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hyperrogue/crystal.cpp

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// Hyperbolic Rogue -- Crystal geometries
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file crystal.cpp
* \brief Multi-dimensional (aka crystal) geometries.
*/
#include "hyper.h"
namespace hr {
EX namespace crystal {
#if HDR
static const int MAXDIM = 7;
static const int MAX_EDGE_CRYSTAL = 2 * MAXDIM;
struct coord : public array<int, MAXDIM> {
coord operator + (coord b) { for(int i=0; i<MAXDIM; i++) b[i] += self[i]; return b; }
coord operator - (coord b) { for(int i=0; i<MAXDIM; i++) b[i] = self[i] - b[i]; return b; }
coord operator * (int x) { coord res; for(int i=0; i<MAXDIM; i++) res[i] = x * self[i]; return res; }
};
static const coord c0 = {};
struct ldcoord : public array<ld, MAXDIM> {
friend ldcoord operator + (ldcoord a, ldcoord b) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] + b[i]; return r; }
friend ldcoord operator - (ldcoord a, ldcoord b) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] - b[i]; return r; }
friend ldcoord operator * (ldcoord a, ld v) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] * v; return r; }
friend ldcoord operator / (ldcoord a, ld v) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] / v; return r; }
friend ld operator | (ldcoord a, ldcoord b) { ld r=0; for(int i=0; i<MAXDIM; i++) r += a[i] * b[i]; return r; }
};
static const ldcoord ldc0 = {};
#endif
#if CAP_CRYSTAL
/** Crystal can be bitruncated either by changing variation to bitruncated.
* In case of the 4D Crystal, the standard HyperRogue bitruncation becomes
* confused by having both the original and new vertices of degree 8.
* Hence Crystal implements its own bitruncation, which is selected/checked
* by setting ginf[gCrystal].vertex to 3. Additionally, this lets us double
* bitruncate.
* Function pure() checks for both kinds of bitruncation (or any other variations).
*/
EX bool pure() {
return PURE && ginf[gCrystal].vertex == 4;
}
EX bool view_coordinates = false;
bool view_east = false;
EX bool used_compass_inside;
EX ldcoord told(coord c) { ldcoord a; for(int i=0; i<MAXDIM; i++) a[i] = c[i]; return a; }
// strange number to prevent weird acting in case of precision errors
coord roundcoord(ldcoord c) { coord a; for(int i=0; i<MAXDIM; i++) a[i] = floor(c[i] + .5136); return a; }
EX ld compass_probability = 1;
int tocode(int cname) { return (1 << (cname >> 1)); }
void resize2(vector<vector<int>>& v, int a, int b, int z) {
v.clear();
v.resize(a);
for(auto& w: v) w.resize(b, z);
}
/** in the "pure" form, the adjacent vertices are internaly spaced by 2 */
const int FULLSTEP = 2;
/** to make space for the additional vertices which are added in the bitruncated version */
const int HALFSTEP = 1;
/** with variations, the connections of the vertex at coordinate v+FULLSTEP mirror the connections
* of the vertex at coordinate v. Therefore, the period of our construction is actually 2*FULLSTEP. */
const int PERIOD = 2 * FULLSTEP;
struct crystal_structure {
int dir;
int dim;
vector<vector<int>> cmap;
vector<vector<int>> next;
vector<vector<int>> prev;
vector<vector<int>> order;
void coord_to_next() {
resize2(next, 1<<dim, 2*dim, -1);
for(int a=0; a<(1<<dim); a++)
for(int b=0; b<dir; b++)
next[a][cmap[a][b]] = cmap[a][(b+1)%dir];
println(hlog, next);
}
void next_to_coord() {
resize2(cmap, 1<<dim, dir, -1);
for(int a=0; a<(1<<dim); a++) {
int at = 0;
for(int b=0; b<dir; b++) {
cmap[a][b] = at;
at = next[a][at];
}
}
println(hlog, "coordinate map is:\n", cmap);
}
void next_to_prev() {
resize2(prev, 1<<dim, 2*dim, -1);
for(int a=0; a<(1<<dim); a++)
for(int b=0; b<dir; b++) {
if(next[a][b] != -1)
prev[a][next[a][b]] = b;
}
}
void coord_to_order() {
println(hlog, dir, dim);
resize2(order, 1<<dim, 2*dim, -1);
for(int a=0; a<(1<<dim); a++)
for(int b=0; b<dir; b++)
order[a][cmap[a][b]] = b;
println(hlog, order);
}
int count_bugs() {
int bugcount = 0;
for(int a=0; a<(1<<dim); a++)
for(int b=0; b<2*dim; b++) {
if(next[a][b] == -1) continue;
int qa = a, qb = b;
for(int i=0; i<4; i++) {
if(i == 2 && (qb != (b^1))) bugcount++;
qa ^= tocode(qb);
qb ^= 1;
qb = next[qa][qb];
}
if(a != qa || b != qb) bugcount++;
}
return bugcount;
}
void next_insert(int a, int at, int val) {
int pd = next[a].size();
next[a].resize(pd + 2);
next[a][val] = next[a][at];
next[a][at] = val;
next[a][val^1] = next[a][at^1];
next[a][at^1] = val^1;
prev[a].resize(pd + 2);
prev[a][val] = at;
prev[a][next[a][val]] = val;
prev[a][val^1] = at^1;
prev[a][next[a][val^1]] = val^1;
}
void prev_insert(int a, int at, int val) {
next_insert(a, prev[a][at], val);
}
int errors;
crystal_structure() { errors = 0; }
bool may_next_insert(int a, int at, int val) {
if(isize(next[a]) != dir) {
next_insert(a, at, val);
return true;
}
else if(next[a][at] != val) errors++;
return false;
}
bool may_prev_insert(int a, int at, int val) {
if(isize(prev[a]) != dir) {
prev_insert(a, at, val);
return true;
}
else if(prev[a][at] != val) errors++;
return false;
}
void add_dimension_to(crystal_structure& poor) {
dir = poor.dir + 2;
dim = poor.dim + 1;
printf("Building dimension %d\n", dim);
next.resize(1<<dim);
prev.resize(1<<dim);
int mask = (1<<poor.dim) - 1;
int mm = tocode(poor.dir);
for(int i=0; i<(1<<dim); i++) {
if(i < mm)
next[i] = poor.next[i&mask], prev[i] = poor.prev[i&mask];
else
next[i] = poor.prev[i&mask], prev[i] = poor.next[i&mask];
}
next_insert(0, 0, poor.dir);
for(int s=2; s<1<<(dim-2); s+=2) {
if(next[s][0] < 4)
prev_insert(s, 0, poor.dir);
else
next_insert(s, 0, poor.dir);
}
// printf("next[%d][%d] = %d\n", 4, 2, next[4][2]);
