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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 {
// 2D Euclidean space
// --- euclidean geometry ---
// NOTE: patterns assume that pair_to_vec(0,1) % 3 == 2!
// Thus, pair_to_vec(0,1) must not be e.g. a power of four
EX int cell_to_vec(cell *c);
EX int pair_to_vec(int x, int y) {
return x + (y << 15);
}
EX pair<int, int> vec_to_pair(int vec) {
int x = vec & ((1<<15)-1);
int y = (vec >> 15);
if(x >= (1<<14)) x -= (1<<15), y++;
return {x, y};
}
EX namespace torusconfig {
// the configuration of the torus topology.
// torus cells are indexed [0..qty),
// where the cell to the right from i is indexed i+dx,
// and the cell to the down-right is numbered i+dy
// Changed with command line option: -tpar <qty>,<dx>,<dy>
// Ideally, qty, dx, and dy should have the same "modulo 3"
// values as the default -- otherwise the three-color
// pattern breaks. Also, they should have no common
// prime divisor.
EX int def_qty = 127*3;
EX int dx = 1;
EX int def_dy = -11*2;
EX int qty = def_qty;
EX int dy = def_dy;
EX int sdx = 12;
EX int sdy = 12;
#if HDR
enum eTorusMode : char {
tmSingleHex,
tmSingle,
tmSlantedHex,
tmStraight,
tmStraightHex,
tmKlein,
tmKleinHex,
tmCylinder,
tmCylinderHex,
tmMobius,
tmMobiusHex,
};
struct torusmode_info {
string name;
flagtype flags;
};
enum : flagtype {
TF_SINGLE = 1,
TF_SIMPLE = 2,
TF_WEIRD = 4,
TF_HEX = 16,
TF_SQUARE = 32,
TF_CYL = 64,
TF_KLEIN = 256,
};
#endif
// new values to change
EX int newqty, newdy, newsdx, newsdy;
EX int torus_cx, torus_cy;
EX vector<torusmode_info> tmodes = {
{"single row (hex)", TF_SINGLE | TF_HEX},
{"single row (squares)", TF_SINGLE | TF_SQUARE},
{"parallelogram (hex)", TF_SIMPLE | TF_HEX},
{"rectangle (squares)", TF_SIMPLE | TF_SQUARE},
{"rectangle (hex)", TF_WEIRD | TF_HEX},
{"Klein bottle (squares)", TF_SIMPLE | TF_KLEIN | TF_SQUARE},
{"Klein bottle (hex)", TF_WEIRD | TF_KLEIN | TF_HEX},
{"cylinder (squares)", TF_SIMPLE | TF_CYL },
{"cylinder (hex)", TF_SIMPLE | TF_CYL | TF_HEX},
{"Möbius band (squares)", TF_SIMPLE | TF_CYL | TF_KLEIN},
{"Möbius band (hex)", TF_SIMPLE | TF_CYL | TF_HEX | TF_KLEIN},
};
EX eTorusMode torus_mode;
EX eTorusMode newmode;
EX flagtype tmflags() { return tmodes[torus_mode].flags; }
EX int getqty() {
if(tmflags() & TF_SINGLE)
return qty;
else
return sdx * sdy;
}
int getvec(int x, int y) {
if(tmflags() & TF_SINGLE)
return x * dx + y * dy;
else if(tmflags() & TF_SIMPLE)
return pair_to_vec(x, y);
else
return pair_to_vec(-y - 2 * x, 3 * y);
}
int id_to_vec(int id, bool mirrored = false) {
if(tmflags() & TF_SINGLE)
return id;
else {
int dx = id % sdx;
int dy = id / sdx;
if(mirrored)
dy = -dy, dx += sdx;
if(tmflags() & TF_SIMPLE)
return pair_to_vec(dx, dy);
else
return pair_to_vec(- 2 * dx - (dy & 1), 3 * dy);
}
}
pair<int, bool> vec_to_id_mirror(int vec) {
if(tmflags() & TF_SINGLE) {
return {gmod(vec, qty), false};
}
else {
int x, y;
tie(x,y) = vec_to_pair(vec);
bool mirror = false;
if(tmflags() & TF_KLEIN) {
if(tmflags() & TF_WEIRD) {
x = gmod(x, 4 * sdx);
mirror = x > 0 && x <= 2 * sdx;
}
else {
x = gmod(x, 2 * sdx);
mirror = x >= sdx;
}
if(mirror) y = -y;
}
if(tmflags() & TF_WEIRD) {
