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hyperrogue/reg3.cpp
2019-09-12 22:38:43 +02:00

459 lines
14 KiB
C++

// Hyperbolic Rogue -- regular honeycombs
// works with spherical and hyperbolic ones -- Euclidean cubic tiling implemented in euclid.cpp
// hyperbolic honeycombs rely on binary:: to deal with floating point errors (just like archimedean)
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
namespace hr {
#if MAXMDIM >= 4
transmatrix cpush(int cid, ld alpha);
transmatrix cspin(int a, int b, ld alpha);
extern
vector<hpcshape> shWall3D, shMiniWall3D;
namespace binary {
void build_tmatrix();
void virtualRebaseSimple(heptagon*& base, transmatrix& at);
int celldistance3(heptagon *c1, heptagon *c2);
hyperpoint deparabolic3(hyperpoint h);
}
namespace reg3 {
int loop, face;
vector<hyperpoint> cellshape;
transmatrix spins[12], adjmoves[12];
template<class T> ld binsearch(ld dmin, ld dmax, const T& f) {
for(int i=0; i<200; i++) {
ld d = (dmin + dmax) / 2;
if(f(d)) dmax = d;
else dmin = d;
}
return dmin;
}
void generate() {
using namespace hyperpoint_vec;
if(S7 == 4) face = 3;
if(S7 == 6) face = 4;
if(S7 == 12) face = 5;
if(S7 == 8) face = 3;
/* icosahedron not implemented */
loop = ginf[geometry].tiling_name[5] - '0';
println(hlog, "face = ", face, " loop = ", loop, " S7 = ", S7);
ld dual_angle = binsearch(0, M_PI, [&] (ld d) {
hyperpoint h0 = cpush(0, 1) * C0;
hyperpoint h1 = cspin(0, 1, d) * h0;
hyperpoint h2 = cspin(1, 2, 2*M_PI/loop) * h1;
return hdist(h0, h1) > hdist(h1, h2);
});
ld dodecahedron_angle = binsearch(0, M_PI, [&] (ld d) {
hyperpoint h0 = cpush(0, 1) * C0;
hyperpoint h1 = cspin(0, 1, d) * h0;
hyperpoint h2 = cspin(1, 2, 2*M_PI/face) * h1;
return hdist(h0, h1) > hdist(h1, h2);
});
if(S7 == 8) {
/* 24-cell is a special case because it is the only one with '4' in the middle of the Schlaefli symbol. */
/* The computations above assume 3 */
hyperpoint h1 = hpxy3(.5,.5,.5);
hyperpoint h2 = hpxy3(.5,.5,-.5);
dual_angle = hdist(h1, h2);
}
println(hlog, "dodecahedron angle = ", dodecahedron_angle);
println(hlog, "dual angle = ", dual_angle);
ld inp_length = binsearch(0, 1.55, [&] (ld d) {
hyperpoint h = xpush(-d) * spin(2*M_PI/face) * xpush0(d);
ld alpha = M_PI - atan2(-h[1], h[0]);
return (alpha < dual_angle / 2) ? hyperbolic : sphere;
});
println(hlog, "inp length = ", inp_length);
ld edge_length = hdist(xpush0(inp_length), spin(2*M_PI/face) * xpush0(inp_length));
if(S7 == 8) edge_length = hdist(normalize(hpxyz3(1,1,0,0)), normalize(hpxyz3(1,0,1,0)));
println(hlog, "edge length = ", edge_length);
hyperpoint h0 = cpush(0, 1) * C0;
hyperpoint h1 = cspin(0, 1, dodecahedron_angle) * h0;
hyperpoint h2 = cspin(1, 2, 2*M_PI/face) * h1;
hyperpoint h3 = cspin(1, 2, -2*M_PI/face) * h1;
hyperpoint a2 = S7 == 8 ? normalize(h1 + h2) : normalize(h0 + h1 + h2);
hyperpoint a3 = S7 == 8 ? normalize(h1 + h3) : normalize(h0 + h1 + h3);
println(hlog, "S7 = ", S7);
ld whereonline = binsearch(0, 5, [&] (ld d) {
// sometimes breaks in elliptic
dynamicval<eGeometry> g(geometry, elliptic ? gCell120 : geometry);
