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new geometry: gSeifertCover

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This commit is contained in:
Zeno Rogue 2020-01-06 20:53:09 +01:00
parent a3fd44f9a9
commit 88e6043e1b
2 changed files with 171 additions and 42 deletions
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3
classes.cpp
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@ -723,7 +723,7 @@ enum eGeometry {
gKiteDart2, gKiteDart3, gNil, gProduct, gRotSpace,
gTernary, gNIH, gSolN, gInfOrder, gSpace336, gSpace344, gCrystal344,
gArnoldCat, gArbitrary, gInfOrder4, gCrystal534,
gSpace535, gSpace536,
gSpace535, gSpace536, gSeifertCover,
gGUARD};
enum eGeometryClass { gcHyperbolic, gcEuclid, gcSphere, gcSolNIH, gcNil, gcProduct, gcSL2 };
@ -892,6 +892,7 @@ EX vector<geometryinfo> ginf = {
{"{5,3,4}","Crystal", "6D crystal in H3", "Cryst6" , 12, 4, qANYQ | qCRYSTAL, giHyperb3, 0x52000, {{7, 3}}, eVariation::pure},
{"{5,3,5}","none", "{5,3,5} hyperbolic honeycomb", "535", 12, 5, 0, giHyperb3, 0x31400, {{7, 2}}, eVariation::pure},
{"{5,3,6}","none", "{5,3,6} hyperbolic honeycomb", "536", 12, 6, qIDEAL, giHyperb3, 0x31400, {{7, 2}}, eVariation::pure},
{"{5,3,5}","SWh", "{5,3,5} quotient", "535c", 12, 5, qsSMALLB | qANYQ, giHyperb3, 0x31400, {{7, 2}}, eVariation::pure},
};
// bits: 9, 10, 15, 16, (reserved for later) 17, 18

