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SolN manifold

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This commit is contained in:
Zeno Rogue
2019-10-03 20:10:48 +02:00
parent 4872ad01f4
commit d69cb4e946
12 changed files with 176 additions and 120 deletions
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225
nonisotropic.cpp
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@@ -25,11 +25,15 @@ EX namespace nisot {
return slr::translate(h);
transmatrix T = Id;
for(int i=0; i<GDIM; i++) T[i][LDIM] = h[i];
if(sol) {
if(sol && nih) {
T[0][0] = pow(2, -h[2]);
T[1][1] = pow(3, h[2]);
}
else if(sol) {
T[0][0] = exp(-h[2]);
T[1][1] = exp(+h[2]);
}
if(nih) {
else if(nih) {
T[0][0] = pow(2, h[2]);
T[1][1] = pow(3, h[2]);
}
@@ -52,6 +56,8 @@ EX namespace solnihv {
void load();
hyperpoint get(ld ix, ld iy, ld iz, bool lazy);
nisot::ptlow& get_int(int ix, int iy, int iz) { return tab[(iz*PRECY+iy)*PRECX+ix]; }
GLuint texture_id;
bool toload;
@@ -84,7 +90,7 @@ EX namespace solnihv {
hyperpoint res;
if(lazy) {
auto r = tab[(int(iz)*PRECY+int(iy))*PRECX+int(ix)];
auto r = get_int(int(ix), int(iy), int(iz));
for(int i=0; i<3; i++) res[i] = r[i];
}
@@ -98,7 +104,7 @@ EX namespace solnihv {
int ay = iy, by = ay+1;
int az = iz, bz = az+1;
#define S0(x,y,z) tab[(z*PRECY+y)*PRECX+x][t]
#define S0(x,y,z) get_int(x, y, z)[t]
#define S1(x,y) (S0(x,y,az) * (bz-iz) + S0(x,y,bz) * (iz-az))
#define S2(x) (S1(x,ay) * (by-iy) + S1(x,by) * (iy-ay))
@@ -244,8 +250,10 @@ EX namespace solnihv {
parent->c.connect(d, g, d1, false);
return g;
};
switch(geometry){
if(sol) switch(d) {
case gSol: switch(d) {
case 0: // right
return rule(altstep(pf, 2), ps, 4);
case 1: // up
@@ -266,7 +274,7 @@ EX namespace solnihv {
return NULL;
}
else switch(d) {
case gNIH: switch(d) {
case 0: // right
return rule(altstep(pf, 2), ps, 2);
case 1: // up
@@ -280,6 +288,26 @@ EX namespace solnihv {
default:
return rule(altstep(pf, (d-5) % 2), altstep3(ps, (d-5)/2), 4);
}
case gSolN: switch(d) {
case 0: // right
return rule(altstep(pf, 2), ps, 2);
case 1: // up
return rule(pf, altstep3(ps, 3), 3);
case 2: // left
return rule(altstep(pf, 4), ps, 0);
case 3: // down
return rule(pf, altstep3(ps, 5), 1);
case 4: case 5:
return rule(altstep(pf, d-4), altstep3(ps, 4), ps->zebraval + 6);
case 6: case 7: case 8:
return rule(altstep(pf, 3), altstep3(ps, d-6), pf->zebraval + 4);
default:
return NULL;
}
default: throw "not solnihv";
}
}
~hrmap_solnih() {
@@ -289,23 +317,23 @@ EX namespace solnihv {
}
transmatrix adjmatrix(int i, int j) {
if(sol) {
switch(geometry) {
case gSol: {
ld z = log(2);
ld bw = vid.binary_width * z;
ld bwh = bw / 4;
switch(i) {
case 0: return xpush(+bw);
case 1: return ypush(+bw);
case 2: return xpush(-bwh) * zpush(+z) * ypush(j == 6 ? +bwh : -bwh);
case 3: return xpush(+bwh) * zpush(+z) * ypush(j == 6 ? +bwh : -bwh);
case 2: case 3:
return ypush(bw*(6.5-j)) * zpush(+z) * xpush(bw*(i-2.5));
case 4: return xpush(-bw);
case 5: return ypush(-bw);
case 6: return ypush(-bwh) * zpush(-z) * xpush(j == 2 ? +bwh : -bwh);
case 7: return ypush(+bwh) * zpush(-z) * xpush(j == 2 ? +bwh : -bwh);
case 6: case 7:
return xpush(bw*(2.5-j)) * zpush(-z) * ypush(bw*(i-6.5));
default:return Id;
}
}
else {
case gNIH: {
ld bw = vid.binary_width;
switch(i) {
case 0: return xpush(+bw);
@@ -378,31 +406,40 @@ EX namespace solnihv {
" return 0.5 - atan((0.5-x) / y) / 3.1415926535897932384626433832795;"
" }";
EX }
