling) dv = 2;
int hash = 0;
for(int a=0; a<3; a++) hash = 1317 * hash + co[a] / 4;
set_euland3(c, co[0]*120, co[1]*120, (co[1]+co[2]) / dv, hash);
}
EX int dist_relative(cell *c) {
auto m = cubemap();
auto& cc = m->camelot_center;
int r = roundTableRadius(NULL);
cell *start = m->gamestart();
if(!cc) {
cc = start;
while(euc::celldistance(cc, start) < r + 5)
cc = cc->cmove(hrand(cc->type));
}
return euc::celldistance(cc, c) - r;
}
/* quotient spaces */
int determinant(const intmatrix T) {
int det = 0;
for(int i=0; i<3; i++)
det += T[0][i] * T[1][(i+1)%3] * T[2][(i+2)%3];
for(int i=0; i<3; i++)
det -= T[0][i] * T[1][(i+2)%3] * T[2][(i+1)%3];
return det;
}
intmatrix scaled_inverse(const intmatrix T) {
intmatrix T2;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
T2[j][i] = (T[(i+1)%3][(j+1)%3] * T[(i+2)%3][(j+2)%3] - T[(i+1)%3][(j+2)%3] * T[(i+2)%3][(j+1)%3]);
return T2;
}
EX torus_config torus3(int x, int y, int z) {
intmatrix T0 = euzeroall;
tie(T0[0][0], T0[1][1], T0[2][2]) = make_tuple(x, y, z);
return {T0, 0};
}
EX torus_config clear_torus3() {
return {euzeroall, 0};
}
coord torus_config_full::compute_cat(coord coo) {
coord cat = euzero;
auto& T2 = inverse_axes;
for(int i=0; i<3; i++) {
int val = T2[0][i] * coo[0] + T2[1][i] * coo[1] + T2[2][i] * coo[2];
if(i < WDIM - infinite_dims) val = gmod(val, det);
cat += val * main_axes[i];
}
return cat;
}
EX bool valid_third_turn(const intmatrix& m) {
if(m[0][2] != -m[0][0]-m[0][1]) return false;
if(m[1][0] != m[0][1]) return false;
if(m[1][1] != m[0][2]) return false;
if(m[1][2] != m[0][0]) return false;
if(m[2][0] != m[2][1]) return false;
if(m[2][0] != m[2][2]) return false;
return true;
}
EX torus_config make_hantzsche_wendt(int v) {
intmatrix im;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++) im[i][j] = 0;
for(int i=0; i<3; i++) {
im[i][i] = v;
im[i][(i+1)%3] = v;
}
return {im, 32};
}
EX bool valid_hantzsche_wendt(const intmatrix& m) {
return m[0][0] > 0 && m == make_hantzsche_wendt(m[0][0]).user_axes;
}
EX torus_config make_third_turn(int a, int b, int c) {
intmatrix T0;
T0[0][0] = a;
T0[0][1] = b;
T0[2][0] = c;
T0[0][2] = -T0[0][0]-T0[0][1];
T0[1][0] = T0[0][1];
T0[1][1] = T0[0][2];
T0[1][2] = T0[0][0];
T0[2][1] = T0[2][2] = c;
return {T0, 8};
}
EX torus_config make_quarter_turn(int a, int b, int c) {
intmatrix T0 = euzeroall;
T0[0][0] = a;
T0[0][1] = b;
T0[2][0] = c;
return {T0, 5};
}
void torus_config_full::add(coord val) {
auto cat = compute_cat(val); if(hash.count(cat)) return; hash[cat] = isize(seq); seq.push_back(val);
}
coord torus_config_full::get(coord x) {
auto cat = compute_cat(x);
auto& st = cubemap()->shifttable;
while(!hash.count(cat)) {
if(index == isize(seq)) throw hr_exception();
auto v = seq[index++];
for(auto s: st) add(v + s);
}
return seq[hash[cat]];
}
EX bool valid_irr_torus() {
#if CAP_IRR
if(!IRREGULAR) return true;
if(eu.twisted) return false;
for(int i=0; i<2; i++) {
auto x = eu.user_axes[i];
coord dm = eutester;
transmatrix dummy = Id;
bool mirr = false;
irr::base_config.canonicalize(x, dm, dummy, mirr);
auto x0 = eu.user_axes[i];
auto dm0 = eutester;
eu.canonicalize(x0, dm0, dummy, mirr);
if(x0 != euzero || dm0 != eutester) return false;
}
#endif
