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hyperrogue/kite.cpp

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// Hyperbolic Rogue -- Kite-and-dart tiling
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file kite.cpp
* \brief Kite-and-dart tiling, both in R^2 and H^3
*/
#include "hyper.h"
namespace hr {
EX namespace kite {
EX bool in() { return cgflags & qKITE; }
#if CAP_BT
#if HDR
enum pshape {pDart, pKite};
#endif
transmatrix meuscale(ld z) {
if(meuclid) {
transmatrix T = Id;
T[0][0] = z;
T[1][1] = z;
return T;
}
else
return xpush(log(z));
}
transmatrix mspin(ld alpha) {
if(meuclid)
return spin(alpha);
else
return cspin(1, 2, alpha);
}
const ld euscale = 0.5;
transmatrix meupush(ld x, ld y) {
if(meuclid)
return eupush(euscale * x, euscale * y);
else
return bt::parabolic3(x, y);
}
hyperpoint mhpxy(ld x, ld y) {
if(meuclid) return hpxy(euscale * x, euscale * y);
else return bt::parabolic3(x, y) * C0;
}
const ld phi = golden_phi;
const ld rphi = 1 / phi;
const ld down = 1 / tan(36._deg);
const ld up = 1 / tan(72._deg);
const ld dart_center = (down + 2 * up) / 3;
const ld kite_center = up;
EX pshape getshape(heptagon *h) { return pshape(h->s); }
EX pair<vector<vector<hyperpoint>>, vector<vector<ld>>> make_walls() {
vector<vector<hyperpoint>> kv;
vector<vector<ld>> weights;
for(pshape sh: {pDart, pKite}) {
bool kite = sh == pKite;
int t = kite ? 1 : -1;
ld shf = kite ? kite_center : dart_center;
hyperpoint left = mhpxy(-1, shf);
hyperpoint right = mhpxy( 1, shf);
hyperpoint top = mhpxy( 0, shf + t*up);
hyperpoint bottom = mhpxy( 0, shf-down);
hyperpoint dleft = meupush(-1, shf) * meuscale(rphi) * C0;
hyperpoint dright = meupush( 1, shf) * meuscale(rphi) * C0;
hyperpoint dtop = meupush( 0, shf+t*up) * meuscale(rphi) * C0;
hyperpoint dbottom = meupush( 0, shf-down) * meuscale(rphi) * C0;
hyperpoint dleftmid = (!kite) ? meupush(0, shf-down) * meuscale(rphi) * meupush(-1, down) * C0 : meupush(0, shf-down) * meuscale(rphi) * mspin(-36._deg) * meupush(0, down - up) * C0;
hyperpoint drightmid = (!kite) ? meupush(0, shf-down) * meuscale(rphi) * meupush(1, down) * C0 : meupush(0, shf-down) * meuscale(rphi) * mspin(36._deg) * meupush(0, down - up) * C0;
hyperpoint dcenter = meupush( 0, shf-up) * meuscale(rphi) * C0;
auto pw = [&] (int id, const vector<hyperpoint> v, const vector<ld> w) { kv.push_back(v); weights.push_back(w); };
pw(0, {left, bottom, dbottom, dleftmid, dleft}, {1,1,1,1,1});
pw(1, {bottom, right, dright, drightmid, dbottom}, {1,1,1,1,1});
pw(2, {right, top, dtop, dright}, {1,1,1,1});
pw(3, {top, left, dleft, dtop}, {1,1,1,1});
ld b = 10; // big weight
pw(4, {left, bottom, top}, {1,b,b});
pw(5, {right, bottom, top}, {1,b,b});
if(kite) {
pw(6, {dcenter, drightmid, dright}, {b,1,1});
pw(7, {dcenter, dright, dtop}, {b,1,1});
pw(8, {dcenter, dleft, dleftmid}, {b,1,1});
pw(9, {dcenter, dtop, dleft}, {b,1,1});
pw(10,{dbottom, drightmid, dcenter}, {1,1,b});
pw(11,{dbottom, dcenter, dleftmid}, {1,b,1});
}
else {
pw(6, {dbottom, dtop, dleftmid}, {1,b,1});