for(int s=0; s<8; s++) for(int a=0; a<(1<<dim); a++) if(isize(next[a]) > poor.dir) {
int which = next[a][poor.dir];
int a1 = a ^ tocode(which);
may_next_insert(a1, which^1, poor.dir);
may_next_insert(a ^ mm, which, poor.dir^1);
which = prev[a][poor.dir];
a1 = a ^ tocode(which);
may_prev_insert(a1, which^1, poor.dir);
}
// println(hlog, next);
if(errors) { printf("errors: %d\n", errors); exit(1);; }
int unf = 0;
for(int a=0; a<(1<<dim); a++) if(isize(next[a]) == poor.dir) {
if(!unf) printf("unf: ");
printf("%d ", a);
unf ++;
}
if(unf) { printf("\n"); exit(2); }
for(int a=0; a<(1<<dim); a++) for(int b=0; b<dir; b++)
if(prev[a][next[a][b]] != b) {
println(hlog, next[a], prev[a]);
printf("next/prev %d\n", a);
exit(3);
}
if(count_bugs()) {
printf("bugs reported: %d\n", count_bugs());
exit(4);
}
}
void remove_half_dimension() {
dir--;
for(int i=0; i<(1<<dim); i++) {
int take_what = dir-1;
if(i >= (1<<(dim-1))) take_what = dir;
next[i][prev[i][take_what]] = next[i][take_what],
prev[i][next[i][take_what]] = prev[i][take_what],
next[i].resize(dir),
prev[i].resize(dir);
}
}
void build() {
dir = 4;
dim = 2;
next.resize(4, {2,3,1,0});
next_to_prev();
while(dir < S7) {
crystal_structure csx = move(*this);
add_dimension_to(csx);
}
if(dir > S7) remove_half_dimension();
next_to_coord();
coord_to_order();
coord_to_next();
if(count_bugs()) {
printf("bugs found\n");
}
if(dir > MAX_EDGE_CRYSTAL || dim > MAXDIM) {
printf("Dimension or directions exceeded -- I have generated it, but won't play");
exit(0);
}
}
};
struct lwalker {
crystal_structure& cs;
int id;
int spin;
lwalker(crystal_structure& cs) : cs(cs) {}
void operator = (const lwalker& x) { id = x.id; spin = x.spin; }
constexpr lwalker(const lwalker& l) : cs(l.cs), id(l.id), spin(l.spin) {}
};
lwalker operator +(lwalker a, int v) { a.spin = gmod(a.spin + v, a.cs.dir); return a; }
lwalker operator +(lwalker a, wstep_t) {
a.spin = a.cs.cmap[a.id][a.spin];
a.id ^= tocode(a.spin);
a.spin = a.cs.order[a.id][a.spin^1];
return a;
}
coord add(coord c, lwalker a, int val) {
int code = a.cs.cmap[a.id][a.spin];
c[code>>1] += ((code&1) ? val : -val);
return c;
}
coord add(coord c, int cname, int val) {
int dim = (cname>>1);
c[dim] = (c[dim] + (cname&1?val:-val));
return c;
}
ld sqhypot2(crystal_structure& cs, ldcoord co1, ldcoord co2) {
int result = 0;
for(int a=0; a<cs.dim; a++) result += (co1[a] - co2[a]) * (co1[a] - co2[a]);
return result;
}
static const int Modval = 64;
struct east_structure {
map<coord, int> data;
int Xmod, cycle;
int zeroshift;
int coordid;
};
int fiftyrule(coord c) {
int res[256] = {
1,-1,32,-1,-1, 2,-1,35,32,-1, 1,-1,-1,35,-1, 2,
-1,-1,-1,-1, 4,-1,36,-1,-1,-1,-1,-1,36,-1, 4,-1,
32,-1, 1,-1,-1,34,-1, 3, 1,-1,32,-1,-1, 3,-1,34,
-1,-1,-1,-1,36,-1, 4,-1,-1,-1,-1,-1, 4,-1,36,-1,
-1, 4,-1,36,-1,-1,-1,-1,-1,36,-1, 4,-1,-1,-1,-1,
3,-1,35,-1,-1,-1,-1,-1,35,-1, 3,-1,-1,-1,-1,-1,
-1,36,-1, 4,-1,-1,-1,-1,-1, 4,-1,36,-1,-1,-1,-1,
34,-1, 2,-1,-1,-1,-1,-1, 2,-1,34,-1,-1,-1,-1,-1,
32,-1, 1,-1,-1,34,-1, 3, 1,-1,32,-1,-1, 3,-1,34,
-1,-1,-1,-1,36,-1, 4,-1,-1,-1,-1,-1, 4,-1,36,-1,
1,-1,32,-1,-1, 2,-1,35,32,-1, 1,-1,-1,35,-1, 2,
-1,-1,-1,-1, 4,-1,36,-1,-1,-1,-1,-1,36,-1, 4,-1,
-1,36,-1, 4,-1,-1,-1,-1,-1, 4,-1,36,-1,-1,-1,-1,
34,-1, 2,-1,-1,-1,-1,-1, 2,-1,34,-1,-1,-1,-1,-1,
-1, 4,-1,36,-1,-1,-1,-1,-1,36,-1, 4,-1,-1,-1,-1,
3,-1,35,-1,-1,-1,-1,-1,35,-1, 3,-1,-1,-1,-1,-1,
};
int index = 0;
for(int i=0; i<4; i++) index += (c[i] & 3) << (2 * i);
if(res[index] == -1) exit(1);
return res[index];
}
bool is_bi(crystal_structure& cs, coord co);
#if MAXMDIM >= 4
typedef array<coord, 12> shifttable;
int ctable[64][6] = {
{0, 1, 2, 3, 4, 5, },
{6, 1, 5, 4, 3, 2, },
{0, 7, 5, 4, 3, 2, },
{6, 7, 2, 3, 4, 5, },
{0, 1, 5, 4, 3, 8, },
{6, 1, 8, 3, 4, 5, },
{0, 7, 8, 3, 4, 5, },
{6, 7, 5, 4, 3, 8, },
{0, 1, 5, 4, 9, 2, },
{6, 1, 2, 9, 4, 5, },
{0, 7, 2, 9, 4, 5, },
{6, 7, 5, 4, 9, 2, },
{0, 1, 8, 9, 4, 5, },
{6, 1, 5, 4, 9, 8, },
{0, 7, 5, 4, 9, 8, },
{6, 7, 8, 9, 4, 5, },
{0, 1, 5, 10, 3, 2, },
{6, 1, 2, 3, 10, 5, },
{0, 7, 2, 3, 10, 5, },
{6, 7, 5, 10, 3, 2, },
{0, 1, 8, 3, 10, 5, },
{6, 1, 5, 10, 3, 8, },
{0, 7, 5, 10, 3, 8, },
{6, 7, 8, 3, 10, 5, },
{0, 1, 2, 9, 10, 5, },
{6, 1, 5, 10, 9, 2, },
{0, 7, 5, 10, 9, 2, },
{6, 7, 2, 9, 10, 5, },
{0, 1, 5, 10, 9, 8, },
{6, 1, 8, 9, 10, 5, },
{0, 7, 8, 9, 10, 5, },
{6, 7, 5, 10, 9, 8, },
{0, 1, 11, 4, 3, 2, },
{6, 1, 2, 3, 4, 11, },
{0, 7, 2, 3, 4, 11, },
{6, 7, 11, 4, 3, 2, },
{0, 1, 8, 3, 4, 11, },
{6, 1, 11, 4, 3, 8, },
{0, 7, 11, 4, 3, 8, },
{6, 7, 8, 3, 4, 11, },
{0, 1, 2, 9, 4, 11, },
{6, 1, 11, 4, 9, 2, },
{0, 7, 11, 4, 9, 2, },
{6, 7, 2, 9, 4, 11, },
{0, 1, 11, 4, 9, 8, },
{6, 1, 8, 9, 4, 11, },
{0, 7, 8, 9, 4, 11, },
{6, 7, 11, 4, 9, 8, },
{0, 1, 2, 3, 10, 11, },
{6, 1, 11, 10, 3, 2, },
{0, 7, 11, 10, 3, 2, },
{6, 7, 2, 3, 10, 11, },
{0, 1, 11, 10, 3, 8, },
{6, 1, 8, 3, 10, 11, },
{0, 7, 8, 3, 10, 11, },
{6, 7, 11, 10, 3, 8, },
{0, 1, 11, 10, 9, 2, },
{6, 1, 2, 9, 10, 11, },
{0, 7, 2, 9, 10, 11, },
{6, 7, 11, 10, 9, 2, },
{0, 1, 8, 9, 10, 11, },
{6, 1, 11, 10, 9, 8, },
{0, 7, 11, 10, 9, 8, },
{6, 7, 8, 9, 10, 11, },
};
shifttable get_canonical(coord co) {
shifttable res;
if(S7 == 12) {
int eid = 0;
for(int a=0; a<6; a++) if(co[a] & 2) eid += (1<<a);
for(int i=0; i<12; i++) res[i] = c0;
for(int i=0; i<6; i++) {
int c = ctable[eid][i];
res[i][c % 6] = (c>=6) ? -2 : 2;
res[6+i][c % 6] = (c>=6) ? 2 : -2;
}
}
else {
for(int i=0; i<4; i++) {
res[i] = c0;
res[i][i] = 2;
res[i+4] = c0;
res[i+4][i] = -2;
}
for(int a=0; a<4; a++) if(co[a] & 2) swap(res[a], res[a+4]);
int bts = 0;
for(int a=0; a<4; a++) if(co[a] & 2) bts++;
if(bts & 1) swap(res[2], res[3]), swap(res[6], res[7]);
}
return res;
}
#endif
EX int crystal_period = 0;
