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new tiling: Arnold's cat
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Zeno Rogue
239
asonov.cpp
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239
asonov.cpp
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// Hyperbolic Rogue -- Arnold's cat map
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// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
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/** \file asonov.cpp
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* \brief Arnold's cat map
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*/
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#include "hyper.h"
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//#include <cstdio>
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//#include <cmath>
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namespace hr {
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EX namespace asonov {
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EX hyperpoint tx, ty, tz;
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EX int period_xy = 8;
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EX int period_z = 8;
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struct coord: public array<int,3> {
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coord() {}
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coord(int x, int y, int z) : array<int,3>(make_array(zgmod(x, period_xy), zgmod(y, period_xy), zgmod(z, period_z))) {}
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coord shift(int x, int y, int z=0) { return coord(self[0]+x, self[1]+y, self[2]+z); }
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coord up() { return coord(self[0]*2-self[1], self[1]-self[0], self[2]+1); }
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coord down() { return coord(self[0]+self[1], self[0]+self[1]*2, self[2]-1); }
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coord addmove(int d) {
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switch(d) {
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case 0: return up().shift(0, 0);
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case 1: return up().shift(1, -1);
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case 2: return up().shift(-1, 0);
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case 3: return up().shift(0, -1);
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case 4: return shift(1, 0);
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case 5: return shift(0, 1);
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case 6: return down().shift(0, 0);
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case 7: return down().shift(0, 1);
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case 8: return down().shift(1, 1);
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case 9: return down().shift(1, 2);
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case 10: return shift(-1, 0);
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case 11: return shift(0, -1);
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default: throw "error";
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}
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}
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};
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EX void prepare() {
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using namespace hr;
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transmatrix A = Id;
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A[0][0] = 1;
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A[0][1] = 1;
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A[1][0] = 1;
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A[1][1] = 2;
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static bool first = true;
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if(first) println(hlog, "amain");
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// if(true) {
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double det = hr::det(A);
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if(det != 1) { printf("wrong det\n"); return; }
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// (a00-x)(a11-x) - a01*a10 = 0
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// x^2 - (a00+a11) x + 1 = 0
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double b = (A[0][0] + A[1][1]) / 2;
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// x^2 - 2b x + b^2 = b^2-1
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// if(b*b <= 1) { printf("imaginary eigenvalues\n"); return 0; }
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// x = b + sqrt(b^2-1)
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hyperpoint lambda;
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lambda[0] = b + sqrt(b*b-1);
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lambda[1] = b - sqrt(b*b-1);
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if(first) println(hlog, "lambda = ", lambda);
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transmatrix eigen = Id;
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for(int i: {0,1}) {
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eigen[0][i] = 1;
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eigen[1][i] = (lambda[i] - A[0][0]) / A[0][1];
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}
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if(first) println(hlog, "eigen = ", eigen);
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if(first) println(hlog, "A*eigen = ", A*eigen);
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transmatrix ieigen = inverse(eigen);
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if(first) println(hlog, "ieigen = ", ieigen);
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if(first) println(hlog, "ieigen*A = ", ieigen * A);
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tx = point3(ieigen[0][0], ieigen[1][0], 0);
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ty = point3(ieigen[0][1], ieigen[1][1], 0);
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tz = -point3(0, 0, log(lambda[0]));
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println(hlog, "tx = ", tx);
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println(hlog, "ty = ", ty);
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println(hlog, "tz = ", tz);
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for(int a=0; a<12; a++) {
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int b = (a+6) % 12;
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coord test(1, 10, 100);
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auto test1 = test.addmove(a).addmove(b);
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println(hlog, test == test1 ? "OK" : "BAD", " : ", test, " vs ", test1, " ## ", test.addmove(a));
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}
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}
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struct hrmap_asonov : hrmap {
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unordered_map<coord, heptagon*> at;
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unordered_map<heptagon*, coord> coords;
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heptagon *getOrigin() override { return get_at(coord(0,0,0)); }
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hrmap_asonov() { prepare(); }
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~hrmap_asonov() {
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for(auto& p: at) clear_heptagon(p.second);
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}
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heptagon *get_at(coord c) {