EX namespace solv {
EX ld solrange_xy = 15;
EX ld solrange_z = 4;
EX bool in_table_range(hyperpoint h) {
return abs(h[0]) < solrange_xy && abs(h[1]) < solrange_xy && abs(h[2]) < solrange_z;
}
EX solnihv::tabled_inverses solt = solnihv::tabled_inverses("solv-geodesics.dat");
hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
return hpxyz3(
-velocity[2] * transported[0] - velocity[0] * transported[2],
velocity[2] * transported[1] + velocity[1] * transported[2],
velocity[0] * transported[0] * exp(2*at[2]) - velocity[1] * transported[1] * exp(-2*at[2]),
0
);
constexpr ld l2 = log(2);
constexpr ld l3 = log(3);
switch(geometry) {
case gSolN:
return hpxyz3(
-(velocity[2] * transported[0] + velocity[0] * transported[2]) * l2,
(velocity[2] * transported[1] + velocity[1] * transported[2]) * l3,
velocity[0] * transported[0] * exp(2*l2*at[2]) * l2 - velocity[1] * transported[1] * exp(-2*l3*at[2]) * l3,
0
);
case gSol:
return hpxyz3(
-velocity[2] * transported[0] - velocity[0] * transported[2],
velocity[2] * transported[1] + velocity[1] * transported[2],
velocity[0] * transported[0] * exp(2*at[2]) - velocity[1] * transported[1] * exp(-2*at[2]),
0
);
case gNIH:
return hpxyz3(
(velocity[2] * transported[0] + velocity[0] * transported[2]) * l2,
(velocity[2] * transported[1] + velocity[1] * transported[2]) * l3,
-(velocity[0] * transported[0] * exp(-2*l2*at[2]) * l2 + velocity[1] * transported[1] * exp(-2*l3*at[2]) * l3),
0
);
default:
throw "christoffel not in solnihv";
}
}
EX hyperpoint get_inverse_exp(hyperpoint h, bool lazy, bool just_direction) {
solt.load();
EX hyperpoint get_inverse_exp_symsol(hyperpoint h, bool lazy, bool just_direction) {
auto& s = get_tabled();
s.load();
ld ix = h[0] >= 0. ? solnihv::x_to_ix(h[0]) : solnihv::x_to_ix(-h[0]);
ld iy = h[1] >= 0. ? solnihv::x_to_ix(h[1]) : solnihv::x_to_ix(-h[1]);
@@ -410,7 +447,7 @@ EX namespace solv {
if(h[2] < 0.) { iz = -iz; swap(ix, iy); }
hyperpoint res = solt.get(ix, iy, iz, lazy);
hyperpoint res = s.get(ix, iy, iz, lazy);
if(h[2] < 0.) { swap(res[0], res[1]); res[2] = -res[2]; }
if(h[0] < 0.) res[0] = -res[0];
@@ -425,7 +462,29 @@ EX namespace solv {
return res;
}
EX string solshader = solnihv::common +
EX hyperpoint get_inverse_exp_nsym(hyperpoint h, bool lazy, bool just_direction) {
auto& s = get_tabled();
s.load();
ld ix = h[0] >= 0. ? solnihv::x_to_ix(h[0]) : solnihv::x_to_ix(-h[0]);
ld iy = h[1] >= 0. ? solnihv::x_to_ix(h[1]) : solnihv::x_to_ix(-h[1]);
ld iz = (tanh(h[2]/4)+1)/2;
hyperpoint res = s.get(ix, iy, iz, lazy);
if(h[0] < 0.) res[0] = -res[0];
if(h[1] < 0.) res[1] = -res[1];
if(!just_direction) {
ld r = hypot_d(3, res);
if(r == 0.) return res;
return res * atanh(r) / r;
}
return res;
}
EX string shader_symsol = solnihv::common +
"vec4 inverse_exp(vec4 h) {"
@@ -456,57 +515,7 @@ EX namespace solv {
"return res;"
"}";
EX int approx_distance(heptagon *h1, heptagon *h2) {
auto m = (solnihv::hrmap_solnih*) currentmap;
dynamicval<eGeometry> g(geometry, gBinary4);
dynamicval<hrmap*> cm(currentmap, m->binary_map);
int d1 = binary::celldistance3_approx(m->coords[h1].first, m->coords[h2].first);
int d2 = binary::celldistance3_approx(m->coords[h1].second, m->coords[h2].second);
return d1 + d2 - abs(h1->distance - h2->distance);
}
EX }
EX namespace nihv {
EX solnihv::tabled_inverses niht = solnihv::tabled_inverses("h23-geodesics.dat");
hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
static const ld l2 = log(2);