struct hrmap_crystal : hrmap_standard {
heptagon *getOrigin() override { return get_heptagon_at(c0, S7); }
map<heptagon*, coord> hcoords;
map<coord, heptagon*> heptagon_at;
map<int, eLand> landmemo;
map<coord, eLand> landmemo4;
map<cell*, map<cell*, int>> distmemo;
map<cell*, ldcoord> sgc;
cell *camelot_center;
ldcoord camelot_coord;
ld camelot_mul;
crystal_structure cs;
east_structure east;
lwalker makewalker(coord c, int d) {
lwalker a(cs);
a.id = 0;
for(int i=0; i<cs.dim; i++) if(c[i] & FULLSTEP) a.id += (1<<i);
a.spin = d;
return a;
}
bool crystal3() { return WDIM == 3; }
hrmap_crystal() {
#if MAXMDIM >= 4
if(crystal3()) reg3::generate(), cs.dim = S7 / 2; else
#endif
cs.build();
camelot_center = NULL;
}
~hrmap_crystal() {
clearfrom(getOrigin());
}
heptagon *get_heptagon_at(coord c, int deg) {
if(heptagon_at.count(c)) return heptagon_at[c];
heptagon*& h = heptagon_at[c];
h = init_heptagon(deg);
h->c7 = newCell(deg, h);
/* in {6,4} we need emeraldval for some patterns, including (bitruncated) football and (bitruncated) three-color */
h->emeraldval = (c[0] ^ c[1] ^ c[2]) & 2;
h->emeraldval ^= (c[1] & 4);
h->emeraldval ^= (c[0] & 4);
h->emeraldval ^= (c[2] & 4);
h->emeraldval ^= ((c[2] & 2) << 1);
if(c[0] & 2) h->emeraldval ^= 1;
if(ginf[gCrystal].vertex == 3)
h->fiftyval = fiftyrule(c);
for(int i=0; i<cs.dim; i++) h->distance += abs(c[i]);
h->distance /= 2;
hcoords[h] = c;
// for(int i=0; i<6; i++) crystalstep(h, i);
return h;
}
ldcoord get_coord(cell *c) {
// in C++14?
// auto b = sgc.emplace(c, ldc0);
// ldcoord& res = b.first->second;
if(sgc.count(c)) return sgc[c];
ldcoord& res = (sgc[c] = ldc0);
{ // if(b.second) {
if(BITRUNCATED && c->master->c7 != c) {
for(int i=0; i<c->type; i+=2)
res = res + told(hcoords[c->cmove(i)->master]);
res = res * 2 / c->type;
}
else if(GOLDBERG && c->master->c7 != c) {
auto m = gp::get_masters(c);
auto H = gp::get_master_coordinates(c);
for(int i=0; i<cs.dim; i++)
res = res + told(hcoords[m[i]]) * H[i];
}
else
res = told(hcoords[c->master]);
}
return res;
}
coord long_representant(cell *c);
int get_east(cell *c);
void build_east(int cid);
void verify() override { }
void prepare_east();
void apply_period(coord& co) {
for(int a=0; a<cs.dim; a++)
co[a] = szgmod(co[a], 2*crystal_period);
}
heptagon *create_step(heptagon *h, int d) override {
if(!hcoords.count(h)) {
printf("not found\n");
return NULL;
}
auto co = hcoords[h];
#if MAXMDIM >= 4
if(crystal3()) {
auto st = get_canonical(co);
auto co1 = co + st[d];
apply_period(co1);
auto h1 = get_heptagon_at(co1, S7);
auto st1 = get_canonical(co1);
for(int d1=0; d1<S7; d1++) if(st1[d1] == st[d])
h->c.connect(d, h1, (d1+S7/2) % S7, false);
return h1;
}
#endif
if(is_bi(cs, co)) {
heptspin hs(h, d);
(hs + 1 + wstep + 1).cpeek();
return h->move(d);
}
auto lw = makewalker(co, d);
if(ginf[gCrystal].vertex == 4) {
auto c1 = add(co, lw, FULLSTEP);
auto lw1 = lw+wstep;
apply_period(c1);
h->c.connect(d, heptspin(get_heptagon_at(c1, S7), lw1.spin));
}
else {
auto coc = add(add(co, lw, HALFSTEP), lw+1, HALFSTEP);
auto hc = get_heptagon_at(coc, 8);
apply_period(coc);
for(int a=0; a<8; a+=2) {
hc->c.connect(a, heptspin(h, lw.spin));
if(h->modmove(lw.spin-1)) {
hc->c.connect(a+1, heptspin(h, lw.spin) - 1 + wstep - 1);
}
co = add(co, lw, FULLSTEP);
apply_period(co);
lw = lw + wstep + (-1);
h = get_heptagon_at(co, S7);
}
}
return h->move(d);
}
#if MAXMDIM >= 4
map<int, transmatrix> adjs;
transmatrix adj(heptagon *h, int d) override {
if(!crystal3()) return hrmap_standard::adj(h, d);
auto co = hcoords[h];
int id = 0;
for(int a=0; a<S7/2; a++) id = (2*id) + ((co[a]>>1) & 1);
id = S7*id + d;
if(adjs.count(id)) return adjs[id];
transmatrix T = cgi.adjmoves[d];
reg3::generate_cellrotations();
auto st = get_canonical(co);
auto co1 = co + st[d];
auto st1 = get_canonical(co1);
int qty = 0;
transmatrix res;
ld gdist = S7 == 12 ? hdist0(tC0(cgi.adjmoves[0])) : cgi.strafedist;
for(auto& cr: cgi.cellrotations) {
transmatrix U = T * cr.M;
ld go = hdist0(U * tC0(cgi.adjmoves[h->c.spin(d)]));
if(go > 1e-2) continue;
for(int s=0; s<S7; s++)
if(cgi.dirs_adjacent[d][s])
for(int t=0; t<S7; t++)
if(st1[t] == st[s]) {
if(hdist(U * tC0(cgi.adjmoves[t]), tC0(cgi.adjmoves[s])) > gdist + .1)
goto wrong;
}
res = U;
qty++;
wrong: ;
}
adjs[id] = res;
if(qty == 1) return res;
println(hlog, "qty = ", qty);
exit(1);
}
transmatrix adj(cell *c, int d) override {
if(crystal3()) return adj(c->master, d);
return hrmap_standard::adj(c, d);
}
void draw_at(cell *at, const shiftmatrix& where) override {
if(!crystal3()) { hrmap_standard::draw_at(at, where); return; }
else hrmap::draw_at(at, where);
}
virtual transmatrix relative_matrix(cell *h2, cell *h1, const hyperpoint& hint) override {
if(!crystal3()) return hrmap_standard::relative_matrix(h2, h1, hint);
if(h2 == h1) return Id;
for(int i=0; i<S7; i++) if(h2 == h1->move(i)) return adj(h1->master, i);
if(gmatrix0.count(h2) && gmatrix0.count(h1))
return inverse_shift(gmatrix0[h1], gmatrix0[h2]);
println(hlog, "unknown relmatrix, distance = ", celldistance(h1, h2));
return xpush(999);
}
virtual transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
if(!crystal3()) return hrmap::relative_matrix(h2, h1, hint);
return relative_matrix(h2->c7, h1->c7, hint);
}
#endif
};
hrmap_crystal *crystal_map() {
return (hrmap_crystal*) currentmap;
}
EX heptagon *get_heptagon_at(coord c) { return crystal_map()->get_heptagon_at(c, S7); }
EX coord get_coord(heptagon *h) { return crystal_map()->hcoords[h]; }
EX ldcoord get_ldcoord(cell *c) { return crystal_map()->get_coord(c); }
EX int get_dim() { return crystal_map()->cs.dim; }
#if MAXMDIM >= 4
EX transmatrix get_adj(heptagon *h, int d) { return crystal_map()->adj(h, d); }
