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hyperrogue/nonisotropic.cpp

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// Hyperbolic Rogue -- nonisotropic spaces (Solv and Nil)
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file nonisotropic.cpp
* \brief nonisotropic spaces (Solv and Nil)
*/
#include "hyper.h"
namespace hr {
EX namespace nisot {
EX bool local_perspective_used;
EX bool geodesic_movement = true;
EX transmatrix translate(hyperpoint h, ld co IS(1)) {
if(sl2 || sphere)
return co > 0 ? stretch::translate(h) : stretch::itranslate(h);
transmatrix T = Id;
for(int i=0; i<GDIM; i++) T[i][LDIM] = h[i];
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]);
}
else if(nih) {
T[0][0] = pow(2, h[2]);
T[1][1] = pow(3, h[2]);
}
if(nil) {
T[2][1] = h[0] * (nilv::model_used + 1) / 2;
T[2][0] = h[1] * (nilv::model_used - 1) / 2;
}
if(co < 0) return iso_inverse(T);
return T;
}
EX }
#if !CAP_SOLV
EX namespace sn {
EX always_false in() { return always_false(); }
EX }
#endif
#if CAP_SOLV
EX namespace sn {
EX bool in() { return among(cgclass, gcSol, gcNIH, gcSolN); }
EX eGeometryClass geom() {
return cgclass;
}
#if HDR
typedef array<float, 3> compressed_point;
inline hyperpoint decompress(compressed_point p) { return point3(p[0], p[1], p[2]); }
inline compressed_point compress(hyperpoint h) { return make_array<float>(h[0], h[1], h[2]); }
struct tabled_inverses {
int PRECX, PRECY, PRECZ;
vector<compressed_point> tab;
string fname;
bool loaded;
void load();
hyperpoint get(ld ix, ld iy, ld iz, bool lazy);
compressed_point& get_int(int ix, int iy, int iz) { return tab[(iz*PRECY+iy)*PRECX+ix]; }
GLuint texture_id;
bool toload;
GLuint get_texture_id();
tabled_inverses(string s) : fname(s), texture_id(0), toload(true) {}
};
#endif
void tabled_inverses::load() {
if(loaded) return;
FILE *f = fopen(fname.c_str(), "rb");
if(!f) f = fopen((rsrcdir + fname).c_str(), "rb");
if(!f) { addMessage(XLAT("geodesic table missing")); pmodel = mdPerspective; return; }
hr::ignore(fread(&PRECX, 4, 1, f));
hr::ignore(fread(&PRECY, 4, 1, f));
hr::ignore(fread(&PRECZ, 4, 1, f));
tab.resize(PRECX * PRECY * PRECZ);
hr::ignore(fread(&tab[0], sizeof(compressed_point) * PRECX * PRECY * PRECZ, 1, f));
fclose(f);
loaded = true;
}
hyperpoint tabled_inverses::get(ld ix, ld iy, ld iz, bool lazy) {
ix *= PRECX-1;
iy *= PRECY-1;
iz *= PRECZ-1;
hyperpoint res;
if(lazy) {
if(isnan(ix) || isnan(iy) || isnan(iz)) return Hypc;
return decompress(get_int(int(ix+.5), int(iy+.5), int(iz+.5)));
}
else {
if(ix >= PRECX-1 || isnan(ix)) ix = PRECX-2;
if(iy >= PRECX-1 || isnan(iy)) iy = PRECX-2;
if(iz >= PRECZ-1 || isnan(iz)) iz = PRECZ-2;
int ax = ix, bx = ax+1;
int ay = iy, by = ay+1;
int az = iz, bz = az+1;
#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))
for(int t=0; t<3; t++)
res[t] = S2(ax) * (bx-ix) + S2(bx) * (ix-ax);
res[3] = 0;
}
return res;
}
GLuint tabled_inverses::get_texture_id() {
#if CAP_GL
if(!toload) return texture_id;
load();
if(!loaded) return 0;
println(hlog, "installing table");
toload = false;
if(texture_id == 0) glGenTextures(1, &texture_id);
glBindTexture( GL_TEXTURE_3D, texture_id);
glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_WRAP_R, GL_CLAMP_TO_EDGE);
auto xbuffer = new glvertex[PRECZ*PRECY*PRECX];
for(int z=0; z<PRECZ*PRECY*PRECX; z++) {
auto& t = tab[z];
xbuffer[z] = glhr::makevertex(t[0], t[1], t[2]);
}
#if !ISWEB
glTexImage3D(GL_TEXTURE_3D, 0, 34836 /*GL_RGBA32F*/, PRECX, PRECX, PRECZ, 0, GL_RGBA, GL_FLOAT, xbuffer);
#else
// glTexStorage3D(GL_TEXTURE_3D, 1, 34836 /*GL_RGBA32F*/, PRECX, PRECX, PRECZ);
// glTexSubImage3D(GL_TEXTURE_3D, 0, 0, 0, 0, PRECX, PRECY, PRECZ, GL_RGBA, GL_FLOAT, xbuffer);
#endif
delete[] xbuffer;
#endif
return texture_id;
}
EX ld x_to_ix(ld u) {
if(u == 0.) return 0.;
ld diag = u*u/2.;
ld x = diag;
ld y = u;
ld z = diag+1.;
x /= (1.+z);
y /= (1.+z);
return 0.5 - atan((0.5-x) / y) / M_PI;
}
EX ld ix_to_x(ld ix) {
ld minx = 0;
while(x_to_ix(minx) <= ix) minx++;
ld maxx = minx; minx--;
for(int it=0; it<20; it++) {
ld x = (minx + maxx) / 2;
if(x_to_ix(x) < ix) minx = x;
else maxx = x;
}
return minx;
}
EX ld z_to_iz(ld z) {
z = sinh(z) / (1 + cosh(z));
if(nih) z = (z+1) / 2;
return z;
}
EX ld iz_to_z(ld iz) {
ld minz = 0;
while(z_to_iz(minz) <= iz) minz++;
while(z_to_iz(minz) > iz) minz--;
ld maxz = minz + 1;
for(int it=0; it<20; it++) {
ld z = (minz + maxz) / 2;
if(z_to_iz(z) < iz) minz = z;
else maxz = z;
}
return (minz+maxz) / 2;
}
EX hyperpoint azeq_to_table(hyperpoint x) {
// azimuthal equidistant to Poincare
ld r = hypot_d(3, x);
if(r == 0) return point3(0,0,0);
ld make_r = sinh(r) / (1 + cosh(r));
ld d = make_r / r;
return x * d;
}
EX hyperpoint table_to_azeq(hyperpoint x) {
// Poincare to azimuthal equidistant
ld hr = sqhypot_d(3, x);
if(hr < 1e-5) return x * 2;
if(hr >= 1) return x * 60;
ld hz = (1 + hr) / (1 - hr);
ld d = (hz+1) * acosh(hz) / sinh(acosh(hz));
return x * d;
}
struct hrmap_solnih : hrmap {
hrmap *binary_map;
hrmap *ternary_map; /* nih only */
map<pair<heptagon*, heptagon*>, heptagon*> at;
map<heptagon*, pair<heptagon*, heptagon*>> coords;
heptagon *origin;
heptagon *getOrigin() override { return origin; }
heptagon *get_at(heptagon *x, heptagon *y) {
auto& h = at[make_pair(x, y)];
if(h) return h;
h = init_heptagon(S7);
h->c7 = newCell(S7, h);
coords[h] = make_pair(x, y);
h->distance = x->distance;
h->zebraval = x->emeraldval;
h->emeraldval = y->emeraldval;
return h;
}
hrmap_solnih() {
heptagon *alt;
heptagon *alt3;
if(true) {
dynamicval<eGeometry> g(geometry, gBinary4);
alt = init_heptagon(S7);
alt->s = hsOrigin;
alt->alt = alt;
binary_map = bt::new_alt_map(alt);
}
if(nih) {
dynamicval<eGeometry> g(geometry, gTernary);
alt3 = init_heptagon(S7);
alt3->s = hsOrigin;
alt3->alt = alt3;
ternary_map = bt::new_alt_map(alt3);
}
else {
alt3 = alt;
ternary_map = nullptr;
}
origin = get_at(alt, alt3);
}
heptagon *altstep(heptagon *h, int d) {
dynamicval<eGeometry> g(geometry, gBinary4);
dynamicval<hrmap*> cm(currentmap, binary_map);
return h->cmove(d);
}
heptagon *altstep3(heptagon *h, int d) {
dynamicval<eGeometry> g(geometry, gTernary);
dynamicval<hrmap*> cm(currentmap, ternary_map);
return h->cmove(d);
}
heptagon *create_step(heptagon *parent, int d) override {
auto p = coords[parent];
auto pf = p.first, ps = p.second;
auto rule = [&] (heptagon *c1, heptagon *c2, int d1) {
auto g = get_at(c1, c2);
parent->c.connect(d, g, d1, false);
return g;
};
switch(geometry){
case gSol: switch(d) {
case 0: // right
return rule(altstep(pf, 2), ps, 4);
case 1: // up
return rule(pf, altstep(ps, 2), 5);
case 2: // front left
return rule(altstep(pf, 0), altstep(ps, 3), ps->zebraval ? 7 : 6);
case 3: // front right
return rule(altstep(pf, 1), altstep(ps, 3), ps->zebraval ? 7 : 6);
case 4: // left
return rule(altstep(pf, 4), ps, 0);
case 5: // down
return rule(pf, altstep(ps, 4), 1);
case 6: // back down
return rule(altstep(pf, 3), altstep(ps, 0), pf->zebraval ? 3 : 2);
case 7: // back up
return rule(altstep(pf, 3), altstep(ps, 1), pf->zebraval ? 3 : 2);
default:
return NULL;
}
case gNIH: 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: // back
return rule(altstep(pf, 3), altstep3(ps, 4), 5 + pf->zebraval + 2 * ps->zebraval);
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 hr_exception("not solnihv");
}
}
~hrmap_solnih() {
delete binary_map;
if(ternary_map) delete ternary_map;
for(auto& p: at) clear_heptagon(p.second);
}
transmatrix adjmatrix(int i, int j) {
switch(geometry) {
case gSol: {
ld z = log(2);
ld bw = vid.binary_width * z;
switch(i) {
case 0: return xpush(+bw);
case 1: return ypush(+bw);
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: case 7:
return xpush(bw*(2.5-j)) * zpush(-z) * ypush(bw*(i-6.5));
default:return Id;
}
}
case gNIH: {
ld bw = vid.binary_width;
switch(i) {
case 0: return xpush(+bw);
case 1: return ypush(+bw);
case 2: return xpush(-bw);
case 3: return ypush(-bw);
case 4: return xpush(-((j-5)%2-.5)*bw) * ypush(-((j-5)/2-1)*bw) * zpush(1);
default:
return zpush(-1) * xpush(((i-5)%2-.5)*bw) * ypush(((i-5)/2-1)*bw);
}
}
case gSolN: {
ld bw = vid.binary_width;
switch(i) {
case 0: return xpush(+bw);
case 1: return ypush(+bw);
case 2: return xpush(-bw);
case 3: return ypush(-bw);
case 4:
case 5:
return ypush(bw*(7-j)) * zpush(+1) * xpush(bw*(i-4.5));
case 6:
case 7:
case 8:
return xpush(bw*(4.5-j)) * zpush(-1) * ypush(bw*(i-7));
default:
throw hr_exception("wrong dir");
}
}
default: throw hr_exception("wrong geometry");
}
}
transmatrix adj(heptagon *h, int d) override {
h->cmove(d); return adjmatrix(d, h->c.spin(d));
}
transmatrix relative_matrixh(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
for(int i=0; i<h1->type; i++) if(h1->move(i) == h2) return adjmatrix(i, h1->c.spin(i));
if(gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7))
return inverse_shift(gmatrix0[h1->c7], gmatrix0[h2->c7]);
transmatrix front = Id, back = Id;
int up, down;
switch(geometry) {
case gSol: up = 2; down = 6; break;
case gSolN: up = 4; down = 7; break;
case gNIH: up = 4; down = 4; break;
default: throw hr_exception("not nihsolv");
}
while(h1->distance > h2->distance) front = front * adj(h1, down), h1 = h1->cmove(down);
while(h1->distance < h2->distance) back = iadj(h2, down) * back, h2 = h2->cmove(down);
while(coords[h1].first != coords[h2].first) front = front * adj(h1, down), back = iadj(h2, down) * back, h1 = h1->cmove(down), h2 = h2->cmove(down);
while(coords[h1].second != coords[h2].second) front = front * adj(h1, up), back = iadj(h2, up) * back, h1 = h1->cmove(up), h2 = h2->cmove(up);
return front * back;
}
};
EX pair<heptagon*,heptagon*> getcoord(heptagon *h) {
return ((hrmap_solnih*)currentmap)->coords[h];
}
EX heptagon *get_at(heptagon *h1, heptagon *h2, bool gen) {