y /= 3; x = (x + (y&1)) / -2;
}
x = gmod(x, sdx), y = gmod(y, sdy);
return {y * sdx + x, mirror};
}
}
EX int vec_to_id(int vec) {
return vec_to_id_mirror(vec).first;
}
void torus_test() {
printf("Testing torus vec_to_pair/pair_to_vec...\n");
for(int x=-10; x<=10; x++)
for(int y=-10; y<=10; y++) {
auto p = vec_to_pair(pair_to_vec(x, y));
if(p.first != x || p.second != y)
printf("Failed for (%d,%d) -> [%d] -> (%d,%d)\n", x, y, pair_to_vec(x,y), p.first, p.second);
}
printf("Testing id_to_vec / vec_to_id...\n");
for(int i=0; i < getqty(); i++)
for(int m=0; m< (torus_mode == tmKlein ? 2 : 1); m++)
if(vec_to_id_mirror(id_to_vec(i, m)) != pair<int,bool> (i,m))
printf("Failed for id %d.%d [%d] (%d.%d)\n", i, m, id_to_vec(i,m), vec_to_id(id_to_vec(i,m)), vec_to_id_mirror(id_to_vec(i,m)).second);
}
int tester = addHook(hooks_tests, 0, torus_test);
EX void activate() {
auto& gi(ginf[gTorus]);
if(tmflags() & TF_HEX)
gi.vertex = 3, gi.sides = 6, gi.tiling_name = "{6,3}";
else
gi.vertex = 4, gi.sides = 4, gi.tiling_name = "{4,4}";
flagtype& flags = gi.flags;
set_flag(flags, qNONORIENTABLE, tmflags() & TF_KLEIN);
set_flag(flags, qBOUNDED, !(tmflags() & TF_CYL));
int i = 0;
if(tmflags() & TF_KLEIN) i++;
if(tmflags() & TF_CYL) i+=2;
const char *quonames[4] = {"torus", "Klein bottle", "cylinder", "Möbius band"};
gi.quotient_name = quonames[i];
}
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 dcross(gp::loc e1, gp::loc e2) {
return e1.first * e2.second - e1.second*e2.first;
}
EX gp::loc sdxy() { return gp::loc(sdx, sdy); }
EX int mobius_dir_basic() {
int dscalars[6];
for(int a=0; a<SG6; a++)
dscalars[a] = dscalar(gp::eudir(a), sdxy());
for(int a=0; a<SG6; a++)
for(int b=0; b<SG6; b++)
if(a != b && dscalars[a] == dscalars[b]) {
return (a + b) % SG6;
}
return -1;
}
EX bool mobius_symmetric(bool square, int dx, int dy) {
dynamicval<eGeometry> g(geometry, square ? gEuclidSquare : gEuclid);
dynamicval<int> gx(sdx, dx);
dynamicval<int> gy(sdy, dy);
return mobius_dir_basic() != -1;
}
void mobius_flip(int&x, int& y) {
int d = mobius_dir_basic();
int a, b;
if(d == 0) a = 1, b = SG6-1;
else a = 0, b = d;
auto p1 = gp::eudir(a);
auto p2 = gp::eudir(b);
// x = sdx * s + px * t
// y = sdy * s + py * t
// py * x = py * sdx * s + px * py * t
// px * y = px * sdy * s + px + py * t
// py * x - px * y = py * sdx * s - px * sdy * s
// s = (py * x - px * y) / (py * sdx - px * sdy)
int det = p1.second * sdx - p1.first * sdy;
int smul = p1.second * x - p1.first * y;
int tmul = sdx * y - sdy * x;
x = (tmul * p2.first + smul * sdx) / det;
y = (tmul * p2.second + smul * sdy) / det;
// println(hlog, make_pair(ox,oy), " [", d, "] ", make_pair(x,y), " p1 = ", p1, " p2 = ", p2, " det = ", det, " smul = ", smul, " tmul = ", tmul);
}
EX int mobius_dir(cell *c) {
if(c->type == 8) return mobius_dir_basic() * 2;
else return mobius_dir_basic();
}
EX bool be_canonical(int& x, int& y) {
using namespace torusconfig;
int periods = gdiv(dscalar(gp::loc(x,y), sdxy()), dscalar(sdxy(), sdxy()));
y -= sdy * periods;
x -= sdx * periods;
bool b = false;
if(nonorientable && (periods & 1)) {
mobius_flip(x, y);
b = true;
}
return b;
}
EX int cyldist(int id1, int id2) {
int x1, y1, x2, y2;