#endif
bool is_bi(crystal_structure& cs, coord co) {
for(int i=0; i<cs.dim; i++) if(co[i] & HALFSTEP) return true;
return false;
}
array<array<int,2>, MAX_EDGE_CRYSTAL> distlimit_table = {{
{{SEE_ALL,SEE_ALL}}, {{SEE_ALL,SEE_ALL}}, {{SEE_ALL,SEE_ALL}}, {{SEE_ALL,SEE_ALL}}, {{15, 10}},
{{6, 4}}, {{5, 3}}, {{4, 3}}, {{4, 3}}, {{3, 2}}, {{3, 2}}, {{3, 2}}, {{3, 2}}, {{3, 2}}
}};
EX color_t colorize(cell *c, char whichCanvas) {
auto m = crystal_map();
ldcoord co = ldc0;
int dim = 3;
if(cryst) co = m->get_coord(c), dim = m->cs.dim;
#if MAXMDIM >= 4
else if(geometry == gSpace344) {
co = told(reg3::decode_coord(c->master->fieldval)), dim = 4;
for(int a=0; a<4; a++) if(co[a] > 4) co[a] -= 8;
}
else if(geometry == gSeifertCover) {
int i = c->master->fieldval;
for(int a=0; a<3; a++) co[a] = i%5, i /= 5;
}
#endif
else if(euc::in()) {
auto tab = euc::get_ispacemap()[c->master];
for(int a=0; a<3; a++) co[a] = tab[a];
if(PURE) for(int a=0; a<3; a++) co[a] *= 2;
dim = 3;
}
color_t res = 0;
coord ico = roundcoord(co);
int ones = 0;
for(int i=0; i<dim; i++) if((ico[i] & 2) == 2) ones++;
switch(whichCanvas) {
case 'K':
for(int i=0; i<3; i++)
res |= ((int)(((i == 2 && S7 == 5) ? (128 + co[i] * 50) : (255&int(128 + co[i] * 25))))) << (8*i);
return res;
case '@': {
if(ico[dim-1] == 2 && (ones & 1)) return 0x1C0FFC0;
if(ico[dim-1] == 2 && !(ones & 1)) return 0x180FF80;
if(ico[dim-1] == -4 && (ones & 1)) return 0x180C0FF;
if(ico[dim-1] == -4 && !(ones & 1)) return 0x14080FF;
return 0x101010;
}
case '=':
if(ico[dim-1] == 2 && (ones & 1)) return 0x1C0FFC0;
if(ico[dim-1] == 2 && !(ones & 1)) return 0x180FF80;
if(ico[dim-1] == -2 && (ones & 1)) return 0x180C0FF;
if(ico[dim-1] == -2 && !(ones & 1)) return 0x14080FF;
return 0x101010;
case '#': {
bool grid = false;
ico[dim-1] -= 2;
for(int d=dim; d<MAXDIM; d++) ico[d] = 0;
for(int i=0; i<dim; i++) if((ico[i] & 6) == 4) grid = true;
for(int i=0; i<3; i++) part(res, i) = 0xFF + 0x18 * (ico[i]/2-2);
if(grid) res |= 0x1000000;
else if(GDIM == 2) res = (res & 0xFEFEFE) >> 1;
if(ico == c0) res = 0x1FFD500;
return res;
}
case 'O': {
for(int i=0; i<3; i++) part(res, i) = 0xFF + 0x18 * (ico[i]/2-2);
c->landparam = res;
if(ones == dim-1) res |= 0x1000000;
else if(GDIM == 2) res = (res & 0xFEFEFE) >> 1;
return res;
}
case '/': {
int s = 0;
for(int a=0; a<dim; a++) s += ico[a];
if(s > 0) return 0x1FF20FF;
else if (s < -2) return 0x1C0C0C0;
}
}
return res;
}
EX colortable coordcolors = {0xD04040, 0x40D040, 0x4040D0, 0xFFD500, 0xF000F0, 0x00F0F0, 0xF0F0F0 };
EX ld compass_angle() {
bool bitr = ginf[gCrystal].vertex == 3;
return (bitr ? M_PI/8 : 0) - master_to_c7_angle();
}
EX bool crystal_cell(cell *c, shiftmatrix V) {
if(!cryst) return false;
if(view_east && cheater) {
int d = dist_alt(c);
queuestr(V, 0.3, its(d), 0xFFFFFF, 1);
}
if(view_coordinates && WDIM == 2 && cheater) {
auto m = crystal_map();
if(c->master->c7 == c && !is_bi(m->cs, m->hcoords[c->master])) {
ld dist = cellgfxdist(c, 0);
for(int i=0; i<S7; i++) {
shiftmatrix T = V * spin(compass_angle() - 2 * M_PI * i / S7) * xpush(dist*.3);
auto co = m->hcoords[c->master];
auto lw = m->makewalker(co, i);
int cx = m->cs.cmap[lw.id][i];
queuestr(T, 0.3, its(co[cx>>1] / FULLSTEP), coordcolors[cx>>1], 1);
}
}
}
return false;
}
EX vector<cell*> build_shortest_path(cell *c1, cell *c2) {
auto m = crystal_map();
ldcoord co1 = m->get_coord(c1);
ldcoord co2 = m->get_coord(c2) - co1;
// draw a cylinder from co1 to co2, and find the solution by going through that cylinder
ldcoord mul = co2 / sqrt(co2|co2);
ld mmax = (co2|mul);
vector<cell*> p;
vector<int> parent_id;
manual_celllister cl;
cl.add(c2);
parent_id.push_back(-1);
int steps = 0;
int nextsteps = 1;
for(int i=0; i<isize(cl.lst); i++) {
if(i == nextsteps) steps++, nextsteps = isize(cl.lst);
cell *c = cl.lst[i];
forCellCM(c3, c) if(!cl.listed(c3)) {
if(c3 == c1) {
p.push_back(c1);
while(c3 != c2) {
while(i) {
p.push_back(c3);
i = parent_id[i];
c3 = cl.lst[i];
}
}
p.push_back(c3);
return p;
}
auto h = m->get_coord(c3) - co1;
ld dot = (h|mul);
if(dot > mmax + PERIOD/2 + .1) continue;
for(int k=0; k<m->cs.dim; k++) if(abs(h[k] - dot * mul[k]) > PERIOD + .1) goto next3;
cl.add(c3);
parent_id.push_back(i);
next3: ;
}
}
println(hlog, "Error: path not found");
return p;
}
EX int precise_distance(cell *c1, cell *c2) {
if(c1 == c2) return 0;
auto m = crystal_map();
if(pure()) {
coord co1 = m->hcoords[c1->master];
coord co2 = m->hcoords[c2->master];
int result = 0;
for(int a=0; a<m->cs.dim; a++) result += abs(co1[a] - co2[a]);
return result / FULLSTEP;
}
auto& distmemo = m->distmemo;
if(c2 == currentmap->gamestart()) swap(c1, c2);
else if(isize(distmemo[c2]) > isize(distmemo[c1])) swap(c1, c2);
if(distmemo[c1].count(c2)) return distmemo[c1][c2];
int zmin = 999999, zmax = -99;
forCellEx(c3, c2) if(distmemo[c1].count(c3)) {
int d = distmemo[c1][c3];
if(d < zmin) zmin = d;
if(d > zmax) zmax = d;
}
if(zmin+1 < zmax-1) println(hlog, "zmin < zmax");
if(zmin+1 == zmax-1) return distmemo[c1][c2] = zmin+1;
ldcoord co1 = m->get_coord(c1);
ldcoord co2 = m->get_coord(c2) - co1;
// draw a cylinder from co1 to co2, and find the solution by going through that cylinder
ldcoord mul = co2 / sqrt(co2|co2);
ld mmax = (co2|mul);
manual_celllister cl;
cl.add(c2);
int steps = 0;
int nextsteps = 1;
for(int i=0; i<isize(cl.lst); i++) {
if(i == nextsteps) steps++, nextsteps = isize(cl.lst);
cell *c = cl.lst[i];
forCellCM(c3, c) if(!cl.listed(c3)) {
if(c3 == c1) {
return distmemo[c1][c2] = distmemo[c2][c1] = 1 + steps;
}
auto h = m->get_coord(c3) - co1;
ld dot = (h|mul);
if(dot > mmax + PERIOD/2 + .1) continue;