auto m = ((hrmap_solnih*)currentmap);
if(!gen && !m->at.count(make_pair(h1, h2))) return nullptr;
return m->get_at(h1, h2);
}
EX string common =
"uniform mediump sampler3D tInvExpTable;"
"uniform mediump float PRECX, PRECY, PRECZ;"
"float x_to_ix(float u) {"
" if(u < 1e-6) return 0.;"
" float diag = u*u/2.;"
" float x = diag;"
" float y = u;"
" float z = diag+1.;"
" x /= (1.+z);"
" y /= (1.+z);"
" return 0.5 - atan((0.5-x) / y) / 3.1415926535897932384626433832795;"
" }"
"float z_to_iz_s(float z) {"
"return sinh(z) / (1. + cosh(z));"
"}"
"float z_to_iz_ns(float z) {"
"z = sinh(z) / (1. + cosh(z));"
"return (z+1.)/2.;"
"}";
hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
const ld l2 = log(2);
const ld l3 = log(3);
switch(geom()) {
case gcSolN:
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 gcSol:
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 gcNIH:
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 hr_exception("christoffel not in solnihv");
}
}
EX hyperpoint get_inverse_exp_symsol(hyperpoint h, flagtype flags) {
auto& s = get_tabled();
s.load();
ld ix = h[0] >= 0. ? sn::x_to_ix(h[0]) : sn::x_to_ix(-h[0]);
ld iy = h[1] >= 0. ? sn::x_to_ix(h[1]) : sn::x_to_ix(-h[1]);
ld iz = sn::z_to_iz(h[2]);
if(h[2] < 0.) { iz = -iz; swap(ix, iy); }
hyperpoint res = s.get(ix, iy, iz, flags & pfNO_INTERPOLATION);
if(h[2] < 0.) { swap(res[0], res[1]); res[2] = -res[2]; }
if(h[0] < 0.) res[0] = -res[0];
if(h[1] < 0.) res[1] = -res[1];
if(flags & pfNO_DISTANCE) return res;
return table_to_azeq(res);
}
EX hyperpoint get_inverse_exp_nsym(hyperpoint h, flagtype flags) {
auto& s = get_tabled();
s.load();
ld ix = h[0] >= 0. ? sn::x_to_ix(h[0]) : sn::x_to_ix(-h[0]);
ld iy = h[1] >= 0. ? sn::x_to_ix(h[1]) : sn::x_to_ix(-h[1]);
ld iz = sn::z_to_iz(h[2]);
hyperpoint res = s.get(ix, iy, iz, flags & pfNO_INTERPOLATION);
if(h[0] < 0.) res[0] = -res[0];
if(h[1] < 0.) res[1] = -res[1];
if(flags & pfNO_DISTANCE) return res;
return table_to_azeq(res);
}
EX string shader_symsol = sn::common +
"vec4 inverse_exp(vec4 h) {"
"float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);"
"float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);"
"float iz = z_to_iz_s(h[2]);"
"if(h[2] < 1e-6) { iz = -iz; float s = ix; ix = iy; iy = s; }"
"if(iz < 0.) iz = 0.;"
"vec4 res;"
"float cx = ix*(1.-1./PRECX) + .5/PRECX;"
"float cy = iy*(1.-1./PRECY) + .5/PRECY;"
"float cz = iz*(1.-1./PRECZ) + .5/PRECZ;"
// "if(ix > .5 && iy > .6 && ix < iy + .05 && iz < .2 && iz < (iy - 0.5) * 0.6)"
"\n#ifndef SOLV_ALL\n"
"bool ok = true;"
// hard to tell which triangles fall on the other sides
"if(iz < .03 && ix > .65 && iy > .65) ok = false;"
"if(iz < .013 && ix > .55 && iy > .55) ok = false;"
"if(iz < .0075 && ix > .45 && iy > .45) ok = false;"
"if(iz > 0.004 && ix > 0.4 && iy > 0.4 && ix < .6 && iy < .6) ok = true;"
"if(iz > 0.000004 && ix > 0.4 && ix < 0.7 && iy > 0.4 && iy < 0.7) ok = true;"
"if(iz < 0.04 && ix > 0.70 && ix < 0.8 && iy > 0.5 && iy < 0.7) ok = false;"
"if(iz < 0.05 && ix > .45 && iy > .75 && ix < .55 && iy < .95) ok = false;"
"if(iz < 0.05 && ix > .85 && iy > .45 && iy < .75) ok = false;"
"if(iz < 0.025 && ix > .65 && iy > .65 && ix < .8 && iy < .8) ok = false;"
"if(!ok) res = vec4(0./0.,0./0.,0./0.,1);"
"else "
"\n#endif\n"
"res = texture3D(tInvExpTable, vec3(cx, cy, cz));"
"if(h[2] < 1e-6) { res.xy = res.yx; res[2] = -res[2]; }"
"if(h[0] < 0.) res[0] = -res[0];"
"if(h[1] < 0.) res[1] = -res[1];"
"return res;"
"}";
EX string shader_nsymsol = sn::common + R"*(
vec4 inverse_exp(vec4 h) {
float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);
float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);
float iz = z_to_iz_ns(h[2]);
vec4 res;
float cx = ix*(1.-1./PRECX) + .5/PRECX;
float cy = iy*(1.-1./PRECY) + .5/PRECY;
float cz = iz*(1.-1./PRECZ) + .5/PRECZ;
if(ix > .65 && iy > .5 && iz > .45 && iz < .55)
res = vec4(0.,0.,0.,1.);
else if(ix > .55 && iy > .75 && ix < .7 && iz > .45 && iz < .55)
res = vec4(0.,0.,0.,1.);
else if(ix > .45 && iy > .75 && ix < .7 && iz > .4 && iz < .5)
res = vec4(0.,0.,0.,1.);
else if(ix > .85 && iy > .5 && iz > .55 && iz < .75)
res = vec4(0.,0.,0.,1.);
else if(ix > .7 && iy > .55 && iz > .42 && iz < .58)
res = vec4(0.,0.,0.,1.);
else if(iz > 0.45 && ix > 0.8 && iy > 0.3 && iy < 0.6)
res = vec4(0.,0.,0.,1.);
else if(iz > 0.45 && ix > 0.8 && iy > 0.3 && iy < 0.6)
res = vec4(0.,0.,0.,1.);
else if(iz > .4 && iz < .55 && ix > .7 && iy > .36 && iy < .5 && ix < .8 && ix+iy > 1.2)
res = vec4(0.,0.,0.,1.);
else res = texture3D(tInvExpTable, vec3(cx, cy, cz));
if(h[0] < 0.) res[0] = -res[0];
if(h[1] < 0.) res[1] = -res[1];
return res;
})*";
EX string shader_nsym = sn::common +
"vec4 inverse_exp(vec4 h) {"
"float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);"
"float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);"
"float iz = z_to_iz_ns(h[2]);"
"vec4 res;"
"float cx = ix*(1.-1./PRECX) + .5/PRECX;"
"float cy = iy*(1.-1./PRECY) + .5/PRECY;"
"float cz = iz*(1.-1./PRECZ) + .5/PRECZ;"
"res = texture3D(tInvExpTable, vec3(cx, cy, cz));"
"if(h[0] < 0.) res[0] = -res[0];"
"if(h[1] < 0.) res[1] = -res[1];"
"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 = sn::tabled_inverses("solv-geodesics.dat");
EX tabled_inverses niht = sn::tabled_inverses("shyp-geodesics.dat");
EX tabled_inverses sont = sn::tabled_inverses("ssol-geodesics.dat");
EX tabled_inverses& get_tabled() {
switch(geom()) {
case gcSol: return solt;
case gcNIH: return niht;
case gcSolN: return sont;
default: throw hr_exception("not solnih");
}
}
EX int approx_distance(heptagon *h1, heptagon *h2) {
auto m = (sn::hrmap_solnih*) currentmap;
dynamicval<eGeometry> g(geometry, gBinary4);
dynamicval<hrmap*> cm(currentmap, m->binary_map);
int d1 = bt::celldistance3_approx(m->coords[h1].first, m->coords[h2].first);
int d2 = bt::celldistance3_approx(m->coords[h1].second, m->coords[h2].second);
return d1 + d2 - abs(h1->distance - h2->distance);
}
EX void create_faces() {
if(geometry == gSol) {
ld zstep = -log(2) / 2;
ld bwh = vid.binary_width * zstep;
auto pt = [&] (int x, int y, int z) { return xpush(bwh*x) * ypush(bwh*y) * zpush(zstep*z) * C0; };
add_wall(0, {pt(-1,-1,-1), pt(-1,-1,+1), pt(-1,00,+1), pt(-1,+1,+1), pt(-1,+1,-1)});
add_wall(1, {pt(-1,-1,-1), pt(00,-1,-1), pt(+1,-1,-1), pt(+1,-1,+1), pt(-1,-1,+1)});
add_wall(2, {pt(+1,+1,-1), pt(+1,-1,-1), pt(00,-1,-1), pt(00,+1,-1)});
add_wall(3, {pt(00,+1,-1), pt(00,-1,-1), pt(-1,-1,-1), pt(-1,+1,-1)});
add_wall(4, {pt(+1,-1,-1), pt(+1,-1,+1), pt(+1,00,+1), pt(+1,+1,+1), pt(+1,+1,-1)});
add_wall(5, {pt(-1,+1,-1), pt(00,+1,-1), pt(+1,+1,-1), pt(+1,+1,+1), pt(-1,+1,+1)});
add_wall(6, {pt(-1,+1,+1), pt(+1,+1,+1), pt(+1,00,+1), pt(-1,00,+1)});
add_wall(7, {pt(-1,00,+1), pt(+1,00,+1), pt(+1,-1,+1), pt(-1,-1,+1)});
}
if(geometry == gNIH) {
ld zstep = .5;
ld bwh = vid.binary_width / 6;
auto pt = [&] (int x, int y, int z) { return xpush(bwh*x) * ypush(bwh*y) * zpush(zstep*z) * C0; };
add_wall(0, {pt(+3,-3,-1), pt(+3,-3,+1), pt(+3,+3,+1), pt(+3,+3,-1), pt(+3,+1,-1), pt(+3,-1,-1) });
add_wall(1, {pt(-3,+3,-1), pt(-3,+3,+1), pt(+3,+3,+1), pt(+3,+3,-1), pt(+0,+3,-1) });
add_wall(2, {pt(-3,-3,-1), pt(-3,-3,+1), pt(-3,+3,+1), pt(-3,+3,-1), pt(-3,+1,-1), pt(-3,-1,-1) });
add_wall(3, {pt(-3,-3,-1), pt(-3,-3,+1), pt(+3,-3,+1), pt(+3,-3,-1), pt(+0,-3,-1)});
add_wall(4, {pt(-3,-3,+1), pt(-3,+3,+1), pt(+3,+3,+1), pt(+3,-3,+1)});
for(int i=0; i<6; i++) {
int x = -3 + (i%2) * 3;
int y = -3 + (i/2) * 2;
add_wall(5+i, {pt(x,y,-1), pt(x+3,y,-1), pt(x+3,y+2,-1), pt(x,y+2,-1)});
}
}
if(geometry == gSolN) {
ld zstep = -.5;
ld bwh = vid.binary_width / 6;
auto pt = [&] (int x, int y, int z) { return xpush(bwh*x) * ypush(bwh*y) * zpush(zstep*z) * C0; };
add_wall(0, {pt(+3,-3,-1), pt(+3,-3,+1), pt(+3,-1,+1), pt(+3,+1,+1), pt(+3,+3,+1), pt(+3,+3,-1)});
add_wall(1, {pt(-3,+3,-1), pt(00,+3,-1), pt(+3,+3,-1), pt(+3,+3,+1), pt(-3,+3,+1)});
add_wall(2, {pt(-3,-3,-1), pt(-3,-3,+1), pt(-3,-1,+1), pt(-3,+1,+1), pt(-3,+3,+1), pt(-3,+3,-1)});
add_wall(3, {pt(-3,-3,-1), pt(00,-3,-1), pt(+3,-3,-1), pt(+3,-3,+1), pt(-3,-3,+1)});
add_wall(4, {pt(-3,+3,-1), pt(-3,-3,-1), pt(00,-3,-1), pt(00,+3,-1)});
add_wall(5, {pt(00,+3,-1), pt(00,-3,-1), pt(+3,-3,-1), pt(+3,+3,-1)});
add_wall(6, {pt(-3,-3,+1), pt(+3,-3,+1), pt(+3,-1,+1), pt(-3,-1,+1)});
add_wall(7, {pt(-3,-1,+1), pt(+3,-1,+1), pt(+3,+1,+1), pt(-3,+1,+1)});
add_wall(8, {pt(-3,+1,+1), pt(+3,+1,+1), pt(+3,+3,+1), pt(-3,+3,+1)});
}
get_hsh().compute_hept();
}
EX }
#endif
EX namespace nilv {
#if HDR
/** nmSym is the rotationally symmetric model of Nil, while nmHeis is the Heisenberg model. */
constexpr ld nmSym = 0, nmHeis = 1;
#endif
/** HyperRogue currently uses nmSym by default, but some parts are still written in nmHeis */
EX ld model_used = nmSym;
/** a helper function for model conversions */
EX ld sym_to_heis_bonus(const hyperpoint& H) {
return H[0] * H[1] / 2;
}
EX hyperpoint convert(hyperpoint H, ld from, ld to) {
H[2] += sym_to_heis_bonus(H) * (to - from);
return H;
}
EX void convert_ref(hyperpoint& H, ld from, ld to) {
H[2] += sym_to_heis_bonus(H) * (to - from);
}
EX void convert_tangent_ref(hyperpoint at, hyperpoint& v, ld from, ld to) {
v[2] += (at[0] * v[1] + at[1] * v[0]) * (to - from) / 2;
}
EX void convert_ref(transmatrix& T, ld from, ld to) {
auto T1 = transpose(T);
convert_ref(T1[3], from, to);
for(int i: {0, 1, 2})
convert_tangent_ref(T1[3], T1[i], from, to);
T = transpose(T1);
}
EX hyperpoint checked_convert(hyperpoint H, ld from, ld to) {
if(nil) return convert(H, from, to);
return H;
}
hyperpoint christoffel(const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported, ld model = model_used) {
hyperpoint c; c[3] = 0;
ld x = Position[0]; ld y = Position[1];
auto mu = model;