210
reg3.cpp
View File

@ -40,6 +40,9 @@ EX namespace reg3 {
EX ld strafedist;
EX bool dirs_adjacent[16][16];
/** for adjacent directions a,b, next_dir[a][b] is the next direction adjacent to a, in (counter?)clockwise order from b */
EX int next_dir[16][16];
template<class T> ld binsearch(ld dmin, ld dmax, const T& f) {
for(int i=0; i<200; i++) {
ld d = (dmin + dmax) / 2;
@ -203,6 +206,15 @@ EX namespace reg3 {
for(hyperpoint h2: vertices_only) if(hdist(h, h2) < 1e-6) found = true;
if(!found) vertices_only.push_back(h);
}
for(int a=0; a<12; a++)
for(int b=0; b<12; b++)
if(reg3::dirs_adjacent[a][b])
for(int c=0; c<12; c++)
if(reg3::dirs_adjacent[a][c] && reg3::dirs_adjacent[b][c]) {
transmatrix t = build_matrix(tC0(reg3::adjmoves[a]), tC0(reg3::adjmoves[b]), tC0(reg3::adjmoves[c]), C0);
if(det(t) > 1e-3) reg3::next_dir[a][b] = c;
}
}
void binary_rebase(heptagon *h, const transmatrix& V) {
@ -210,13 +222,57 @@ EX namespace reg3 {
void test();
#if HDR
struct hrmap_quotient3 : hrmap {
vector<heptagon*> allh;
vector<vector<transmatrix>> tmatrices;
transmatrix adj(heptagon *h, int d) { return tmatrices[h->fieldval][d]; }
};
heptagon *getOrigin() override { return allh[0]; }
void draw() override;
transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override;
};
#endif
void hrmap_quotient3::draw() {
sphereflip = Id;
// for(int i=0; i<S6; i++) queuepoly(ggmatrix(cwt.at), shWall3D[i], 0xFF0000FF);
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(in_wallopt() && isWall3(c) && isize(dq::drawqueue) > 1000) continue;
for(int d=0; d<S7; d++)
dq::enqueue_by_matrix(h->move(d), V * tmatrices[h->fieldval][d]);
}
}
transmatrix hrmap_quotient3::relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) {
if(h1 == h2) return Id;
int d = hr::celldistance(h2->c7, h1->c7);
for(int a=0; a<S7; a++) if(hr::celldistance(h1->move(a)->c7, h2->c7) < d)
return adj(h1, a) * relative_matrix(h2, h1->move(a), hint);
println(hlog, "error in hrmap_quotient3:::relative_matrix");
return Id;
}
int encode_coord(const crystal::coord& co) {
int c = 0;
for(int i=0; i<4; i++) c |= ((co[i]>>1) & 3) << (2*i);
@ -548,45 +604,6 @@ EX namespace reg3 {
}
}
void draw() override {
sphereflip = Id;
// for(int i=0; i<S6; i++) queuepoly(ggmatrix(cwt.at), shWall3D[i], 0xFF0000FF);
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(in_wallopt() && isWall3(c) && isize(dq::drawqueue) > 1000) continue;
for(int d=0; d<S7; d++)
dq::enqueue_by_matrix(h->move(d), V * tmatrices[h->fieldval][d]);
}
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
if(h1 == h2) return Id;
int d = hr::celldistance(h2->c7, h1->c7);
for(int a=0; a<S7; a++) if(hr::celldistance(h1->move(a)->c7, h2->c7) < d)
return adj(h1, a) * relative_matrix(h2, h1->move(a), hint);
println(hlog, "error in hrmap_field3:::relative_matrix");
return Id;
}
heptagon *getOrigin() override { return allh[0]; }
vector<cell*>& allcells() override { return acells; }
vector<hyperpoint> get_vertices(cell* c) override {
@ -594,6 +611,116 @@ EX namespace reg3 {
}
};
/** homology cover of the Seifert-Weber space */
namespace seifert_weber {
using crystal::coord;
vector<coord> periods;
int flip(int x) { return (x+6) % 12; }
void build_reps() {
reg3::generate();
// start_game();
for(int a=0; a<12; a++)
for(int b=0; b<12; b++)
if(reg3::dirs_adjacent[a][b])
for(int c=0; c<12; c++)
if(reg3::dirs_adjacent[a][c] && reg3::dirs_adjacent[b][c]) {
transmatrix t = build_matrix(tC0(reg3::adjmoves[a]), tC0(reg3::adjmoves[b]), tC0(reg3::adjmoves[c]), C0);
if(det(t) > 0) next_dir[a][b] = c;
}
set<coord> boundaries;
for(int a=0; a<12; a++)
for(int b=0; b<12; b++) if(reg3::dirs_adjacent[a][b]) {
coord res = crystal::c0;
int sa = a, sb = b;
do {
// printf("%d ", sa);
if(sa < 6) res[sa]++; else res[sa-6]--;
sa = flip(sa);
sb = flip(sb);
swap(sa, sb);
sb = next_dir[sa][sb];
// sb = next_dirsa][sb];
}
while(a != sa || b != sb);
// printf("\n");
if(res > crystal::c0)
boundaries.insert(res);
}
periods.clear();
for(int index = 5; index >= 0; index--) {
for(auto k: boundaries) println(hlog, k);
println(hlog, "simplifying...");
for(auto by: boundaries) if(among(by[index], 1, -1)) {
println(hlog, "simplifying by ", by);
periods.push_back(by);
set<coord> nb;
for(auto v: boundaries)
if(v == by) ;
else if(v[index] % by[index] == 0)
nb.insert(v - by * (v[index] / by[index]));
else println(hlog, "error");
boundaries = move(nb);
break;
}
}
}
int get_rep(coord a) {
a = a - periods[0] * (a[5] / periods[0][5]);
a = a - periods[1] * (a[4] / periods[1][4]);
a = a - periods[2] * (a[3] / periods[2][3]);
for(int i=0; i<3; i++) a[i] = gmod(a[i], 5);
return a[2] * 25 + a[1] * 5 + a[0];
}
coord decode(int id) {
coord res = crystal::c0;
for(int a=0; a<3; a++) res[a] = id % 5, id /= 5;
return res;
}
struct hrmap_seifert_cover : hrmap_quotient3 {
hrmap_seifert_cover() {
if(periods.empty()) build_reps();
allh.resize(125);
tmatrices.resize(125);
for(int a=0; a<125; a++) {
allh[a] = tailored_alloc<heptagon> (S7);
allh[a]->c7 = newCell(S7, allh[a]);
allh[a]->fieldval = a;
allh[a]->zebraval = 0;
allh[a]->alt = NULL;
}
for(int a=0; a<125; a++) {
tmatrices[a].resize(12);
for(int b=0; b<12; b++) {
coord x = decode(a);
if(b < 6) x[b]++;
else x[b-6]--;
int a1 = get_rep(x);
allh[a]->c.connect(b, allh[a1], flip(b), false);
transmatrix T = reg3::adjmoves[b];
hyperpoint p = tC0(T);
tmatrices[a][b] = rspintox(p) * xpush(hdist0(p)) * cspin(2, 1, 108 * degree) * spintox(p);
}
}
}
};
}
struct hrmap_reg3 : hrmap {
heptagon *origin;
@ -897,6 +1024,7 @@ EX namespace reg3 {
};
EX hrmap* new_map() {
if(geometry == gSeifertCover) return new seifert_weber::hrmap_seifert_cover;
if(quotient && !sphere) return new hrmap_field3;
return new hrmap_reg3;
}
@ -945,7 +1073,7 @@ EX bool pseudohept(cell *c) {
return c->master->distance & 1;
if(geometry == gField534)
return hr::celldistance(c, currentmap->gamestart()) & 1;
if(geometry == gCrystal344 || geometry == gCrystal534)
if(geometry == gCrystal344 || geometry == gCrystal534 || geometry == gSeifertCover)
return false;
if(hyperbolic) {
heptagon *h = m->reg_gmatrix[c->master].first;