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hyperrogue/sphere.cpp
? a847f0f040 3d:: wax model in sphere3
2019-09-12 22:38:40 +02:00

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// Hyperbolic Rogue -- spherical spaces
// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details
namespace hr {
// --- spherical geometry ---
int spherecells() {
if(S7 == 5) return (elliptic?6:12);
if(S7 == 4) return (elliptic?3:6);
if(S7 == 3 && S3 == 4) return (elliptic?4:8);
if(S7 == 3) return 4;
if(S7 == 2) return (elliptic?1:2);
if(S7 == 1) return 1;
return 12;
}
vector<int> siblings;
struct hrmap_spherical : hrmap {
heptagon *dodecahedron[12];
eVariation mvar;
hrmap_spherical() {
mvar = variation;
for(int i=0; i<spherecells(); i++) {
heptagon& h = *(dodecahedron[i] = tailored_alloc<heptagon> (S7));
h.s = hsOrigin;
h.emeraldval = i;
h.zebraval = i;
h.fiftyval = i;
h.rval0 = h.rval1 = 0;
h.alt = NULL;
h.cdata = NULL;
h.c.fullclear();
h.fieldval = i;
if(!IRREGULAR) h.c7 = newCell(S7, &h);
}
if(S7 == 5)
siblings = {1, 0, 10, 4, 3, 8, 9, 11, 5, 6, 2, 7};
else
siblings = {1, 0, 3, 2, 5, 4};
if(S7 == 3 && S3 == 4) {
for(int i=0; i<8; i++) {
dodecahedron[i]->move(0) = dodecahedron[i^1];
dodecahedron[i]->c.setspin(0, 0, false);
dodecahedron[i]->move(1) = dodecahedron[i^2];
dodecahedron[i]->c.setspin(1, 1, false);
dodecahedron[i]->move(2) = dodecahedron[i^4];
dodecahedron[i]->c.setspin(2, 2, false);
}
for(int i=0; i<8; i++) {
int s = (i&1)+((i&2)>>1)+((i&4)>>2);
if((s&1) == 1) {
swap(dodecahedron[i]->move(1), dodecahedron[i]->move(2));
int a = dodecahedron[i]->c.spin(1);
int b = dodecahedron[i]->c.spin(2);
dodecahedron[i]->c.setspin(1, b, false);
dodecahedron[i]->c.setspin(2, a, false);
dodecahedron[i]->move(1)->c.setspin(b, 1, false);
dodecahedron[i]->move(2)->c.setspin(a, 2, false);
}
}
for(int i=0; i<8; i++)
for(int j=0; j<3; j++)
if(dodecahedron[i]->move(j)->move(dodecahedron[i]->c.spin(j)) != dodecahedron[i])
println(hlog, "8");
}
else if(S7 == 4 && elliptic) {
for(int i=0; i<3; i++) {
int i1 = (i+1)%3;
int i2 = (i+2)%3;
dodecahedron[i]->move(0) = dodecahedron[i1];
dodecahedron[i]->c.setspin(0, 1, false);
dodecahedron[i]->move(1) = dodecahedron[i2];
dodecahedron[i]->c.setspin(1, 0, false);
dodecahedron[i]->move(2) = dodecahedron[i1];
dodecahedron[i]->c.setspin(2, 3, true);
dodecahedron[i]->move(3) = dodecahedron[i2];
dodecahedron[i]->c.setspin(3, 2, true);
}
}
else for(int i=0; i<S7; i++) {
dodecahedron[0]->move(i) = dodecahedron[i+1];
dodecahedron[0]->c.setspin(i, 0, false);
dodecahedron[i+1]->move(0) = dodecahedron[0];
dodecahedron[i+1]->c.setspin(0, i, false);
dodecahedron[i+1]->move(1) = dodecahedron[(i+S7-1)%S7+1];
dodecahedron[i+1]->c.setspin(1, S7-1, false);
dodecahedron[i+1]->move(S7-1) = dodecahedron[(i+1)%S7+1];
dodecahedron[i+1]->c.setspin(S7-1, 1, false);
if(S7 == 5 && elliptic) {
dodecahedron[i+1]->move(2) = dodecahedron[(i+2)%S7+1];
dodecahedron[i+1]->c.setspin(2, 3, true);
dodecahedron[i+1]->move(3) = dodecahedron[(i+3)%S7+1];
dodecahedron[i+1]->c.setspin(3, 2, true);
}
else if(S7 == 5) {
dodecahedron[6]->move(i) = dodecahedron[7+i];
dodecahedron[6]->c.setspin(i, 0, false);
dodecahedron[7+i]->move(0) = dodecahedron[6];
dodecahedron[7+i]->c.setspin(0, i, false);
dodecahedron[i+7]->move(1) = dodecahedron[(i+4)%5+7];
