mirror of
https://github.com/zenorogue/hyperrogue.git
synced 2024-11-30 23:49:53 +00:00
337 lines
9.5 KiB
C++
337 lines
9.5 KiB
C++
// This generates the 'solv-geodesics.dat' file.
|
|
// You may change the _PREC* values for more precise geodesics.
|
|
|
|
#include "../hyper.h"
|
|
|
|
#include <thread>
|
|
#include <mutex>
|
|
|
|
namespace hr {
|
|
|
|
const int _PRECX = 64;
|
|
const int _PRECY = 64;
|
|
const int _PRECZ = 64;
|
|
|
|
transmatrix parabolic1(ld u);
|
|
|
|
namespace solv {
|
|
|
|
typedef hyperpoint pt;
|
|
typedef array<float, 3> ptlow;
|
|
|
|
ptlow be_low(pt x) { return ptlow({float(x[0]), float(x[1]), float(x[2])}); }
|
|
|
|
template<class T> void parallelize(int threads, int Nmin, int Nmax, T action) {
|
|
std::vector<std::thread> v;
|
|
for(int k=0; k<threads; k++)
|
|
v.emplace_back([&,k] () {
|
|
for(int i=Nmin+k; i < Nmax; i += threads) action(k, i);
|
|
});
|
|
for(std::thread& t:v) t.join();
|
|
}
|
|
|
|
hyperpoint sol1(pt v) {
|
|
auto [x,y,z,t] = (array<ld,4>&) v;
|
|
if(x == 0 && z == 0) return C0;
|
|
hyperpoint h = parabolic1(x) * xpush(-z) * C0;
|
|
ld d = acosh(h[2]) / sqrt(h[0] * h[0] + h[1] * h[1]);
|
|
return hyperpoint({h[1]*d, 0, -h[0]*d,1});
|
|
}
|
|
|
|
hyperpoint sol2(pt v) {
|
|
auto [x,y,z,t] = (array<ld,4>&) v;
|
|
if(y == 0 && z == 0) return C0;
|
|
hyperpoint h = parabolic1(y) * xpush(z) * C0;
|
|
ld d = acosh(h[2]) / sqrt(h[0] * h[0] + h[1] * h[1]);
|
|
return hyperpoint({0, h[1]*d, +h[0]*d,1});
|
|
}
|
|
|
|
ld x_to_ix(ld u);
|
|
|
|
ld solerror(pt ok, pt chk) {
|
|
auto zok = point3( x_to_ix(ok[0]), x_to_ix(ok[1]), tanh(ok[2]) );
|
|
auto zchk = point3( x_to_ix(chk[0]), x_to_ix(chk[1]), tanh(chk[2]) );
|
|
return hypot_d(3, zok - zchk);
|
|
}
|
|
|
|
ld eucerror(pt ok, pt chk) {
|
|
return pow(ok[0]-chk[0], 2) + pow(ok[1]-chk[1], 2) + pow(ok[2]-chk[2], 2);
|
|
}
|
|
|
|
pt iterative_solve(pt xp, pt candidate, int prec, ld minerr, bool debug = false) {
|
|
|
|
transmatrix T = Id; T[0][1] = 8; T[2][2] = 5;
|
|
|
|
auto f = [&] (hyperpoint x) { return nisot::numerical_exp(x, prec); }; // T * x; };
|
|
|
|
auto ver = f(candidate);
|
|
ld err = solerror(xp, ver);
|
|
auto at = candidate;
|
|
|
|
ld eps = 1e-6;
|
|
|
|
pt c[3];
|
|
for(int a=0; a<3; a++) c[a] = point3(a==0, a==1, a==2);
|
|
|
|
while(err > minerr) {
|
|
if(debug) println(hlog, "\n\nf(", at, "?) = ", ver, " (error ", err, ")");
|
|
array<hyperpoint, 3> pnear;
|
|
for(int a=0; a<3; a++) {
|
|
auto x = at + c[a] * eps;
|
|
if(debug) println(hlog, "f(", x, ") = ", f(x), " = y + ", f(x)-ver );
|
|
pnear[a] = (f(x) - ver) / eps; // (direct_exp(at + c[a] * eps, prec) - ver) / eps;
|
|
}
|
|
|
|
transmatrix U = Id;
|
|
for(int a=0; a<3; a++)
|
|
for(int b=0; b<3; b++)
|
|
U[a][b] = pnear[b][a];
|
|
|
|
hyperpoint diff = (xp - ver);
|
|
|
|
hyperpoint bonus = inverse(U) * diff;
|
|
|
|
if(hypot_d(3, bonus) > 0.1) bonus = bonus * 0.1 / hypot_d(3, bonus);
|
|
|
|
int fixes = 0;
|
|
|
|
if(debug)
|
|
println(hlog, "\nU = ", U, "\ndiff = ", diff, "\nbonus = ", bonus, "\n");
|
|
|
|
nextfix:
|
|
hyperpoint next = at + bonus;
|
|
hyperpoint nextver = f(next);
|
|
ld nexterr = solerror(xp, nextver);
|
|
if(debug) println(hlog, "f(", next, ") = ", nextver, ", error = ", nexterr);
