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https://github.com/zenorogue/hyperrogue.git
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567 lines
15 KiB
C++
567 lines
15 KiB
C++
// Hyperbolic Rogue -- Euclidean geometry, including 2D, 3D, and quotient spaces
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// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details
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namespace hr {
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// 2D Euclidean space
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// --- euclidean geometry ---
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// NOTE: patterns assume that pair_to_vec(0,1) % 3 == 2!
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// Thus, pair_to_vec(0,1) must not be e.g. a power of four
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int pair_to_vec(int x, int y) {
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return x + (y << 15);
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}
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pair<int, int> vec_to_pair(int vec) {
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int x = vec & ((1<<15)-1);
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int y = (vec >> 15);
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if(x >= (1<<14)) x -= (1<<15), y++;
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return {x, y};
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}
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namespace torusconfig {
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// the configuration of the torus topology.
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// torus cells are indexed [0..qty),
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// where the cell to the right from i is indexed i+dx,
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// and the cell to the down-right is numbered i+dy
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// Changed with command line option: -tpar <qty>,<dx>,<dy>
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// Ideally, qty, dx, and dy should have the same "modulo 3"
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// values as the default -- otherwise the three-color
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// pattern breaks. Also, they should have no common
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// prime divisor.
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int def_qty = 127*3, dx = 1, def_dy = -11*2;
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int qty = def_qty, dy = def_dy;
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int sdx = 12, sdy = 12;
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// new values to change
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int newqty, newdy, newsdx, newsdy;
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int torus_cx, torus_cy;
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vector<torusmode_info> tmodes = {
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{"single row (hex)", TF_SINGLE | TF_HEX},
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{"single row (squares)", TF_SINGLE | TF_SQUARE},
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{"parallelogram (hex)", TF_SIMPLE | TF_HEX},
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{"rectangle (squares)", TF_SIMPLE | TF_SQUARE},
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{"rectangle (hex)", TF_WEIRD | TF_HEX},
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{"Klein bottle (squares)", TF_SIMPLE | TF_KLEIN | TF_SQUARE},
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{"Klein bottle (hex)", TF_WEIRD | TF_KLEIN | TF_HEX},
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{"cylinder (squares)", TF_SIMPLE | TF_CYL },
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{"cylinder (hex)", TF_SIMPLE | TF_CYL | TF_HEX},
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{"Möbius band (squares)", TF_SIMPLE | TF_CYL | TF_KLEIN},
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{"Möbius band (hex)", TF_SIMPLE | TF_CYL | TF_HEX | TF_KLEIN},
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};
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eTorusMode torus_mode, newmode;
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flagtype tmflags() { return tmodes[torus_mode].flags; }
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int getqty() {
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if(tmflags() & TF_SINGLE)
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return qty;
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else
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return sdx * sdy;
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}
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int getvec(int x, int y) {
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if(tmflags() & TF_SINGLE)
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return x * dx + y * dy;
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else if(tmflags() & TF_SIMPLE)
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return pair_to_vec(x, y);
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else
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return pair_to_vec(-y - 2 * x, 3 * y);
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}
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int id_to_vec(int id, bool mirrored = false) {
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if(tmflags() & TF_SINGLE)
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return id;
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else {
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int dx = id % sdx;
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int dy = id / sdx;
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if(mirrored)
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dy = -dy, dx += sdx;
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if(tmflags() & TF_SIMPLE)
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return pair_to_vec(dx, dy);
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else
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return pair_to_vec(- 2 * dx - (dy & 1), 3 * dy);
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}
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}
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pair<int, bool> vec_to_id_mirror(int vec) {
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if(tmflags() & TF_SINGLE) {
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return {gmod(vec, qty), false};
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}
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else {
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int x, y;
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tie(x,y) = vec_to_pair(vec);
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bool mirror = false;
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if(tmflags() & TF_KLEIN) {
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if(tmflags() & TF_WEIRD) {
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x = gmod(x, 4 * sdx);
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mirror = x > 0 && x <= 2 * sdx;
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}
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else {
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x = gmod(x, 2 * sdx);
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mirror = x >= sdx;
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}
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if(mirror) y = -y;
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}
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if(tmflags() & TF_WEIRD) {
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y /= 3; x = (x + (y&1)) / -2;
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}
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x = gmod(x, sdx), y = gmod(y, sdy);
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return {y * sdx + x, mirror};
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}
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}
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int vec_to_id(int vec) {
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return vec_to_id_mirror(vec).first;
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}
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void torus_test() {
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printf("Testing torus vec_to_pair/pair_to_vec...\n");
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for(int x=-10; x<=10; x++)
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for(int y=-10; y<=10; y++) {
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auto p = vec_to_pair(pair_to_vec(x, y));
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if(p.first != x || p.second != y)
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printf("Failed for (%d,%d) -> [%d] -> (%d,%d)\n", x, y, pair_to_vec(x,y), p.first, p.second);
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}
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printf("Testing id_to_vec / vec_to_id...\n");