return true;
}
EX void build_torus3(eGeometry g) {
int dim = ginf[g].g.gameplay_dimension;
eu.user_axes = eu_input.user_axes;
if(dim == 2) eu.user_axes[2] = euzero;
eu.optimal_axes = eu.user_axes;
again:
for(int i=0; i<dim; i++) if(eu.optimal_axes[i] < euzero) eu.optimal_axes[i] = -eu.optimal_axes[i];
if(eu.optimal_axes[0] < eu.optimal_axes[1]) swap(eu.optimal_axes[0], eu.optimal_axes[1]);
if(eu.optimal_axes[1] < eu.optimal_axes[dim-1]) swap(eu.optimal_axes[1], eu.optimal_axes[dim-1]);
if(eu.optimal_axes[0] < eu.optimal_axes[1]) swap(eu.optimal_axes[0], eu.optimal_axes[1]);
for(int i=0; i<3; i++) {
int i1 = (i+1) % 3;
int i2 = (i+2) % 3;
for(int a=-10; a<=10; a++)
for(int b=-10; b<=10; b++) {
coord cand = eu.optimal_axes[i] + eu.optimal_axes[i1] * a + eu.optimal_axes[i2] * b;
if(celldistance(cand) < celldistance(eu.optimal_axes[i])) {
eu.optimal_axes[i] = cand;
goto again;
}
}
}
eu.regular_axes = eu.optimal_axes;
eu.infinite_dims = dim;
for(int i=0; i<dim; i++) if(eu.optimal_axes[i] != euzero) eu.infinite_dims--;
int attempt = 0;
next_attempt:
for(int i=dim-eu.infinite_dims; i<3; i++)
eu.regular_axes[i] = main_axes[(attempt+i)%3];
eu.det = determinant(eu.regular_axes);
if(eu.det == 0) {
attempt++;
if(attempt == 3) {
println(hlog, "weird singular!\n");
exit(1);
}
goto next_attempt;
}
if(eu.det < 0) eu.det = -eu.det;
eu.inverse_axes = scaled_inverse(eu.regular_axes);
eu.reset();
eu.add(euzero);
eu.twisted = eu_input.twisted;
if(dim == 3) {
auto &T0 = eu.user_axes;
if(valid_third_turn(eu.user_axes)) {
eu.twisted &= 16;
if(g == gRhombic3 && (T0[2][2]&1)) eu.twisted = 0;
if(g == gBitrunc3 && (T0[0][0]&1)) eu.twisted = 0;
if(g == gBitrunc3 && (T0[1][1]&1)) eu.twisted = 0;
}
else if(valid_hantzsche_wendt(eu.user_axes)) {
eu.twisted &= 32;
if(g == gBitrunc3 && (T0[0][0]&1)) eu.twisted = 0;
}
else {
eu.twisted &= 7;
if(g != gCubeTiling && ((T0[0][0]+T0[2][2]) & 1)) eu.twisted &=~ 1;
if(g != gCubeTiling && ((T0[1][1]+T0[2][2]) & 1)) eu.twisted &=~ 2;
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
if(i != j && T0[i][j]) eu.twisted = 0;
if(T0[2][2] == 0) eu.twisted = 0;
if(T0[0][0] != T0[1][1]) eu.twisted &= 3;
}
}
else {
eu.twisted &= 8;
eu.twisted_vec = to_loc(eu.user_axes[1]);
eu.ortho_vec = to_loc(eu.user_axes[0]);
if(eu.twisted_vec == gp::loc{0,0}) eu.twisted = 0;
if(chiral(eu.twisted_vec)) eu.twisted = 0;
if(dscalar(eu.twisted_vec, eu.ortho_vec))
eu.twisted = 0;
}
set_flag(ginf[g].flags, qANYQ, eu.infinite_dims < dim);
set_flag(ginf[g].flags, qBOUNDED, eu.infinite_dims == 0);
set_flag(ginf[g].flags, qSMALL, eu.infinite_dims == 0 && eu.det <= 4096);
bool nonori = false;
if(eu.twisted&1) nonori = !nonori;
if(eu.twisted&2) nonori = !nonori;
if(eu.twisted&4) nonori = !nonori;
if(eu.twisted&8) nonori = !nonori;
set_flag(ginf[g].flags, qNONORIENTABLE, nonori);
}
EX void build_torus3() {
for(eGeometry g: { gEuclid, gEuclidSquare, gCubeTiling, gRhombic3, gBitrunc3})
build_torus3(g);
}
void swap01(transmatrix& M) {
for(int i=0; i<4; i++) swap(M[i][0], M[i][1]);
}
gp::loc ort1() { return (S3 == 3 ? gp::loc(1, -2) : gp::loc(0, 1)); }
int diagonal_cross(const coord& a, const coord& b) {
return a[0]*b[1] + a[1]*b[2] + a[2]*b[0]
- b[0]*a[1] - b[1]*a[2] - b[2]*a[0];