tie(x1, y1) = vec_to_pair(id1);
tie(x2, y2) = vec_to_pair(id2);
be_canonical(x1, y1);
be_canonical(x2, y2);
int dist = 1000000000;
for(int a1=-1; a1<=1; a1++)
for(int a2=-1; a2<=1; a2++) {
int ax1 = x1 + sdx * a1;
int ay1 = y1 + sdy * a1;
if(nonorientable && a1) mobius_flip(ax1, ay1);
int ax2 = x2 + sdx * a2;
int ay2 = y2 + sdy * a2;
if(nonorientable && a2) mobius_flip(ax2, ay2);
dist = min(dist, eudist(ax1 - ax2, ay1 - ay2));
}
return dist;
}
EX }
EX int euclid_getvec(int dx, int dy) {
if(euwrap) return torusconfig::getvec(dx, dy);
else return pair_to_vec(dx, dy);
}
template<class T> void build_euclidean_moves(cell *c, int vec, const T& builder) {
int x, y;
tie(x,y) = vec_to_pair(vec);
c->type = a4 ? (PURE || ((x^y^1) & 1) ? 4 : 8) : 6;
if(c->type == 4) {
int m = PURE ? 1 : 2;
builder(euclid_getvec(+1,+0), 0, 2 * m);
builder(euclid_getvec(+0,+1), 1, 3 * m);
builder(euclid_getvec(-1,+0), 2, 0 * m);
builder(euclid_getvec(+0,-1), 3, 1 * m);
}
else if(c->type == 8) {
builder(euclid_getvec(+1,+0), 0, 2);
builder(euclid_getvec(+1,+1), 1, 5);
builder(euclid_getvec(+0,+1), 2, 3);
builder(euclid_getvec(-1,+1), 3, 7);
builder(euclid_getvec(-1,+0), 4, 0);
builder(euclid_getvec(-1,-1), 5, 1);
builder(euclid_getvec(+0,-1), 6, 1);
builder(euclid_getvec(+1,-1), 7, 3);
}
else /* 6 */ {
builder(euclid_getvec(+1,+0), 0, 3);
builder(euclid_getvec(+0,+1), 1, 4);
builder(euclid_getvec(-1,+1), 2, 5);
builder(euclid_getvec(-1,+0), 3, 0);
builder(euclid_getvec(+0,-1), 4, 1);
builder(euclid_getvec(+1,-1), 5, 2);
}
}
struct hrmap_euclid_any : hrmap_standard {
void draw() override;
};
struct hrmap_torus : hrmap_euclid_any {
vector<cell*> all;
vector<int> dists;
virtual vector<cell*>& allcells() { return all; }
cell *gamestart() {
return all[0];
}
hrmap_torus() {
using namespace torusconfig;
int q = getqty();
all.resize(q);
for(int i=0; i<q; i++) {
all[i] = newCell(8, encodeId(i));
}
for(int i=0; i<q; i++) {
int iv = id_to_vec(i);
build_euclidean_moves(all[i], iv, [&] (int delta, int d, int d2) {
auto im = vec_to_id_mirror(iv + delta);
all[i]->move(d) = all[im.first];
all[i]->c.setspin(d, d2, im.second);
});
}
if(nonorientable) for(cell *c: all) for(int d=0; d<c->type; d++) {
cell *c2 = c->move(d);
for(int d2=0; d2<c2->type; d2++)
if(c2->move(d2) == c)
c->c.setspin(d, d2, c->c.mirror(d));
}
celllister cl(gamestart(), 100, 100000000, NULL);
dists.resize(q);
for(int i=0; i<isize(cl.lst); i++)
dists[decodeId(cl.lst[i]->master)] = cl.dists[i];
}
~hrmap_torus() {
for(cell *c: all) tailored_delete(c);
}
transmatrix relative_matrix(cell *c2, cell *c1, const hyperpoint& point_hint) {
transmatrix t = Id;
// if(whateveri) printf("[%p,%d] ", c2, celldistance(c2, c1));
int d = celldistance(c2, c1);
while(d) {
forCellIdEx(cc, i, c1) {
int d1 = celldistance(cc, c2);
if(d1 < d) {
t = t * adj(c1, i);
c1 = cc;
d = d1;
goto again;
}
}
printf("ERROR not reached\n");
break;
again: ;
}
return t;
}
};
hrmap_torus *torusmap() {
return dynamic_cast<hrmap_torus*> (currentmap);
}
/* cell *getTorusId(int id) {
hrmap_torus *cur = torusmap();
if(!cur) return NULL;
return cur->all[id];
} */
struct hrmap_euclidean : hrmap_euclid_any {
cell *gamestart() {
return *(euclideanAtCreate(0).first);
