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euclid.cpp
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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> {
explicit coord() = default;
constexpr explicit coord(int x, int y, int z) : array<int,3> {{x,y,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 constexpr 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:
case gMengerSponge:
shifttable = { +D0, +D1, +D2 };
break;
case gRhombic3:
case gSierpinskiTet:
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:
case gSierpinski3:
case gSixFlake:
shifttable = { D0, D1, D1-D0, -D0, -D1, D0-D1 };
break;
case gEuclidSquare:
case gSierpinski4:
shifttable = { D0, D1, -D0, -D1 };
break;
default:
throw hr_exception("euc::get_shifttable() called in geometry that is not euclid3");
}
// 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() {
cgi.require_basics();
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(closed_manifold && !disksize) {
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 = init_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
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(dont_inverse()) return adj(c->master, i);
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++) {
auto V1 = V * adj(h, i);
if(geom3::apply_break_cylinder && cgi.emb->break_cylinder(V, V1)) continue;
dq::enqueue_by_matrix(h->move(i), optimized_shift(V1));
}
}
}
transmatrix relative_matrixh(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);
}
subcellshape& get_cellshape(cell* c) override {
return *cgi.heptshape;
}
int pattern_value(cell *c) override {
if(WDIM == 2) {
auto p = euc2_coordinates(c);
if(closed_manifold) return p.first + p.second * (1 << 16);
return gmod(p.first - 22 * p.second, 3*127);
}
else {
auto co = ispacemap[c->master];
if(closed_manifold) return co[0] + (co[1] << 10) + (co[2] << 20);
return gmod(co[0] + 3 * co[1] + 9 * co[2], 3*127);
}
}
};
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, qCLOSED, 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();
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::get_di().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}));