for(int k=0; k<m->cs.dim; k++) if(abs(h[k] - dot * mul[k]) > PERIOD + .1) goto next3;
cl.add(c3);
next3: ;
}
}
println(hlog, "Error: distance not found");
return 999999;
}
EX ld space_distance(cell *c1, cell *c2) {
auto m = crystal_map();
ldcoord co1 = m->get_coord(c1);
ldcoord co2 = m->get_coord(c2);
return sqrt(sqhypot2(m->cs, co1, co2));
}
EX ld space_distance_camelot(cell *c) {
auto m = crystal_map();
return m->camelot_mul * sqrt(sqhypot2(m->cs, m->get_coord(c), m->camelot_coord));
}
EX int dist_relative(cell *c) {
auto m = crystal_map();
auto& cc = m->camelot_center;
int r = roundTableRadius(NULL);
cell *start = m->gamestart();
if(!cc) {
println(hlog, "Finding Camelot center...");
cc = start;
while(precise_distance(cc, start) < r + 5)
cc = cc->cmove(hrand(cc->type));
m->camelot_coord = m->get_coord(m->camelot_center);
if(m->cs.dir % 2)
m->camelot_coord[m->cs.dim-1] = 1;
m->camelot_mul = 1;
m->camelot_mul *= (r+5) / space_distance_camelot(start);
}
if(pure())
return precise_distance(c, cc) - r;
ld dis = space_distance_camelot(c);
if(dis < r)
return int(dis) - r;
else {
forCellCM(c1, c) if(space_distance_camelot(c1) < r)
return 0;
return int(dis) + 1 - r;
}
}
coord hrmap_crystal::long_representant(cell *c) {
auto& coordid = east.coordid;
auto co = roundcoord(get_coord(c) * Modval/PERIOD);
for(int s=0; s<coordid; s++) co[s] = gmod(co[s], Modval);
for(int s=coordid+1; s<cs.dim; s++) {
int v = gdiv(co[s], Modval);
co[s] -= v * Modval;
co[coordid] += v * Modval;
}
return co;
}
int hrmap_crystal::get_east(cell *c) {
auto& coordid = east.coordid;
auto& Xmod = east.Xmod;
auto& data = east.data;
auto& cycle = east.cycle;
coord co = long_representant(c);
int cycles = gdiv(co[coordid], Xmod);
co[coordid] -= cycles * Xmod;
return data[co] + cycle * cycles;
}
void hrmap_crystal::build_east(int cid) {
auto& coordid = east.coordid;
auto& Xmod = east.Xmod;
auto& data = east.data;
auto& cycle = east.cycle;
coordid = cid;
map<coord, int> full_data;
manual_celllister cl;
for(int i=0; i<(1<<cid); i++) {
auto co = c0;
for(int j=0; j<cid; j++) co[j] = ((i>>j)&1) * 2;
cell *cc = get_heptagon_at(co, cs.dir)->c7;
cl.add(cc);
}
map<coord, int> stepat;
int steps = 0, nextstep = isize(cl.lst);
cycle = 0;
int incycle = 0;
int needcycle = 16 + nextstep;
int elongcycle = 0;
Xmod = Modval;
int modmul = 1;
for(int i=0; i<isize(cl.lst); i++) {
if(incycle > needcycle * modmul) break;
if(i == nextstep) steps++, nextstep = isize(cl.lst);
cell *c = cl.lst[i];
auto co = long_representant(c);
if(co[coordid] < -Modval) continue;
if(full_data.count(co)) continue;
full_data[co] = steps;
auto co1 = co; co1[coordid] -= Xmod;
auto co2 = co; co2[coordid] = gmod(co2[coordid], Xmod);
if(full_data.count(co1)) {
int ncycle = steps - full_data[co1];
if(ncycle != cycle) incycle = 1, cycle = ncycle;
else incycle++;
int dd = gdiv(co[coordid], Xmod);
// println(hlog, co, " set data at ", co2, " from ", data[co2], " to ", steps - dd * cycle, " at step ", steps);
data[co2] = steps - dd * cycle;
elongcycle++;
if(elongcycle > 2 * needcycle * modmul) Xmod += Modval, elongcycle = 0, modmul++;
}
else incycle = 0, needcycle++, elongcycle = 0;
forCellCM(c1, c) cl.add(c1);
}
east.zeroshift = 0;
east.zeroshift = -get_east(cl.lst[0]);
println(hlog, "cycle found: ", cycle, " Xmod = ", Xmod, " on list: ", isize(cl.lst), " zeroshift: ", east.zeroshift);
}
void hrmap_crystal::prepare_east() {
if(east.data.empty()) build_east(1);
}
EX int dist_alt(cell *c) {
auto m = crystal_map();
if(specialland == laCamelot && m->camelot_center) {
if(pure())
return precise_distance(c, m->camelot_center);
if(c == m->camelot_center) return 0;
return 1 + int(2 * space_distance_camelot(c));
}
else {
m->prepare_east();
return m->get_east(c);
}
}
array<array<ld, MAXDIM>, MAXDIM> crug_rotation;
int ho = 1;
ldcoord rug_center;
bool draw_cut = false;
ld cut_level = 0;
EX void init_rotation() {
for(int i=0; i<MAXDIM; i++)
for(int j=0; j<MAXDIM; j++)
crug_rotation[i][j] = i == j ? 1/2. : 0;
auto& cs = crystal_map()->cs;
if(ho & 1) {
for(int i=(draw_cut ? 2 : cs.dim-1); i>=1; i--) {
ld c = cos(M_PI / 2 / (i+1));
ld s = sin(M_PI / 2 / (i+1));
for(int j=0; j<cs.dim; j++)
tie(crug_rotation[j][0], crug_rotation[j][i]) =
make_pair(
crug_rotation[j][0] * s + crug_rotation[j][i] * c,
-crug_rotation[j][i] * s + crug_rotation[j][0] * c
);
}
}
}
EX void random_rotation() {
auto& cs = crystal_map()->cs;
for(int i=0; i<100; i++) {
int a = hrand(cs.dim);
int b = hrand(cs.dim);
if(a == b) continue;
ld alpha = hrand(1000);
ld c = cos(alpha);
ld s = sin(alpha);
for(int u=0; u<cs.dim; u++) {
auto& x = crug_rotation[u][a];
auto& y = crug_rotation[u][b];
tie(x,y) = make_pair(x * c + y * s, y * c - x * s);
}
}
}
EX void next_home_orientation() {
ho++;
init_rotation();
}
EX void flip_z() {
for(int i=0; i<MAXDIM; i++)
crug_rotation[i][2] *= -1;
}
#if CAP_RUG
#if MAXMDIM >= 4
hyperpoint coord_to_flat(ldcoord co, int dim = 3) {
auto& cs = crystal_map()->cs;
hyperpoint res = Hypc;
co = co - rug_center;
for(int a=0; a<cs.dim; a++)
for(int b=0; b<dim; b++)
res[b] += crug_rotation[b][a] * co[a] * rug::modelscale;
return res;
}
#endif
EX void switch_z_coordinate() {
auto& cs = crystal_map()->cs;
for(int i=0; i<cs.dim; i++) {
ld tmp = crug_rotation[i][2];
for(int u=2; u<cs.dim-1; u++) crug_rotation[i][u] = crug_rotation[i][u+1];
crug_rotation[i][cs.dim-1] = tmp;
}
}
EX void apply_rotation(const transmatrix t) {
auto& cs = crystal_map()->cs;
for(int i=0; i<cs.dim; i++) {
hyperpoint h;
for(int j=0; j<3; j++) h[j] = crug_rotation[i][j];
h = t * h;
for(int j=0; j<3; j++) crug_rotation[i][j] = h[j];
}
}
EX void centerrug(ld aspd) {
if(vid.sspeed >= 4.99) aspd = 1000;
auto m = crystal_map();
