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hyperrogue/asonov.cpp

269 lines
7.4 KiB
C++

// Hyperbolic Rogue -- Arnold's cat map
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file asonov.cpp
* \brief Arnold's cat map
*/
#include "hyper.h"
//#include <cstdio>
//#include <cmath>
namespace hr {
EX namespace asonov {
#if !CAP_SOLV
#if HDR
inline bool in() { return false; }
#endif
#endif
EX int period_xy = 8;
EX int period_z = 8;
#if CAP_SOLV
EX bool in() { return cgflags & qCAT; }
EX hyperpoint tx, ty, tz;
EX transmatrix straighten;
#if HDR
struct coord: public array<int,3> {
coord() {}
coord(int x, int y, int z) : array<int,3>(make_array(zgmod(x, period_xy), zgmod(y, period_xy), zgmod(z, period_z))) {}
coord shift(int x, int y, int z=0) { return coord(self[0]+x, self[1]+y, self[2]+z); }
coord up() { return coord(self[0]*2-self[1], self[1]-self[0], self[2]+1); }
coord down() { return coord(self[0]+self[1], self[0]+self[1]*2, self[2]-1); }
coord addmove(int d);
coord operator - (coord b);
};
#endif
coord coord::addmove(int d) {
switch(d) {
case 0: return up().shift(0, 0);
case 1: return up().shift(1, -1);
case 2: return up().shift(-1, 0);
case 3: return up().shift(0, -1);
case 4: return shift(1, 0);
case 5: return shift(0, 1);
case 6: return down().shift(0, 0);
case 7: return down().shift(0, 1);
case 8: return down().shift(1, 1);
case 9: return down().shift(1, 2);
case 10: return shift(-1, 0);
case 11: return shift(0, -1);
default: throw hr_exception("error");
}
}
EX void prepare() {
using namespace hr;
transmatrix A = Id;
A[0][0] = 1;
A[0][1] = 1;
A[1][0] = 1;
A[1][1] = 2;
double det = hr::det(A);
if(det != 1) { printf("wrong det\n"); return; }
// (a00-x)(a11-x) - a01*a10 = 0
// x^2 - (a00+a11) x + 1 = 0
double b = (A[0][0] + A[1][1]) / 2;
// x^2 - 2b x + b^2 = b^2-1
// if(b*b <= 1) { printf("imaginary eigenvalues\n"); return 0; }
// x = b + sqrt(b^2-1)
hyperpoint lambda;
lambda[0] = b + sqrt(b*b-1);
lambda[1] = b - sqrt(b*b-1);
DEBB(DF_GEOM, ("b = ", b, " lambda = ", lambda));
transmatrix eigen = Id;
for(int i: {0,1}) {
eigen[0][i] = 1;
eigen[1][i] = (lambda[i] - A[0][0]) / A[0][1];
}
transmatrix ieigen = inverse(eigen);
tx = point3(ieigen[0][0], ieigen[1][0], 0) * vid.binary_width;
ty = point3(ieigen[0][1], ieigen[1][1], 0) * vid.binary_width;
tz = -point3(0, 0, log(lambda[0]));
DEBB(DF_GEOM, ("tx = ", tx, " ty = ", ty, " tz = ", tz));
straighten = inverse(build_matrix(asonov::tx/2, asonov::ty/2, asonov::tz/2, C0));
}
EX void prepare_walls() {
auto& hsh = get_hsh();
auto& cs = hsh.faces;
cs.clear();
auto pt = [&] (int x, int y, int z) { return asonov::tx*x/2 + asonov::ty*y/2 + asonov::tz*z/2 + C0; };
cs.push_back({pt(-1,-1,+1), pt(00,+1,+1), pt(+1,+1,+1)});
cs.push_back({pt(00,-1,+1), pt(+1,+1,+1), pt(+1,-1,+1)});
cs.push_back({pt(-1,+1,+1), pt(00,+1,+1), pt(-1,-1,+1)});
cs.push_back({pt(-1,-1,+1), pt(+1,+1,+1), pt(00,-1,+1)});
cs.push_back({pt(+1,-1,-1), pt(+1,00,-1), pt(+1,+1,-1), pt(+1,+1,+1), pt(+1,-1,+1)});
cs.push_back({pt(-1,+1,-1), pt(-1,+1,+1), pt(00,+1,+1), pt(+1,+1,+1), pt(+1,+1,-1)});
cs.push_back({pt(-1,-1,-1), pt(-1,00,-1), pt(+1,-1,-1)});
cs.push_back({pt(-1,00,-1), pt(-1,+1,-1), pt(+1,-1,-1)});
cs.push_back({pt(-1,+1,-1), pt(+1,00,-1), pt(+1,-1,-1)});
cs.push_back({pt(-1,+1,-1), pt(+1,+1,-1), pt(+1,00,-1)});