hyperpoint z2 = a2 * d + C0 * (1-d);
if(hyperbolic && intval(z2, Hypc) >= 0) return true;
hyperpoint b2 = normalize(z2);
hyperpoint z3 = a3 * d + C0 * (1-d);
hyperpoint b3 = normalize(z3);
return hdist(b2, b3) >= edge_length;
});
println(hlog, "whereonline = ", whereonline);
a2 = normalize(a2 * whereonline + C0 * (1-whereonline));
a3 = normalize(a3 * whereonline + C0 * (1-whereonline));
hyperpoint mid = Hypc;
for(int i=0; i<face; i++) mid += cspin(1, 2, 2*i*M_PI/face) * a2;
mid = normalize(mid);
ld between_centers = 2 * hdist0(mid);
println(hlog, "between_centers = ", between_centers);
if(S7 == 12 || S7 == 8) {
spins[0] = Id;
spins[1] = cspin(0, 1, dodecahedron_angle) * cspin(1, 2, M_PI);
for(int a=2; a<face+1; a++) spins[a] = cspin(1, 2, 2*M_PI*(a-1)/face) * spins[1];
for(int a=S7/2; a<S7; a++) spins[a] = cspin(0, 1, M_PI) * spins[a-S7/2];
}
if(S7 == 6) {
spins[0] = Id;
spins[1] = cspin(0, 1, dodecahedron_angle) * cspin(1, 2, M_PI);
spins[2] = cspin(1, 2, M_PI/2) * spins[1];
for(int a=S7/2; a<S7; a++) spins[a] = spins[a-S7/2] * cspin(0, 1, M_PI);
}
if(S7 == 4) {
spins[0] = Id;
spins[1] = cspin(0, 1, dodecahedron_angle) * cspin(1, 2, M_PI);
for(int a=2; a<face+1; a++) spins[a] = cspin(1, 2, 2*M_PI*(a-1)/face) * spins[1];
}
cellshape.clear();
for(int a=0; a<S7; a++)
for(int b=0; b<face; b++)
cellshape.push_back(spins[a] * cspin(1, 2, 2*M_PI*b/face) * a2);
adjmoves[0] = cpush(0, between_centers) * cspin(0, 2, M_PI);
for(int i=1; i<S7; i++) adjmoves[i] = spins[i] * adjmoves[0];
for(int a=0; a<S7; a++)
println(hlog, "center of ", a, " is ", tC0(adjmoves[a]));
println(hlog, "doublemove = ", tC0(adjmoves[0] * adjmoves[0]));
// exit(1);
}
void binary_rebase(heptagon *h, const transmatrix& V) {
}
void test();
struct hrmap_reg3 : hrmap {
heptagon *origin;
hrmap *binary_map;
unordered_map<heptagon*, pair<heptagon*, transmatrix>> reg_gmatrix;
unordered_map<heptagon*, vector<pair<heptagon*, transmatrix> > > altmap;
hrmap_reg3() {
generate();
origin = tailored_alloc<heptagon> (S7);
heptagon& h = *origin;
h.s = hsOrigin;
h.cdata = NULL;
h.alt = NULL;
h.distance = 0;
h.c7 = newCell(S7, origin);
worst_error1 = 0, worst_error2 = 0;
dynamicval<hrmap*> cr(currentmap, this);
heptagon *alt = NULL;
transmatrix T = Id;
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gBinary3);
binary::build_tmatrix();
alt = tailored_alloc<heptagon> (S7);
alt->s = hsOrigin;
alt->emeraldval = 0;
alt->zebraval = 0;
alt->distance = 0;
alt->alt = alt;
alt->cdata = NULL;
binary_map = newAltMap(alt);
T = xpush(.01241) * spin(1.4117) * xpush(0.1241) * cspin(0, 2, 1.1249) * xpush(0.07) * Id;
}
reg_gmatrix[origin] = make_pair(alt, T);
altmap[alt].emplace_back(origin, T);
}
ld worst_error1, worst_error2;
heptagon *getOrigin() {
return origin;
}
#define DEB 0
heptagon *createStep(heptagon *parent, int d) {
auto& p1 = reg_gmatrix[parent];
if(DEB) println(hlog, "creating step ", parent, ":", d, ", at ", p1.first, tC0(p1.second));
heptagon *alt = p1.first;
transmatrix T = p1.second * adjmoves[d];
transmatrix T1 = T;