dodecahedron[i+7]->c.setspin(1, 4, false);
dodecahedron[i+7]->move(4) = dodecahedron[(i+1)%5+7];
dodecahedron[i+7]->c.setspin(4, 1, false);
dodecahedron[i+1]->move(2) = dodecahedron[7+(10-i)%5];
dodecahedron[i+1]->c.setspin(2, 2, false);
dodecahedron[7+(10-i)%5]->move(2) = dodecahedron[1+i];
dodecahedron[7+(10-i)%5]->c.setspin(2, 2, false);
dodecahedron[i+1]->move(3) = dodecahedron[7+(9-i)%5];
dodecahedron[i+1]->c.setspin(3, 3, false);
dodecahedron[7+(9-i)%5]->move(3) = dodecahedron[i+1];
dodecahedron[7+(9-i)%5]->c.setspin(3, 3, false);
}
if(S7 == 4) {
dodecahedron[5]->move(3-i) = dodecahedron[i+1];
dodecahedron[5]->c.setspin(3-i, 2, false);
dodecahedron[i+1]->move(2) = dodecahedron[5];
dodecahedron[i+1]->c.setspin(2, 3-i, false);
}
}
#if CAP_IRR
if(IRREGULAR) {
irr::link_start(dodecahedron[0]);
for(int i=0; i<spherecells(); i++)
for(int j=0; j<S7; j++)
irr::may_link_next(dodecahedron[i], j);
}
#endif
}
heptagon *getOrigin() { return dodecahedron[0]; }
~hrmap_spherical() {
dynamicval<eVariation> ph(variation, mvar);
for(int i=0; i<spherecells(); i++) clearHexes(dodecahedron[i]);
for(int i=0; i<spherecells(); i++) tailored_delete(dodecahedron[i]);
}
void verify() {
for(int i=0; i<spherecells(); i++) for(int k=0; k<S7; k++) {
heptspin hs(dodecahedron[i], k, false);
heptspin hs2 = hs + wstep + (S7-1) + wstep + (S7-1) + wstep + (S7-1);
if(S3 == 4) hs2 = hs2 + wstep + (S7-1);
if(hs2.at != hs.at) printf("error %d,%d\n", i, k);
}
for(int i=0; i<spherecells(); i++) verifycells(dodecahedron[i]);
}
};
heptagon *getDodecahedron(int i) {
hrmap_spherical *s = dynamic_cast<hrmap_spherical*> (currentmap);
if(!s) return NULL;
return s->dodecahedron[i];
}
namespace sphere3 {
vector<hyperpoint> vertices120;
array<transmatrix, 120> vmatrix120;
vector<int> adj0;
array<array<int, 4>, 120> js;
array<hyperpoint, 60> dodefaces;
hyperpoint zero4;
ld norm(hyperpoint a, hyperpoint b) {
ld res = 0;
for(int i=0; i<4; i++) res += pow(a[i]-b[i], 2);
return res;
}
void gen600() {
vertices120.clear();
/// coordinates taken from Wikipedia
for(int a=0; a<16; a++) {
hyperpoint v = zero4;
for(int i=0; i<4; i++) v[i] = ((a >> i) & 1) ? .5 : -.5;
vertices120.push_back(v);
}
for(int i=0; i<4; i++) for(int q: {-1, 1}) {
hyperpoint v = zero4;
v[i]=q;
vertices120.push_back(v);
}
ld phi = (1 + sqrt(5)) / 2;
array<ld, 4> coo = {1, phi, 1/phi, 0};
// all permutations
array<int, 4> tab;
for(int i=0; i<4; i++) tab[i] = i;
do {
// check the permutation's sign
auto tabs = tab;
int inv = 0;
for(int i=0; i<4; i++) while(tabs[i] != i) {
swap(tabs[i], tabs[tabs[i]]);
inv++;
}
if(inv&1) goto again;
// 8 vertices for each permutation
for(int sg=0; sg<8; sg++) {
hyperpoint v;
for(int i=0; i<4; i++)
v[i] = (((sg >> tab[i])&1) ? 1 : -1) * coo[tab[i]]/2;
vertices120.push_back(v);
}
again: ;
}
while(std::next_permutation(tab.begin(), tab.end()));
if(isize(vertices120) != 120) {
printf("error: wrong number of vertices\n");
exit(1);
}
// we add edges between vertices which are close to each other
// ((specifically in distance 1/phi/phi)
bool inedge[120][120];
for(int i=0; i<120; i++)
for(int j=0; j<120; j++) {
ld d = hdist(vertices120[i], vertices120[j]);
inedge[i][j] = (i != j) && d < sqrt(.4);
}
vector<hyperpoint> cellvertices;
for(int i=0; i<120; i++)
for(int j=0; j<120; j++) if(inedge[i][j])