c[ 0 ] = 0
+ Velocity[ 0 ] * Transported[ 1 ] * ( y*(mu - 1)/4 )
+ Velocity[ 1 ] * Transported[ 0 ] * ( y*(mu - 1)/4 )
+ Velocity[ 1 ] * Transported[ 1 ] * ( x*(mu + 1)/2 )
+ Velocity[ 1 ] * Transported[ 2 ] * ( -1/2. )
+ Velocity[ 2 ] * Transported[ 1 ] * ( -1/2. );
c[ 1 ] = 0
+ Velocity[ 0 ] * Transported[ 0 ] * ( y*(1 - mu)/2 )
+ Velocity[ 0 ] * Transported[ 1 ] * ( -x*(mu + 1)/4 )
+ Velocity[ 0 ] * Transported[ 2 ] * ( 1/2. )
+ Velocity[ 1 ] * Transported[ 0 ] * ( -x*(mu + 1)/4 )
+ Velocity[ 2 ] * Transported[ 0 ] * ( 1/2. );
c[ 2 ] = 0
+ Velocity[ 0 ] * Transported[ 0 ] * ( x*y*(1 - mu*mu)/4 )
+ Velocity[ 0 ] * Transported[ 1 ] * ( -mu*mu*x*x/8 + mu*mu*y*y/8 - mu*x*x/4 - mu*y*y/4 + mu/2 - x*x/8 + y*y/8 )
+ Velocity[ 0 ] * Transported[ 2 ] * ( x*(mu + 1)/4 )
+ Velocity[ 1 ] * Transported[ 0 ] * ( -mu*mu*x*x/8 + mu*mu*y*y/8 - mu*x*x/4 - mu*y*y/4 + mu/2 - x*x/8 + y*y/8 )
+ Velocity[ 1 ] * Transported[ 1 ] * ( x*y*(mu*mu - 1)/4 )
+ Velocity[ 1 ] * Transported[ 2 ] * ( y*(1 - mu)/4 )
+ Velocity[ 2 ] * Transported[ 0 ] * ( x*(mu + 1)/4 )
+ Velocity[ 2 ] * Transported[ 1 ] * ( y*(1 - mu)/4 );
return c;
}
EX hyperpoint formula_exp(hyperpoint v) {
// copying Modelling Nil-geometry in Euclidean Space with Software Presentation
// v[0] = c cos alpha
// v[1] = c sin alpha
// v[2] = w
if(v[0] == 0 && v[1] == 0) return point31(v[0], v[1], v[2]);
if(v[2] == 0) return convert(point31(v[0], v[1], 0), nmSym, model_used);
ld alpha = atan2(v[1], v[0]);
ld w = v[2];
ld c = hypot(v[0], v[1]) / v[2];
return convert(point31(
2 * c * sin(w/2) * cos(w/2 + alpha),
2 * c * sin(w/2) * sin(w/2 + alpha),
w * (1 + (c*c/2) * ((1 - sin(w)/w) + (1-cos(w))/w * sin(w + 2 * alpha)))
), nmHeis, model_used);
}
EX hyperpoint get_inverse_exp(hyperpoint h, flagtype prec IS(pNORMAL)) {
ld wmin, wmax;
ld side = convert(h, model_used, nmSym)[2];
convert_ref(h, model_used, nmHeis);
if(hypot_d(2, h) < 1e-6) return point3(h[0], h[1], h[2]);
else if(side > 1e-6) {
wmin = 0, wmax = TAU;
}
else if(side < -1e-6) {
wmin = - TAU, wmax = 0;
}
else return point3(h[0], h[1], 0);
ld alpha_total = h[0] ? atan(h[1] / h[0]) : 90._deg;
ld b;
if(abs(h[0]) > abs(h[1]))
b = h[0] / 2 / cos(alpha_total);
else
b = h[1] / 2 / sin(alpha_total);
ld s = sin(2 * alpha_total);
int max_iter = (prec & pfLOW_BS_ITER) ? 5 : 20;
for(int it=0;; it++) {
ld w = (wmin + wmax) / 2;
ld z = b * b * (s + (sin(w) - w)/(cos(w) - 1)) + w;
if(it == max_iter) {
ld alpha = alpha_total - w/2;
ld c = b / sin(w/2);
return point3(c * w * cos(alpha), c * w * sin(alpha), w);
}
if(h[2] > z) wmin = w;
else wmax = w;
}
}
EX string nilshader() {
return "vec4 inverse_exp(vec4 h) {"
"float wmin, wmax;"
"h[2] += h[0] * h[1] / 2. * " + glhr::to_glsl(1-model_used) + ";"
"float side = h[2] - h[0] * h[1] / 2.;"
"if(h[0]*h[0] + h[1]*h[1] < 1e-12) return vec4(h[0], h[1], h[2], 1);"
"if(side > 1e-6) { wmin = 0.; wmax = 2.*PI; }"
"else if(side < -1e-6) { wmin = -2.*PI; wmax = 0.; }"
"else return vec4(h[0], h[1], 0., 1.);"
"float at = h[0] != 0. ? atan(h[1] / h[0]) : PI/2.;"
"float b = abs(h[0]) > abs(h[1]) ? h[0] / 2. / cos(at) : h[1] / 2. / sin(at);"
"float s = sin(2. * at);"
"for(int it=0; it<50; it++) {"
"float w = (wmin + wmax) / 2.;"
// the formula after ':' produces visible numerical artifacts for w~0
"float z = b * b * (s + (abs(w) < .1 ? w/3. + w*w*w/90. + w*w*w*w*w/2520.: (sin(w) - w)/(cos(w) - 1.))) + w;"
"if(h[2] > z) wmin = w;"
"else wmax = w;"
"}"
"float w = (wmin + wmax) / 2.;"
"float alpha = at - w/2.;"
"float c = b / sin(w/2.);"
"return vec4(c*w*cos(alpha), c*w*sin(alpha), w, 1.);"
"}";
}
#if HDR
struct mvec : array<int, 3> {
/** these are in nmHeis */
explicit mvec() = default;
constexpr explicit mvec(int x, int y, int z) : array<int, 3>{{x, y, z}} {}
mvec inverse() {
auto& a = *this;
return mvec(-a[0], -a[1], -a[2]+a[1] * a[0]);
}
mvec operator * (const mvec b) {
auto& a = *this;
return mvec(a[0] + b[0], a[1] + b[1], a[2] + b[2] + a[0] * b[1]);
}
};
#endif
static constexpr mvec mvec_zero = mvec(0, 0, 0);
EX ld nilwidth = 1;
hyperpoint mvec_to_point(mvec m) { return convert(hpxy3(m[0] * nilwidth, m[1] * nilwidth, m[2] * nilwidth * nilwidth), nmHeis, model_used); }
#if HDR
struct nilstructure {
vector<mvec> movevectors;
vector<vector<hyperpoint>> facevertices;
};
#endif
EX hyperpoint heis(ld x, ld y, ld z) { return convert(point31(x, y, z), nmHeis, model_used); }
nilstructure ns6 = {
{{ mvec(-1,0,0), mvec(0,-1,0), mvec(0,0,-1), mvec(1,0,0), mvec(0,1,0), mvec(0,0,1) }},
{{
{ heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,0.75), heis(-0.5,0.5,0.25), heis(-0.5,0.5,-0.75), },
{ heis(0.5,-0.5,-0.5), heis(0.5,-0.5,0.5), heis(-0.5,-0.5,0.5), heis(-0.5,-0.5,-0.5), },
{ heis(0,0,-0.5), heis(-0.5,0.5,-0.75), heis(-0.5,-0.5,-0.25), heis(0,0,-0.5), heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,-0.5), heis(0,0,-0.5), heis(-0.5,-0.5,-0.5), heis(0.5,-0.5,-0.5), heis(0,0,-0.5), heis(0.5,-0.5,-0.5), heis(0.5,-0.5,-0.75), heis(0,0,-0.5), heis(0.5,-0.5,-0.75), heis(0.5,0.5,-0.25), heis(0,0,-0.5), heis(0.5,0.5,-0.25), heis(0.5,0.5,-0.5), heis(0,0,-0.5), heis(0.5,0.5,-0.5), heis(-0.5,0.5,-0.5), heis(0,0,-0.5), heis(-0.5,0.5,-0.5), heis(-0.5,0.5,-0.75), },
{ heis(0.5,0.5,-0.25), heis(0.5,0.5,0.75), heis(0.5,-0.5,0.25), heis(0.5,-0.5,-0.75), },
{ heis(-0.5,0.5,-0.5), heis(-0.5,0.5,0.5), heis(0.5,0.5,0.5), heis(0.5,0.5,-0.5), },
{ heis(0,0,0.5), heis(-0.5,0.5,0.25), heis(-0.5,-0.5,0.75), heis(0,0,0.5), heis(-0.5,-0.5,0.75), heis(-0.5,-0.5,0.5), heis(0,0,0.5), heis(-0.5,-0.5,0.5), heis(0.5,-0.5,0.5), heis(0,0,0.5), heis(0.5,-0.5,0.5), heis(0.5,-0.5,0.25), heis(0,0,0.5), heis(0.5,-0.5,0.25), heis(0.5,0.5,0.75), heis(0,0,0.5), heis(0.5,0.5,0.75), heis(0.5,0.5,0.5), heis(0,0,0.5), heis(0.5,0.5,0.5), heis(-0.5,0.5,0.5), heis(0,0,0.5), heis(-0.5,0.5,0.5), heis(-0.5,0.5,0.25), },
}}
};
nilstructure ns8 = {
{{ mvec(-1,0,0), mvec(-1,0,1), mvec(0,-1,0), mvec(0,0,-1), mvec(1,0,0), mvec(1,0,-1), mvec(0,1,0), mvec(0,0,1) }},
{{
{ heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,0.75), heis(-0.5,0.5,-0.25), },
{ heis(-0.5,-0.5,0.75), heis(-0.5,0.5,0.75), heis(-0.5,0.5,-0.25), },
{ heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,0.75), heis(0.5,-0.5,0.25), heis(0.5,-0.5,-0.75), },
{ heis(-0.5,-0.5,-0.25), heis(-0.5,0.5,-0.25), heis(0.5,0.5,-0.75), heis(0.5,-0.5,-0.75), },
{ heis(0.5,0.5,0.25), heis(0.5,-0.5,0.25), heis(0.5,-0.5,-0.75), },
{ heis(0.5,0.5,-0.75), heis(0.5,0.5,0.25), heis(0.5,-0.5,-0.75), },
{ heis(-0.5,0.5,0.75), heis(-0.5,0.5,-0.25), heis(0.5,0.5,-0.75), heis(0.5,0.5,0.25), },
{ heis(-0.5,-0.5,0.75), heis(-0.5,0.5,0.75), heis(0.5,0.5,0.25), heis(0.5,-0.5,0.25), },
}}
};
EX nilstructure& current_ns() { return S7 == 6 ? ns6 : ns8; }
EX array<int,3> nilperiod, nilperiod_edit;
int S7_edit;
EX transmatrix adjmatrix(int i) {
return nisot::translate(mvec_to_point(current_ns().movevectors[i]));
}
struct hrmap_nil : hrmap {
map<mvec, heptagon*> at;
map<heptagon*, mvec> coords;
heptagon *getOrigin() override { return get_at(mvec_zero); }
~hrmap_nil() {
for(auto& p: at) clear_heptagon(p.second);
}
heptagon *get_at(mvec c) {
auto& h = at[c];
if(h) return h;
h = init_heptagon(S7);
h->c7 = newCell(S7, h);
coords[h] = c;
h->zebraval = c[0];
h->emeraldval = c[1];
h->fieldval = c[2];
return h;
}
heptagon *create_step(heptagon *parent, int d) override {
auto p = coords[parent];
auto q = p * current_ns().movevectors[d];
for(int a=0; a<3; a++) q[a] = zgmod(q[a], nilperiod[a]);
auto child = get_at(q);
parent->c.connect(d, child, (d + S7/2) % S7, false);
return child;
}
transmatrix adj(heptagon *h, int i) override { return adjmatrix(i); }
transmatrix relative_matrixh(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
for(int a=0; a<S7; a++) if(h2 == h1->move(a)) return adjmatrix(a);
auto p = coords[h1].inverse() * coords[h2];
for(int a=0; a<3; a++) p[a] = szgmod(p[a], nilperiod[a]);
return nisot::translate(mvec_to_point(p));
}
};
EX mvec get_coord(heptagon *h) { return ((hrmap_nil*)currentmap)->coords[h]; }
EX heptagon *get_heptagon_at(mvec m) { return ((hrmap_nil*)currentmap)->get_at(m); }
EX void set_flags() {
int coords = 0;
for(int a=0; a<3; a++) if(nilperiod[a]) coords++;
set_flag(ginf[gNil].flags, qANYQ, coords);
set_flag(ginf[gNil].flags, qCLOSED, coords == 3);
set_flag(ginf[gNil].flags, qSMALL, coords == 3 && nilperiod[0] * nilperiod[1] * nilperiod[2] <= 4096);
}
EX hyperpoint on_geodesic(hyperpoint s0, hyperpoint s1, ld x) {
hyperpoint local = nisot::translate(s0, -1) * s1;
hyperpoint h = get_inverse_exp(local);
return nisot::translate(s0) * formula_exp(h * x);
}
EX color_t colorize(cell *c, char whichCanvas) {
mvec at = ((hrmap_nil*)currentmap)->coords[c->master];
color_t res = 0;
auto setres = [&] (int z, color_t which) {
if(zgmod(at[2] - z, nilperiod[2]) == 0) res = which;
if(zgmod(at[2] - z-1, nilperiod[2]) == 0) res = which;
};
if(at[1] == 0 && at[0] >=0 && at[0] < 4)
setres(-at[0], gradient(0x1FF0000, 0x10000FF, 0, at[0], 4));
else if(at[0] == 4 && at[1] >= 0 && at[1] < 4)
setres(at[1]*3-4, gradient(0x10000FF, 0x100FF00, 0, at[1], 4));
else if(at[1] == 4 && at[0] >= 0 && at[0] <= 4)
setres(4+at[0], gradient(0x100FF00, 0x1FFFF00, 4, at[0], 0));
else if(at[0] == 0 && at[1] >= 0 && at[1] <= 4)
setres(at[1], gradient(0x1FFFF00, 0x1FF0000, 4, at[1], 0));
return res;
}
EX void prepare_niltorus3() {
nilperiod_edit = nilperiod;
S7_edit = ginf[gNil].sides;
}
EX void show_niltorus3() {
cmode = sm::SIDE | sm::MAYDARK;
gamescreen();
dialog::init(XLAT("Nil quotient spaces"));
for(int a=0; a<3; a++) {
string title = XLAT("%1 period", s0+char('X'+a));
dialog::addSelItem(title, its(nilperiod_edit[a]), 'x');
dialog::add_action([=] {
dialog::editNumber(nilperiod_edit[a], 0, 60, 1, 0, title,
XLAT("Set to 0 to make it non-periodic.")