pw(7, {dbottom, drightmid, dtop}, {1,1,b});
pw(8, {dleftmid, dtop, dleft}, {b,b,1});
pw(9, {drightmid, dright, dtop}, {b,1,b});
}
}
return {kv, weights};
}
inline void print(hstream& hs, pshape sh) { print(hs, sh == pKite ? "pKite" : "pDart"); }
EX bool no_adj;
struct hrmap_kite : hrmap {
transmatrix pKite1, pKite2, pKite3, pDart1, pDart2, ipKite1, ipKite2, ipKite3, ipDart1, ipDart2;
heptagon *origin;
heptagon *getOrigin() override { return origin; }
void find_cell_connection(cell *c, int d) override {
kite::find_cell_connection(c, d);
}
hyperpoint get_corner(cell *c, int cid, ld cf) override {
bool kite = getshape(c->master) == pKite;
int t = kite ? 1 : -1;
ld shf = kite ? kite_center : dart_center;
ld mul = 3/cf;
switch(cid & 3) {
case 0: return mhpxy(-mul, (shf)*mul);
case 1: return mhpxy(0, (shf-down)*mul);
case 2: return mhpxy(+mul, shf*mul);
case 3: return mhpxy(0, (shf + t*up)*mul);
}
return C0; /* unreachable! */
}
int shvid(cell *c) override {
return kite::getshape(c->master);
}
heptagon *newtile(pshape s, int dist) {
heptagon *h = init_heptagon(8);
h->s = hstate(s);
h->dm4 = h->distance = dist;
if(bt::in() || dist == 0)
h->c7 = newCell(meuclid ? 4 : s == pKite ? 12 : 10, h);
return h;
}
heptagon *hspawn(heptagon *of, int our, int their, pshape s) {
auto h = newtile(s, of->distance + (our ? 1 : -1));
if(bt::in()) bt::make_binary_lands(of, h);
of->c.connect(our, h, their, false);
return h;
}
heptagon *create_step(heptagon *of, int dir) override {
if(of->move(dir)) return of->move(dir);
auto sh = getshape(of);
if(sh == pKite && dir == 0) return hspawn(of, 0, 1, pKite);
if(sh == pKite && dir == 1) return hspawn(of, 1, 0, pKite);
if(sh == pKite && dir == 2) return hspawn(of, 2, 0, pKite);
if(sh == pKite && dir == 3) return hspawn(of, 3, 0, pDart);
if(sh == pDart && dir == 1) return hspawn(of, 1, 0, pKite);
if(sh == pDart && dir == 2) return hspawn(of, 2, 0, pDart);
if(sh == pDart && dir == 3) of->c.connect(3, of, 3, false); /* illegal */
/* generated by findmore */
#define RULEFOR(sh0, dir0, z, dir1) if(sh == sh0 && dir == dir0) { heptagon *at = of; if(z true) of->c.connect(dir0, at, dir1, false); }
#define GO(our, shape) (at = at->cmove(our)) && getshape(at) == shape &&
#define GOIF(our, shape, their) at->cmove(our) && at->c.spin(our) == their && getshape(at->move(our)) == shape && (at = at->move(our), true) &&
RULEFOR(pDart, 5, GOIF(0, pDart, 2) GO(4, pKite) GO(3, pDart), 4)
RULEFOR(pDart, 5, GOIF(0, pDart, 2) GO(4, pDart) GO(6, pKite) GO(2, pKite), 5)
RULEFOR(pDart, 5, GOIF(0, pDart, 2) GO(7, pKite) GO(6, pKite) GO(2, pKite), 5)
RULEFOR(pDart, 5, GOIF(0, pKite, 3) GO(5, pKite) GO(3, pDart), 4)
RULEFOR(pDart, 5, GOIF(0, pKite, 3) GO(5, pDart) GO(6, pKite) GO(2, pKite), 5)
RULEFOR(pDart, 4, GOIF(0, pDart, 2) GO(7, pKite) GO(1, pKite), 4)
RULEFOR(pDart, 4, GOIF(0, pKite, 3) GO(4, pDart) GO(2, pDart), 5)
RULEFOR(pDart, 4, GOIF(0, pKite, 3) GO(4, pKite) GO(3, pDart), 5)
RULEFOR(pDart, 6, GOIF(0, pDart, 2) GO(4, pDart) GO(1, pKite), 6)