ldcoord at = m->get_coord(cwt.at) - rug_center;
ld R = sqrt(at|at);
if(R < 1e-9) rug_center = m->get_coord(cwt.at);
else {
aspd *= (2+3*R*R);
if(aspd > R) aspd = R;
rug_center = rug_center + at * aspd / R;
}
}
void cut_triangle2(const hyperpoint pa, const hyperpoint pb, const hyperpoint pc, const hyperpoint ha, const hyperpoint hb, const hyperpoint hc) {
ld zac = pc[3] / (pc[3] - pa[3]);
hyperpoint pac = pa * zac + pc * (1-zac);
hyperpoint hac = ha * zac + hc * (1-zac);
ld zbc = pc[3] / (pc[3] - pb[3]);
hyperpoint pbc = pb * zbc + pc * (1-zbc);
hyperpoint hbc = hb * zbc + hc * (1-zbc);
pac[3] = pbc[3] = 1;
rug::rugpoint *rac = rug::addRugpoint(shiftless(hac), 0);
rug::rugpoint *rbc = rug::addRugpoint(shiftless(hbc), 0);
rac->native = pac;
rbc->native = pbc;
rac->valid = true;
rbc->valid = true;
rug::triangles.push_back(rug::triangle(rac, rbc, NULL));
}
void cut_triangle(const hyperpoint pa, const hyperpoint pb, const hyperpoint pc, const hyperpoint ha, const hyperpoint hb, const hyperpoint hc) {
if((pa[3] >= 0) == (pb[3] >= 0))
cut_triangle2(pa, pb, pc, ha, hb, hc);
else if((pa[3] >= 0) == (pc[3] >= 0))
cut_triangle2(pc, pa, pb, hc, ha, hb);
else
cut_triangle2(pb, pc, pa, hb, hc, ha);
}
#if MAXMDIM >= 4
EX void build_rugdata() {
using namespace rug;
rug::clear_model();
rug::good_shape = true;
rug::vertex_limit = 0;
auto m = crystal_map();
for(const auto& gp: gmatrix) {
cell *c = gp.first;
if(c->wall == waInvisibleFloor) continue;
const shiftmatrix& V = gp.second;
auto co = m->get_coord(c);
vector<ldcoord> vcoord(c->type);
for(int i=0; i<c->type; i++)
if(valence() == 4)
vcoord[i] = ((m->get_coord(c->cmove(i)) + m->get_coord(c->cmodmove(i-1))) / 2);
else
vcoord[i] = ((m->get_coord(c->cmove(i)) + m->get_coord(c->cmodmove(i-1)) + co) / 3);
if(!draw_cut) {
rugpoint *v = addRugpoint(tC0(V), 0);
v->native = coord_to_flat(co);
v->valid = true;
rugpoint *p[MAX_EDGE_CRYSTAL];
for(int i=0; i<c->type; i++) {
p[i] = addRugpoint(V * get_corner_position(c, i), 0);
p[i]->valid = true;
p[i]->native = coord_to_flat(vcoord[i]);
}
for(int i=0; i<c->type; i++) addTriangle(v, p[i], p[(i+1) % c->type]);
}
else {
hyperpoint hco = coord_to_flat(co, 4);
hco[3] -= cut_level * rug::modelscale;
vector<hyperpoint> vco(c->type);
for(int i=0; i<c->type; i++) {
vco[i] = coord_to_flat(vcoord[i], 4);
vco[i][3] -= cut_level * rug::modelscale;
}
for(int i=0; i<c->type; i++) {
int j = (i+1) % c->type;
if((vco[i][3] >= 0) != (hco[3] >= 0) || (vco[j][3] >= 0) != (hco[3] >= 0)) {
cut_triangle(hco, vco[i], vco[j], unshift(tC0(V)), unshift(V * get_corner_position(c, i)), unshift(V * get_corner_position(c, j)));
}
}
}
}
println(hlog, "cut ", cut_level, "r ", crug_rotation);
}
#endif
#endif
EX void set_land(cell *c) {
setland(c, specialland);
auto m = crystal_map();
auto co = m->get_coord(c);
auto co1 = roundcoord(co * 60);
coord cx = roundcoord(co / 8);
int hash = 0;
for(int a=0; a<m->cs.dim; a++) hash = 1317 * hash + cx[a];
set_euland3(c, co1[0], co1[1], dist_alt(c), hash);
}
EX void set_crystal(int sides) {
stop_game();
set_geometry(gCrystal);
set_variation(eVariation::pure);
ginf[gCrystal].sides = sides;
ginf[gCrystal].vertex = 4;
static char buf[20];
sprintf(buf, "{%d,4}", sides);
ginf[gCrystal].tiling_name = buf;
ginf[gCrystal].distlimit = distlimit_table[min(sides, MAX_EDGE_CRYSTAL-1)];
}
void test_crt() {
start_game();
auto m = crystal_map();
manual_celllister cl;
cl.add(m->camelot_center);
for(int i=0; i<isize(cl.lst); i++)
forCellCM(c1, cl.lst[i]) {
setdist(c1, 7, m->gamestart());
if(c1->land == laCamelot && c1->wall == waNone)
cl.add(c1);
}
println(hlog, "actual = ", isize(cl.lst), " algorithm = ", get_table_volume());
if(its(isize(cl.lst)) != get_table_volume()) exit(1);
}
void unit_test_tables() {
stop_game();
specialland = laCamelot;
set_crystal(5);
test_crt();
set_crystal(6);
test_crt();
set_crystal(5); set_variation(eVariation::bitruncated);
test_crt();
set_crystal(6); set_variation(eVariation::bitruncated);
test_crt();
set_crystal(8); set_variation(eVariation::bitruncated); set_variation(eVariation::bitruncated);
test_crt();
}
EX void set_crystal_period_flags() {
crystal_period &= ~1;
for(auto& g: ginf)
if(g.flags & qCRYSTAL) {
set_flag(ginf[gNil].flags, qSMALL, crystal_period && crystal_period <= 8);
set_flag(ginf[gNil].flags, qBOUNDED, crystal_period);
}
}
#if CAP_COMMANDLINE
int readArgs() {
using namespace arg;
if(0) ;
else if(argis("-crystal")) {
PHASEFROM(2);
shift(); set_crystal(argi());
}
else if(argis("-cview")) {
view_coordinates = true;
}
else if(argis("-ceast")) {
view_east = true;
}
else if(argis("-cprob")) {
PHASEFROM(2); shift_arg_formula(compass_probability);
}
else if(argis("-ccut")) {
draw_cut = true;
PHASEFROM(2); shift_arg_formula(cut_level);
}
else if(argis("-ccutoff")) {
draw_cut = false;
}
else if(argis("-cho")) {
shift(); ho = argi();
init_rotation();
}
else if(argis("-chrr")) {
random_rotation();
}
else if(argis("-test:crt")) {
test_crt();
}
else if(argis("-crystal_period")) {
if(cryst) stop_game();
shift(); crystal_period = argi();
set_crystal_period_flags();
}
else if(argis("-d:crystal"))
launch_dialog(show);
else if(argis("-cvcol")) {
shift(); int d = argi();
shift(); coordcolors[d] = arghex();
}
else return 1;
return 0;
}
#endif
EX hrmap *new_map() {
return new hrmap_crystal;
}
EX string compass_help() {
return XLAT(
"Lands in this geometry are usually built on North-South or West-East axis. "
"Compasses always point North, and all the cardinal directions to the right from compass North are East (this is not "
"true in general, but it is true for the cells where compasses are generated). "
"North is the first coordinate, while East is the sum of other coordinates."