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gBinary3);
binary::virtualRebaseSimple(alt, T);
}
fixmatrix(T);
auto hT = tC0(T);
if(DEB) println(hlog, "searching at ", alt, ":", hT);
if(DEB) for(auto& p2: altmap[alt]) println(hlog, "for ", tC0(p2.second), " intval is ", intval(tC0(p2.second), hT));
ld err;
for(auto& p2: altmap[alt]) if((err = intval(tC0(p2.second), hT)) < 1e-3) {
if(err > worst_error1) println(hlog, format("worst_error1 = %lg", double(worst_error1 = err)));
// println(hlog, "YES found in ", isize(altmap[alt]));
if(DEB) println(hlog, "-> found ", p2.first);
int fb = 0;
hyperpoint old = T * (inverse(T1) * tC0(p1.second));
for(int d2=0; d2<S7; d2++) {
hyperpoint back = p2.second * tC0(adjmoves[d2]);
if((err = intval(back, old)) < 1e-3) {
if(err > worst_error2) println(hlog, format("worst_error2 = %lg", double(worst_error2 = err)));
if(p2.first->move(d2)) println(hlog, "error: repeated edge");
p2.first->c.connect(d2, parent, d, false);
fb++;
}
}
if(fb != 1) {
println(hlog, "found fb = ", fb);
println(hlog, old);
for(int d2=0; d2<S7; d2++) {
println(hlog, p2.second * tC0(adjmoves[d2]), " in distance ", intval(p2.second * tC0(adjmoves[d2]), old));
}
parent->c.connect(d, parent, d, false);
return parent;
}
return p2.first;
}
if(DEB) println(hlog, "-> not found");
heptagon *created = tailored_alloc<heptagon> (S7);
created->c7 = newCell(S7, created);
created->alt = NULL;
created->zebraval = hrand(10);
fixmatrix(T);
reg_gmatrix[created] = make_pair(alt, T);
altmap[alt].emplace_back(created, T);
created->c.connect(0, parent, d, false);
return created;
}
};
hrmap* new_map() {
return new hrmap_reg3;
}
hrmap_reg3* regmap() {
return ((hrmap_reg3*) currentmap);
}
heptagon *createStep(heptagon *parent, int d) {
return regmap()->createStep(parent, d);
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1) {
auto m = regmap();
auto p1 = m->reg_gmatrix[h1];
auto p2 = m->reg_gmatrix[h2];
transmatrix T = Id;
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gBinary3);
T = binary::relative_matrix(p2.first, p1.first);
}
return inverse(p1.second) * T * p2.second;
}
void draw() {
sphereflip = Id;
// for(int i=0; i<S6; i++) queuepoly(ggmatrix(cwt.at), shWall3D[i], 0xFF0000FF);
dq::visited.clear();
dq::enqueue(viewctr.at, cview());
while(!dq::drawqueue.empty()) {
auto& p = dq::drawqueue.front();
heptagon *h = get<0>(p);
transmatrix V = get<1>(p);
dynamicval<ld> b(band_shift, get<2>(p));
bandfixer bf(V);
dq::drawqueue.pop();
cell *c = h->c7;
if(!do_draw(c, V)) continue;
drawcell(c, V, 0, false);
for(int i=0; i<S7; i++)
dq::enqueue(h->move(i), V * relative_matrix(h->move(i), h));
}
}
int celldistance(cell *c1, cell *c2) {
if(c1 == c2) return 0;
auto r = regmap();
dynamicval<eGeometry> g(geometry, gBinary3);
return 1 + binary::celldistance3(r->reg_gmatrix[c1->master].first, r->reg_gmatrix[c2->master].first);
}
bool pseudohept(cell *c) {
if(sphere) {
hyperpoint h = tC0(relative_matrix(c->master, regmap()->origin));
if(S7 == 12) {
hyperpoint h1 = cspin(0, 1, atan2(16, 69) + M_PI/4) * h;