}
void torus_config_full::canonicalize(coord& x, coord& d, transmatrix& M, bool& mirr) {
if(!twisted) {
if(infinite_dims == WDIM) return;
if(infinite_dims == WDIM-1) {
auto& o = optimal_axes;
while(celldistance(x + o[0]) <= celldistance(x)) x += o[0];
while(celldistance(x - o[0]) < celldistance(x)) x -= o[0];
return;
}
x = get(x);
return;
}
auto& T0 = user_axes;
if(twisted & 32) {
int period = T0[0][0];
auto& coo = x;
while(true) {
restart:
/* These coordinates cause the algorithm below to go in circles. We simply break if they are detected */
if(coo[0] >= 0 && coo[1] == period - coo[0] && coo[2] == -coo[1] && coo[0]*2 > period && coo[0] < period) return;
if(coo[0]*2 <= -period && coo[0] >= -period && coo[2] == period+coo[0] && coo[2] == -coo[1]) return;
/* apply periods */
for(int i=0; i<3; i++) {
int j = (i+1) % 3;
int k = (i+2) % 3;
int v1 = coo[i] + coo[j];
int v2 = coo[i] - coo[j];
if(v1 >= period) {
coo[i] -= period; coo[j] -= period;
}
else if(v1 < -period) {
coo[i] += period; coo[j] += period;
}
else if(v2 >= period) {
coo[i] -= period; coo[j] += period;
}
else if(v2 < -period) {
coo[i] += period; coo[j] -= period;
}
else continue;
d[j] = -d[j]; d[k] = -d[k];
coo[j] = -coo[j]; coo[k] = -coo[k];
transmatrix S = Id;
S[j][j] = -1; S[k][k] = -1;
M = M * S;
goto restart;
}
return;
}
}
#if MAXMDIM >= 4
if(twisted & 16) {
int period = T0[2][2];
transmatrix RotYZX = Zero;
RotYZX[1][0] = 1;
RotYZX[2][1] = 1;
RotYZX[0][2] = 1;
RotYZX[3][3] = 1;
auto& coo = x;
while(true) {
auto coosum = coo[0] + coo[1] + coo[2];
if(coosum >= 3 * period) {
coo[0] -= period, coo[1] -= period, coo[2] -= period;
tie(d[0], d[1], d[2]) = make_tuple(d[1], d[2], d[0]);
tie(coo[0], coo[1], coo[2]) = make_tuple(coo[1], coo[2], coo[0]);
M = M * RotYZX;
}
else if(coosum < 0) {
coo[0] += period, coo[1] += period, coo[2] += period;
tie(d[0], d[1], d[2]) = make_tuple(d[2], d[0], d[1]);
tie(coo[0], coo[1], coo[2]) = make_tuple(coo[2], coo[0], coo[1]);
M = M * RotYZX * RotYZX;
}
else break;
}
if(T0[0] != euzero) {
while(diagonal_cross(coo, T0[1]) < 0) coo -= T0[0];
while(diagonal_cross(coo, T0[1]) > 0) coo += T0[0];
while(diagonal_cross(coo, T0[0]) > 0) coo -= T0[1];
while(diagonal_cross(coo, T0[0]) < 0) coo += T0[1];
}
return;
}
#endif
if(WDIM == 3) {
#if MAXMDIM >= 4
auto& coo = x;
while(coo[2] >= T0[2][2]) {
coo[2] -= T0[2][2];
if(twisted & 1) coo[0] *= -1, d[0] *= -1, M = M * MirrorX;
if(twisted & 2) coo[1] *= -1, d[1] *= -1, M = M * MirrorY;
if(twisted & 4) swap(coo[0], coo[1]), swap01(M), swap(d[0], d[1]);
}
while(coo[2] < 0) {
coo[2] += T0[2][2];
if(twisted & 4) swap(coo[0], coo[1]), swap(d[0], d[1]), swap01(M);
if(twisted & 1) coo[0] *= -1, d[0] *= -1, M = M * MirrorX;
if(twisted & 2) coo[1] *= -1, d[1] *= -1, M = M * MirrorY;
}
for(int i: {0,1})
if(T0[i][i]) coo[i] = gmod(coo[i], T0[i][i]);
return;
#endif
}
else {
gp::loc coo = to_loc(x);
gp::loc ort = ort1() * twisted_vec;
int dsc = dscalar(twisted_vec, twisted_vec);
gp::loc d0 (d[0], d[1]);
hyperpoint h = eumove(to_coord(twisted_vec)) * C0;
while(true) {
int dsx = dscalar(coo, twisted_vec);
if(dsx >= dsc) coo = coo - twisted_vec;
else if (dsx < 0) coo = coo + twisted_vec;
else break;