}
struct euclideanSlab {
cell* a[256][256];
euclideanSlab() {
for(int y=0; y<256; y++) for(int x=0; x<256; x++)
a[y][x] = NULL;
}
~euclideanSlab() {
for(int y=0; y<256; y++) for(int x=0; x<256; x++)
if(a[y][x]) tailored_delete(a[y][x]);
}
};
static const int slabs = max_vec / 256;
euclideanSlab* euclidean[slabs][slabs];
hrmap_euclidean() {
for(int y=0; y<slabs; y++) for(int x=0; x<slabs; x++)
euclidean[y][x] = NULL;
}
euc_pointer at(int vec) {
auto p = vec_to_pair(vec);
int x = p.first, y = p.second;
bool mobius = false;
if(euwrap)
mobius = torusconfig::be_canonical(x, y);
euclideanSlab*& slab = euclidean[(y>>8)&(slabs-1)][(x>>8)&(slabs-1)];
if(!slab) slab = new hrmap_euclidean::euclideanSlab;
return make_pair(&(slab->a[y&255][x&255]), mobius);
}
map<int, struct cdata> eucdata;
~hrmap_euclidean() {
for(int y=0; y<slabs; y++) for(int x=0; x<slabs; x++)
if(euclidean[y][x]) {
tailored_delete(euclidean[y][x]);
euclidean[y][x] = NULL;
}
eucdata.clear();
}
transmatrix relative_matrix(cell *c2, cell *c1, const hyperpoint& point_hint) {
return eumove(cell_to_vec(c2) - cell_to_vec(c1));
}
};
EX cellwalker vec_to_cellwalker(int vec) {
if(!fulltorus) {
auto p = euclideanAtCreate(vec);
if(p.second)
return cellwalker(*p.first, torusconfig::mobius_dir(*p.first), true);
else
return cellwalker(*p.first, 0, false);
}
else {
hrmap_torus *cur = torusmap();
if(!cur) return cellwalker(NULL, 0);
auto p = torusconfig::vec_to_id_mirror(vec);
return cellwalker(cur->all[p.first], 0, p.second);
}
}
EX int cellwalker_to_vec(cellwalker cw) {
int id = decodeId(cw.at->master);
if(!fulltorus) {
if(nonorientable) {
auto ep = euclideanAt(id);
if(ep.second != cw.mirrored) {
int x, y;
tie(x, y) = vec_to_pair(id);
x += torusconfig::sdx;
y += torusconfig::sdy;
torusconfig::mobius_flip(x, y);
return pair_to_vec(x, y);
}
}
return id;
}
return torusconfig::id_to_vec(id, cw.mirrored);
}
EX int cell_to_vec(cell *c) {
int id = decodeId(c->master);
if(!fulltorus) return id;
return torusconfig::id_to_vec(id, false);
}
EX pair<int, int> cell_to_pair(cell *c) {
return vec_to_pair(cell_to_vec(c));
}
union heptacoder {
heptagon *h;
int id;
};
EX int decodeId(heptagon* h) {
heptacoder u;
u.h = h; return u.id;
}
EX heptagon* encodeId(int id) {
heptacoder u;
u.id = id;
return u.h;
}
// 3D Euclidean space
#if MAXMDIM == 4
EX namespace euclid3 {
#if HDR
typedef long long coord;
constexpr long long COORDMAX = (1<<16);
#endif
typedef array<coord, 3> axes;
typedef array<array<int, 3>, 3> intmatrix;
static const axes main_axes = make_array<coord>(1, COORDMAX, COORDMAX * COORDMAX );
EX array<int, 3> getcoord(coord x) {
array<int, 3> res;
for(int k=0; k<3; k++) {
int next = x % COORDMAX;
if(next>COORDMAX/2) next -= COORDMAX;
if(next<-COORDMAX/2) next += COORDMAX;
res[k] = next;
x -= next;
x /= COORDMAX;
}
return res;
}
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;
switch(geometry) {
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;
default:
printf("euclid3::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;
}
coord canonicalize(coord x);
EX void build_torus3();
coord twist(coord x, transmatrix& M);
EX int twisted;
intmatrix T0;
struct hrmap_euclid3 : hrmap {