);
dialog::bound_low(0);
});
}
dialog::addSelItem(XLAT("honeycomb"), its(S7_edit), 'h');
dialog::add_action([] { S7_edit = S7_edit ^ 6 ^ 8; });
bool ok = (!nilperiod_edit[1]) || (nilperiod_edit[2] && nilperiod_edit[1] % nilperiod_edit[2] == 0);
dialog::addBreak(50);
if(ok) {
dialog::addItem(XLAT("activate"), 'a');
dialog::add_action([] {
stop_game();
nilperiod = nilperiod_edit;
ginf[gNil].sides = S7_edit;
set_flags();
geometry = gNil;
start_game();
});
}
else dialog::addInfo(XLAT("Y period must be divisible by Z period"));
dialog::addBreak(50);
dialog::addBack();
dialog::display();
}
EX void create_faces() {
for(int i=0; i<S7; i++) {
vector<hyperpoint> fvs = nilv::current_ns().facevertices[i];
using nilv::nilwidth;
for(auto& h: fvs) h[0] *= nilwidth, h[1] *= nilwidth, h[2] *= nilwidth * nilwidth;
add_wall(i, fvs);
}
get_hsh().compute_hept();
}
EX }
EX bool in_s2xe() { return gproduct && hybrid::under_class() == gcSphere; }
EX bool in_h2xe() { return gproduct && hybrid::under_class() == gcHyperbolic; }
EX bool in_e2xe() { return gproduct && hybrid::under_class() == gcEuclid; }
EX namespace hybrid {
EX eGeometry underlying;
EX geometry_information *underlying_cgip;
EX eGeometryClass under_class() {
if(embedded_plane) {
auto c = geom3::ginf_backup[geometry].cclass;
if(c == gcEuclid) c = cginf.g.sig[2] > 0 ? gcSphere : gcHyperbolic;
return c;
}
return ginf[hybrid::underlying].cclass;
}
EX int csteps;
EX int disc_quotient = 0;
EX map<heptagon*, short> altmap_heights;
EX void configure(eGeometry g) {
if(WDIM == 3) return;
ray::reset_raycaster();
check_cgi();
cgi.require_basics();
underlying = geometry;
underlying_cgip = cgip;
bool sph = sphere;
auto keep = ginf[g].menu_displayed_name;
ginf[g] = ginf[underlying];
ginf[g].menu_displayed_name = keep;
if(g == gRotSpace) {
ginf[g].g = sph ? giSphere3 : giSL2;
ginf[g].tiling_name = "Iso(" + ginf[g].tiling_name + ")";
string& qn = ginf[g].quotient_name;
if(csteps && csteps != (sph ? cgi.psl_steps*2 : 0)) {
string qplus;
if(csteps == cgi.psl_steps)
qplus = sph ? "elliptic" : "PSL";
else if(csteps == 2 * cgi.psl_steps && !sph)
qplus = "SL";
else qplus = its(csteps);
if(qn == "none") qn = qplus;
else qn = qn + "/" + qplus;
}
if(sph) ginf[g].flags |= qELLIPTIC;
if(csteps && csteps != cgi.psl_steps && csteps != 2*cgi.psl_steps)
ginf[g].flags |= qANYQ;
}
else {
ginf[g].cclass = g == gRotSpace ? gcSL2 : gcProduct;
ginf[g].g.gameplay_dimension++;
ginf[g].g.graphical_dimension++;
ginf[g].tiling_name += "xZ";
if(csteps) ginf[g].flags |= qANYQ, ginf[g].tiling_name += its(csteps);
}
ginf[g].flags |= qHYBRID;
}
EX void reconfigure() {
if(!mhybrid) return;
stop_game();
auto g = geometry;
geometry = underlying;
configure(g);
geometry = g;
}
EX hrmap *pmap;
EX geometry_information *pcgip;
EX eGeometry actual_geometry;
#if HDR
template<class T> auto in_actual(const T& t) -> decltype(t()) {
if(pmap == nullptr) return t();
dynamicval<eGeometry> g(geometry, actual_geometry);
dynamicval<geometry_information*> gc(cgip, pcgip);
dynamicval<hrmap*> gu(currentmap, pmap);
dynamicval<hrmap*> gup(pmap, NULL);
return t();
}
#define PIA(x) hr::hybrid::in_actual([&] { return (x); })
#endif
struct hrmap_hybrid : hrmap {
hrmap *underlying_map;
bool twisted;
map<cell*, pair<cellwalker, cellwalker>> spins;
map<pair<cell*, int>, cell*> at;
map<cell*, pair<cell*, int>> where;
heptagon *getOrigin() override { return underlying_map->getOrigin(); }
const int SHIFT_UNKNOWN = 30000;
map<cell*, vector<int>> shifts;
EX vector<int>& make_shift(cell *c) {
auto& res = shifts[c];
if(res.empty()) res = vector<int> (c->type+1, SHIFT_UNKNOWN);
return res;
}
EX int& get_shift_current(cellwalker cw) {
return make_shift(cw.at)[cw.spin];
}
EX bool have_shift(cellwalker cw) {
return shifts.count(cw.at) && get_shift_current(cw) != SHIFT_UNKNOWN;
}
EX int get_shift(cellwalker cw0) {
if(S3 >= OINF) return 0;
auto& v = get_shift_current(cw0);
if(v != SHIFT_UNKNOWN) return v;
vector<int> candidates;
for(int a: {1, -1}) {
cellwalker cw = cw0;
cw += wstep; cw += a;
int s = 0;
while(cw != cw0) {
if(!have_shift(cw)) goto next;
s += shifts[cw.at][cw.spin];
cw += wstep;
cw += a;
}
candidates.push_back(-a * cgi.single_step * (sphere ? -1 : 1) - s);
next: ;
}
if(candidates.size() == 2 && candidates[0] != candidates[1]) {
int val = candidates[0] - candidates[1];
if(disc_quotient == 0) disc_quotient = val;
disc_quotient = gcd(val, disc_quotient);
if(disc_quotient < 0) disc_quotient = -disc_quotient;
}
int val = 0;
auto cw1 = cw0+wstep;
if(1) {
/* the value from PSL, helps to draw the underlying space correctly */
auto ps = cgi.psl_steps;
val = cw0.spin*ps / cw0.at->type - cw1.spin*ps / cw1.at->type + ps/2;
}
if(!candidates.empty()) val = candidates[0];
v = val;
get_shift_current(cw1) = -val;
return val;
}
EX void ensure_shifts(cell *c) {
if(S3 >= OINF) return;
if(!make_shift(c)[c->type]) return;
forCellEx(c1, c)
for(int a=0; a<c->type; a++) {
cellwalker cw0(c, a);
cellwalker cw = cw0;
while(cw != cw0) {
get_shift(cw);
cw += wstep;
cw += a;
}
}
make_shift(c)[c->type] = 0;
}
EX int cycle_discrepancy(cellwalker cw0) {
int total = 0;
auto cw = cw0;
do {
total += get_shift(cw);
cw += wstep;
cw++;
}
while(cw != cw0);
return total + cgi.single_step * (sphere ? -1 : 1);
}
EX void fix_bounded_cycles() {
if(!rotspace) return;
if(!closed_manifold) return;
in_underlying([&] {
cellwalker final(currentmap->gamestart(), 0);
auto& ac = currentmap->allcells();
for(cell *c: ac) for(int i=0; i<c->type; i++) {
cellwalker cw(c, i);
int cd = cycle_discrepancy(cw);
if(!cd) continue;
while(cw != final) {
if(celldist(cw.peek()) < celldist(cw.at)) {
cw += wstep;
cw++;
}
else {
get_shift_current(cw) -= cd;
get_shift_current(cw+wstep) += cd;
cw++;
}
}
}
disc_quotient = abs(cycle_discrepancy(final));
if(debugflags & DF_GEOM) for(cell *c: ac) for(int i=0; i<c->type; i++) {
cellwalker cw(c, i);
if(cycle_discrepancy(cw)) println(hlog, cw, cycle_discrepancy(cw));
}
});
}
template<class T> auto in_underlying(const T& t) -> decltype(t()) {
pcgip = cgip;
dynamicval<hrmap*> gpm(pmap, this);
dynamicval<eGeometry> gag(actual_geometry, geometry);
dynamicval<eGeometry> g(geometry, underlying);
dynamicval<int> gss(underlying_cgip->single_step, cgi.single_step);
dynamicval<int> gsp(underlying_cgip->psl_steps, cgi.psl_steps);
dynamicval<geometry_information*> gc(cgip, underlying_cgip);
dynamicval<hrmap*> gu(currentmap, underlying_map);
return t();
}
cell *getCell(cell *u, int h) {
if(twisted) {
if(!spins.count(u))
println(hlog, "link missing: ", u);
else {
while(h >= csteps) h -= csteps, u = spins[u].first.at;
while(h < 0) h += csteps, u = spins[u].second.at;
}
}
h = zgmod(h, csteps);
cell*& c = at[make_pair(u, h)];
if(!c) { c = newCell(u->type+2, u->master); where[c] = {u, h}; }
return c;
}
cell* gamestart() override { return getCell(underlying_map->gamestart(), 0); }
hrmap_hybrid() {
underlying_map = nullptr;
twisted = false;
disc_quotient = 0;
in_underlying([this] { initcells(); underlying_map = currentmap; });
for(hrmap*& m: allmaps) if(m == underlying_map) m = NULL;
fix_bounded_cycles();
}
~hrmap_hybrid() {
in_underlying([] { delete currentmap; });
for(auto& p: at) destroy_cell(p.second);
}
void find_cell_connection(cell *c, int d) override {
hybrid::find_cell_connection(c, d);
}
int shvid(cell *c) override {
cell *c1 = hybrid::get_where(c).first;
return PIU( hr::shvid(c1) );
}
int full_shvid(cell *c) override {
cell *c1 = hybrid::get_where(c).first;
return PIU( currentmap->full_shvid(c1) );
}
transmatrix spin_to(cell *c, int d, ld bonus) override { if(d >= c->type-2) return Id; c = get_where(c).first; return fix4_f( in_underlying([&] { return currentmap->spin_to(c, d, bonus); }) ); }
transmatrix spin_from(cell *c, int d, ld bonus) override { if(d >= c->type-2) return Id; c = get_where(c).first; return fix4_f( in_underlying([&] { return currentmap->spin_from(c, d, bonus); }) ); }
subcellshape& get_cellshape(cell *c) override {
int id = full_shvid(c);
return generate_subcellshape_if_needed(c, id);
}
};
hrmap_hybrid* hmap() { return (hrmap_hybrid*) currentmap; }
EX cell *get_at(cell *base, int level) {
return hmap()->getCell(base, level);
}
EX pair<cell*, int> get_where(cell *c) { return hmap()->where[c]; }
EX void find_cell_connection(cell *c, int d) {
auto m = hmap();
if(d >= c->type - 2) {
int s = cgi.single_step;
int lev = m->where[c].second + (d == c->type-1 ? s : -s);
cell *c1 = get_at(m->where[c].first, lev);
c->c.connect(d, c1, c1->type - 3 + c->type - d, false);
}
else {
auto cu = m->where[c].first;
auto cu1 = m->in_underlying([&] { return cu->cmove(d); });
int d1 = cu->c.spin(d);
int s = 0;
if(geometry == gRotSpace) {
auto cm = (hrmap_hybrid*)currentmap;
m->in_underlying([&] { cm->ensure_shifts(cu); });
s = ((hrmap_hybrid*)currentmap)->get_shift(cellwalker(cu, d));
}
cell *c1 = get_at(cu1, m->where[c].second + s);
c->c.connect(d, c1, d1, cu->c.mirror(d));
}
}
EX hrmap* get_umap() { if(!dynamic_cast<hrmap_hybrid*>(currentmap)) return nullptr; else return ((hrmap_hybrid*)currentmap)->underlying_map; }
#if HDR
template<class T> auto in_underlying_geometry(const T& f) -> decltype(f()) {
if(!mhybrid && !gproduct) return f();
if(embedded_plane) {
if(cgi.emb->is_euc_in_product()) {
dynamicval<eGeometryClass> dgc(cginf.g.kind, cginf.g.sig[2] < 0 ? gcHyperbolic : gcSphere);
return f();
}
if(cgi.emb->is_cylinder()) {
dynamicval<eGeometryClass> dgc(cginf.g.kind, cginf.g.sig[2] < 0 ? gcHyperbolic : gcSphere);
return f();