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auto& h = at[c];
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if(h) return h;
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h = tailored_alloc<heptagon> (S7);
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h->c7 = newCell(S7, h);
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coords[h] = c;
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h->dm4 = 0;
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h->distance = c[2];
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h->zebraval = c[0];
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h->emeraldval = c[1];
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h->cdata = NULL;
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h->alt = NULL;
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return h;
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}
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heptagon *create_step(heptagon *parent, int d) override {
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auto p = coords[parent];
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auto q = p.addmove(d);
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auto child = get_at(q);
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parent->c.connect(d, child, (d + 6) % 12, false);
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return child;
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}
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transmatrix adjmatrix(int i) {
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coord c = coord(0,0,0).addmove(i);
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if(c[0] > period_xy/2) c[0] -= period_xy;
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if(c[1] > period_xy/2) c[1] -= period_xy;
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if(c[2] > period_z/2) c[2] -= period_z;
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transmatrix T = eupush(tz * c[2]) * eupush(tx * c[0] + ty * c[1]);;
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if(i < 4) return T * eupush(ty/2);
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if(i >= 6 && i < 10) return eupush(-ty/2) * T;
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return T;
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}
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virtual transmatrix relative_matrix(heptagon *h2, heptagon *h1) override {
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for(int a=0; a<S7; a++) if(h2 == h1->move(a)) return adjmatrix(a);
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return Id;
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}
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void draw() override {
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dq::visited_by_matrix.clear();
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dq::enqueue_by_matrix(viewctr.at, cview());
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while(!dq::drawqueue.empty()) {
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auto& p = dq::drawqueue.front();
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heptagon *h = get<0>(p);
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transmatrix V = get<1>(p);
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dq::drawqueue.pop();
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cell *c = h->c7;
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if(!do_draw(c, V)) continue;
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drawcell(c, V);
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if(wallopt && isWall3(c) && isize(dq::drawqueue) > 1000) continue;
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for(int i=0; i<S7; i++)
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dq::enqueue_by_matrix(h->cmove(i), V * adjmatrix(i));
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}
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}
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};
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EX hrmap *new_map() { return new hrmap_asonov; }
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EX int period_xy_edit, period_z_edit;
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EX void set_flags() {
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auto& flag = ginf[gArnoldCat].flags;
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set_flag(flag, qANYQ, period_xy || period_z);
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set_flag(flag, qBOUNDED, period_xy && period_z);
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set_flag(flag, qSMALL, period_xy && period_z && (period_xy * period_xy * period_z <= 4096));
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}
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EX void prepare_config() {
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period_xy_edit = period_xy;
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period_z_edit = period_z;
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}
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EX void show_config() {
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cmode = sm::SIDE | sm::MAYDARK;
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gamescreen(1);
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dialog::init(XLAT("Solv quotient spaces"));
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dialog::addSelItem(XLAT("%1 period", "X/Y"), its(period_xy_edit), 'x');
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dialog::add_action([=] {
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dialog::editNumber(period_xy_edit, 0, 64, 1, 0, XLAT("%1 period", "X/Y"),
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XLAT("Note: the value 0 functions effectively as the size of int (2^32).")
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);
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dialog::bound_low(0);
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});
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dialog::addSelItem(XLAT("%1 period", "Z"), its(period_z_edit), 'z');
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dialog::add_action([=] {
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dialog::editNumber(period_z_edit, 0, 64, 1, 0, XLAT("%1 period", "Z"),
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XLAT("Set to 0 to make it non-periodic.")
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);
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dialog::bound_low(0);
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});
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dialog::addBreak(50);
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dialog::addItem(XLAT("activate"), 'a');
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dialog::add_action([] {
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stop_game();
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period_xy = period_xy_edit;
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period_z = period_z_edit;
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set_flags();
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geometry = gArnoldCat;
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start_game();
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});
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dialog::addBreak(50);
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dialog::addBack();
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dialog::display();
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}
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}
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}
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