vector<coord> shifttable;
vector<transmatrix> tmatrix;
map<coord, heptagon*> spacemap;
map<heptagon*, coord> ispacemap;
cell *camelot_center;
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_euclid3() {
shifttable = get_shifttable();
tmatrix.resize(S7);
for(int i=0; i<S7; i++) tmatrix[i] = Id;
for(int i=0; i<S7; i++) for(int j=0; j<3; j++)
tmatrix[i][j][LDIM] = getcoord(shifttable[i])[j];
camelot_center = NULL;
build_torus3();
}
heptagon *getOrigin() override {
return get_at(0);
}
heptagon *get_at(coord at) {
if(spacemap.count(at))
return spacemap[at];
else {
auto h = tailored_alloc<heptagon> (S7);
h->c7 = newCell(S7, h);
h->distance = 0;
h->cdata = NULL;
h->alt = NULL;
auto co = getcoord(at);
if(S7 != 14)
h->zebraval = gmod(co[0] + co[1] * 2 + co[2] * 4, 5);
else
h->zebraval = co[0] & 1;
spacemap[at] = h;
ispacemap[h] = at;
return h;
}
}
heptagon *build(heptagon *parent, int d, coord at) {
auto h = get_at(at);
int d1 = (d+S7/2)%S7;
if(twisted) {
coord a = ispacemap[parent];
coord b = ispacemap[h];
for(int i=0; i<S7; i++)
if(canonicalize(b + shifttable[i]) == a)
d1 = i;
}
h->c.connect(d1, parent, d, false);
return h;
}
heptagon *create_step(heptagon *parent, int d) override {
return build(parent, d, canonicalize(ispacemap[parent] + shifttable[d]));
}
transmatrix get_move(cell *c, int i) {
if(!twisted) return tmatrix[i];
transmatrix res = tmatrix[i];
coord id = ispacemap[c->master];
id += shifttable[i];
twist(id, res);
return res;
}
void draw() override {
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(wallopt && isWall3(c) && isize(dq::drawqueue) > 1000) continue;
for(int i=0; i<S7; i++)
dq::enqueue_by_matrix(h->move(i), V * get_move(h->c7, i));
}
}
transmatrix warppush(coord dif) {
auto v = getcoord(dif);
for(int i: {0, 1})
if(T0[i][i])
v[i] = gmod(v[i] + T0[i][i] / 2, T0[i][i]) - T0[i][i] / 2;
return eupush3(v[0], v[1], v[2]);
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1) override {
if(twisted) {
coord c1 = ispacemap[h1];
coord c2 = ispacemap[h2];
transmatrix T = warppush(c2 - c1);
for(int d: {-1, 1}) {
transmatrix I = Id;
coord cs = c1;
for(int s=0; s<3; s++) {
cs += d * T0[2][2] * main_axes[2];
I = I * eupush3(0, 0, d * T0[2][2]);
cs = twist(cs, I);
transmatrix T1 = I * warppush(c2 - cs);
if(hdist0(tC0(T1)) < hdist0(tC0(T)))
T = T1;
}
}
return T;
}
auto d = ispacemap[h2] - ispacemap[h1];
d = canonicalize(d);
auto v = getcoord(d);
return eupush3(v[0], v[1], v[2]);
}
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_euclid3* cubemap() {
return ((hrmap_euclid3*) currentmap);
}
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 hrmap* new_map() {
return new hrmap_euclid3;
}
EX transmatrix move_matrix(cell *c, int i) {
return cubemap()->get_move(c, i);
}
EX bool pseudohept(cell *c) {
coord co = cubemap()->ispacemap[c->master];
auto v = getcoord(co);
if(S7 == 12) {
for(int i=0; i<3; i++) if((v[i] & 1)) return false;
}
else {
for(int i=0; i<3; i++) if(!(v[i] & 1)) return false;
}
return true;
}
EX int dist_alt(cell *c) {
if(specialland == laCamelot) return dist_relative(c) + roundTableRadius(c);
coord co = cubemap()->ispacemap[c->master];
auto v = getcoord(co);