cs.push_back({pt(-1,+1,-1), pt(-1,00,-1), pt(-1,-1,-1), pt(-1,-1,+1), pt(-1,+1,+1)});
cs.push_back({pt(+1,-1,-1), pt(+1,-1,+1), pt(00,-1,+1), pt(-1,-1,+1), pt(-1,-1,-1)});
hsh.compute_hept();
}
transmatrix coord_to_matrix(coord c, coord zero) {
transmatrix T = Id;
while(zero[2] != c[2]) {
int z = szgmod(c[2] - zero[2], period_z);
if(z > 0) zero = zero.up(), T = eupush(tz) * eupush(ty/2) * T;
else zero = zero.down(), T = eupush(-ty/2) * eupush(-tz) * T;
}
return T * eupush(tx * szgmod(c[0]-zero[0], period_xy) + ty * szgmod(c[1]-zero[1], period_xy));
}
coord coord::operator - (coord b) {
auto c = self;
while(b[2]) {
int z = szgmod(b[2], period_z);
if(z > 0) b = b.down(), c = c.down();
else if(z < 0) b = b.up(), c = c.up();
}
c[0] = zgmod(c[0]-b[0], period_xy); b[0] = 0;
c[1] = zgmod(c[1]-b[1], period_xy); b[1] = 0;
return c;
}
EX transmatrix adjmatrix(int i) {
dynamicval<int> pxy(period_xy, 64);
dynamicval<int> pz(period_z, 64);
coord zero(0,0,0);
coord c = zero.addmove(i);
return coord_to_matrix(c, zero);
}
struct hrmap_asonov : hrmap {
map<coord, heptagon*> at;
map<heptagon*, coord> coords;
heptagon *getOrigin() override { return get_at(coord(0,0,0)); }
hrmap_asonov() { prepare(); }
~hrmap_asonov() {
for(auto& p: at) clear_heptagon(p.second);
}
heptagon *get_at(coord c) {
auto& h = at[c];
if(h) return h;
h = init_heptagon(S7);
h->c7 = newCell(S7, h);
coords[h] = c;
h->distance = c[2];
h->zebraval = c[0];
h->emeraldval = c[1];
return h;
}
heptagon *create_step(heptagon *parent, int d) override {
auto p = coords[parent];
auto q = p.addmove(d);
auto child = get_at(q);
parent->c.connect(d, child, (d + 6) % 12, 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);
return coord_to_matrix(coords[h2], coords[h1]);
}
};
EX hrmap *new_map() { return new hrmap_asonov; }
EX coord get_coord(heptagon *h) { return ((hrmap_asonov*)currentmap)->coords[h]; }
EX heptagon *get_at(coord where) { return ((hrmap_asonov*)currentmap)->at[where]; }
EX int period_xy_edit, period_z_edit;
EX void set_flags() {
auto& flag = ginf[gArnoldCat].flags;
set_flag(flag, qANYQ, period_xy || period_z);
set_flag(flag, qCLOSED, period_xy && period_z);
set_flag(flag, qSMALL, period_xy && period_z && (period_xy * period_xy * period_z <= 4096));
set_flag(flag, qHUGE_BOUNDED, period_xy * period_xy * period_z > 16384);
}
EX void prepare_config() {
period_xy_edit = period_xy;
period_z_edit = period_z;
}
EX void show_config() {
cmode = sm::SIDE | sm::MAYDARK;
gamescreen();
dialog::init(XLAT("Solv quotient spaces"));
dialog::addSelItem(XLAT("%1 period", "X/Y"), its(period_xy_edit), 'x');
dialog::add_action([=] {
dialog::editNumber(period_xy_edit, 0, 64, 1, 0, XLAT("%1 period", "X/Y"),
XLAT("Note: the value 0 functions effectively as the size of int (2^32).")
);
dialog::bound_low(0);
});
dialog::addSelItem(XLAT("%1 period", "Z"), its(period_z_edit), 'z');
dialog::add_action([=] {
dialog::editNumber(period_z_edit, 0, 64, 1, 0, XLAT("%1 period", "Z"),
XLAT("Set to 0 to make it non-periodic.")
);
dialog::bound_low(0);
});
dialog::addBreak(50);
dialog::addItem(XLAT("activate"), 'a');
dialog::add_action([] {
stop_game();
period_xy = period_xy_edit;
period_z = period_z_edit;
set_flags();
geometry = gArnoldCat;
start_game();
});
dialog::addBreak(50);
dialog::addBack();
dialog::display();
}
#endif
}
}