RULEFOR(pDart, 6, GOIF(0, pDart, 2) GO(4, pKite) GO(1, pKite), 6)
RULEFOR(pDart, 6, GOIF(0, pKite, 3) GO(5, pDart) GO(1, pKite), 6)
RULEFOR(pDart, 6, GOIF(0, pKite, 3) GO(5, pKite) GO(1, pKite), 6)
RULEFOR(pDart, 7, GOIF(0, pDart, 2) GO(1, pKite), 7)
RULEFOR(pDart, 7, GOIF(0, pKite, 3) GO(2, pKite), 7)
RULEFOR(pKite, 5, GOIF(0, pDart, 1) GO(5, pDart) GO(1, pKite), 4)
RULEFOR(pKite, 5, GOIF(0, pDart, 1) GO(5, pKite) GO(2, pKite), 4)
RULEFOR(pKite, 5, GOIF(0, pKite, 1) GO(4, pDart) GO(1, pKite), 4)
RULEFOR(pKite, 5, GOIF(0, pKite, 1) GO(4, pKite) GO(2, pKite), 4)
RULEFOR(pKite, 5, GOIF(0, pKite, 2) GO(6, pKite) GO(1, pKite), 4)
RULEFOR(pKite, 5, GOIF(0, pKite, 2) GO(6, pDart) GO(5, pDart) GO(2, pDart), 5)
RULEFOR(pKite, 5, GOIF(0, pKite, 2) GO(6, pDart) GO(5, pKite) GO(3, pDart), 5)
RULEFOR(pKite, 5, GOIF(0, pKite, 2) GO(7, pKite) GO(7, pDart) GO(2, pDart), 5)
RULEFOR(pKite, 4, GOIF(0, pDart, 1) GO(4, pDart) GO(1, pKite), 5)
RULEFOR(pKite, 4, GOIF(0, pDart, 1) GO(4, pKite) GO(1, pKite), 5)
RULEFOR(pKite, 4, GOIF(0, pKite, 1) GO(7, pDart) GO(2, pDart), 4)
RULEFOR(pKite, 4, GOIF(0, pKite, 1) GO(7, pKite) GO(2, pKite), 5)
RULEFOR(pKite, 4, GOIF(0, pKite, 2) GO(5, pDart) GO(1, pKite), 5)
RULEFOR(pKite, 4, GOIF(0, pKite, 2) GO(5, pKite) GO(1, pKite), 5)
RULEFOR(pKite, 6, GOIF(0, pDart, 1) GO(5, pDart) GO(2, pDart), 6)
RULEFOR(pKite, 6, GOIF(0, pDart, 1) GO(5, pKite) GO(3, pDart), 6)
RULEFOR(pKite, 6, GOIF(0, pKite, 1) GO(4, pDart) GO(2, pDart), 6)
RULEFOR(pKite, 6, GOIF(0, pKite, 1) GO(4, pKite) GO(3, pDart), 6)
RULEFOR(pKite, 6, GOIF(0, pKite, 2) GO(1, pKite), 7)
RULEFOR(pKite, 7, GOIF(0, pDart, 1) GO(2, pDart), 7)
RULEFOR(pKite, 7, GOIF(0, pKite, 1) GO(2, pKite), 6)
RULEFOR(pKite, 7, GOIF(0, pKite, 2) GO(3, pDart), 7)
#undef RULEFOR
#undef GO
#undef GOIF
return of->move(dir);
}
map<int, transmatrix> graphrules;
int encode(pshape s0, int d0, pshape s1, int d1) {
return d0 + d1 * 16 + s0 * 256 + s1 * 512;
}
void graphrule(pshape s0, int d0, pshape s1, int d1, transmatrix T) {
graphrules[encode(s0, d0, s1, d1)] = T;
}
void make_graphrules() {
bool f = geom3::flipped;
bool emb = embedded_plane;
if(emb) geom3::light_flip(true);
pKite1 = meupush(-1, kite_center + 0) * mspin(108._deg) * meuscale(rphi) * meupush(0, down - kite_center);
pKite2 = meupush(1, kite_center + 0) * mspin(-108._deg) * meuscale(rphi) * meupush(0, down - kite_center);
pKite3 = meupush(0, kite_center - down) * mspin(36._deg) * meuscale(rphi) * meupush(0, down - dart_center);
pDart1 = meupush(0, dart_center-down) * meuscale(rphi) * meupush(0, down - kite_center);
pDart2 = meupush(-1, dart_center+0) * mspin(144._deg) * meuscale(rphi) * meupush(0, down - dart_center);
ipKite1 = inverse(pKite1);
ipKite2 = inverse(pKite2);
ipKite3 = inverse(pKite3);
ipDart1 = inverse(pDart1);
ipDart2 = inverse(pDart2);
/* generated with facelift */
graphrule(pDart, 0, pDart, 1, ipKite3 * ipKite1 * ipKite1 * pKite2 * pKite2 * pKite3); // ipKite3 * ipKite1 * ipDart1 * pDart2 * pDart2 * pDart2);