}
geom3::light_flip(true);
finalizer ff([] { geom3::light_flip(false); });
return f();
}
if(geom3::flipped) throw hr_exception("called in_underlying_geometry in flipped");
pcgip = cgip;
dynamicval<eGeometry> gag(actual_geometry, geometry);
dynamicval<eGeometry> g(geometry, underlying);
dynamicval<int> gss(underlying_cgip->single_step, cgi.single_step);
dynamicval<int> gsp(underlying_cgip->psl_steps, cgi.psl_steps);
dynamicval<geometry_information*> gc(cgip, underlying_cgip);
dynamicval<hrmap*> gpm(pmap, currentmap);
dynamicval<hrmap*> gm(currentmap, get_umap());
return f();
}
#define PIU(x) hr::hybrid::in_underlying_geometry([&] { return (x); })
#endif
/** like in_underlying_geometry but does not return */
EX void switch_to_underlying() {
if(!mhybrid && !gproduct) return;
if(embedded_plane) throw hr_exception("switch_to_underlying in embedded_plane");
auto m = hmap();
pmap = m;
actual_geometry = geometry;
geometry = underlying;
underlying_cgip->single_step = cgi.single_step;
underlying_cgip->psl_steps = cgi.psl_steps;
pcgip = cgip;
cgip = underlying_cgip;
currentmap = m->underlying_map;
}
/** like in_actual but does not return */
EX void switch_to_actual() {
if(!pmap) return;
geometry = actual_geometry;
cgip = pcgip;
currentmap = pmap;
pmap = nullptr;
}
// next: 0 = i-th corner, 1 = next corner, 2 = center of the wall
EX hyperpoint get_corner(cell *c, int i, int next, ld z) {
ld lev = cgi.plevel * z / 2;
if(WDIM == 2) {
ld zz = lerp(cgi.FLOOR, cgi.WALL, (1+z) / 2);
hyperpoint h = orthogonal_move(get_corner_position(c, i+next), zz);
return h;
}
if(gproduct) {
dynamicval<eGeometry> g(geometry, hybrid::underlying);
dynamicval<geometry_information*> gc(cgip, hybrid::underlying_cgip);
dynamicval<hrmap*> gm(currentmap, ((hrmap_hybrid*)currentmap)->underlying_map);
return scale_point(get_corner_position(c, i+next), exp(lev));
}
else {
#if MAXMDIM >= 4
ld tf, he, alpha;
in_underlying_geometry([&] {
hyperpoint h1 = get_corner_position(c, i);
hyperpoint h2 = get_corner_position(c, i+1);
hyperpoint hm;
if(next == 2) {
hm = h1;
he = 0;
}
else {
hyperpoint hm = mid(h1, h2);
he = hdist(hm, h2)/2;
if(next) he = -he;
}
tf = hdist0(hm)/2;
alpha = atan2(hm[1], hm[0]);
});
return spin(alpha) * rots::uxpush(tf) * rots::uypush(he) * rots::uzpush(lev) * C0;
#else
throw hr_exception();
#endif
}
}
auto clear_samples = addHook(hooks_clearmemory, 40, [] () {
for(auto& c: cgis) for(auto& v: c.second.walloffsets)
v.second = nullptr;
altmap_heights.clear();
});
EX vector<pair<int, cell*>> gen_sample_list() {
if(!mhybrid && WDIM != 2 && PURE)
return {make_pair(0, centerover), make_pair(centerover->type, nullptr)};
vector<pair<int, cell*>> result;
for(auto& v: cgi.walloffsets) if(v.first >= 0) result.push_back(v);
sort(result.begin(), result.end());
int last = 0;
for(auto& r: result) if(r.second) last = r.first + r.second->type + (WDIM == 2 ? 2 : 0);
result.emplace_back(last, nullptr);
return result;
}
vector<cell*> to_link;
EX void will_link(cell *c) { if(pmap && ((hrmap_hybrid*) pmap)->twisted) to_link.push_back(c); }
EX bool in_link = false;
EX void link() {
if(in_link) return;
dynamicval<bool> b(in_link, true);
auto pm = (hrmap_hybrid*) pmap;
if(!pm) return;
auto& ss = pm->spins;
int success = -1;
while(success) {
vector<cell*> xlink = std::move(to_link);
success = 0;
for(cell *c: xlink) {
bool success_here = ss.count(c);
if(!success_here) forCellIdEx(c2, i, c) if(ss.count(c2)) {
ss[c].first = ss[c2].first + c->c.spin(i) + wstep - i;
ss[c].second = ss[c2].second + c->c.spin(i) + wstep - i;
success++;
success_here = true;
break;
}
if(!success_here) to_link.push_back(c);
}
}
}
EX int celldistance(cell *c1, cell *c2) {
if(sl2) {
auto w1 = hybrid::get_where(c1), w2 = hybrid::get_where(c2);
return PIU (hr::celldistance(w1.first, w2.first));
}
else if(csteps == 0) {
auto w1 = hybrid::get_where(c1), w2 = hybrid::get_where(c2);
return PIU (hr::celldistance(w1.first, w2.first)) + abs(w1.second - w2.second);
}
else {
int s = 0;
int a = 999999, b = -999999;
auto c = c1;
do {
auto w1 = hybrid::get_where(c), w2 = hybrid::get_where(c2);
if(w1.second == w2.second) {
int d = PIU(hr::celldistance(w1.first, w2.first));
a = min(s+d, a);
b = max(s-d, b);
}
c = c->cmove(c1->type-1); s++;
}
while(c != c1);
return min(a, s-b);
}
}
EX void configure_period() {
static int s;
s = csteps / cgi.single_step;
string str = "";
if(rotspace)
str = XLAT(
"If the 2D underlying manifold is bounded, the period should be a divisor of the 'rotation space' "
"value (PSL(2,R)) times the Euler characteristics of the underlying manifold. "
"For unbounded underlying manifold, any value should work (theoretically, "
"the current implementation in HyperRogue is not perfect).\n\n"
"We won't stop you from trying illegal numbers, but they won't work correctly.");
dialog::editNumber(s, 0, 16, 1, 0, XLAT("%1 period", "Z"), str);
dialog::bound_low(0);
auto set_s = [] (int s1, bool ret) {
return [s1,ret] {
if(ret) popScreen();
if(csteps == s1) return;
stop_game();
csteps = s1 * cgi.single_step;
hybrid::reconfigure();
start_game();
};
};
dialog::get_di().extra_options = [=] () {
if(rotspace) {
int e_steps = cgi.psl_steps / gcd(cgi.single_step, cgi.psl_steps);
bool ubounded = PIU(closed_manifold);
dialog::addSelItem( sphere ? XLAT("elliptic") : XLAT("PSL(2,R)"), its(e_steps), 'P');
dialog::add_action(set_s(e_steps, true));
dialog::addSelItem( sphere ? XLAT("sphere") : XLAT("SL(2,R)"), its(2*e_steps), 'P');
dialog::add_action(set_s(2*e_steps, true));
if(sl2 && !ubounded) {
dialog::addSelItem( XLAT("universal cover"), its(0), 'P');
dialog::add_action(set_s(0, true));
}
dialog::addSelItem(ubounded ? XLAT("maximum") : XLAT("works correctly so far"), its(disc_quotient), 'Q');
dialog::add_action(set_s(disc_quotient, true));
}
else {
dialog::addSelItem( XLAT("non-periodic"), its(0), 'N');
dialog::add_action(set_s(0, true));
}
dialog::get_di().reaction_final = set_s(s, false);
};
}
EX }
EX namespace product {
int z0;
struct hrmap_product : hybrid::hrmap_hybrid {
transmatrix relative_matrixc(cell *c2, cell *c1, const hyperpoint& hint) override {
return in_underlying([&] { return calc_relative_matrix(where[c2].first, where[c1].first, hint); }) * cpush(2, cgi.plevel * szgmod(where[c2].second - where[c1].second, hybrid::csteps));
}
transmatrix adj(cell *c, int i) override {
if(twisted && i == c->type-1 && where[c].second == hybrid::csteps-1) {
auto b = spins[where[c].first].first;
transmatrix T = cpush(2, cgi.plevel);
T = T * spin(TAU * b.spin / b.at->type);
if(b.mirrored) T = T * Mirror;
return T;
}
if(twisted && i == c->type-2 && where[c].second == 0) {
auto b = spins[where[c].first].second;
transmatrix T = cpush(2, -cgi.plevel);
T = T * spin(TAU * b.spin / b.at->type);
if(b.mirrored) T = T * Mirror;
return T;
}
if(i == c->type-1) return cpush(2, cgi.plevel);
else if(i == c->type-2) return cpush(2, -cgi.plevel);
c = where[c].first;
return PIU(currentmap->adj(c, i));
}
hrmap_product() {
current_spin_invalid = false;
using hybrid::csteps;
if((cspin || cmirror) && csteps) {
in_underlying([&] {
twisted = validate_spin();
if(!twisted) { current_spin_invalid = true; return; }
auto ugs = currentmap->gamestart();
spins[ugs] = make_pair(
cellwalker(ugs, gmod(+cspin, ugs->type), cmirror),
cellwalker(ugs, gmod(-cspin, ugs->type), cmirror)
);
manual_celllister cl;
cl.add(ugs);
for(int i=0; i<isize(cl.lst); i++) {
cell *c = cl.lst[i];
hybrid::will_link(c);
forCellEx(c2, c) cl.add(c2);
}
hybrid::link();
});
}
}
transmatrix ray_iadj(cell *c, int i) override {
if(i == c->type-2) return (cpush(2, +cgi.plevel));
if(i == c->type-1) return (cpush(2, -cgi.plevel));
transmatrix T;
cell *cw = hybrid::get_where(c).first;
hybrid::in_underlying_geometry([&] {
T = currentmap->ray_iadj(cw, i);
});
return T;
}
};
EX bool current_spin_invalid, cmirror;
EX int cspin;
/* todo might need a shiftpoint version */
EX hyperpoint inverse_exp(hyperpoint h) {
hyperpoint res;
res[2] = zlevel(h);
h = h * exp(-res[2]);
ld r = hypot_d(2, h);
if(hybrid::under_class() == gcEuclid) {
res[0] = h[0];
res[1] = h[1];
}
else if(r < 1e-6) {
res[0] = h[0];
res[1] = h[1];
}
else {
auto c = acos_auto_clamp(h[2]);
r = c / r;
res[0] = h[0] * r;
res[1] = h[1] * r;
}
return res;
}
EX hyperpoint direct_exp(hyperpoint h) {
hyperpoint res;
ld d = hypot_d(2, h);
ld cd = d == 0 ? 0 : sin_auto(d) / d;
res[0] = h[0] * cd;
res[1] = h[1] * cd;
res[2] = cos_auto(d);
return res * exp(h[2]);
}
EX bool validate_spin() {
if(mproduct) return hybrid::in_underlying_geometry(validate_spin);
if(aperiodic) return false;
if(!quotient && !arcm::in()) return true;
map<cell*, cellwalker> cws;
manual_celllister cl;
cell *start = currentmap->gamestart();
cl.add(start);
cws[start] = cellwalker(start, gmod(cspin, start->type), cmirror);
for(int i=0; i<isize(cl.lst); i++) {
cell *c = cl.lst[i];
cellwalker cwc = cws.at(c);
forCellIdEx(c2, j, c) {
cellwalker cwc2 = cwc + j + wstep - c->c.spin(j);
if(!cws.count(c2)) cws[c2] = cwc2;
else if(cws[c2] != cwc2) return false;
cl.add(c2);
}
}
return true;
}
EX void show_config() {
cmode = sm::SIDE | sm::MAYDARK;
gamescreen();
dialog::init(XLAT("quotient product spaces"));
dialog::addSelItem(XLAT("%1 period", "Z"), its(hybrid::csteps), 'z');
dialog::add_action(hybrid::configure_period);
dialog::addSelItem(XLAT("rotation"), its(cspin), 'r');
dialog::add_action([] {
static int s;
dialog::editNumber(s, 0, 16, 1, 0, XLAT("rotation", "Z"),
XLAT("Works if the underlying space is symmetric.")