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 = getcoord(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 co) {
auto v = getcoord(co);
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 co) {
auto v = getcoord(co);
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();
return celldistance(canonicalize(cm->ispacemap[c1->master] - cm->ispacemap[c2->master]));
}
EX void set_land(cell *c) {
setland(c, specialland);
auto m = cubemap();
auto co = getcoord(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(euclid3::celldistance(cc, start) < r + 5)
cc = cc->cmove(hrand(cc->type));
}
return euclid3::celldistance(cc, c) - r;
}
/* quotient spaces */
intmatrix make_intmatrix(axes a) {
intmatrix T;
T[0] = getcoord(a[0]);
T[1] = getcoord(a[1]);
T[2] = getcoord(a[2]);
return T;
}
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;
}
axes user_axes;
axes optimal_axes;
axes regular_axes;
intmatrix T, T2, T_edit;
int det;
int coords;
int twisted0, twisted_edit;
EX void set_torus3(int x, int y, int z) {
for(int i=0; i<3; i++) for(int j=0; j<3; j++) T0[i][j] = 0;
tie(T0[0][0], T0[1][1], T0[2][2]) = make_tuple(x, y, z);
twisted = 0;
build_torus3();
}
EX void clear_torus3() {
set_torus3(0, 0, 0);
}
unordered_map<coord, int> canonical_hash;
vector<coord> canonical_seq;
int canonical_index;
coord compute_cat(coord co) {
auto coo = getcoord(co);
coord cat = 0;
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 < coords) val = gmod(val, det);
cat += val * main_axes[i];
}
return cat;
};
void add_canonical(coord val) {
auto cat = compute_cat(val);
if(canonical_hash.count(cat)) return;
canonical_hash[cat] = isize(canonical_seq);
canonical_seq.push_back(val);
}
void build_torus3() {
for(int i=0; i<3; i++) {
user_axes[i] = 0;
for(int j=0; j<3; j++) user_axes[i] += main_axes[j] * T0[i][j];
}
optimal_axes = user_axes;
again:
for(int i=0; i<3; i++) if(optimal_axes[i] < 0) optimal_axes[i] = -optimal_axes[i];
if(optimal_axes[0] < optimal_axes[1]) swap(optimal_axes[0], optimal_axes[1]);
if(optimal_axes[1] < optimal_axes[2]) swap(optimal_axes[1], optimal_axes[2]);
if(optimal_axes[0] < optimal_axes[1]) swap(optimal_axes[0], 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 = optimal_axes[i] + optimal_axes[i1] * a + optimal_axes[i2] * b;
if(celldistance(cand) < celldistance(optimal_axes[i])) {
optimal_axes[i] = cand;
goto again;
}
}
}
regular_axes = optimal_axes;
coords = 0;
for(int i=0; i<3; i++) if(optimal_axes[i]) coords++;
int attempt = 0;
next_attempt:
for(int i=coords; i<3; i++)
regular_axes[i] = main_axes[(attempt+i)%3];
T = make_intmatrix(regular_axes);
det = determinant(T);
if(det == 0) {
attempt++;
if(attempt == 3) {
println(hlog, "weird singular!\n");
exit(1);
}
goto next_attempt;
}
if(det < 0) det = -det;
T2 = scaled_inverse(T);
canonical_hash.clear();
canonical_seq.clear();
canonical_index = 0;
add_canonical(0);
twisted = twisted0;
if(geometry != gCubeTiling && ((T0[0][0]+T0[2][2]) & 1)) twisted &=~ 1;
if(geometry != gCubeTiling && ((T0[1][1]+T0[2][2]) & 1)) twisted &=~ 2;
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
if(i != j && T0[i][j]) twisted = 0;
if(T0[2][2] == 0) twisted = 0;
if(T0[0][0] != T0[1][1]) twisted &= 3;