for(int k=0; k<120; k++) if(inedge[i][k] && inedge[k][j])
for(int l=0; l<120; l++) if(inedge[i][l] && inedge[j][l] && inedge[k][l]) {
array<int, 4> ijkl = {i, j, k, l};
transmatrix T;
for(int z=0; z<4; z++) set_column(T, z, vertices120[ijkl[z]]);
if(det(T) > 0) js[i] = ijkl;
}
/* transmatrix src;
for(int z=0; z<4; z++) set_column(src, z, vertices120[js[0][z]]); */
for(int i=0; i<120; i++)
for(int z=0; z<4; z++) set_column(vmatrix120[i], z, vertices120[js[i][z]]);
for(int i=0; i<120; i++) println(hlog, i, ": ", js[i], " -> ", vmatrix120[i]);
adj0.clear();
for(int i=0; i<120; i++) if(inedge[0][i]) adj0.push_back(i);
using namespace hyperpoint_vec;
int id = 0;
for(int i=0; i<12; i++) {
int ot = adj0[i];
vector<int> pentagon;
for(int j: adj0) if(inedge[ot][j]) pentagon.push_back(j);
println(hlog, i, ": ", pentagon);
int illegal = -1;
int at = pentagon[0];
for(int d=0; d<5; d++) {
for(int s: pentagon) if(inedge[at][s] && s != illegal) {
hyperpoint m = vertices120[0] + vertices120[ot] + vertices120[at] + vertices120[s];
m = mid(m, m);
println(hlog, id, ": ", m);
dodefaces[id++] = m;
illegal = at;
at = s;
break;
}
}
}
printf("id = %d\n", id);
}
struct hrmap_spherical3 : hrmap {
heptagon* cells[120];
hrmap_spherical3() {
gen600();
for(int i=0; i<120; i++) {
cells[i] = tailored_alloc<heptagon> (12);
heptagon& h = *(cells[i]);
h.s = hsOrigin;
h.emeraldval = i;
h.zebraval = i;
h.fiftyval = i;
h.rval0 = h.rval1 = 0;
h.alt = NULL;
h.cdata = NULL;
h.c.fullclear();
h.fieldval = i;
h.c7 = newCell(12, &h);
}
for(int i=0; i<120; i++) {
for(int k=0; k<12; k++) {
hyperpoint which = vmatrix120[i] * inverse(vmatrix120[0]) * vertices120[adj0[k]];
for(int s=0; s<120; s++) if(hdist(which, vertices120[s]) < 1e-6) {
cells[i]->move(k) = cells[s];
println(hlog, i,".",k, " -> ", s, " ; ", js[i]);
}
}
}
for(int i=0; i<120; i++)
for(int k=0; k<12; k++)
for(int l=0; l<12; l++)
if(cells[i]->move(k)->move(l) == cells[i])
cells[i]->c.setspin(k, l, false);
}
heptagon *getOrigin() { return cells[0]; }
~hrmap_spherical3() {
for(int i=0; i<120; i++) tailored_delete(cells[i]);
}
};
void draw() {
auto m = (hrmap_spherical3*) currentmap;
int old = viewctr.at->zebraval;
for(int i=0; i<120; i++)
drawcell(m->cells[i]->c7, View * vmatrix120[0] * inverse(vmatrix120[old]) * vmatrix120[i] * inverse(vmatrix120[0]), 0, false);
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1) {
return vmatrix120[0] * inverse(vmatrix120[h1->zebraval]) * vmatrix120[h2->zebraval] * inverse(vmatrix120[0]);
}
void makewax(int x) {
auto m = (hrmap_spherical3*) currentmap;
for(int i=0; i<120; i++) m->cells[i]->c7->wall = waNone;
m->cells[70]->c7->wall = waDune;
int cols[16] = {0x202020, 0x2020A0, 0x20A020, 0x20A0A0, 0xA02020, 0xA020A0, 0xA0A020, 0xA0A0A0,
0x606060, 0x6060FF, 0x60FF60, 0x60FFFF, 0xFF6060, 0xFF60FF, 0xFFFF60, 0xFFFFFF };
if(x) for(int i=0; i<12; i++) {
m->cells[70]->c7->move(i)->wall = waWaxWall;
m->cells[70]->c7->move(i)->landparam = cols[i];
}
}
#if CAP_COMMANDLINE
int readArgs() {
using namespace arg;
if(argis("-wax1")) {
PHASE(3);
start_game();
makewax(1);
}
else if(argis("-wax0")) {
PHASE(3);
start_game();
makewax(0);
}
else return 1;
return 0;
}
auto hook =
addHook(hooks_args, 100, readArgs);
#endif
}
}
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