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arbitrile.cpp
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arbitrile.cpp
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// Hyperbolic Rogue -- Arbitrary Tilings
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file arbitrile.cpp
* \brief Arbitrary tilings
*
* Arbitrary tilings, defined in .tes files.
*/
#include "hyper.h"
namespace hr {
EX namespace arb {
EX int affine_limit = 200;
#if HDR
/** a type used to specify the connections between shapes */
struct connection_t {
/** the index of the connected shape in the 'shapes' table */
int sid;
/** the index of the edge in the 'shapes' table */
int eid;
/** 1 if this connection mirrored, 0 otherwise. do_unmirror() removes all mirrors by doubling shapes */
int mirror;
bool operator == (const arb::connection_t& b) const { return tie(sid, eid, mirror) == tie(b.sid, b.eid, b.mirror); }
bool operator < (const arb::connection_t& b) const { return tie(sid, eid, mirror) < tie(b.sid, b.eid, b.mirror); }
};
inline void print(hstream& hs, const connection_t& conn) { print(hs, tie(conn.sid, conn.eid, conn.mirror)); }
/** \brief each shape of the arb tessellation
* note: the usual HyperRogue convention is: vertex 0, edge 0, vertex 1, edge 1, ...
* note: the tesfile convention is: edge 0, vertex 0, edge 1, vertex 1, ...
*/
/** edge with infinite end on the left */
constexpr ld INFINITE_LEFT = -1;
/** edge with infinite end on the right */
constexpr ld INFINITE_RIGHT = -2;
/** edge with two infinite ends */
constexpr ld INFINITE_BOTH = -3;
struct shape {
/** index in the arbi_tiling::shapes */
int id;
/** index in the original file */
int orig_id;
/** flags such as sfLINE and sfPH */
int flags;
/** list of vertices in the usual convention */
vector<hyperpoint> vertices;
/** list of angles in the tesfile convention */
vector<ld> angles;
/** list of edge lengths */
vector<ld> edges;
/** list of input edges */
vector<ld> in_edges;
/** list of input angles */
vector<ld> in_angles;
/** (ultra)ideal markers */
vector<bool> ideal_markers;
/** list of edge connections */
vector<connection_t> connections;
int size() const { return isize(vertices); }
void build_from_angles_edges(bool is_comb);
vector<pair<int, int> > sublines;
vector<pair<ld, ld>> stretch_shear;
/** '*inf' was applied to represent an apeirogon/pseudogon */
bool apeirogonal;
/** connections repeat `repeat_value` times */
int repeat_value;
/** 0 if the no mirror symmetries are declared; otherwise, edge i is the mirror of edge gmod(symmetric_value-i, size()). Make sure symmetric_value != 0, e.g., by adding size() */
int symmetric_value;
/** if a tile/edge combination may be connected to edges j1 and j2 of this, j1-j2 must be divisible by cycle_length */
int cycle_length;
/** list of valences of vertices in the tesfile convention */
vector<int> vertex_valence;
/** list of periods of vertices in the tesfile convention */
vector<int> vertex_period;
/** list of angles at vertices in the tesfile convention */
vector<vector<ld>> vertex_angles;
/** football types */
int football_type;
/** is it a mirrored version of an original tile */
bool is_mirrored;
/** auxiliary function for symmetric_value: is the edge index reflectable? */
bool reflectable(int id) {
if(!symmetric_value) return false;
if(apeirogonal && gmod(id, size()) >= size() - 2) return false;
return true;
}
/** reflect a reflectable reflect index */
int reflect(int id) {
return gmod(symmetric_value - id, size() - (apeirogonal ? 2 : 0));
}
};
struct slider {
string name;
ld zero;
ld current;
ld min;
ld max;
};
struct intslider {
string name;
int zero;
int current;
int min;
int max;
};
struct arbi_tiling {
int order;
/* line flags have been marked for tiles */
bool have_line;
/* pseudohept flags have been marked for tiles (1), or the tiling is football-colorable (2), or neither (0) */
int have_ph;
/* is the tree structure given in the tes file */
bool have_tree;
/* is the valence data reliable */
bool have_valence;
/* use "star." if the tessellation includs star polygons */
bool is_star;
/* use "combinatorial." for combinatorial tessellations; vertex valences computed based on their angles. Currently only rulegen works for combinatorial tessellations */
bool is_combinatorial;
/* reserved for future flags */
bool res0, res1, res2, res3;
int yendor_backsteps;
vector<shape> shapes;
string name;
string comment;
vector<slider> sliders;
vector<intslider> intsliders;
ld cscale;
int range;
ld floor_scale;
ld boundary_ratio;
string filename;
int mirror_rules;
vector<string> options;
int min_valence, max_valence;
bool is_football_colorable;
bool was_unmirrored;
bool was_split_for_football;