for(eGeometry g: {gCubeTiling, gRhombic3, gBitrunc3}) {
set_flag(ginf[g].flags, qANYQ, coords);
set_flag(ginf[g].flags, qBOUNDED, coords == 3);
bool nonori = false;
if(twisted&1) nonori = !nonori;
if(twisted&2) nonori = !nonori;
if(twisted&4) nonori = !nonori;
set_flag(ginf[g].flags, qNONORIENTABLE, nonori);
}
}
void swap01(transmatrix& M) {
for(int i=0; i<4; i++) swap(M[i][0], M[i][1]);
}
coord twist(coord x, transmatrix& M) {
auto coo = getcoord(x);
while(coo[2] >= T0[2][2]) {
coo[2] -= T0[2][2];
if(twisted & 1) coo[0] *= -1, M = M * MirrorX;
if(twisted & 2) coo[1] *= -1, M = M * MirrorY;
if(twisted & 4) swap(coo[0], coo[1]), swap01(M);
}
while(coo[2] < 0) {
coo[2] += T0[2][2];
if(twisted & 4) swap(coo[0], coo[1]), swap01(M);
if(twisted & 1) coo[0] *= -1, M = M * MirrorX;
if(twisted & 2) coo[1] *= -1, M = M * MirrorY;
}
for(int i: {0,1})
if(T0[i][i]) coo[i] = gmod(coo[i], T0[i][i]);
return coo[0] * main_axes[0] + coo[1] * main_axes[1] + coo[2] * main_axes[2];
}
coord canonicalize(coord x) {
if(twisted) {
transmatrix M = Id;
return twist(x, M);
}
if(coords == 0) return x;
if(coords == 1) {
while(celldistance(x + optimal_axes[0]) <= celldistance(x)) x += optimal_axes[0];
while(celldistance(x - optimal_axes[0]) < celldistance(x)) x -= optimal_axes[0];
return x;
}
auto cat = compute_cat(x);
auto& st = cubemap()->shifttable;
while(!canonical_hash.count(cat)) {
if(canonical_index == isize(canonical_seq)) throw hr_exception();
auto v = canonical_seq[canonical_index++];
for(auto s: st) add_canonical(v + s);
}
return canonical_seq[canonical_hash[cat]];
}
EX void prepare_torus3() {
T_edit = T0;
twisted_edit = twisted0;
}
EX void show_torus3() {
cmode = sm::SIDE | sm::MAYDARK;
gamescreen(1);
dialog::init(XLAT("3D Euclidean spaces"));
for(int y=0; y<4; y++)
dialog::addBreak(100);
dialog::addBreak(50);
bool nondiag = false;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
if(T_edit[i][j] && i != j) nondiag = true;
if(nondiag) {
dialog::addInfo(XLAT("twisting implemented only for diagonal matrices"));
dialog::addBreak(200);
}
else if(T_edit[2][2] == 0) {
dialog::addInfo(XLAT("nothing to twist"));
dialog::addInfo(XLAT("change the bottom left corner"));
dialog::addBreak(100);
}
else {
if(geometry == 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([] { twisted_edit ^= 1; });
if(geometry == 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([] { twisted_edit ^= 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([] { twisted_edit ^= 4; });
}
dialog::addBreak(50);
char xch = 'p';
for(eGeometry g: {gCubeTiling, gRhombic3, gBitrunc3}) {
dialog::addItem(XLAT(ginf[g].menu_displayed_name), xch++);
dialog::add_action([g] {
stop_game();
set_geometry(g);
T0 = T_edit;
twisted0 = twisted_edit;
start_game();
});
}
dialog::addBreak(50);
dialog::addBack();
dialog::display();
int i = -1;
for(auto& v: dialog::items) if(v.type == dialog::diBreak) {
if(i >= 0 && i < 3) {
for(int j=0; j<3; j++) {
char ch = 'a' + i * 3 + j;
if(displayfr(dialog::dcenter + dialog::dfspace * 4 * (j-1), v.position, 2, dialog::dfsize, its(T_edit[j][i]), 0xFFFFFF, 8))
getcstat = ch;
dialog::add_key_action(ch, [=] {
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.)"