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for(int i=0; i < getqty(); i++)
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for(int m=0; m< (torus_mode == tmKlein ? 2 : 1); m++)
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if(vec_to_id_mirror(id_to_vec(i, m)) != pair<int,bool> (i,m))
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printf("Failed for id %d.%d [%d] (%d.%d)\n", i, m, id_to_vec(i,m), vec_to_id(id_to_vec(i,m)), vec_to_id_mirror(id_to_vec(i,m)).second);
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}
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int tester = addHook(hooks_tests, 0, torus_test);
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void activate() {
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auto& gi(ginf[gTorus]);
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if(tmflags() & TF_HEX)
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gi.vertex = 3, gi.sides = 6, gi.tiling_name = "{6,3}";
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else
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gi.vertex = 4, gi.sides = 4, gi.tiling_name = "{4,4}";
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flagtype& flags = gi.flags;
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set_flag(flags, qNONORIENTABLE, tmflags() & TF_KLEIN);
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set_flag(flags, qBOUNDED, !(tmflags() & TF_CYL));
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int i = 0;
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if(tmflags() & TF_KLEIN) i++;
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if(tmflags() & TF_CYL) i+=2;
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const char *quonames[4] = {"torus", "Klein bottle", "cylinder", "Möbius band"};
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gi.quotient_name = quonames[i];
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}
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int dscalar(gp::loc e1, gp::loc e2) {
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return 2 * (e1.first * e2.first + e1.second*e2.second) + (S3 == 3 ? e1.first*e2.second + e2.first * e1.second : 0);
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}
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int dcross(gp::loc e1, gp::loc e2) {
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return e1.first * e2.second - e1.second*e2.first;
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}
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gp::loc sdxy() { return gp::loc(sdx, sdy); }
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int mobius_dir_basic() {
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int dscalars[6];
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for(int a=0; a<SG6; a++)
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dscalars[a] = dscalar(gp::eudir(a), sdxy());
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for(int a=0; a<SG6; a++)
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for(int b=0; b<SG6; b++)
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if(a != b && dscalars[a] == dscalars[b]) {
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return (a + b) % SG6;
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}
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return -1;
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}
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bool mobius_symmetric(bool square, int dx, int dy) {
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dynamicval<eGeometry> g(geometry, square ? gEuclidSquare : gEuclid);
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dynamicval<int> gx(sdx, dx);
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dynamicval<int> gy(sdy, dy);
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return mobius_dir_basic() != -1;
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}
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void mobius_flip(int&x, int& y) {
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int d = mobius_dir_basic();
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int a, b;
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if(d == 0) a = 1, b = SG6-1;
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else a = 0, b = d;
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auto p1 = gp::eudir(a);
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auto p2 = gp::eudir(b);
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// x = sdx * s + px * t
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// y = sdy * s + py * t
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// py * x = py * sdx * s + px * py * t
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// px * y = px * sdy * s + px + py * t
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// py * x - px * y = py * sdx * s - px * sdy * s
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// s = (py * x - px * y) / (py * sdx - px * sdy)
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int det = p1.second * sdx - p1.first * sdy;
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int smul = p1.second * x - p1.first * y;
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int tmul = sdx * y - sdy * x;
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x = (tmul * p2.first + smul * sdx) / det;
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y = (tmul * p2.second + smul * sdy) / det;
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// println(hlog, make_pair(ox,oy), " [", d, "] ", make_pair(x,y), " p1 = ", p1, " p2 = ", p2, " det = ", det, " smul = ", smul, " tmul = ", tmul);
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}
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int mobius_dir(cell *c) {
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if(c->type == 8) return mobius_dir_basic() * 2;
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else return mobius_dir_basic();
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}
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bool be_canonical(int& x, int& y) {
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using namespace torusconfig;
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int periods = gdiv(dscalar(gp::loc(x,y), sdxy()), dscalar(sdxy(), sdxy()));
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y -= sdy * periods;
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x -= sdx * periods;
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bool b = false;
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if(nonorientable && (periods & 1)) {
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mobius_flip(x, y);
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b = true;
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}
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return b;
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}
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int cyldist(int id1, int id2) {
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int x1, y1, x2, y2;
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tie(x1, y1) = vec_to_pair(id1);
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tie(x2, y2) = vec_to_pair(id2);
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be_canonical(x1, y1);
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be_canonical(x2, y2);
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int dist = 1000000000;
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for(int a1=-1; a1<=1; a1++)
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for(int a2=-1; a2<=1; a2++) {
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int ax1 = x1 + sdx * a1;
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int ay1 = y1 + sdy * a1;
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if(nonorientable && a1) mobius_flip(ax1, ay1);
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int ax2 = x2 + sdx * a2;
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int ay2 = y2 + sdy * a2;
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if(nonorientable && a2) mobius_flip(ax2, ay2);
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dist = min(dist, eudist(ax1 - ax2, ay1 - ay2));
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}
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return dist;
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}
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}
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int euclid_getvec(int dx, int dy) {
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if(euwrap) return torusconfig::getvec(dx, dy);
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else return pair_to_vec(dx, dy);
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}
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template<class T> void build_euclidean_moves(cell *c, int vec, const T& builder) {
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int x, y;
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tie(x,y) = vec_to_pair(vec);
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c->type = a4 ? (PURE || ((x^y^1) & 1) ? 4 : 8) : 6;
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if(c->type == 4) {