for(int i=0; i<4; i++) if(abs(abs(h1[i]) - .5) > .01) return false;
return true;
}
if(S7 == 8)
return h[3] >= .99 || h[3] <= -.99 || abs(h[3]) < .01;
if(loop == 3 && face == 3 && S7 == 4)
return c == currentmap->gamestart();
if(loop == 4 && face == 3)
return abs(h[3]) > .9;
if(loop == 3 && face == 4)
return abs(h[3]) > .9;
if(loop == 5 && face == 3)
return abs(h[3]) > .99 || abs(h[0]) > .99 || abs(h[1]) > .99 || abs(h[2]) > .99;
}
if(hyperbolic) {
heptagon *h = regmap()->reg_gmatrix[c->master].first;
return (h->zebraval == 1) && (h->distance & 1);
}
return false;
}
int dist_alt(cell *c) {
return regmap()->reg_gmatrix[c->master].first->distance;
}
#endif
#if 0
/* More precise, but very slow distance. Not used/optimized for now */
ld adistance(cell *c) {
hyperpoint h = tC0(regmap()->reg_gmatrix[c->master].second);
h = binary::deparabolic3(h);
return regmap()->reg_gmatrix[c->master].first->distance * log(2) - h[0];
}
int bucketer(ld x) {
return int(x * 10 + 100000.5) - 100000;
}
int bucketer(hyperpoint h) {
return bucketer(h[0]) + 1000 * bucketer(h[1]) + 1000000 * bucketer(h[2]);
}
map<int, int> close_distances;
unordered_map<pair<cell*, cell*>, int> memo;
bool cdd;
int celldistance(cell *c1, cell *c2) {
if(memo.count(make_pair(c1, c2))) return memo[make_pair(c1, c2)];
if(c1 == c2) return 0;
vector<cell*> v[2];
v[0].push_back(c1);
v[1].push_back(c2);
int steps = 0;
map<cell*, int> visited;
visited[c1] = 1;
visited[c2] = 2;
while(true) {
if(cdd) {
println(hlog, "state ", steps, "/",isize(v[0]), "/", isize(v[1]));
println(hlog, " A: ", v[0]);
println(hlog, " B: ", v[1]);
}
for(int i: {0,1}) {
vector<cell*> new_v;
for(cell *c: v[i]) forCellCM(cn, c) if(adistance(cn) < adistance(c)) {
auto &vi = visited[cn];
if((vi&3) == 0) {
vi = 4 * (steps+1);
vi |= (1<<i);
new_v.push_back(cn);
}
else if((vi&3) == 2-i) {
vector<pair<cell*, int>> ca1, ca2;
int b1 = 4*steps-4;
int b2 = ((vi>>2)<<2) - 4;
for(auto p: visited) {
if(cdd) println(hlog, p);
int ps = p.second & 3;
if(ps == 1+i && p.second >= b1)
ca1.emplace_back(p.first, p.second/4);
if(ps == 2-i && p.second >= b2 && p.second <= b2+8)
ca2.emplace_back(p.first, p.second/4);
}
int bound = 1<<16;
for(auto p1: ca1) for(auto p2: ca2) {
hyperpoint h = tC0(relative_matrix(p1.first->master, p2.first->master));
int b = bucketer(h);
if(close_distances.count(b)) {
int d = close_distances[b] + p1.second + p2.second;
if(cdd) println(hlog, "candidate: close=", close_distances[b], p1, p2, "; h = ", h);
if(d < bound) bound = d;
}
else if(cdd) println(hlog, "bucket missing");
}
return memo[make_pair(c1, c2)] = bound;
return bound;
}
}
v[i] = std::move(new_v);
}
steps++;
}
}
cellwalker target;
int tsteps;
int dist_alt(cell *c) {
if(!target.at) {
target = cellwalker(currentmap->gamestart(), 0);
tsteps = 0;
for(int i=0; i<30; i++) target += wstep, target += rev, tsteps++;
}
if(specialland == laCamelot) return reg3::celldistance(c, target.at);
else {
int d = reg3::celldistance(c, target.at) - tsteps;
if(d < 10) target += wstep, target += rev, tsteps++;
return d;
}
}
#endif
}
}