);
}
string make_help() {
return XLAT(
"This space essentially lets you play in a d-dimensional grid. Pick three "
"dimensions and '3D display' to see how it works -- we are essentially playing on a periodic surface in "
"three dimensions, made of hexagons; each hexagon connects to six other hexagons, in each of the 6 "
"possible directions. Normally, the game visualizes this from the point of view of a creature living inside "
"the surface (regularized and smoothened somewhat), assuming that light rays are also restricted to the surface -- "
"this will look exactly like the {2d,4} tiling, except that the light rays may thus "
"sometimes make a loop, causing you to see images of yourself in some directions (in other words, "
"the d-dimensional grid is a quotient of the hyperbolic plane). The same construction works in other dimensions. "
"Half dimensions are interpreted in the following way: the extra dimension only has two 'levels', for example 2.5D "
"has a top plane and a bottom plane.\n\n"
"You may also bitruncate this tessellation -- which makes it work better with the rules of HyperRogue, but a bit harder to understand."
);
}
EX void crystal_knight_help() {
gamescreen(1);
dialog::init();
dialog::addHelp(XLAT(
"This is a representation of four-dimensional geometry. Can you find the Holy Grail in the center of the Round Table?\n\n"
"In 'Knight of the 16-Cell Table', each cell has 8 adjacent cells, "
"which correspond to 8 adjacent points in the four-dimensional grid. The Round Table has the shape of a 16-cell.\n\n"
"In 'Knight of the 3-Spherical Table', it is the same map, but double bitruncated. The Round Table has the shape of a hypersphere.\n\n"
));
dialog::addItem(XLAT("let me understand how the coordinates work"), 'e');
dialog::add_action([] { cheater = true; view_coordinates = true; compass_probability = 1; restart_game(); popScreenAll(); });
dialog::addItem(XLAT("thanks, I need no hints (achievement)"), 't');
dialog::add_action([] { view_coordinates = false; compass_probability = 0; restart_game(); popScreenAll(); });
dialog::addItem(XLAT("more about this geometry..."), 'm');
dialog::add_action([] { popScreenAll(); pushScreen(show); });
dialog::display();
}
EX void show() {
cmode = sm::SIDE | sm::MAYDARK;
gamescreen(0);
dialog::init(XLAT("dimensional crystal"));
for(int i=5; i<=14; i++) {
string s;
if(i % 2) s = its(i/2) + ".5D";
else s = its(i/2) + "D";
dialog::addBoolItem(s, cryst && ginf[gCrystal].sides == i && ginf[gCrystal].vertex == 4, 'a' + i - 5);
dialog::add_action(dialog::add_confirmation([i]() { set_crystal(i); start_game(); }));
}
dialog::addBoolItem(XLAT("4D double bitruncated"), ginf[gCrystal].vertex == 3, 'D');
dialog::add_action(dialog::add_confirmation([]() { set_crystal(8); set_variation(eVariation::bitruncated); set_variation(eVariation::bitruncated); start_game(); }));
dialog::addBreak(50);
dialog::addBoolItem_action(XLAT("view coordinates in the cheat mode"), view_coordinates, 'v');
dialog::addSelItem(XLAT("compass probability"), fts(compass_probability), 'p');
if(geometry == gCrystal344) dialog::lastItem().value += " (N/A)";
dialog::add_action([]() {
dialog::editNumber(compass_probability, 0, 1, 0.1, 1, XLAT("compass probability"), compass_help());
dialog::bound_low(0);
});
#if CAP_RUG
if(cryst && WDIM == 2) {
dialog::addBoolItem(XLAT("3D display"), rug::rugged, 'r');
dialog::add_action_push(rug::show);
}
else
dialog::addBreak(100);
if(rug::rugged && cryst && ginf[gCrystal].sides == 8 && WDIM == 2) {
dialog::addBoolItem(XLAT("render a cut"), draw_cut, 'x');
dialog::add_action([]() {
draw_cut = true;
dialog::editNumber(cut_level, -1, 1, 0.1, 0, XLAT("cut level"), "");
dialog::extra_options = [] {
dialog::addItem(XLAT("disable"), 'D');
dialog::add_action([] { draw_cut = false; popScreen(); });
};
});
}
else dialog::addBreak(100);
#endif
dialog::addSelItem(XLAT("Crystal torus"), its(crystal_period), 'C');
dialog::add_action([] {
dialog::editNumber(crystal_period, 0, 16, 2, 0, XLAT("Crystal torus"),
XLAT("Z_k^d instead of Z^d. Only works with k even."));
dialog::reaction_final = [] {
if(cryst) stop_game();
set_crystal_period_flags();
if(cryst) start_game();
};
});
dialog::addBack();
dialog::addHelp();
dialog::add_action([] { gotoHelp(make_help()); });
dialog::display();
}
auto crystalhook =
#if CAP_COMMANDLINE
addHook(hooks_args, 100, readArgs)
#endif
+ addHook(hooks_drawcell, 100, crystal_cell)
+ addHook(hooks_tests, 200, unit_test_tables);
map<pair<int, int>, bignum> volume_memo;
bignum& compute_volume(int dim, int rad) {
auto p = make_pair(dim, rad);
int is = volume_memo.count(p);
auto& m = volume_memo[p];
if(is) return m;
if(dim == 0) { m = 1; return m; }
m = compute_volume(dim-1, rad);
for(int r=0; r<rad; r++)
m.addmul(compute_volume(dim-1, r), 2);
return m;
}
// shift_data_zero.children[x1].children[x2]....children[xk].result[r2]
// is the number of grid points in distance at most sqrt(r2) from (x1,x2,...,xk)
struct eps_comparer {
bool operator() (ld a, ld b) const { return a < b-1e-6; }
};
struct shift_data {
shift_data *parent;
ld shift;
map<ld, shift_data, eps_comparer> children;
map<ld, bignum, eps_comparer> result;
shift_data() { parent = NULL; }
bignum& compute(ld rad2) {
if(result.count(rad2)) return result[rad2];
// println(hlog, "compute ", format("%p", this), " [shift=", shift, "], r2 = ", rad2);
// indenter i(2);
auto& b = result[rad2];
if(!parent) {
if(rad2 >= 0) b = 1;
}
else if(rad2 >= 0) {
for(int x = -2-sqrt(rad2); x <= sqrt(rad2)+2; x++) {
ld ax = x - shift;
if(ax*ax <= rad2)
b.addmul(parent->compute(rad2 - (ax*ax)), 1);
}
}
// println(hlog, "result = ", b.get_str(100));
return b;
}
};
shift_data shift_data_zero;
EX string get_table_volume() {