)
);
});
}
}
i++;
}
}
#if CAP_COMMANDLINE
int euArgs() {
using namespace arg;
if(0) ;
else if(argis("-t3")) {
PHASEFROM(2);
stop_game();
for(int i=0; i<3; i++)
for(int j=0; j<3; j++) {
shift(); T0[i][j] = argi();
}
build_torus3();
}
else if(argis("-twist3")) {
PHASEFROM(2);
stop_game();
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(); twisted0 = argi();
build_torus3();
}
else if(argis("-twisttest")) {
start_game();
celllister cl(cwt.at, 10000, 10000, NULL);
for(cell *c: cl.lst) {
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(c->move(i) && c->move(k) && c->move(i)->move(j) == c->move(k)->move(l) && c->move(i)->move(j)) {
transmatrix T1 = move_matrix(c, i) * move_matrix(c->move(i), j);
transmatrix T2 = move_matrix(c, k) * move_matrix(c->move(k), l);
if(!eqmatrix(T1, T2)) {
println(hlog, c, " @ ", getcoord(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 }
#endif
EX ld matrixnorm(const transmatrix& Mat) {
return Mat[0][LDIM] * Mat[0][LDIM] + Mat[1][LDIM] * Mat[1][LDIM] + Mat[2][LDIM] * Mat[2][LDIM];
}
void hrmap_euclid_any::draw() {
DEBB(DF_GRAPH, ("drawEuclidean\n"));
sphereflip = Id;
// printf("centerover = %p player = %p [%d,%d]-[%d,%d]\n", lcenterover, cwt.c,
// mindx, mindy, maxdx, maxdy);
int pvec = cellwalker_to_vec(cellwalker(centerover));
typedef pair<int, int> euspot;
const euspot zero = {0,0};
set<euspot> visited = {zero};
vector<euspot> dfs = {zero};
auto View0 = cview();
for(int i=0; i<isize(dfs); i++) {
int dx, dy;
tie(dx, dy) = dfs[i];
cellwalker cw = vec_to_cellwalker(pvec + euclid_getvec(dx, dy));
if(!cw.at) continue;
transmatrix Mat = View0 * eumove(dx, dy);
torusconfig::torus_cx = dx;
torusconfig::torus_cy = dy;
if(do_draw(cw.at, Mat)) {
drawcell(cw, cw.mirrored ? Mat * spin(-2*M_PI*cw.spin / cw.at->type) * Mirror : Mat);
for(int x=-1; x<=+1; x++)
for(int y=-1; y<=+1; y++) {
euspot p(dx+x, dy+y);
if(!visited.count(p)) visited.insert(p), dfs.push_back(p);
}
}
}
}
EX euc_pointer euclideanAt(int vec) {
if(fulltorus) { printf("euclideanAt called\n"); exit(1); }
hrmap_euclidean* euc = dynamic_cast<hrmap_euclidean*> (currentmap);
return euc->at(vec);
}
EX euc_pointer euclideanAtCreate(int vec) {
euc_pointer ep = euclideanAt(vec);
cell*& c = *ep.first;
if(!c) {
if(euwrap) {
int x, y;
tie(x, y) = vec_to_pair(vec);
torusconfig::be_canonical(x, y);
vec = pair_to_vec(x, y);
}
c = newCell(8, encodeId(vec));
// euclideanAt(vec) = c;
build_euclidean_moves(c, vec, [c,vec] (int delta, int d, int d2) {
euc_pointer ep2 = euclideanAt(vec + delta);
cell* c2 = *ep2.first;
if(!c2) return;
// if(ep.second) d = c->c.fix(torusconfig::mobius_dir(c) - d);
if(ep2.second) d2 = c2->c.fix(torusconfig::mobius_dir(c2) - d2);
eumerge(c, d, c2, d2, ep2.second);
});
}
return ep;
}
EX hrmap* new_torus_map() { return new hrmap_torus; }
EX hrmap* new_euclidean_map() { return new hrmap_euclidean; }
EX int get_torus_dist(int id) { return torusmap()->dists[id]; }
EX map<int, cdata>& get_cdata() { return ((hrmap_euclidean*) (currentmap))->eucdata; }
}
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