|
|
|
|
if(nexterr < err) {
|
|
// println(hlog, "reduced error ", err, " to ", nexterr);
|
|
at = next;
|
|
ver = nextver;
|
|
err = nexterr;
|
|
continue;
|
|
}
|
|
else {
|
|
bonus /= 2;
|
|
fixes++;
|
|
if(fixes > 10) {
|
|
if(err > 999) {
|
|
for(ld s = 1; abs(s) > 1e-9; s *= 0.5)
|
|
for(int k=0; k<27; k++) {
|
|
int kk = k;
|
|
next = at;
|
|
for(int i=0; i<3; i++) { if(kk%3 == 1) next[i] += s; if(kk%3 == 2) next[i] -= s; kk /= 3; }
|
|
// next = at + c[k] * s;
|
|
nextver = f(next);
|
|
nexterr = solerror(xp, nextver);
|
|
// println(hlog, "f(", next, ") = ", nextver, ", error = ", nexterr);
|
|
if(nexterr < err) { at = next; ver = nextver; err = nexterr; goto nextiter; }
|
|
}
|
|
println(hlog, "cannot improve error ", err);
|
|
exit(1);
|
|
}
|
|
break;
|
|
}
|
|
goto nextfix;
|
|
}
|
|
|
|
nextiter: ;
|
|
}
|
|
|
|
return at;
|
|
}
|
|
|
|
ptlow solution[_PRECZ][_PRECY][_PRECX];
|
|
|
|
ptlow mlow(ld x, ld y, ld z) { return ptlow({float(x), float(y), float(z)}); }
|
|
|
|
pt atxyz(ld x, ld y, ld z) { return hyperpoint({x, y, z, 1}); }
|
|
|
|
ptlow operator +(ptlow a, ptlow b) { return mlow(a[0]+b[0], a[1]+b[1], a[2]+b[2]); }
|
|
ptlow operator -(ptlow a, ptlow b) { return mlow(a[0]-b[0], a[1]-b[1], a[2]-b[2]); }
|
|
ptlow operator *(ptlow a, ld x) { return mlow(a[0]*x, a[1]*x, a[2]*x); }
|
|
|
|
ptlow can(pt x) {
|
|
// azimuthal equidistant to Klein
|
|
ld r = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
|
|
if(r == 0) return mlow(0,0,0);
|
|
ld make_r = tanh(r);
|
|
ld d = make_r / r;
|
|
return mlow(x[0]*d, x[1]*d, x[2]*d);
|
|
}
|
|
|
|
pt uncan(ptlow x) {
|
|
ld r = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
|
|
if(r == 0) return atxyz(0,0,0);
|
|
ld make_r = atanh(r);
|
|
if(r == 1) make_r = 30;
|
|
ld d = make_r / r;
|
|
return atxyz(x[0]*d, x[1]*d, x[2]*d);
|
|
}
|
|
|
|
pt uncan_info(ptlow x) {
|
|
ld r = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
|
|
println(hlog, "r = ", r);
|
|
if(r == 0) return atxyz(0,0,0);
|
|
ld make_r = atanh(r);
|
|
println(hlog, "make_r = ", make_r);
|
|
ld d = make_r / r;
|
|
println(hlog, "d = ", d);
|
|
return atxyz(x[0]*d, x[1]*d, x[2]*d);
|
|
}
|
|
|
|
void fint(FILE *f, int x) { fwrite(&x, sizeof(x), 1, f); }
|
|
void ffloat(FILE *f, float x) { fwrite(&x, sizeof(x), 1, f); }
|
|
|
|
void write_table(const char *fname) {
|
|
FILE *f = fopen(fname, "wb");
|
|
fint(f, _PRECX);
|
|
fint(f, _PRECY);
|
|
fint(f, _PRECZ);
|
|
fwrite(solution, sizeof(solution), 1, f);
|
|
fclose(f);
|
|
}
|
|
|
|
void load_table(const char *fname) {
|
|
int s;
|
|
FILE *f = fopen(fname, "rb");
|
|
fread(&s, 4, 1, f);
|
|
fread(&s, 4, 1, f);
|
|
fread(&s, 4, 1, f);
|
|
fread(solution, sizeof(solution), 1, f);
|
|
fclose(f);
|
|
}
|
|
|
|
ld ix_to_x(ld ix) {
|
|
ld minx = 0, maxx = 1;
|
|
for(int it=0; it<100; it++) {
|
|
ld x = (minx + maxx) / 2;
|
|
if(x_to_ix(atanh(x)) < ix) minx = x;
|
|
else maxx = x;
|
|
}
|
|
return atanh(minx);
|
|
}
|
|
|
|
ld iz_to_z(ld z) {
|
|
return atanh(z); // atanh(z * 2 - 1);
|
|
}
|
|
|
|
ld z_to_iz(ld z) {
|
|
return tanh(z); // (tanh(z) + 1) / 2;
|
|
}
|
|
|
|
int last_x = _PRECX-1, last_y = _PRECY-1, last_z = _PRECZ-1;
|
|
|
|
ld ptd(ptlow p) {
|
|