if(!pure()) {
auto m = crystal_map();
bignum res;
manual_celllister cl;
cl.add(m->gamestart());
ld rad2 = pow(roundTableRadius(NULL) / m->camelot_mul / PERIOD, 2) + 1e-4;
for(int i=0; i<isize(cl.lst); i++) {
cell *c = cl.lst[i];
ld mincoord = 9, maxcoord = -9;
auto co = m->get_coord(c);
for(int i=0; i<m->cs.dim; i++) {
if(co[i] < mincoord) mincoord = co[i];
if(co[i] > maxcoord) maxcoord = co[i];
}
static const ld eps = 1e-4;
if(mincoord >= 0-eps && maxcoord < PERIOD-eps) {
ld my_rad2 = rad2;
auto cshift = (co - m->camelot_coord) / PERIOD;
auto sd = &shift_data_zero;
for(int i=0; i<m->cs.dim; i++) {
if(i == m->cs.dim-1 && (m->cs.dir&1)) {
my_rad2 -= pow(cshift[i] / m->camelot_mul, 2);
}
else {
ld val = cshift[i] - floor(cshift[i]);
if(!sd->children.count(val)) {
sd->children[val].parent = sd;
sd->children[val].shift = val;
}
sd = &sd->children[val];
}
}
res.addmul(sd->compute(my_rad2), 1);
}
if(mincoord < -2 || maxcoord > 6) continue;
forCellCM(c2, c) cl.add(c2);
}
return res.get_str(100);
}
int s = ginf[gCrystal].sides;
int r = roundTableRadius(NULL);
if(s % 2 == 0)
return compute_volume(s/2, r-1).get_str(100);
else
return (compute_volume(s/2, r-1) + compute_volume(s/2, r-2)).get_str(100);
}
EX string get_table_boundary() {
if(!pure()) return "";
int r = roundTableRadius(NULL);
int s = ginf[gCrystal].sides;
if(s % 2 == 0)
return (compute_volume(s/2, r) - compute_volume(s/2, r-1)).get_str(100);
else
return (compute_volume(s/2, r) - compute_volume(s/2, r-2)).get_str(100);
}
EX void may_place_compass(cell *c) {
if(c != c->master->c7) return;
if(WDIM == 3) return;
auto m = crystal_map();
auto co = m->hcoords[c->master];
for(int i=0; i<m->cs.dim; i++)
if(co[i] % PERIOD)
return;
if(hrandf() < compass_probability)
c->item = itCompass;
}
#endif
#if CAP_CRYSTAL && MAXMDIM >= 4
euc::coord crystal_to_euclid(coord x) {
return euc::coord(x[0]/2, x[1]/2, x[2]/2);
}
coord euclid3_to_crystal(euc::coord x) {
coord res;
for(int i=0; i<3; i++) res[i] = x[i] * 2;
for(int i=3; i<MAXDIM; i++) res[i] = 0;
return res;
}
void transform_crystal_to_euclid () {
euc::clear_torus3();
geometry = gCubeTiling;
auto e = euc::new_map();
auto m = crystal_map();
auto infront = cwt.cpeek();
auto& spacemap = euc::get_spacemap();
auto& ispacemap = euc::get_ispacemap();
auto& camelot_center = euc::get_camelot_center();
auto& shifttable = euc::get_current_shifttable();
for(auto& p: m->hcoords) {
auto co = crystal_to_euclid(p.second);
spacemap[co] = p.first;
ispacemap[p.first] = co;
cell* c = p.first->c7;
// rearrange the monster directions
if(c->mondir < S7 && c->move(c->mondir)) {
auto co1 = crystal_to_euclid(m->hcoords[c->move(c->mondir)->master]) - co;
for(int i=0; i<6; i++)
if(co1 == shifttable[i])
c->mondir = i;
}
for(int i=0; i<S7; i++) c->move(i) = NULL;
}
if(m->camelot_center)
camelot_center = spacemap[crystal_to_euclid(m->hcoords[m->camelot_center->master])]->c7;
// clean hcoords and heptagon_at so that the map is not deleted when we delete m
m->hcoords.clear();
m->heptagon_at.clear();
delete m;
for(int i=0; i<isize(allmaps); i++)
if(allmaps[i] == m)
allmaps[i] = e;
currentmap = e;
// connect the cubes
for(auto& p: spacemap) {
auto& co = p.first;
auto& h = p.second;
for(int i=0; i<S7; i++)
if(spacemap.count(co + shifttable[i]))
h->move(i) = spacemap[co + shifttable[i]],
h->c.setspin(i, (i + 3) % 6, false),
h->c7->move(i) = h->move(i)->c7,
h->c7->c.setspin(i, (i + 3) % 6, false);
}
clearAnimations();
cwt.spin = neighborId(cwt.at, infront);
View = iddspin(cwt.at, cwt.spin, M_PI/2);
if(!flipplayer) View = cspin(0, 2, M_PI) * View;
if(pmodel == mdDisk) pmodel = mdPerspective;
}
void transform_euclid_to_crystal () {
geometry = gCrystal;
ginf[gCrystal].sides = 6;
ginf[gCrystal].vertex = 4;
ginf[gCrystal].tiling_name = "{6,4}";
ginf[gCrystal].distlimit = distlimit_table[6];
auto e = currentmap;
auto m = new hrmap_crystal;
auto infront = cwt.cpeek();
auto& spacemap = euc::get_spacemap();
auto& ispacemap = euc::get_ispacemap();
auto& camelot_center = euc::get_camelot_center();
for(auto& p: ispacemap) {
auto co = euclid3_to_crystal(p.second);
m->heptagon_at[co] = p.first;
m->hcoords[p.first] = co;
}
for(auto& p: ispacemap) {
cell *c = p.first->c7;
if(c->mondir < S7 && c->move(c->mondir)) {
auto co = euclid3_to_crystal(p.second);
for(int d=0; d<S7; d++) {
auto lw = m->makewalker(co, d);
auto co1 = add(co, lw, FULLSTEP);
if(m->heptagon_at.count(co1) && m->heptagon_at[co1] == c->move(c->mondir)->master)
c->mondir = d;
}
}
for(int i=0; i<S7; i++) c->move(i) = NULL;
}
if(camelot_center)
m->camelot_center = m->heptagon_at[euclid3_to_crystal(ispacemap[camelot_center->master])]->c7;
spacemap.clear();
ispacemap.clear();
delete e;
for(int i=0; i<isize(allmaps); i++)
if(allmaps[i] == e)
allmaps[i] = m;
currentmap = m;
// connect the cubes
for(auto& p: m->heptagon_at) {
auto& co = p.first;
auto& h = p.second;
for(int i=0; i<S7; i++) {
auto lw = m->makewalker(co, i);
auto co1 = add(co, lw, FULLSTEP);
if(m->heptagon_at.count(co1)) {
auto lw1 = lw+wstep;
h->move(i) = m->heptagon_at[co1],
h->c.setspin(i, lw1.spin, false),
h->c7->move(i) = h->move(i)->c7;
h->c7->c.setspin(i, h->c.spin(i), false);
}
}
}
View = Id;
clearAnimations();
cwt.spin = neighborId(cwt.at, infront);
if(pmodel == mdPerspective) pmodel = mdDisk;
}
EX void add_crystal_transform(char c) {
if(shmup::on) return;
if(cryst && ginf[gCrystal].sides == 6 && geometry != gCrystal344) {
dialog::addItem("convert Crystal to 3D", c);
dialog::add_action(transform_crystal_to_euclid);
}
if(geometry == gCubeTiling && !quotient) {
dialog::addItem("convert 3D to Crystal", c);
dialog::add_action(transform_euclid_to_crystal);
}
}
#endif
}
}
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