);
dialog::get_di().reaction_final = [] {
if(s == cspin) return;
stop_game();
cspin = s;
start_game();
};
});
dialog::addBoolItem(XLAT("reflect"), cmirror, 'f');
dialog::add_action([]{
stop_game();
cmirror = !cmirror;
start_game();
});
if(current_spin_invalid)
dialog::addInfo("the current rotation is invalid");
else
dialog::addBreak(100);
dialog::addBreak(50);
dialog::addBack();
dialog::display();
}
EX }
EX namespace slr {
/** in what range are we rendering SL(2,R) */
EX ld range_xy = 2;
/** in what Z range are we rendering SL(2,R) */
EX ld range_z = 2;
/** the number of steps for inverse_exp in the shader */
EX int shader_iterations = 15;
EX transmatrix translate(hyperpoint h) {
return matrix4(
h[3], -h[2], h[1], h[0],
h[2], h[3], -h[0], h[1],
h[1], -h[0], h[3], h[2],
h[0], h[1], -h[2], h[3]
);
}
EX hyperpoint polar(ld r, ld theta, ld phi) {
return hyperpoint(sinh(r) * cos(theta-phi), sinh(r) * sin(theta-phi), cosh(r) * sin(phi), cosh(r) * cos(phi));
}
EX hyperpoint xyz_point(ld x, ld y, ld z) {
ld r = hypot(x, y);
ld f = r ? sinh(r) / r : 1;
return hyperpoint(x * f * cos(z) + y * f * sin(z), y * f * cos(z) - x * f * sin(z), cosh(r) * sin(z), cosh(r) * cos(z));
}
EX hyperpoint get_inverse_exp(shiftpoint h) {
ld xy = hypot_d(2, h.h);
ld phi = atan2(h[2], h[3]) + h.shift;
if(xy < 1e-6) return point31(0.,0.,phi);
bool flipped = phi > 0;
if(flipped) phi = -phi;
ld SV = stretch::not_squared();
ld K = -1;
ld alpha = flipped ? atan2(h[1], h[0]) - h.shift : atan2(h[1], -h[0]) + h.shift;
hyperpoint res;
ld fiber_barrier = atan(1/SV);
ld flip_barrier = atan( 1 / tanh(asinh(xy)) / SV);
// test the side of the flip barrier
int part = -1;
if(1) {
ld kk = flip_barrier;
ld x_part = cos(kk);
ld z_part = sin(kk);
ld rparam = x_part / z_part / SV;
ld r = atanh(rparam);
ld cr = cosh(r);
ld sr = sinh(r);
// sinh(r) = xy
// r = tanh(sinh(xy))
ld z = cr * (K - 1/SV/SV);
ld k = 90._deg;
ld a = k / K;
ld zw = xy * cr / sr;
ld u = z * a;
ld phi1 = atan2(zw, cos(k)) - u;
if(phi < phi1) part = 2;
}
if(part == -1) {
ld zw = xy;
ld u = xy * (K - 1/SV/SV) / K;
ld phi1 = atan2(zw, 1) - u;
if(phi > phi1) part = 0; else part = 1;
}
if(part == 2) {
ld min_k = fiber_barrier;
ld max_k = flip_barrier;
for(int it=0; it<30; it++) {
ld kk = (min_k + max_k) / 2;
ld x_part = cos(kk);
ld z_part = sin(kk);
ld rparam = x_part / z_part / SV;
assert(rparam <= 1);
ld r = atanh(rparam);
ld cr = cosh(r);
ld sr = sinh(r);
ld z = cr * (K - 1/SV/SV);
ld k = M_PI - asin(xy / sr);
ld a = k / K;
ld len = a * hypot(sr, cr/SV);
ld zw = xy * cr / sr;
ld u = z * a;
ld phi1 = atan2(zw, cos(k)) - u;
if(phi < phi1) max_k = kk;
else min_k = kk;
ld r_angle = alpha + u;
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
}
}
if(part == 0) {
ld min_k = 0;
ld max_k = fiber_barrier;
for(int it=0; it<30; it++) {
ld kk = (min_k + max_k) / 2;
ld x_part = cos(kk);
ld z_part = sin(kk);
ld rparam = x_part / z_part / SV;
ld cr = 1 / sqrt(rparam*rparam - 1);
ld sr = rparam * cr;
ld z = cr * (K - 1/SV/SV);
ld k = asinh(xy / sr);
ld a = k / K;
ld len = a * hypot(sr, cr/SV);
ld zw = xy * cr / sr;
ld u = z * a;
ld phi1 = atan2(zw, cosh(k)) - u;
if(phi > phi1) max_k = kk; else min_k = kk;
ld r_angle = alpha + u;
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
}
}
if(part == 1) {
ld min_k = fiber_barrier;
ld max_k = flip_barrier;
for(int it=0; it<30; it++) {
ld kk = (min_k + max_k) / 2;
ld x_part = cos(kk);
ld z_part = sin(kk);
ld rparam = x_part / z_part / SV;
ld r = atanh(rparam);
ld cr = cosh(r);
ld sr = sinh(r);
ld z = cr * (K - 1/SV/SV);
ld k = asin(xy / sr);
ld a = k / K;
ld len = a * hypot(sr, cr/SV);
ld zw = xy * cr / sr;
ld u = z * a;
ld phi1 = atan2(zw, cos(k)) - u;
if(isnan(phi1)) max_k = kk;
else if(phi > phi1) max_k = kk;
else min_k = kk;
ld r_angle = alpha + u;
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
}
}
if(flipped) res[0] *= -1, res[2] *= -1;
return res;
}
#if ISWEB
#define ITERATE " for(int it=0; it<50; it++) { if(it >= uIterations) break; "
#else
#define ITERATE " for(int it=0; it<uIterations; it++) {"
#endif
EX string slshader =
"uniform mediump float uIndexSL;"
"uniform mediump int uIterations;"
"uniform mediump float uSV;"
"vec4 inverse_exp(vec4 h) {"
"float xy = length(h.xy);"
"float phi = atan2(h[2], h[3]) + uIndexSL;"
"if(xy < 1e-6) return vec4(0.,0.,phi,1.);"
"vec4 res = vec4(sqrt(-1.),sqrt(-1.),sqrt(-1.),sqrt(-1.));"
"bool flipped = phi > 0.;"
"if(flipped) phi = -phi;"
"float alpha = flipped ? atan2(h[1], h[0]) - uIndexSL : atan2(h[1], -h[0]) + uIndexSL;"
"float fiber_barrier = atan(1./uSV);"
"float flip_barrier = atan(1. / tanh(asinh(xy)) / uSV);"
"int part = 0;"
"if(true) {"
"float x_part = cos(flip_barrier);"
"float z_part = sin(flip_barrier);"
"float rparam = x_part / z_part / uSV;"
"float r = atanh(rparam);"
"float cr = cosh(r);"
"float sr = sinh(r);"
"float z = cr * (-1.-1./uSV/uSV);"
"float k = PI/2.;"
"float a = -k;"
"float zw = xy * cr / sr;"
"float u = z * a;"
"float phi1 = atan2(zw, cos(k)) - u;"
"if(phi < phi1) part = 2;"
"}\n"
"if(part == 0) {"
"float zw = xy;"
"float u = xy * (1. + 1./uSV/uSV);"
"float phi1 = atan2(zw, 1.) - u;"
"if(phi > phi1) part = 0; else part = 1;"
"}\n"
"if(part == 2) {"
"float min_k = fiber_barrier;"
"float max_k = flip_barrier;"
ITERATE
"float kk = (min_k + max_k) / 2.;"
"float x_part = cos(kk);"
"float z_part = sin(kk);"
"float rparam = x_part / z_part / uSV;"
"float r = atanh(rparam);"
"float cr = cosh(r);"
"float sr = sinh(r);"
"float z = cr * (-1. - 1./uSV/uSV);"
"float k = PI - asin(xy / sr);"
"float a = -k;"
"float len = a * length(vec2(sr, cr/uSV));"
"float zw = xy * cr / sr;"
"float u = z * a;"
"float phi1 = atan2(zw, cos(k)) - u;"
"if(phi < phi1) max_k = kk; else min_k = kk;"
"float r_angle = alpha + u;"
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
"}"
"}\n"
"if(part == 0) {"
"float min_k = 0.;"
"float max_k = fiber_barrier;"
ITERATE
"float kk = (min_k + max_k) / 2.;"
"float x_part = cos(kk);"
"float z_part = sin(kk);"
"float rparam = x_part / z_part / uSV;"
"float cr = 1. / sqrt(rparam*rparam - 1.);"
"float sr = rparam * cr;"
"float z = cr * (-1. - 1./uSV/uSV);"
"float k = asinh(xy / sr);"
"float a = -k;"
"float len = a * length(vec2(sr, cr/uSV));"
"float zw = xy * cr / sr;"
"float u = z * a;"
"float phi1 = atan2(zw, cosh(k)) - u;"
"if(phi > phi1) max_k = kk; else min_k = kk;"
"float r_angle = alpha + u;"
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
"}"
"}\n"
"if(part == 1) {"
"float min_k = fiber_barrier;"
"float max_k = flip_barrier;"
ITERATE
"float kk = (min_k + max_k) / 2.;"
"float x_part = cos(kk);"
"float z_part = sin(kk);"
"float rparam = x_part / z_part / uSV;"
"float r = atanh(rparam);"
"float cr = cosh(r);"
"float sr = sinh(r);"
"float z = cr * (-1. - 1./uSV/uSV);"
"float k = asin(xy / sr);"
"float a = -k;"
"float len = a * length(vec2(sr, cr/uSV));"
"float zw = xy * cr / sr;"
"float u = z * a;"
"float phi1 = atan2(zw, cos(k)) - u;"
"if(phi > phi1) max_k = kk;"
"else min_k = kk;"
"float r_angle = alpha + u;"
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
"}"
"}\n"
"if(flipped) res[0] *= -1., res[2] *= -1.;"
"return res;"
"}";
EX }
EX namespace rots {
EX ld underlying_scale = 0;
#if MAXMDIM >= 4
EX transmatrix uxpush(ld x) {
if(sl2) return xpush(x);
return cspin(1, 3, x) * cspin(0, 2, x);
}
EX transmatrix uypush(ld y) {
if(sl2) return ypush(y);
return cspin(0, 3, -y) * cspin(1, 2, y);
}
EX transmatrix uzpush(ld z) {
if(sl2) return zpush(z);
return cspin(3, 2, -z) * cspin(0, 1, -z);
}
EX transmatrix lift_matrix(const transmatrix& T) {
hyperpoint d;
ld alpha, beta, distance;
transmatrix Spin;
hybrid::in_underlying_geometry([&] {
hyperpoint h = tC0(T);
Spin = iso_inverse(gpushxto0(h) * T);
d = hr::inverse_exp(shiftless(h));
alpha = atan2(Spin[0][1], Spin[0][0]);
distance = hdist0(h);
beta = atan2(h[1], h[0]);
});
for(int k=0; k<3; k++) Spin[3][k] = Spin[k][3] = 0; Spin[3][3] = 1;
return spin(beta) * uxpush(distance/2) * spin(-beta+alpha);
}
EX std::map<int, transmatrix> saved_matrices_ray;
struct hrmap_rotation_space : hybrid::hrmap_hybrid {
std::map<int, transmatrix> saved_matrices;
transmatrix adj(cell *c1, int i) override {
if(i == c1->type-2) return uzpush(-cgi.plevel) * spin(-2*cgi.plevel);
if(i == c1->type-1) return uzpush(+cgi.plevel) * spin(+2*cgi.plevel);
cell *c2 = c1->cmove(i);
#if CAP_ARCM
int id1 = hybrid::underlying == gArchimedean ? arcm::id_of(c1->master) + 20 * arcm::parent_index_of(c1->master) : shvid(c1);
int id2 = hybrid::underlying == gArchimedean ? arcm::id_of(c2->master) + 20 * arcm::parent_index_of(c2->master) : shvid(c2);
#else
int id1 = shvid(c1);
int id2 = shvid(c2);
#endif
int j = c1->c.spin(i);
int id = id1 + (id2 << 10) + (i << 20) + (j << 26);
auto &M = saved_matrices[id];
if(M[3][3]) return M;
cell *cw = where[c1].first;
return M = lift_matrix(PIU(currentmap->adj(cw, i)));
}
transmatrix relative_matrixc(cell *c2, cell *c1, const hyperpoint& hint) override {
if(c1 == c2) return Id;
if(gmatrix0.count(c2) && gmatrix0.count(c1))
return inverse_shift(gmatrix0[c1], gmatrix0[c2]);
for(int i=0; i<c1->type; i++) if(c1->move(i) == c2) return adj(c1, i);
return Id; // not implemented yet
}
transmatrix ray_iadj(cell *c1, int i) override {
if(i == c1->type-1) return uzpush(-cgi.plevel) * spin(-2*cgi.plevel);
if(i == c1->type-2) return uzpush(+cgi.plevel) * spin(+2*cgi.plevel);
cell *c2 = c1->cmove(i);
#if CAP_ARCM
int id1 = hybrid::underlying == gArchimedean ? arcm::id_of(c1->master) + 20 * arcm::parent_index_of(c1->master) : shvid(c1);
int id2 = hybrid::underlying == gArchimedean ? arcm::id_of(c2->master) + 20 * arcm::parent_index_of(c2->master) : shvid(c2);
#else
int id1 = shvid(c1);
int id2 = shvid(c2);
#endif
int j = c1->c.spin(i);
int id = id1 + (id2 << 10) + (i << 20) + (j << 26);
auto &M = saved_matrices_ray[id];
if(M[3][3]) return M;
cell *cw = hybrid::get_where(c1).first;
transmatrix T;
hybrid::in_underlying_geometry([&] {
hyperpoint h0 = get_corner_position(cw, i);
hyperpoint h1 = get_corner_position(cw, (i+1));
T = to_other_side(h0, h1);
});
return M = lift_matrix(T);
}
};
/** reinterpret the given point of rotspace as a rotation matrix in the underlying geometry (note: this is the inverse) */
EX transmatrix qtm(hyperpoint h) {
ld& x = h[0];
ld& y = h[1];
ld& z = h[2];
ld& w = h[3];
ld xx = x*x;
ld yy = y*y;
ld zz = z*z;
ld ww = w*w;
ld xy = x*y;
ld xz = x*z;
ld xw = x*w;
ld yz = y*z;
ld yw = y*w;
ld zw = z*w;
transmatrix M;
M[0][0] = +xx - yy - zz + ww;
M[1][1] = -xx + yy - zz + ww;
M[2][2] = -xx - yy + zz + ww;
M[0][1] = -2 * (xy + zw);
M[1][0] = -2 * (xy - zw);
M[0][2] = 2 * (xz - yw);
M[2][0] = 2 * (xz + yw);
M[1][2] = -2 * (yz + xw);
M[2][1] = -2 * (yz - xw);
if(hyperbolic) {
swap(M[0][2], M[1][2]);
swap(M[2][0], M[2][1]);
M[1][2] *= -1;
M[2][0] *= -1;
M[2][2] = xx + yy + zz + ww;