static const ld l3 = log(3);
return hpxyz3(
(velocity[2] * transported[0] + velocity[0] * transported[2]) * l2,
(velocity[2] * transported[1] + velocity[1] * transported[2]) * l3,
-(velocity[0] * transported[0] * exp(-2*l2*at[2]) * l2 + velocity[1] * transported[1] * exp(-2*l3*at[2]) * l3),
// (-velocity[2] * transported[0] - velocity[0] * transported[2]) * l2,
// (-velocity[2] * transported[1] - velocity[1] * transported[2]) * l3,
// velocity[0] * transported[0] * exp(2*l2*at[2]) * l2 + velocity[1] * transported[1] * exp(2*l3*at[2]) * l3,
0
);
}
EX hyperpoint get_inverse_exp(hyperpoint h, bool lazy, bool just_direction) {
niht.load();
ld ix = h[0] >= 0. ? solnihv::x_to_ix(h[0]) : solnihv::x_to_ix(-h[0]);
ld iy = h[1] >= 0. ? solnihv::x_to_ix(h[1]) : solnihv::x_to_ix(-h[1]);
ld iz = (tanh(h[2]/4)+1)/2;
hyperpoint res = niht.get(ix, iy, iz, lazy);
if(h[0] < 0.) res[0] = -res[0];
if(h[1] < 0.) res[1] = -res[1];
if(!just_direction) {
ld r = hypot_d(3, res);
if(r == 0.) return res;
return res * atanh(r) / r;
}
return res;
}
EX string nihshader = solnihv::common +
EX string shader_nsym = solnihv::common +
"vec4 inverse_exp(vec4 h) {"
@@ -527,6 +536,35 @@ EX namespace nihv {
"return res;"
"}";
EX ld solrange_xy = 15;
EX ld solrange_z = 4;
EX bool in_table_range(hyperpoint h) {
return abs(h[0]) < solrange_xy && abs(h[1]) < solrange_xy && abs(h[2]) < solrange_z;
}
EX tabled_inverses solt = solnihv::tabled_inverses("solv-geodesics.dat");
EX tabled_inverses niht = solnihv::tabled_inverses("h23-geodesics.dat");
EX tabled_inverses sont = solnihv::tabled_inverses("sont-geodesics.dat");
EX tabled_inverses& get_tabled() {
switch(geometry) {
case gSol: return solt;
case gNIH: return niht;
case gSolN: return sont;
default: throw "not solnih";
}
}
EX int approx_distance(heptagon *h1, heptagon *h2) {
auto m = (solnihv::hrmap_solnih*) currentmap;
dynamicval<eGeometry> g(geometry, gBinary4);
dynamicval<hrmap*> cm(currentmap, m->binary_map);
int d1 = binary::celldistance3_approx(m->coords[h1].first, m->coords[h2].first);
int d2 = binary::celldistance3_approx(m->coords[h1].second, m->coords[h2].second);
return d1 + d2 - abs(h1->distance - h2->distance);
}
EX }
#endif
@@ -1513,8 +1551,7 @@ EX namespace nisot {
EX hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
if(nil) return nilv::christoffel(at, velocity, transported);
#if CAP_SOLV
else if(sol) return solv::christoffel(at, velocity, transported);
else if(nih) return nihv::christoffel(at, velocity, transported);
else if(solnih) return solnihv::christoffel(at, velocity, transported);
#endif
else if(sl2) return slr::christoffel(at, velocity, transported);
else return point3(0, 0, 0);
@@ -1522,7 +1559,7 @@ EX namespace nisot {
EX bool in_table_range(hyperpoint h) {
#if CAP_SOLV
if(solnih) return solv::in_table_range(h);
if(sol) return solnihv::in_table_range(h);
#endif
return true;
}
@@ -1625,8 +1662,8 @@ EX namespace nisot {
using namespace arg;
#if CAP_SOLV
if(argis("-solrange")) {
shift_arg_formula(solv::solrange_xy);
shift_arg_formula(solv::solrange_z);
shift_arg_formula(solnihv::solrange_xy);
shift_arg_formula(solnihv::solrange_z);
return 0;
}
#endif
@@ -1636,11 +1673,11 @@ EX namespace nisot {
}
#if CAP_SOLV
else if(argis("-fsol")) {
shift(); solv::solt.fname = args();
shift(); solnihv::solt.fname = args();
return 0;
}
else if(argis("-nihsol")) {
shift(); nihv::niht.fname = args();
shift(); solnihv::niht.fname = args();
return 0;
}
#endif