graphrule(pDart, 0, pKite, 0, ipDart2 * ipDart2 * pDart1 * pKite1);
graphrule(pDart, 1, pDart, 0, ipDart2 * ipDart2 * ipDart2 * pDart1 * pKite1 * pKite3);
graphrule(pDart, 1, pKite, 1, ipDart2 * ipKite3 * pKite1 * pKite2);
graphrule(pDart, 2, pKite, 2, ipDart2 * ipDart2 * ipDart2 * pDart1 * pKite1 * pKite1);
graphrule(pDart, 3, pKite, 3, ipKite3 * pKite2);
graphrule(pKite, 0, pDart, 0, ipKite1 * ipDart1 * pDart2 * pDart2);
graphrule(pKite, 0, pKite, 1, ipKite1 * ipKite1 * pKite2 * pKite2);
graphrule(pKite, 1, pDart, 1, ipKite2 * ipKite1 * pKite3 * pDart2);
graphrule(pKite, 1, pKite, 0, ipKite2 * ipKite2 * pKite1 * pKite1);
graphrule(pKite, 2, pDart, 2, ipDart1 * ipDart2 * ipKite3 * pKite1 * pKite2 * pKite3);
graphrule(pKite, 2, pKite, 3, ipKite2 * pKite1);
graphrule(pKite, 3, pDart, 3, ipDart1 * pDart2);
graphrule(pKite, 3, pKite, 2, ipKite1 * pKite2);
graphrule(pDart, 4, pDart, 8, ipDart2);
graphrule(pDart, 4, pKite, 10, ipKite3);
graphrule(pDart, 5, pDart, 9, ipKite3 * ipKite2 * ipKite1 * pKite3 * pDart2);
graphrule(pDart, 5, pKite, 11, ipDart2 * ipDart2 * ipDart2 * pDart1 * pKite1);
graphrule(pKite, 4, pDart, 6, ipDart1);
graphrule(pKite, 4, pKite, 6, ipKite2);
graphrule(pKite, 4, pKite, 9, ipKite1);
graphrule(pKite, 5, pDart, 7, ipDart1);
graphrule(pKite, 5, pKite, 7, ipKite2);
graphrule(pKite, 5, pKite, 8, ipKite1);
graphrule(pDart, 6, pKite, 4, pDart1);
graphrule(pDart, 7, pKite, 5, pDart1);
graphrule(pDart, 8, pDart, 4, pDart2);
graphrule(pDart, 9, pDart, 5, ipDart2 * ipKite3 * pKite1 * pKite2 * pKite3);
graphrule(pKite, 6, pKite, 4, pKite2);
graphrule(pKite, 7, pKite, 5, pKite2);
graphrule(pKite, 8, pKite, 5, pKite1);
graphrule(pKite, 9, pKite, 4, pKite1);
graphrule(pKite, 10, pDart, 4, pKite3);
graphrule(pKite, 11, pDart, 5, ipKite1 * ipDart1 * pDart2 * pDart2 * pDart2);
if(emb) {
geom3::light_flip(false);
for(auto& g: graphrules) g.second = cgi.emb->base_to_actual(g.second);
geom3::light_flip(f);
}
}
transmatrix adj(cell *c, int dir) override {
if(no_adj) return Id;
auto c1 = c->cmove(dir);
auto code = encode(getshape(c->master), dir, getshape(c1->master), c->c.spin(dir));
if(!graphrules.count(code)) {
println(hlog, "rule missing: ", make_tuple(getshape(c->master), dir, getshape(c1->master), c->c.spin(dir)));
throw 0;
}
return graphrules[code];
}
/* works only for dir = 0,1,2,3 */
transmatrix get_tmatrix(heptagon *h2, int dir, bool inverted) {
if(dir == 0) inverted = !inverted, h2->cmove(dir), tie(dir, h2) = make_pair(h2->c.spin(dir), h2->move(dir));
if(inverted) {
if(dir == 1) return getshape(h2) == pKite ? ipKite1 : ipDart1;
if(dir == 2) return getshape(h2) == pKite ? ipKite2 : ipDart2;
return ipKite3;
}
else {
if(dir == 1) return getshape(h2) == pKite ? pKite1 : pDart1;
if(dir == 2) return getshape(h2) == pKite ? pKite2 : pDart2;
return pKite3;
}
}
transmatrix relative_matrixh(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
if(gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7))
return inverse_shift(gmatrix0[h1->c7], gmatrix0[h2->c7]);