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int m = PURE ? 1 : 2;
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builder(euclid_getvec(+1,+0), 0, 2 * m);
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builder(euclid_getvec(+0,+1), 1, 3 * m);
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builder(euclid_getvec(-1,+0), 2, 0 * m);
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builder(euclid_getvec(+0,-1), 3, 1 * m);
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}
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else if(c->type == 8) {
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builder(euclid_getvec(+1,+0), 0, 2);
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builder(euclid_getvec(+1,+1), 1, 5);
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builder(euclid_getvec(+0,+1), 2, 3);
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builder(euclid_getvec(-1,+1), 3, 7);
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builder(euclid_getvec(-1,+0), 4, 0);
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builder(euclid_getvec(-1,-1), 5, 1);
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builder(euclid_getvec(+0,-1), 6, 1);
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builder(euclid_getvec(+1,-1), 7, 3);
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}
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else /* 6 */ {
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builder(euclid_getvec(+1,+0), 0, 3);
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builder(euclid_getvec(+0,+1), 1, 4);
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builder(euclid_getvec(-1,+1), 2, 5);
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builder(euclid_getvec(-1,+0), 3, 0);
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builder(euclid_getvec(+0,-1), 4, 1);
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builder(euclid_getvec(+1,-1), 5, 2);
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}
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}
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struct hrmap_torus : hrmap {
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vector<cell*> all;
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vector<int> dists;
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virtual vector<cell*>& allcells() { return all; }
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cell *gamestart() {
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return all[0];
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}
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hrmap_torus() {
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using namespace torusconfig;
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int q = getqty();
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all.resize(q);
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for(int i=0; i<q; i++) {
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all[i] = newCell(8, encodeId(i));
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}
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for(int i=0; i<q; i++) {
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int iv = id_to_vec(i);
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build_euclidean_moves(all[i], iv, [&] (int delta, int d, int d2) {
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auto im = vec_to_id_mirror(iv + delta);
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all[i]->move(d) = all[im.first];
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all[i]->c.setspin(d, im.second, false);
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});
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}
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for(cell *c: all) for(int d=0; d<c->type; d++) {
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cell *c2 = c->move(d);
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for(int d2=0; d2<c2->type; d2++)
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if(c2->move(d2) == c)
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c->c.setspin(d, d2, c->c.spin(d));
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}
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celllister cl(gamestart(), 100, 100000000, NULL);
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dists.resize(q);
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for(int i=0; i<isize(cl.lst); i++)
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dists[decodeId(cl.lst[i]->master)] = cl.dists[i];
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}
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~hrmap_torus() {
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for(cell *c: all) tailored_delete(c);
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}
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};
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hrmap_torus *torusmap() {
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return dynamic_cast<hrmap_torus*> (currentmap);
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}
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/* cell *getTorusId(int id) {
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hrmap_torus *cur = torusmap();
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if(!cur) return NULL;
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return cur->all[id];
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} */
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struct hrmap_euclidean : hrmap {
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cell *gamestart() {
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return *(euclideanAtCreate(0).first);
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}
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struct euclideanSlab {
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cell* a[256][256];
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euclideanSlab() {
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for(int y=0; y<256; y++) for(int x=0; x<256; x++)
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a[y][x] = NULL;
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}
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~euclideanSlab() {
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for(int y=0; y<256; y++) for(int x=0; x<256; x++)
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if(a[y][x]) tailored_delete(a[y][x]);
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}
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};
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static const int slabs = max_vec / 256;
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euclideanSlab* euclidean[slabs][slabs];
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hrmap_euclidean() {
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for(int y=0; y<slabs; y++) for(int x=0; x<slabs; x++)
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euclidean[y][x] = NULL;
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}
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euc_pointer at(int vec) {
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auto p = vec_to_pair(vec);
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int x = p.first, y = p.second;
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bool mobius = false;
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if(euwrap)
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mobius = torusconfig::be_canonical(x, y);
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euclideanSlab*& slab = euclidean[(y>>8)&(slabs-1)][(x>>8)&(slabs-1)];
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if(!slab) slab = new hrmap_euclidean::euclideanSlab;
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return make_pair(&(slab->a[y&255][x&255]), mobius);
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}
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map<int, struct cdata> eucdata;
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~hrmap_euclidean() {
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for(int y=0; y<slabs; y++) for(int x=0; x<slabs; x++)
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if(euclidean[y][x]) {
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tailored_delete(euclidean[y][x]);
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euclidean[y][x] = NULL;
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}
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eucdata.clear();
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}
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};
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cellwalker vec_to_cellwalker(int vec) {
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if(!fulltorus) {
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auto p = euclideanAtCreate(vec);
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if(p.second)
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return cellwalker(*p.first, torusconfig::mobius_dir(*p.first), true);
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else
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return cellwalker(*p.first, 0, false);
