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stretched spherical geometry

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Zeno Rogue
2020-05-08 21:18:47 +02:00
parent 02de6fa330
commit 54804bc08b
5 changed files with 312 additions and 27 deletions
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138
nonisotropic.cpp
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@@ -1081,6 +1081,7 @@ EX namespace hybrid {
});
return T;
}
if(rotspace) return inverse(rots::ray_adj(c, i));
return currentmap->iadj(c, i);
}
@@ -1838,6 +1839,8 @@ EX }
EX namespace rots {
EX ld stretch_factor;
EX transmatrix uxpush(ld x) {
if(sl2) return xpush(x);
return cspin(1, 3, x) * cspin(0, 2, x);
@@ -1869,6 +1872,34 @@ EX namespace rots {
return spin(beta) * uxpush(distance/2) * spin(-beta+alpha);
}
std::unordered_map<int, transmatrix> saved_matrices_ray;
EX transmatrix ray_adj(cell *c1, int i) {
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);
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);
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));
hyperpoint hm = mid(h0, h1);
ld d = hdist0(hm);
d *= 2;
T = rspintox(hm) * xpush(d);
});
return M = lift_matrix(T);
}
struct hrmap_rotation_space : hybrid::hrmap_hybrid {
std::unordered_map<int, transmatrix> saved_matrices;
@@ -1968,6 +1999,7 @@ EX namespace rots {
dynamicval<bool> pf(playerfound, true);
dynamicval<cell*> m5(centerover, co);
dynamicval<transmatrix> m2(View, inprod ? pView : ypush(0) * qtm(h));
if(PURE) View = View * pispin;
dynamicval<transmatrix> m3(playerV, Id);
dynamicval<transmatrix> m4(actual_view_transform, Id);
dynamicval<eModel> pm(pmodel, mdDisk);
@@ -1991,6 +2023,64 @@ EX namespace rots {
EX }
/** twisted S2xE */
EX namespace rots_twist {
EX bool applicable() {
return among(geometry, gCell120, gECell120, gCell24, gECell24, gCell8, gECell8);
}
EX bool in() { return rots::stretch_factor && sphere && (rotspace || applicable()); }
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 transmatrix itranslate(hyperpoint h) {
h[0] = -h[0];
h[1] = -h[1];
h[2] = -h[2];
return translate(h);
}
hyperpoint mulz(const hyperpoint at, const hyperpoint velocity, ld factor) {
auto vel = itranslate(at) * velocity;
vel[2] *= factor;
return translate(at) * vel;
}
hyperpoint isometric_to_actual(const hyperpoint at, const hyperpoint velocity) {
return mulz(at, velocity, 1/sqrt(1+rots::stretch_factor));
}
hyperpoint actual_to_isometric(const hyperpoint at, const hyperpoint velocity) {
return mulz(at, velocity, sqrt(1+rots::stretch_factor));
}
hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
auto vel = itranslate(at) * velocity;
auto tra = itranslate(at) * transported;
hyperpoint c;
auto K = rots::stretch_factor;
c[0] = -K * (vel[1] * tra[2] + vel[2] * tra[1]);
c[1] = K * (vel[0] * tra[2] + vel[2] * tra[0]);
c[2] = 0;
c[3] = 0;
return translate(at) * c;
}
EX }
EX namespace nisot {
EX hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
@@ -1999,6 +2089,7 @@ EX namespace nisot {
else if(sn::in()) return sn::christoffel(at, velocity, transported);
#endif
else if(sl2) return slr::christoffel(at, velocity, transported);
else if(rots_twist::in()) return rots_twist::christoffel(at, velocity, transported);
else return point3(0, 0, 0);
}
@@ -2036,12 +2127,14 @@ EX namespace nisot {
EX transmatrix parallel_transport_bare(transmatrix Pos, hyperpoint h) {
h[3] = 0;
bool stretch = rots_twist::in();
if(!stretch) h[3] = 0;
auto tPos = transpose(Pos);
const ld eps = 1e-4;
if(sl2) {
hyperpoint p = slr::to_phigans(tPos[3]);
for(int i=0; i<3; i++)
@@ -2057,6 +2150,18 @@ EX namespace nisot {
auto& at = tPos[3];
auto& vel = h;
array<ld, 4> ms;
if(stretch) {
for(int i=0; i<3; i++) {
ms[i] = sqhypot_d(4, tPos[i]);
tPos[i] = rots_twist::isometric_to_actual(at, tPos[i]);
}
ms[3] = sqhypot_d(4, vel);
if(!ms[3]) return Pos;
vel = rots_twist::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;
@@ -2079,6 +2184,29 @@ EX namespace nisot {
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 = rots_twist::itranslate(at) * h;
h[3] = 0;
ld m1 = h[0] * h[0] + h[1] * h[1] + h[2] * h[2] * (1+rots::stretch_factor);
h /= sqrt(m1/m);
h = rots_twist::translate(at) * h;
};
if(i == 0) println(hlog, vel);
fix(vel, ms[3]);
if(i == 0) println(hlog, vel);
for(int i=0; i<3; i++) fix(tPos[i], ms[i]);
}
}
if(stretch) {
vel = rots_twist::actual_to_isometric(at, vel);
for(int i=0; i<3; i++) tPos[i] = rots_twist::actual_to_isometric(at, tPos[i]);
}
if(sl2) {
@@ -2092,6 +2220,7 @@ EX namespace nisot {
}
EX void fixmatrix(transmatrix& T) {
if(sphere) return hr::fixmatrix(T);
transmatrix push = eupush( tC0(T) );
transmatrix push_back = inverse(push);
transmatrix gtl = push_back * T;
@@ -2221,6 +2350,11 @@ EX namespace nisot {
hybrid::reconfigure();
return 0;
}
else if(argis("-rot-stretch")) {
PHASEFROM(2);
shift_arg_formula(rots::stretch_factor, ray::reset_raycaster);
return 0;
}
else if(argis("-prodturn")) {
PHASEFROM(2);
if(prod) stop_game();