transmatrix gm = Id, where = Id;
while(h1 != h2) {
if(h1->distance <= h2->distance)
where = get_tmatrix(h2, 0, true) * where, h2 = h2->cmove(0);
else
gm = gm * get_tmatrix(h1, 0, false), h1 = h1->cmove(0);
}
return gm * where;
}
int wall_offset(cell *c) override {
if(WDIM == 3)
return kite::getshape(c->master) == kite::pKite ? 10 : 0;
else
return hrmap::wall_offset(c);
}
hrmap_kite() {
make_graphrules();
origin = newtile(pKite, 0);
}
~hrmap_kite() {
clearfrom(origin);
}
};
EX hrmap *new_map() { return new hrmap_kite; }
hrmap_kite *kite_map() { return (hrmap_kite*) currentmap; }
void con(cell *c0, int d0, cell *c1, int d1) {
c0->c.connect(d0, c1, d1, false);
}
EX void find_cell_connection(cell *c, int d) {
auto h0 = c->master;
auto sh = getshape(h0);
auto crule = [&] (pshape s0, int d0, pshape s1, int d1, pshape sparent, int child, int sibling, int rsibling) {
if(sh == s0 && d == d0) {
auto h = h0->cmove(child);
if(getshape(h) != sparent) { printf("bad sparent\n"); exit(1); }
if(sibling != 8) h = h->cmove(sibling);
if(getshape(h) != s1) { printf("bad s1\n"); exit(1); }
con(c, d0, h->c7, d1);
// c->c.connect(d0, h->c7, d1, false);
}
if(sh == s1 && d == d1 && sibling == 8 && getshape(h0->cmove(0)) == s0 && h0->c.spin(0) == child)
con(c, d1, h0->cmove(0)->c7, d0);
// c->c.connect(d1, h0->cmove(0)->c7, d0, false);
if(sh == s1 && d == d1 && sibling != 8 && (h0->cmove(rsibling), h0->c.spin(rsibling) == sibling) && getshape(h0->cmove(rsibling)) == sparent && getshape(h0->cmove(rsibling)->cmove(0)) == s0)
// c->c.connect(d1, h0->cmove(sibling)->cmove(0)->c7, d0, false);
con(c, d1, h0->cmove(rsibling)->cmove(0)->c7, d0);
};
if(d < 4) {
int dx = d;
dx += 4;
heptagon *h1 = h0->cmove(dx);
dx = h0->c.spin(dx);
dx -= 4;
// c->c.connect(d, h1->c7, h0->c.spin(4+d)-4, false);
con(c, d, h1->c7, dx);
return;
}
crule(pDart, 6, pKite, 4, pDart, 2, 7, 7);
crule(pDart, 6, pKite, 4, pKite, 1, 8, 8);
crule(pDart, 7, pKite, 5, pDart, 2, 7, 7);
crule(pDart, 7, pKite, 5, pKite, 1, 8, 8);
crule(pDart, 8, pDart, 4, pDart, 2, 8, 8);
crule(pDart, 8, pDart, 4, pKite, 1, 7, 7);
crule(pDart, 9, pDart, 5, pKite, 1, 6, 6);
crule(pKite, 10, pDart, 4, pDart, 3, 8, 8);
crule(pKite, 10, pDart, 4, pKite, 2, 7, 7);
crule(pKite, 11, pDart, 5, pDart, 3, 4, 5);
crule(pKite, 11, pDart, 5, pKite, 1, 6, 6);
crule(pKite, 6, pKite, 4, pDart, 3, 7, 7);
crule(pKite, 6, pKite, 4, pKite, 1, 7, 6);
crule(pKite, 6, pKite, 4, pKite, 2, 8, 8);
crule(pKite, 7, pKite, 5, pDart, 3, 7, 7);
crule(pKite, 7, pKite, 5, pKite, 1, 7, 6);
crule(pKite, 7, pKite, 5, pKite, 2, 8, 8);
crule(pKite, 8, pKite, 5, pKite, 1, 8, 8);
crule(pKite, 8, pKite, 5, pKite, 2, 6, 7);
crule(pKite, 9, pKite, 4, pKite, 1, 8, 8);
crule(pKite, 9, pKite, 4, pKite, 2, 6, 7);
if(!c->move(d)) {
println(hlog, "connection rule missing: ", d);
throw "connection rule missing";
}
}
auto hooksw = addHook(hooks_swapdim, 100, [] { if(kite::in() && currentmap) kite_map()->make_graphrules(); });
#endif
}}
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