M = M * spintox(h) * MirrorY * rspintox(h);
auto s = ort * dscalar(d0, ort) * 2;
auto v = dscalar(ort, ort);
s.first /= v;
s.second /= v;
d0 = d0 - s;
s = ort * dscalar(coo, ort) * 2;
s.first /= v;
s.second /= v;
coo = coo - s;
mirr = !mirr;
}
if(ortho_vec != gp::loc{0,0}) {
int osc = dscalar(ortho_vec, ortho_vec);
while(true) {
int dsx = dscalar(coo, ortho_vec);
if(dsx >= osc) coo = coo - ortho_vec;
else if(dsx < 0) coo = coo + ortho_vec;
else break;
}
}
d[0] = d0.first; d[1] = d0.second;
x = to_coord(coo);
return;
}
}
coord basic_canonicalize(coord x) {
transmatrix M = Id;
auto dummy = euzero;
bool dm = false;
eu.canonicalize(x, dummy, M, dm);
return x;
}
EX void prepare_torus3() {
eu_edit = eu_input;
}
EX void show_fundamental() {
initquickqueue();
shiftmatrix M = ggmatrix(cwt.at);
shiftpoint h0 = M*C0;
auto& T_edit = eu_edit.user_axes;
hyperpoint ha = M.T*(eumove(T_edit[0]) * C0 - C0) / 2;
hyperpoint hb = M.T*(eumove(T_edit[1]) * C0 - C0) / 2;
if(WDIM == 3) {
hyperpoint hc = M.T*(eumove(T_edit[2]) * C0 - C0) / 2;
for(int d:{-1,1}) for(int e:{-1,1}) {
queueline(h0+d*ha+e*hb-hc, h0+d*ha+e*hb+hc, 0xFFFFFFFF);
queueline(h0+d*hb+e*hc-ha, h0+d*hb+e*hc+ha, 0xFFFFFFFF);
queueline(h0+d*hc+e*ha-hb, h0+d*hc+e*ha+hb, 0xFFFFFFFF);
}
}
else {
queueline(h0+ha+hb, h0+ha-hb, 0xFFFFFFFF);
queueline(h0-ha+hb, h0-ha-hb, 0xFFFFFFFF);
queueline(h0+ha+hb, h0-ha+hb, 0xFFFFFFFF);
queueline(h0+ha-hb, h0-ha-hb, 0xFFFFFFFF);
}
quickqueue();
}
intmatrix on_periods(gp::loc a, gp::loc b) {
intmatrix res;
for(int i=0; i<3; i++) for(int j=0; j<3; j++) res[i][j] = 0;
res[0][0] = a.first;
res[0][1] = a.second;
res[1][0] = b.first;
res[1][1] = b.second;
res[2][2] = 1;
return res;
}
torus_config single_row_torus(int qty, int dy) {
return { on_periods(gp::loc{dy, -1}, gp::loc{qty, 0}), 0 };
}
torus_config regular_torus(gp::loc p) {
return { on_periods(p, gp::loc(0,1) * p), 0 };
}
EX torus_config rectangular_torus(int x, int y, bool klein) {
if(S3 == 3) y /= 2;
return { on_periods(ort1() * gp::loc(y,0), gp::loc(x,0)), klein?8:0 };
}
void torus_config_option(string name, char key, torus_config tc) {
dialog::addBoolItem(name, eu_edit.user_axes == tc.user_axes && eu_edit.twisted == tc.twisted && PURE, key);
dialog::add_action([tc] {
stop_game();
eu_input = eu_edit = tc;
set_variation(eVariation::pure);
start_game();
});
}
EX int quotient_size = 2;
EX void show_torus3() {
int dim = WDIM;
auto& T_edit = eu_edit.user_axes;
auto& twisted_edit = eu_edit.twisted;
cmode = sm::SIDE | sm::MAYDARK | sm::TORUSCONFIG;
gamescreen(1);
dialog::init(XLAT("Euclidean quotient spaces"));
for(int y=0; y<dim+1; y++)
dialog::addBreak(100);
dialog::addInfo(XLAT("columns specify periods"));
dialog::addInfo(XLAT("(vectors you need to take to get back to start)"));
dialog::addBreak(50);
show_fundamental();
if(dim == 3) {
bool nondiag = false;
for(int i=0; i<dim; i++)
for(int j=0; j<dim; j++)
if(T_edit[i][j] && i != j) nondiag = true;
if(valid_third_turn(T_edit)) {
auto g = geometry;
if(g == gCubeTiling ||
(g == gRhombic3 && T_edit[2][2] % 2 == 0) ||
(g == gBitrunc3 && T_edit[0][0] % 2 == 0 && T_edit[1][1] % 2 == 0))
dialog::addBoolItem(XLAT("third-turn space"), twisted_edit & 16, 'x');
else