return p[0]*p[0] + p[1]*p[1] + p[2] * p[2];
|
|
}
|
|
|
|
ptlow zflip(ptlow x) { return mlow(x[1], x[0], -x[2]); }
|
|
|
|
void build_sols() {
|
|
std::mutex file_mutex;
|
|
ld max_err = 0;
|
|
auto act = [&] (int tid, int iz) {
|
|
|
|
auto solve_at = [&] (int ix, int iy) {
|
|
ld x = ix_to_x(ix / (_PRECX-1.));
|
|
ld y = ix_to_x(iy / (_PRECY-1.));
|
|
ld z = iz_to_z(iz / (_PRECZ-1.));
|
|
|
|
auto v = hyperpoint ({x,y,z,1});
|
|
|
|
vector<pt> candidates;
|
|
pt cand;
|
|
|
|
candidates.push_back(atxyz(0,0,0));
|
|
|
|
static constexpr int prec = 100;
|
|
|
|
// sort(candidates.begin(), candidates.end(), [&] (pt a, pt b) { return solerror(v, direct_exp(a, prec)) > solerror(v, direct_exp(b, prec)); });
|
|
|
|
// cand_best = candidates.back();
|
|
|
|
vector<pt> solved_candidates;
|
|
|
|
for(auto c: candidates) {
|
|
auto solt = iterative_solve(v, c, prec, 1e-6);
|
|
solved_candidates.push_back(solt);
|
|
if(solerror(v, nisot::numerical_exp(solt, prec)) < 1e-9) break;
|
|
}
|
|
|
|
sort(solved_candidates.begin(), solved_candidates.end(), [&] (pt a, pt b) { return solerror(v, nisot::numerical_exp(a, prec)) > solerror(v, nisot::numerical_exp(b, prec)); });
|
|
|
|
cand = solved_candidates.back();
|
|
|
|
auto xerr = solerror(v, nisot::numerical_exp(cand, prec));
|
|
|
|
if(xerr > 1e-3) {
|
|
println(hlog, format("[%2d %2d %2d] ", iz, iy, ix));
|
|
println(hlog, "f(?) = ", v);
|
|
println(hlog, "f(", cand, ") = ", nisot::numerical_exp(cand, prec));
|
|
println(hlog, "error = ", xerr);
|
|
println(hlog, "canned = ", can(cand));
|
|
max_err = xerr;
|
|
hyperpoint h1 = uncan(solution[iz][iy-1][ix]);
|
|
hyperpoint h2 = uncan(solution[iz][iy][ix-1]);
|
|
hyperpoint h3 = uncan(solution[iz][iy-1][ix-1]);
|
|
hyperpoint h4 = h1 + h2 - h3;
|
|
solution[iz][iy][ix] = can(h4);
|
|
return;
|
|
}
|
|
|
|
solution[iz][iy][ix] = can(cand);
|
|
|
|
for(int z=0; z<3; z++) if(isnan(solution[iz][iy][ix][z]) || isinf(solution[iz][iy][ix][z])) {
|
|
println(hlog, cand, "canned to ", solution[iz][iy][ix]);
|
|
exit(4);
|
|
}
|
|
};
|
|
|
|
for(int it=0; it<max(last_x, last_y); it++) {
|
|
for(int a=0; a<it; a++) {
|
|
if(it < last_x && a < last_y) solve_at(it, a);
|
|
if(a < last_x && it < last_y) solve_at(a, it);
|
|
}
|
|
if(it < last_x && it < last_y) solve_at(it, it);
|
|
std::lock_guard<std::mutex> fm(file_mutex);
|
|
println(hlog, format("%2d: %2d", iz, it));
|
|
}
|
|
};
|
|
|
|
parallelize(last_z, 0, last_z, act);
|
|
|
|
for(int x=0; x<last_x; x++)
|
|
for(int y=0; y<last_y; y++) {
|
|
for(int z=last_z; z<_PRECZ; z++)
|
|
solution[z][y][x] = solution[z-1][y][x] * 2 - solution[z-2][y][x];
|
|
}
|
|
|
|
for(int x=0; x<last_x; x++)
|
|
for(int y=last_y; y<_PRECY; y++)
|
|
for(int z=0; z<_PRECZ; z++)
|
|
solution[z][y][x] = solution[z][y-1][x] * 2 - solution[z][y-2][x];
|
|
|
|
for(int x=last_x; x<_PRECX; x++)
|
|
for(int y=0; y<_PRECY; y++)
|
|
for(int z=0; z<_PRECZ; z++)
|
|
solution[z][y][x] = solution[z][y][x-1] * 2 - solution[z][y][x-2];
|
|
}
|
|
|
|
int main(int argc, char **argv) {
|
|
|
|
println(hlog);
|
|
|
|
geometry = gSol;
|
|
|
|
build_sols();
|
|
write_table("solv-geodesics-generated.dat");
|
|
|
|
exit(0);
|
|
}
|
|
|
|
int phooks = addHook(hooks_main, 0, main);
|
|
|
|
}
|
|
}
|