return M;
}
return M;
}
EX bool drawing_underlying = false;
EX void draw_underlying(bool cornermode) {
if(underlying_scale <= 0) return;
ld d = hybrid::get_where(centerover).second;
d *= cgi.plevel;
transmatrix T = rots::uzpush(-d) * spin(-2*d);
if(det(T) < 0) T = centralsym * T;
if(mproduct) d = 0;
hyperpoint h = inverse(View * spin(master_to_c7_angle()) * T) * C0;
auto g = std::move(gmatrix);
auto g0 = std::move(gmatrix0);
ld alpha = atan2(ortho_inverse(NLP) * point3(1, 0, 0));
bool inprod = mproduct;
transmatrix pView = View;
if(inprod) {
pView = spin(alpha) * View;
ld z = zlevel(tC0(View));
for(int a=0; a<3; a++) pView[a] *= exp(-z);
}
cell *co = hybrid::get_where(centerover).first;
hybrid::in_underlying_geometry([&] {
cgi.require_shapes();
dynamicval<int> pcc(corner_centering, cornermode ? 1 : 2);
dynamicval<bool> pf(playerfound, true);
dynamicval<cell*> m5(centerover, co);
dynamicval<transmatrix> m2(View, inprod ? pView : ypush(0) * qtm(h));
if(PURE && !inprod) View = View * pispin;
View = inverse(stretch::mstretch_matrix) * spin(2*d) * View;
dynamicval<shiftmatrix> m3(playerV, shiftless(Id));
dynamicval<transmatrix> m4(actual_view_transform, Id);
dynamicval<shiftmatrix> m6(cwtV, shiftless(Id));
dynamicval<eModel> pm(pmodel, mdDisk);
dynamicval<ld> pss(pconf.scale, (sphere ? 10 : euclid ? .4 : 1) * underlying_scale);
dynamicval<ld> psa(pconf.alpha, sphere ? 10 : 1);
dynamicval<hrmap*> p(hybrid::pmap, NULL);
dynamicval<int> psr(sightrange_bonus, 0);
dynamicval<int> psx(vid.use_smart_range, 2);
dynamicval<ld> psy(vid.smart_range_detail, 1);
dynamicval<bool> pdu(drawing_underlying, true);
calcparam();
reset_projection(); current_display->set_all(0, 0);
ptds.clear();
drawthemap();
drawqueue();
displaychr(current_display->xcenter, current_display->ycenter, 0, 24 * mapfontscale / 100, '+', 0xFFFFFFFF);
glflush();
});
gmatrix = std::move(g);
gmatrix0 = std::move(g0);
calcparam();
reset_projection(); current_display->set_all(0, 0);
}
/** @brief exponential function for both slr and Berger sphere */
EX hyperpoint formula_exp(hyperpoint vel) {
bool sp = sphere;
ld K = sp ? 1 : -1;
if(vel[0] == 0 && vel[1] == 0 && vel[2] == 0) return C0;
ld len = hypot_d(3, vel);
if(vel[2] < 0) len = -len;
ld z_part = vel[2]/len;
ld x_part = sqrt(max<ld>(1 - z_part * z_part, 0));
ld SV = stretch::not_squared();
ld rparam = x_part / z_part / SV;
ld beta = atan2(vel[1], vel[0]);
if(len < 0) beta += M_PI;
if(sl2 && rparam > 1) {
ld cr = 1 / sqrt(rparam*rparam - 1); // *i
ld sr = rparam * cr; // *i
if(z_part == 0) cr = 0, sr = 1;
ld z = cr * (K - 1/SV/SV); // *i
ld a = len / hypot(sr, cr/SV); // /i
ld k = K*a; // /i
ld u = z*a;
ld xy = sr * sinh(k);
ld zw = cr * sinh(k);
return hyperpoint(K*xy * cos(u+beta), K*xy * sin(u+beta), zw * cos(u) - cosh(k) * sin(u), zw * sin(u) + cosh(k)*cos(u));
}
else {
ld r = atan_auto(rparam);
ld cr = cos_auto(r);
ld sr = sin_auto(r);
ld z = cr * (K - 1/SV/SV);
ld a = len / hypot(sr, cr/SV);
ld k = K*a;
ld u = z*a;
ld xy = sr * sin(k);
ld zw = cr * sin(k);
return hyperpoint(K*xy * cos(u+beta), K*xy * sin(u+beta), zw * cos(u) - cos(k) * sin(u), zw * sin(u) + cos(k)*cos(u));
}
}
#endif
EX }
/** stretched rotation space (S3 or SLR) */
EX namespace stretch {
EX ld factor;
EX bool mstretch;
EX transmatrix m_itoa, m_atoi, m_pd;
EX ld ms_christoffel[3][3][3];
EX transmatrix mstretch_matrix;
EX void enable_mstretch() {
mstretch = true;
for(int a=0; a<4; a++)
for(int b=0; b<4; b++)
if(a==3 || b==3) m_atoi[a][b] = (a==b);
m_itoa = inverse3(m_atoi);
for(int a=0; a<4; a++)
for(int b=0; b<4; b++)
if(a==3 || b==3)
m_itoa[a][b] = m_atoi[a][b] = 0;
for(int j=0; j<3; j++)
for(int k=0; k<3; k++) {
m_pd[j][k] = 0;
for(int i=0; i<3; i++)
m_pd[j][k] += m_atoi[i][j] * m_atoi[i][k];
}
auto& c = ms_christoffel;
ld A00 = m_pd[0][0];
ld A11 = m_pd[1][1];
ld A22 = m_pd[2][2];
ld A01 = m_pd[0][1] + m_pd[1][0];
ld A02 = m_pd[0][2] + m_pd[2][0];
ld A12 = m_pd[2][1] + m_pd[1][2];
ld B01 = A01 * A01;
ld B02 = A02 * A02;
ld B12 = A12 * A12;
ld B00 = A00 * A00;
ld B11 = A11 * A11;
ld B22 = A22 * A22;
ld den = (-4*A00*A11*A22 + A00*B12 + B01*A22 - A01*A02*A12 + B02*A11);
if(sl2) {
c[ 0 ][ 0 ][ 0 ] = (A01*(A01*A12 - 2*A02*A11) - A02*(2*A01*A22 - A02*A12))/den;
c[ 0 ][ 0 ][ 1 ] = (A00*A01*A12 - 2*A00*A02*A11 - A01*A11*A12 + A01*A12*A22 + 2*A02*B11 + 2*A02*A11*A22 - A02*B12)/-den ;
c[ 0 ][ 0 ][ 2 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 + A22)*(2*A01*A22 - A02*A12))/den;
c[ 0 ][ 1 ][ 0 ] = (A00*A01*A12 - 2*A00*A02*A11 - A01*A11*A12 + A01*A12*A22 + 2*A02*B11 + 2*A02*A11*A22 - A02*B12)/-den ;
c[ 0 ][ 1 ][ 1 ] = -(A01*(A01*A12 - 2*A02*A11) + A12*(4*A11*A22 - B12))/den;
c[ 0 ][ 1 ][ 2 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 + 4*A11*B22 - B12*A22)/-den ;
c[ 0 ][ 2 ][ 0 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 + A22)*(2*A01*A22 - A02*A12))/den;
c[ 0 ][ 2 ][ 1 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 + 4*A11*B22 - B12*A22)/-den ;
c[ 0 ][ 2 ][ 2 ] = -(A02*(2*A01*A22 - A02*A12) + A12*(4*A11*A22 - B12))/den;
c[ 1 ][ 0 ][ 0 ] = (-A01*(2*A00*A12 - A01*A02) + A02*(4*A00*A22 - B02))/den;
c[ 1 ][ 0 ][ 1 ] = (A02*(2*A01*A22 - A02*A12)/2 + A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den;
c[ 1 ][ 0 ][ 2 ] = (-4*B00*A22 + A00*B02 + A00*B12 - 4*A00*B22 - B01*A22 + B02*A22)/-den ;
c[ 1 ][ 1 ][ 0 ] = (A02*(2*A01*A22 - A02*A12)/2 + A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den;
c[ 1 ][ 1 ][ 1 ] = (A01*(2*A00*A12 - A01*A02) + A12*(2*A01*A22 - A02*A12))/den;
c[ 1 ][ 1 ][ 2 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 + A22)*(2*A01*A22 - A02*A12))/den;
c[ 1 ][ 2 ][ 0 ] = (-4*B00*A22 + A00*B02 + A00*B12 - 4*A00*B22 - B01*A22 + B02*A22)/-den ;
c[ 1 ][ 2 ][ 1 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 + A22)*(2*A01*A22 - A02*A12))/den;
c[ 1 ][ 2 ][ 2 ] = (A02*(4*A00*A22 - B02) + A12*(2*A01*A22 - A02*A12))/den;
c[ 2 ][ 0 ][ 0 ] = (A01*(4*A00*A11 - B01) - A02*(2*A00*A12 - A01*A02))/den;
c[ 2 ][ 0 ][ 1 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 + A00*B12 + B01*A11 - B02*A11)/-den ;
c[ 2 ][ 0 ][ 2 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 + A22)*(2*A00*A12 - A01*A02))/den;
c[ 2 ][ 1 ][ 0 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 + A00*B12 + B01*A11 - B02*A11)/-den ;
c[ 2 ][ 1 ][ 1 ] = -(A01*(4*A00*A11 - B01) + A12*(A01*A12 - 2*A02*A11))/den;
c[ 2 ][ 1 ][ 2 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 + A01*A12*A22 - 2*A02*B11 - 2*A02*A11*A22)/-den ;
c[ 2 ][ 2 ][ 0 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 + A22)*(2*A00*A12 - A01*A02))/den;
c[ 2 ][ 2 ][ 1 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 + A01*A12*A22 - 2*A02*B11 - 2*A02*A11*A22)/-den ;
c[ 2 ][ 2 ][ 2 ] = -(A02*(2*A00*A12 - A01*A02) + A12*(A01*A12 - 2*A02*A11))/den;
}
else {
c[ 0 ][ 0 ][ 0 ] = (A01*(A01*A12 - 2*A02*A11) + A02*(2*A01*A22 - A02*A12))/den ;
c[ 0 ][ 0 ][ 1 ] = (A02*(4*A11*A22 - B12)/2 + A12*(2*A01*A22 - A02*A12)/2 - (A00 - A11)*(A01*A12 - 2*A02*A11))/den ;
c[ 0 ][ 0 ][ 2 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 - A22)*(2*A01*A22 - A02*A12))/den ;
c[ 0 ][ 1 ][ 0 ] = (A02*(4*A11*A22 - B12)/2 + A12*(2*A01*A22 - A02*A12)/2 - (A00 - A11)*(A01*A12 - 2*A02*A11))/den ;
c[ 0 ][ 1 ][ 1 ] = (-A01*(A01*A12 - 2*A02*A11) + A12*(4*A11*A22 - B12))/den ;
c[ 0 ][ 1 ][ 2 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 - 4*A11*B22 + B12*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
c[ 0 ][ 2 ][ 0 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 - A22)*(2*A01*A22 - A02*A12))/den ;
c[ 0 ][ 2 ][ 1 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 - 4*A11*B22 + B12*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
c[ 0 ][ 2 ][ 2 ] = -(A02*(2*A01*A22 - A02*A12) + A12*(4*A11*A22 - B12))/den ;
c[ 1 ][ 0 ][ 0 ] = -(A01*(2*A00*A12 - A01*A02) + A02*(4*A00*A22 - B02))/den ;
c[ 1 ][ 0 ][ 1 ] = (-A02*(2*A01*A22 - A02*A12)/2 - A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den ;
c[ 1 ][ 0 ][ 2 ] = (-4*B00*A22 + A00*B02 + A00*B12 + 4*A00*B22 - B01*A22 - B02*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
c[ 1 ][ 1 ][ 0 ] = (-A02*(2*A01*A22 - A02*A12)/2 - A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den ;
c[ 1 ][ 1 ][ 1 ] = (A01*(2*A00*A12 - A01*A02) - A12*(2*A01*A22 - A02*A12))/den ;
c[ 1 ][ 1 ][ 2 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 - A22)*(2*A01*A22 - A02*A12))/den ;
c[ 1 ][ 2 ][ 0 ] = (-4*B00*A22 + A00*B02 + A00*B12 + 4*A00*B22 - B01*A22 - B02*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
c[ 1 ][ 2 ][ 1 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 - A22)*(2*A01*A22 - A02*A12))/den ;
c[ 1 ][ 2 ][ 2 ] = (A02*(4*A00*A22 - B02) + A12*(2*A01*A22 - A02*A12))/den ;
c[ 2 ][ 0 ][ 0 ] = (A01*(4*A00*A11 - B01) + A02*(2*A00*A12 - A01*A02))/den ;
c[ 2 ][ 0 ][ 1 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 - A00*B12 + B01*A11 + B02*A11)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
c[ 2 ][ 0 ][ 2 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 - A22)*(2*A00*A12 - A01*A02))/den ;
c[ 2 ][ 1 ][ 0 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 - A00*B12 + B01*A11 + B02*A11)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
c[ 2 ][ 1 ][ 1 ] = (-A01*(4*A00*A11 - B01) + A12*(A01*A12 - 2*A02*A11))/den ;
c[ 2 ][ 1 ][ 2 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 - A01*A12*A22 - 2*A02*B11 + 2*A02*A11*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
c[ 2 ][ 2 ][ 0 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 - A22)*(2*A00*A12 - A01*A02))/den ;
c[ 2 ][ 2 ][ 1 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 - A01*A12*A22 - 2*A02*B11 + 2*A02*A11*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
c[ 2 ][ 2 ][ 2 ] = -(A02*(2*A00*A12 - A01*A02) + A12*(A01*A12 - 2*A02*A11))/den ;
}
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
for(int k=0; k<3; k++)
if(c[i][j][k])
println(hlog, tie(i,j,k), " : ", c[i][j][k]);
println(hlog, "ATOI = ", m_atoi);
println(hlog, "ITOA = ", m_itoa, " vs ", 1/not_squared());
println(hlog, "PD = ", m_pd, " vs ", factor);
ray::reset_raycaster();
}
EX bool applicable() {
return rotspace || (cgflags & qSTRETCHABLE);
}
EX bool in() {
return (factor || mstretch) && applicable();
}
EX transmatrix translate(hyperpoint h) {
if(!sphere) return slr::translate(h);
return matrix4(
h[3], -h[2], h[1], h[0],
h[2], h[3], -h[0], h[1],
-h[1], h[0], h[3], h[2],
-h[0], -h[1], -h[2], h[3]
);
}
EX transmatrix itranslate(hyperpoint h) {
h[0] = -h[0];
h[1] = -h[1];
h[2] = -h[2];
if(!sphere) return slr::translate(h);
return translate(h);
}
hyperpoint mulz(const hyperpoint at, const hyperpoint velocity, ld zf) {
auto vel = itranslate(at) * velocity;
vel[2] *= zf;
return translate(at) * vel;
}
EX ld squared() {
return abs(1 + factor);
}
EX ld not_squared() {
return sqrt(squared());