dialog::addBoolItem(XLAT("make it even"), twisted_edit & 16, 'x');
dialog::add_action([] { eu_edit.twisted ^= 16; });
}
if(valid_hantzsche_wendt(T_edit)) {
auto g = geometry;
if(g == gCubeTiling || g == gRhombic3 || (g == gBitrunc3 && T_edit[0][0] % 2 == 0))
dialog::addBoolItem(XLAT("Hantzsche-Wendt space"), twisted_edit & 32, 'x');
else
dialog::addBoolItem(XLAT("make it even"), twisted_edit & 32, 'x');
dialog::add_action([] { eu_edit.twisted ^= 32; });
}
if(nondiag) {
dialog::addInfo(XLAT("twisting implemented only for diagonal matrices"));
dialog::addInfo(XLAT("or for columns : (A,B,C), (B,C,A), (D,D,D) where A+B+C=0"));
dialog::addBreak(200);
}
else if(T_edit[dim-1][dim-1] == 0) {
dialog::addInfo(XLAT("nothing to twist"));
dialog::addInfo(XLAT("change the bottom left corner"));
dialog::addBreak(100);
}
else {
auto g = geometry;
if(g == gCubeTiling || (T_edit[0][0]+T_edit[2][2]) % 2 == 0)
dialog::addBoolItem(XLAT("flip X coordinate"), twisted_edit & 1, 'x');
else
dialog::addBoolItem(XLAT("flipping X impossible"), twisted_edit & 1, 'x');
dialog::add_action([] { eu_edit.twisted ^= 1; });
if(g == gCubeTiling || (T_edit[1][1]+T_edit[2][2]) % 2 == 0)
dialog::addBoolItem(XLAT("flip Y coordinate"), twisted_edit & 2, 'y');
else
dialog::addBoolItem(XLAT("flipping Y impossible"), twisted_edit & 2, 'y');
dialog::add_action([] { eu_edit.twisted ^= 2; });
if(T_edit[0][0] == T_edit[1][1])
dialog::addBoolItem(XLAT("swap X and Y"), twisted_edit & 4, 'z');
else
dialog::addBoolItem(XLAT("swapping impossible"), twisted_edit & 4, 'z');
dialog::add_action([] { eu_edit.twisted ^= 4; });
}
dialog::addBreak(50);
dialog::addItem("special manifolds", 'S');
dialog::add_action([] {
dialog::editNumber(quotient_size, 1, 12, 1, 2, "special manifold size", "");
dialog::extra_options = [] {
auto q = quotient_size;
torus_config_option(XLAT("third-turn space"), 'A', make_third_turn(q,0,q));
torus_config_option(XLAT("quarter-turn space"), 'B', make_quarter_turn(q,0,q));
torus_config_option(XLAT("Hantzsche-Wendt space"), 'C', make_hantzsche_wendt(q));
};
});
}
else {
if(T_edit[1][0] == 0 && T_edit[1][1] == 0)
dialog::addInfo(XLAT("change the second column for Möbius bands and Klein bottles"));
else if(chiral(to_loc(T_edit[1])))
dialog::addInfo(XLAT("second period is chiral -- cannot be mirrored"));
else if(dscalar(to_loc(T_edit[1]), to_loc(T_edit[0])))
dialog::addInfo(XLAT("periods must be orthogonal for mirroring"));
else {
dialog::addBoolItem(XLAT("mirror flip in the second period"), twisted_edit & 8, 'x');
dialog::add_action([] { eu_edit.twisted ^= 8; });
}
dialog::addBreak(50);
torus_config_option(XLAT("single-cell torus"), 'A', regular_torus(gp::loc{1,0}));
torus_config_option(XLAT("large regular torus"), 'B', regular_torus(gp::loc{12, 0}));
torus_config_option(XLAT("Klein bottle"), 'C', rectangular_torus(12, 6, true));
torus_config_option(XLAT("cylinder"), 'D', rectangular_torus(6, 0, false));
torus_config_option(XLAT("Möbius band"), 'E', rectangular_torus(6, 0, true));
if(S3 == 3) torus_config_option(XLAT("seven-colorable torus"), 'F', regular_torus(gp::loc{1,2}));
if(S3 == 3) torus_config_option(XLAT("HyperRogue classic torus"), 'G', single_row_torus(381, -22));