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}
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else {
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hrmap_torus *cur = torusmap();
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if(!cur) return cellwalker(NULL, 0);
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auto p = torusconfig::vec_to_id_mirror(vec);
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return cellwalker(cur->all[p.first], 0, p.second);
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}
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}
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int cellwalker_to_vec(cellwalker cw) {
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int id = decodeId(cw.at->master);
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if(!fulltorus) {
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if(nonorientable) {
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auto ep = euclideanAt(id);
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if(ep.second != cw.mirrored) {
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int x, y;
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tie(x, y) = vec_to_pair(id);
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x += torusconfig::sdx;
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y += torusconfig::sdy;
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torusconfig::mobius_flip(x, y);
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return pair_to_vec(x, y);
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}
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}
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return id;
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}
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return torusconfig::id_to_vec(id, cw.mirrored);
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}
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int cell_to_vec(cell *c) {
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int id = decodeId(c->master);
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if(!fulltorus) return id;
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return torusconfig::id_to_vec(id, false);
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}
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pair<int, int> cell_to_pair(cell *c) {
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return vec_to_pair(cell_to_vec(c));
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}
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union heptacoder {
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heptagon *h;
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int id;
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};
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int decodeId(heptagon* h) {
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heptacoder u;
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u.h = h; return u.id;
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}
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heptagon* encodeId(int id) {
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heptacoder u;
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u.id = id;
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return u.h;
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}
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// 3D Euclidean space
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#if MAXDIM == 4
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namespace euclid3 {
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typedef long long coord;
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struct hrmap_euclid3 : hrmap {
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map<coord, heptagon*> spacemap;
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map<heptagon*, coord> ispacemap;
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hrmap_euclid3() {
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getOrigin();
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}
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heptagon *getOrigin() {
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return get_at(0);
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}
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heptagon *get_at(coord at) {
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if(spacemap.count(at))
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return spacemap[at];
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else {
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auto h = tailored_alloc<heptagon> (6);
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h->c7 = newCell(6, h);
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h->distance = 0;
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h->cdata = NULL;
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spacemap[at] = h;
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ispacemap[h] = at;
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return h;
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}
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}
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heptagon *build(heptagon *parent, int d, coord at) {
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auto h = get_at(at);
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h->c.connect(d^1, parent, d, false);
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return h;
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}
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heptagon *createStep(heptagon *parent, int d) {
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int at = ispacemap[parent];
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coord shifttable[6] = { +1, -1, +1000, -1000, +1000000, -1000000 };
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return build(parent, d, at + shifttable[d]);
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}
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};
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hrmap_euclid3* cubemap() {
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return ((hrmap_euclid3*) currentmap);
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}
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hrmap* new_map() {
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return new hrmap_euclid3;
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}
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heptagon *createStep(heptagon *parent, int d) {
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return cubemap()->createStep(parent, d);
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}
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int getcoord(coord x, int a) {
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for(int k=0; k<a; k++) { x -= getcoord(x, 0); x /= 1000; }
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x %= 1000;
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if(x>500) x -= 1000;
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if(x<-500) x += 500;
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return x;
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}
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void draw() {
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dq::visited.clear();
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dq::enqueue(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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dynamicval<ld> b(band_shift, get<2>(p));
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bandfixer bf(V);
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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, 0, false);
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for(int i=0; i<6; i++)
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dq::enqueue(h->move(i), V * cpush(i>>1, (i&1) ? -1 : 1));
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}
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}
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transmatrix relative_matrix(heptagon *h2, heptagon *h1) {
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auto cm = cubemap();
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coord a = cm->ispacemap[h2] - cm->ispacemap[h1];
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return eupush3(getcoord(a, 0), getcoord(a, 1), getcoord(a, 2));
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}
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int celldistance(cell *c1, cell *c2) {
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auto cm = cubemap();
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coord a = cm->ispacemap[c1->master] - cm->ispacemap[c2->master];
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return getcoord(a, 0) + getcoord(a, 1) + getcoord(a, 2);
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}
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}
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#endif
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}
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