}
EX hyperpoint isometric_to_actual(const hyperpoint at, const hyperpoint velocity) {
if(mstretch)
return translate(at) * m_itoa * itranslate(at) * velocity;
else
return mulz(at, velocity, 1/not_squared());
}
EX hyperpoint actual_to_isometric(const hyperpoint at, const hyperpoint velocity) {
if(mstretch)
return translate(at) * m_atoi * itranslate(at) * velocity;
else
return mulz(at, velocity, not_squared());
}
EX hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
auto vel = itranslate(at) * velocity;
auto tra = itranslate(at) * transported;
hyperpoint c;
if(mstretch) {
c = Hypc;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
for(int k=0; k<3; k++)
c[i] += vel[j] * tra[k] * ms_christoffel[i][j][k];
}
else {
auto K = factor;
c[0] = (sphere ? -K : K+2) * (vel[1] * tra[2] + vel[2] * tra[1]);
c[1] = (sphere ? K : -(K+2)) * (vel[0] * tra[2] + vel[2] * tra[0]);
c[2] = 0;
c[3] = 0;
}
return translate(at) * c;
}
EX ld sqnorm(hyperpoint at, hyperpoint h) {
if(sphere)
return sqhypot_d(4, h);
h = itranslate(at) * h;
return h[0] * h[0] + h[1] * h[1] + h[2] * h[2];
}
EX vector<hyperpoint> inverse_exp_all(hyperpoint h, int generations) {
vector<hyperpoint> res;
ld SV = stretch::not_squared();
if(stretch::factor == 0) {
ld d = hypot_d(3, h);
if(h[3] >= 1 || h[3] <= -1|| d == 0) return res;
ld a = acos(h[3]);
res.push_back(point31(h[0] * a / d, h[1] * a / d, h[2] * a / d));
a = a - TAU;
res.push_back(point31(h[0] * a / d, h[1] * a / d, h[2] * a / d));
return res;
}
if(h[0] == 0 && h[1] == 0) {
ld a = atan2(h[2], h[3]);
for(int it=-generations; it<generations; it++) {
res.push_back(point31(0, 0, (a + TAU * it) * SV));
}
return res;
}
ld xy = hypot_d(2, h);
ld base_min_a = asin(xy);
ld base_max_a = M_PI - base_min_a;
ld seek = 90._deg - atan2(h[3], h[2]);
auto ang = [&] (ld a) {
ld rp = xy / sin(a);
ld co = abs(rp) >= 1 ? 0 : sqrt(1-rp*rp);
return atan2(co * sin(a), cos(a)) - co * (1 - 1/SV/SV) * a;
};
for(int shift=-generations; shift<generations; shift++) {
ld min_a = base_min_a + M_PI * shift;
ld max_a = base_max_a + M_PI * shift;
ld ang_min = ang(min_a);
ld ang_max = ang(max_a);
for(int mi=0; mi<2; mi++) {
// 0 : minimum, 1 : maximum
ld tl = min_a, tr = max_a;
for(int it=0; it<20; it++) {
ld t1 = tl * .51 + tr * .49;
ld t2 = tl * .49 + tr * .51;
if((ang(t1) < ang(t2)) == mi)
tr = t1;
else
tl = t2;
}
ld extreme = (tl + tr) / 2;
ld ang_extreme = ang(extreme);
for(int t=0; t<2; t++) {
ld mmin = t == 0 ? min_a : extreme;
ld mmax = t == 0 ? extreme : max_a;
ld vmin = t == 0 ? ang_min : ang_extreme;
ld vmax = t == 0 ? ang_extreme : ang_max;
// make it increasing
if(t != mi) swap(mmin, mmax), swap(vmin, vmax);
// println(hlog, "*** ", mi, t, " ** ", tie(min_a, ang_min), tie(extreme, ang_extreme), tie(max_a, ang_max), " -> ", vmin, " to ", vmax);
int cmin = ceil((vmin - seek) / TAU);
int cmax = floor((vmax - seek) / TAU);
for(int c = cmin; c <= cmax; c++) {
ld cseek = seek + c * TAU;
for(int it=0; it<40; it++) {
ld a = (mmin + mmax) / 2;
ld cros = ang(a);
if(cros > cseek) mmax = a; else mmin = a;
}
ld a = (mmin + mmax) / 2;
ld r = asin_clamp( xy / sin(a) );
ld z_part = 1;
ld x_part = SV * tan(r);
ld db = hypot(x_part, z_part);
x_part /= db;
z_part /= db;
ld alpha = atan2(-h[1], h[0]);
ld z = cos(r) * (1 - 1/SV/SV);
ld u = z * a;
ld r_angle = alpha + u;
ld len = a * hypot(sin_auto(r), cos_auto(r)/SV);
auto answer = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
// int id = (shift << 10) + (mi << 9) + (t << 8) + c;
/*
auto f = formula_exp(answer);
ld err = sqhypot_d(4, f - h);
println(hlog, "************************* ", answer, ": error = ", err, " id = ", id, " params = ", tie(shift, mi, t, c));
*/
res.emplace_back(answer);
}
}
}
}
return res;
}
EX }
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(sn::in()) return sn::christoffel(at, velocity, transported);
#endif
else if(stretch::in() || sl2) return stretch::christoffel(at, velocity, transported);
else return point3(0, 0, 0);
}
EX bool in_table_range(hyperpoint h) {
#if CAP_SOLV
if(sol) return sn::in_table_range(h);
#endif
return true;
}
EX hyperpoint get_acceleration(const hyperpoint& at, const hyperpoint& vel) {
return christoffel(at, vel, vel);
}
EX void geodesic_step(hyperpoint& at, hyperpoint& vel) {
/* RK4 method */
auto acc1 = get_acceleration(at, vel);
auto acc2 = get_acceleration(at + vel/2, vel + acc1/2);
auto acc3 = get_acceleration(at + vel/2 + acc1/4, vel + acc2/2);
auto acc4 = get_acceleration(at + vel + acc2/2, vel + acc3);
at += vel + (acc1+acc2+acc3)/6;
vel += (acc1+2*acc2+2*acc3+acc4)/6;
}
EX int rk_steps = 20;
EX hyperpoint numerical_exp(hyperpoint v) {
hyperpoint at = point31(0, 0, 0);
v /= rk_steps;
v[3] = 0;
for(int i=0; i<rk_steps; i++) geodesic_step(at, v);
return at;
}
EX transmatrix parallel_transport_bare(transmatrix Pos, hyperpoint h) {
bool stretch = stretch::in() || sl2;
h[3] = 0;
if(stretch::in() && stretch::mstretch)
Pos = stretch::mstretch_matrix * Pos;
auto tPos = transpose(Pos);
h = Pos * h;
int steps = rk_steps;
h /= steps;
auto& at = tPos[3];
auto& vel = h;
array<ld, 4> ms;
if(stretch) {
for(int i=0; i<3; i++) {
ms[i] = stretch::sqnorm(at, tPos[i]);
tPos[i] = stretch::isometric_to_actual(at, tPos[i]);
}
ms[3] = stretch::sqnorm(at, vel);
if(!ms[3]) return Pos;
vel = stretch::isometric_to_actual(at, vel);
}
for(int i=0; i<steps; i++) {
auto acc1 = get_acceleration(at, vel);
auto at1 = at + vel/2; auto vel1 = vel + acc1/2;
auto acc2 = get_acceleration(at1, vel1);
auto at2 = at1 + acc1/4; auto vel2 = vel + acc2/2;
auto acc3 = get_acceleration(at2, vel2);
auto at3 = at + vel + acc2/2; auto vel3 = vel + acc3;
auto acc4 = get_acceleration(at3, vel3);
for(int j=0; j<3; j++) {
auto& tra = tPos[j];
auto tacc1 = christoffel(at, vel, tra);
auto tacc2 = christoffel(at1, vel1, tra + tacc1/2);
auto tacc3 = christoffel(at2, vel2, tra + tacc2/2);
auto tacc4 = christoffel(at3, vel3, tra + tacc3);
tra += (tacc1+tacc2*2+tacc3*2+tacc4) / 6;
}
at += vel + (acc1+acc2+acc3)/6;
vel += (acc1+2*acc2+2*acc3+acc4)/6;
if(stretch) {
at = normalize(at);
auto fix = [&] (hyperpoint& h, ld& m) {
h = stretch::itranslate(at) * h;
h[3] = 0;
ld m1;
if(stretch::mstretch) {
m1 = 0;
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
m1 += h[i] * stretch::m_pd[i][j] * h[j];
}
else
m1 = h[0] * h[0] + h[1] * h[1] + h[2] * h[2] * stretch::squared();
h /= sqrt(m1/m);
h = stretch::translate(at) * h;
};
for(int i=0; i<3; i++) fix(tPos[i], ms[i]);
fix(vel, ms[3]);
}
}
if(stretch) {
vel = stretch::actual_to_isometric(at, vel);
for(int i=0; i<3; i++) tPos[i] = stretch::actual_to_isometric(at, tPos[i]);
}
Pos = transpose(tPos);
if(stretch::in() && stretch::mstretch)
Pos = inverse(stretch::mstretch_matrix) * Pos;
return Pos;
}
EX void fixmatrix(transmatrix& T) {
if(sphere) return hr::fixmatrix(T);
transmatrix push = eupush( tC0(T) );
transmatrix push_back = eupush(tC0(T), -1);
transmatrix gtl = push_back * T;
fix_rotation(gtl);
T = push * gtl;
}
EX transmatrix parallel_transport(const transmatrix Position, const hyperpoint direction) {
auto P = Position;
nisot::fixmatrix(P);
return parallel_transport_bare(P, direction);
}
EX transmatrix lie_transport(const transmatrix Position, const hyperpoint direction) {
transmatrix pshift = eupush( tC0(Position) );
transmatrix irot = iso_inverse(pshift) * Position;
hyperpoint tH = unshift(lie_exp(irot * direction));
return pshift * eupush(tH) * irot;
}
EX transmatrix spin_towards(const transmatrix Position, const hyperpoint goal, flagtype prec IS(pNORMAL)) {
hyperpoint at = tC0(Position);
transmatrix push_back = translate(at, -1);
hyperpoint back_goal = push_back * goal;
back_goal = inverse_exp(shiftless(back_goal), prec);
transmatrix back_Position = push_back * Position;
return rspintox(inverse(back_Position) * back_goal);
}
EX hrmap *new_map() {
#if CAP_SOLV
if(sn::in()) return new sn::hrmap_solnih;
#endif
if(mproduct) return new product::hrmap_product;
#if MAXMDIM >= 4
if(nil) return new nilv::hrmap_nil;
if(mhybrid) return new rots::hrmap_rotation_space;
#endif
return NULL;
}
#if CAP_COMMANDLINE
auto config = addHook(hooks_args, 0, [] () {
using namespace arg;
#if CAP_SOLV
if(argis("-solrange")) {
shift_arg_formula(sn::solrange_xy);
shift_arg_formula(sn::solrange_z);
return 0;
}
#endif
if(argis("-slrange")) {
shift_arg_formula(slr::range_xy);
shift_arg_formula(slr::range_z);
return 0;
}
#if CAP_SOLV
else if(argis("-fsol")) {
shift(); sn::solt.fname = args();
return 0;
}
else if(argis("-nihsol")) {
shift(); sn::niht.fname = args();
return 0;
}
#endif
else if(argis("-product")) {
PHASEFROM(2);
set_geometry(gProduct);
return 0;
}
else if(argis("-s2xe")) {
PHASEFROM(2);
shift(); s2xe::qrings = argi();
return 0;
}
else if(argis("-rotspace")) {
PHASEFROM(2);
set_geometry(gRotSpace);
return 0;
}
else if(argis("-rot_uscale")) {
PHASEFROM(2);
shift_arg_formula(rots::underlying_scale);
return 0;
}
else if(argis("-nilperiod")) {
PHASEFROM(2);
if(nil) stop_game();
for(int a=0; a<3; a++) { shift(); nilv::nilperiod[a] = argi(); }
nilv::set_flags();
return 0;
}
else if(argis("-nilwidth")) {
PHASEFROM(2);
shift_arg_formula(nilv::nilwidth);
return 0;
}
else if(argis("-nilh")) {
PHASEFROM(2);
stop_game();
shift(); ginf[gNil].sides = argi();
nilv::set_flags();
start_game();
}
else if(argis("-rk-steps")) {
PHASEFROM(2);
shift(); rk_steps = argi();
return 0;
}
else if(argis("-nilv")) {
PHASEFROM(2);
if(nil) stop_game();
shift();
ginf[gNil].sides = argi();
return 0;
}
#if CAP_SOLV
else if(argis("-catperiod")) {
PHASEFROM(2);
if(sol) stop_game();
shift(); asonov::period_xy = argi();
shift(); asonov::period_z = argi();
asonov::set_flags();
return 0;
}
#endif
else if(argis("-prodperiod")) {
PHASEFROM(2);
if(mproduct) stop_game();
shift(); hybrid::csteps = argi();
hybrid::reconfigure();
return 0;
}
else if(argis("-rot-stretch")) {
PHASEFROM(2);
shift_arg_formula(stretch::factor, ray::reset_raycaster);
return 0;
}
else if(argis("-mstretch")) {
PHASEFROM(2);
auto& M = stretch::m_atoi;
M = Id;
stretch::enable_mstretch();
while(true) {
shift();
string s = args();
if(isize(s) == 2 && among(s[0], 'a', 'b','c') && among(s[1], 'a', 'b', 'c'))
shift_arg_formula(M[s[0]-'a'][s[1]-'a'], stretch::enable_mstretch);
else break;
}
// shift_arg_formula(stretch::yfactor, ray::reset_raycaster);
return 0;
}
else if(argis("-mstretch1")) {
PHASEFROM(2);
auto& M = stretch::m_atoi;
M = Id;
M[2][2] = stretch::not_squared();
stretch::enable_mstretch();
// shift_arg_formula(stretch::yfactor, ray::reset_raycaster);
return 0;
}
else if(argis("-prodturn")) {
PHASEFROM(2);
if(mproduct) stop_game();
shift(); product::cspin = argi();
shift(); product::cmirror = argi();
return 0;
}
else if(argis("-nil-model")) {
shift(); nilv::model_used = argf();
return 0;
}
return 1;
});
#endif
}
}
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