torus_config_option(XLAT("no quotient"), 'H', rectangular_torus(0, 0, false));
}
dialog::addBreak(50);
dialog::addBoolItem(XLAT("standard rotation"), eqmatrix(models::euclidean_spin, Id), 's');
dialog::add_action([] { rotate_view(models::euclidean_spin); });
#if CAP_RUG
if(GDIM == 2) {
dialog::addBoolItem(XLAT("hypersian rug mode"), (rug::rugged), 'u');
dialog::add_action(rug::select);
}
#endif
dialog::addBreak(50);
char xch = 'p';
for(eGeometry g: {gCubeTiling, gRhombic3, gBitrunc3}) {
if(dim == 2) g = geometry;
dialog::addItem(XLAT(ginf[g].menu_displayed_name), xch++);
dialog::add_action([g] {
stop_game();
set_geometry(g);
eu_input = eu_edit;
start_game();
});
if(dim == 2) break;
}
dialog::addBreak(50);
dialog::addBack();
dialog::display();
int i = -1;
for(auto& v: dialog::items) if(v.type == dialog::diBreak) {
if(i >= 0 && i < dim) {
for(int j=0; j < dim; j++) {
char ch = 'a' + i * 3 + j;
if(displayfr(dialog::dcenter + dialog::dfspace * 4 * (j-(dim-1.)/2), v.position, 2, dialog::dfsize, its(T_edit[j][i]), 0xFFFFFF, 8))
getcstat = ch;
dialog::add_key_action(ch, [i, j] {
auto& T_edit = eu_edit.user_axes;
dialog::editNumber(T_edit[j][i], -10, +10, 1, 0, "", XLAT(
"This matrix lets you play on the quotient spaces of three-dimensional. "
"Euclidean space. Every column specifies a translation vector which "
"takes you back to the starting point. For example, if you put "
"set 2, 6, 0 on the diagonal, you get back to the starting point "
"if you move 2 steps in the X direction, 6 steps in the Y direction "
"(the quotient space is infinite in the Z direction).\n\n"
"You can also introduce twists for diagonal matrices: after going "
"the given number of steps in the Z direction, the space is also "
"mirrored or rotated. (More general 'twisted' spaces are currently "
"not implemented.)"
)
);
dialog::extra_options = show_fundamental;
});
}
}
i++;
}
}
#if CAP_COMMANDLINE
int euArgs() {
using namespace arg;
if(0) ;
else if(argis("-t3")) {
PHASEFROM(2);
stop_game();
auto& T0 = eu_input.user_axes;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++) {
shift(); T0[i][j] = argi();
}
build_torus3();
}
else if(argis("-t2")) {
PHASEFROM(2);
stop_game();
auto& T0 = eu_input.user_axes;
for(int i=0; i<2; i++)
for(int j=0; j<2; j++) {
shift(); T0[i][j] = argi();
}
shift(); eu_input.twisted = argi();
build_torus3();
}
else if(argis("-twistthird")) {
PHASEFROM(2);
stop_game();
shift(); int a = argi();
shift(); int b = argi();
shift(); int c = argi();
eu_input = make_third_turn(a, b, c);
build_torus3();
}
else if(argis("-twist3")) {
PHASEFROM(2);
stop_game();
auto& T0 = eu_input.user_axes;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++) T0[i][j] = 0;
for(int i=0; i<3; i++) {
shift(); T0[i][i] = argi();
}
shift(); eu_input.twisted = argi();
build_torus3();
}
else if(argis("-hw")) {
PHASEFROM(2);
stop_game();
shift();
eu_input = make_hantzsche_wendt(argi());
build_torus3();
}
else if(argis("-twisttest")) {
start_game();
celllister cl(cwt.at, 10000, 10000, NULL);
for(cell *c: cl.lst) {
heptagon *h = c->master;
for(int i=0; i<S7; i++)
for(int j=0; j<S7; j++)
for(int k=0; k<S7; k++)
for(int l=0; l<S7; l++)
if(h->move(i) && c->move(k) && h->move(i)->move(j) == h->move(k)->move(l) && h->move(i)->move(j)) {
transmatrix T1 = move_matrix(h, i) * move_matrix(h->move(i), j);
transmatrix T2 = move_matrix(h, k) * move_matrix(h->move(k), l);
if(!eqmatrix(T1, T2)) {
println(hlog, c, " @ ", cubemap()->ispacemap[c->master], " : ", i, "/", j, "/", k, "/", l, " :: ", T1, " vs ", T2);
exit(1);
}
}
}
}
else return 1;
return 0;
}
auto euhook = addHook(hooks_args, 100, euArgs);
#endif
EX int dscalar(gp::loc e1, gp::loc e2) {
return 2 * (e1.first * e2.first + e1.second*e2.second) + (S3 == 3 ? e1.first*e2.second + e2.first * e1.second : 0);
}
EX int dsquare(gp::loc e) { return dscalar(e, e)/2; }
EX int dcross(gp::loc e1, gp::loc e2) {
return e1.first * e2.second - e1.second*e2.first;
}
EX gp::loc full_coords2(cell *c) {
if(INVERSE) {
cell *c1 = gp::get_mapped(c);
return UIU(full_coords2(c1));
}
auto ans = eucmap()->ispacemap[c->master];
if(S7 == 4 && BITRUNCATED) {
if(c == c->master->c7) return to_loc(ans) * gp::loc(1,1);
else {
auto res = full_coords2(c->cmove(0)) + full_coords2(c->cmove(4));
res.first /= 2;
res.second /= 2;
return res;
}
}
if(BITRUNCATED)
return to_loc(ans) * gp::loc(1,1) + (c == c->master->c7 ? gp::loc(0,0) : gp::eudir((c->c.spin(0)+4)%6));
if(GOLDBERG) {
auto li = gp::get_local_info(c);
gp::loc shift(0,0);
if(li.first_dir >= 0) shift = gp::eudir(li.last_dir) * li.relative;
return to_loc(ans) * gp::param + shift;
}
return to_loc(ans);
}
/** this is slow, but we use it only for small p's */
EX cell* at(gp::loc p) {
cellwalker cw(currentmap->gamestart());
while(p.first--) cw += revstep;
cw ++;
while(p.second--) cw += revstep;
return cw.at;
}
EX coord to_coord(gp::loc p) { return coord(p.first, p.second, 0); }
EX gp::loc sdxy() { return to_loc(eu.user_axes[1]) * gp::univ_param(); }
EX pair<bool, string> coord_display(const shiftmatrix& V, cell *c) {
if(c != c->master->c7) return {false, ""};
hyperpoint hx = eumove(main_axes[0]) * C0;
hyperpoint hy = eumove(main_axes[1]) * C0;
hyperpoint hz = WDIM == 2 ? C0 : eumove(main_axes[2]) * C0;
hyperpoint h = kz(inverse(build_matrix(hx, hy, hz, C03)) * inverse_shift(ggmatrix(cwt.at->master->c7), V) * C0);
if(WDIM == 3)
return {true, fts(h[0]) + "," + fts(h[1]) + "," + fts(h[2]) };
else
return {true, fts(h[0]) + "," + fts(h[1]) };
}
EX gp::loc to_loc(const coord& v) { return gp::loc(v[0], v[1]); }
EX map<gp::loc, cdata>& get_cdata() { return eucmap()->eucdata; }
EX transmatrix eumove(coord co) {
const double q3 = sqrt(double(3));
if(WDIM == 3) {
return eupush3(co[0], co[1], co[2]);
}
transmatrix Mat = Id;
if(a4) {
Mat[0][LDIM] += co[0] * cgi.tessf;
Mat[1][LDIM] += co[1] * cgi.tessf;
}
else {
Mat[0][LDIM] += (co[0] + co[1] * .5) * cgi.tessf;
Mat[1][LDIM] += co[1] * q3 /2 * cgi.tessf;
}
return Mat;
}
EX transmatrix eumove(gp::loc co) { return eumove(to_coord(co)); }
EX bool chiral(gp::loc g) {
int x = g.first;
int y = g.second;
if(x == 0) return false;
if(y == 0) return false;
if(x+y == 0) return false;
if(x==y) return false;
if(S3 == 3 && y == -2*x) return false;
if(S3 == 3 && x == -2*y) return false;
return true;
}
EX void twist_once(gp::loc coo) {
coo = coo - eu.twisted_vec * gp::univ_param();
if(eu.twisted&8) {
gp::loc ort = ort1() * eu.twisted_vec * gp::univ_param();
auto s = ort * dscalar(coo, ort) * 2;
auto v = dscalar(ort, ort);
s.first /= v;
s.second /= v;
coo = coo - s;
}
}
EX int dist(int sx, int sy, bool reduce IS(true)) {
int z0 = abs(sx);
int z1 = abs(sy);
if(a4 && BITRUNCATED)
return (z0 == z1 && z0 > 0 && !reduce) ? z0+1: max(z0, z1);
if(a4) return z0 + z1;
int z2 = abs(sx+sy);
return max(max(z0,z1), z2);
}
EX int dist(gp::loc a, gp::loc b) {
return dist(a.first-b.first, a.second-b.second, (a.first ^ a.second)&1);
}
EX int cyldist(gp::loc a, gp::loc b) {
a = to_loc(basic_canonicalize(to_coord(a)));
b = to_loc(basic_canonicalize(to_coord(b)));
if(!quotient) return dist(a, b);
int best = 0;
for(int sa=0; sa<16; sa++) {
auto _a = a, _b = b;
if(sa&1) twist_once(_a);
if(sa&2) twist_once(_b);
if(sa&4) _a = _a + eu.ortho_vec * gp::univ_param();
if(sa&8) _b = _b + eu.ortho_vec * gp::univ_param();
int val = dist(_a, _b);
if(sa == 0 || val < best) best = val;
}
return best;
}
EX void generate() {
#if MAXMDIM >= 4
if(fake::in()) {
fake::generate();
return;
}
auto v = euc::get_shifttable();
auto& cs = cgi.cellshape;
cgi.loop = 4;
cgi.schmid = 3;
cs.clear();
cs.resize(S7);
if(S7 == 6) {
cgi.adjcheck = 1;
cgi.face = 4;
for(int w=0; w<6; w++) {
for(int a=0; a<4; a++) {
int t[3];
t[0] = (w>=3) ? -1 : 1;
t[1] = among(a, 0, 3) ? -1 : 1;
t[2] = among(a, 2, 3) ? -1 : 1;
int x = w%3;
int y = (x+2)%3;
int z = (y+2)%3;
cs[w].push_back(hpxy3(t[x]/2., t[y]/2., t[z]/2.));
}
}
}
if(S7 == 12) {
cgi.adjcheck = sqrt(2);
cgi.face = 4;
for(int w=0; w<12; w++) {
auto co = v[w];
vector<int> valid;
for(int c=0; c<3; c++) if(co[c]) valid.push_back(c);
int third = 3 - valid[1] - valid[0];
hyperpoint v0 = cpush0(valid[0], co[valid[0]] > 0 ? 1 : -1);
hyperpoint v1 = cpush0(valid[1], co[valid[1]] > 0 ? 1 : -1);
cs[w].push_back(v0);
cs[w].push_back(v0/2 + v1/2 + cpush0(third, .5) - C0);
cs[w].push_back(v1);
cs[w].push_back(v0/2 + v1/2 + cpush0(third, -.5) - C0);
}
}
if(S7 == 14) {
cgi.adjcheck = 2;
cgi.face = 4; /* the first face */
auto v = euc::get_shifttable();
for(int w=0; w<14; w++) {
if(w%7 < 3) {
int z = w>=7?-1:1;
cs[w].push_back(cpush0(w%7, z) + cpush0((w%7+1)%3, 1/2.) - C0);
cs[w].push_back(cpush0(w%7, z) + cpush0((w%7+2)%3, 1/2.) - C0);
cs[w].push_back(cpush0(w%7, z) + cpush0((w%7+1)%3,-1/2.) - C0);
cs[w].push_back(cpush0(w%7, z) + cpush0((w%7+2)%3,-1/2.) - C0);
}
else {
auto t = v[w];
ld x = t[0], y = t[1], z = t[2];
for(hyperpoint h: {
hpxy3(x, y/2, 0), hpxy3(x/2, y, 0), hpxy3(0, y, z/2),
hpxy3(0, y/2, z), hpxy3(x/2, 0, z), hpxy3(x, 0, z/2)
}) cs[w].push_back(h);
}
}
}
reg3::make_vertices_only();
#endif
}
/** @brief returns true if the current geometry is based on this module
* (For example, Archimedean, kite, or fake with underlying non-Euclidean geometry returns false)
*/
EX bool in() {
if(fake::in()) return FPIU(in());
return euclid && standard_tiling();
}
EX bool in(int dim) { return in() && WDIM == dim; }
EX bool in(int dim, int s7) { return in(dim) && S7 == s7; }
EX }
EX gp::loc euc2_coordinates(cell *c) {
if(euc::in()) return euc::full_coords2(c);
hyperpoint h = calc_relative_matrix(c, currentmap->gamestart(), C0) * C0;
return gp::loc(floor(h[0]), floor(h[1]));
}
}
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