geometryinfo1& get_geometry();
eGeometryClass get_class() { return get_geometry().kind; }
ld scale();
};
#endif
/** currently loaded tiling */
EX arbi_tiling current;
/** is the currently displayed map current or slided */
EX bool using_slided;
/** for real-valued sliders, current is the tiling used by the map, while slided is the tiling used for the display */
EX arbi_tiling slided;
EX bool in_slided() { return in() && using_slided; }
EX arbi_tiling& current_or_slided() {
return using_slided ? slided : current;
}
/** id of vertex in the arbitrary tiling */
EX short& id_of(heptagon *h) { return h->zebraval; }
#if HDR
struct hr_polygon_error : hr_exception {
vector<transmatrix> v;
eGeometryClass c;
int id;
transmatrix end;
map<string, cld> params;
hr_polygon_error(const vector<transmatrix>& _v, int _id, transmatrix _e) : v(_v), c(cgclass), id(_id), end(_e) {}
~hr_polygon_error() noexcept(true) {}
string generate_error();
};
#endif
string hr_polygon_error::generate_error() {
cld dist = (hdist0(tC0(end)) / params["distunit"]);
bool angle = abs(dist) < 1e-9;
if(angle) dist = (atan2(end * lxpush0(1)) / params["angleunit"]);
return
XLAT("Polygon number %1 did not close correctly (%2 %3). Here is the picture to help you understand the issue.\n\n", its(id),
angle ? "angle" : "distance",
lalign(0, dist)
);
}
struct connection_debug_request : hr_exception {
int id;
eGeometryClass c;
connection_debug_request(int i): id(i), c(cgclass) {}
};
void ensure_geometry(eGeometryClass c) {
stop_game();
if(c != cgclass) {
if(c == gcEuclid) set_geometry(gEuclid);
if(c == gcHyperbolic) set_geometry(gNormal);
if(c == gcSphere) set_geometry(gSphere);
}
if(specialland != laCanvas) {
canvas_default_wall = waInvisibleFloor;
ccolor::set_plain_nowall(0xFFFFFF);
enable_canvas();
}
start_game();
}
void start_poly_debugger(hr_polygon_error& err) {
#if CAP_EDIT
ensure_geometry(err.c);
drawthemap();
mapeditor::drawing_tool = true;
pushScreen(mapeditor::showDrawEditor);
mapeditor::initdraw(cwt.at);
int n = isize(err.v);
mapeditor::dtcolor = 0xFF0000FF;
mapeditor::dtwidth = 0.02;
for(int i=0; i<n-1; i++)
mapeditor::dt_add_line(shiftless(tC0(err.v[i])), shiftless(tC0(err.v[i+1])), 0);
mapeditor::dtcolor = 0xFFFFFFFF;
for(int i=0; i<n; i++)
mapeditor::dt_add_text(shiftless(tC0(err.v[i])), 0.5, its(i));
#endif
}
void shape::build_from_angles_edges(bool is_comb) {
transmatrix at = Id;
int n = isize(in_angles);
hyperpoint ctr = Hypc;
vector<transmatrix> matrices;
for(int i=0; i<n; i++) {
matrices.push_back(at);
if(debugflags & DF_GEOM) println(hlog, "at = ", at);
ctr += tC0(at);
at = at * lxpush(in_edges[i]) * spin(in_angles[i]+M_PI);
}
matrices.push_back(at);
if(is_comb) return;
if(!eqmatrix(at, Id) && !apeirogonal) {
throw hr_polygon_error(matrices, id, at);
}
if(sqhypot_d(3, ctr) < 1e-2) {
// this may happen for some spherical tilings
// try to move towards the center
if(debugflags & DF_GEOM) println(hlog, "special case encountered");
for(int i=0; i<n; i++) {
ctr += at * lxpush(in_edges[i]) * spin((in_angles[i]+M_PI)/2) * lxpush0(.01);
at = at * lxpush(in_edges[i]) * spin(in_angles[i]);
}
if(debugflags & DF_GEOM) println(hlog, "ctr = ", ctr);
}
hyperpoint inf_point;
if(apeirogonal) {
transmatrix U = at;
for(int i=0; i<3; i++) for(int j=0; j<3; j++) U[i][j] -= Id[i][j];
hyperpoint v;
ld det = U[0][1] * U[1][0] - U[1][1] * U[0][0];
v[1] = (U[1][2] * U[0][0] - U[0][2] * U[1][0]) / det;
v[0] = (U[0][2] * U[1][1] - U[1][2] * U[0][1]) / det;
v[2] = 1;
inf_point = v;
ctr = mid(C0, tC0(at));
ctr = towards_inf(ctr, inf_point);
}
ctr = normalize(ctr);
vertices.clear();
angles.clear();
for(int i=0; i<n; i++) {
edges.push_back(in_edges[i]);
if(!ideal_markers[i]) {
vertices.push_back(tC0(gpushxto0(ctr) * matrices[i]));
angles.push_back(in_angles[i]);
}
else {
angles.push_back(0);
hyperpoint a1 = tC0(matrices[i]);
hyperpoint t1 = get_column(matrices[i], 0);
hyperpoint a2 = tC0(matrices[i+2]);
hyperpoint t2 = get_column(matrices[i+2], 0);
a1 /= a1[2];
a2 /= a2[2];
t1 -= a1 * t1[2];
t2 -= a2 * t2[2];
ld c1 = a2[0] - a1[0], c2 = a2[1] - a1[1];
ld v1 = t1[0], v2 = t1[1];
ld u1 = t2[0], u2 = t2[1];
ld r = (u2 * c1 - c2 * u1) / (v1 * u2 - v2 * u1);
// ld s = (v2 * c1 - c2 * v1) / (v1 * u2 - v2 * u1);
hyperpoint v = a1 + r * t1;
// also v == a2 + s * t2;
v[2] = 1;
v = gpushxto0(ctr) * v;
v /= v[2];
vertices.push_back(v);
i++;
}
}
if(apeirogonal) {
vertices.push_back(gpushxto0(ctr) * tC0(at));
hyperpoint v = gpushxto0(ctr) * inf_point;
v /= v[2];
vertices.push_back(v);
auto b = angles.back() / 2;
angles.back() = b;
angles.push_back(0);
angles.push_back(b);
edges.push_back(0);
edges.push_back(0);
}
n = isize(angles);
for(int i=0; i<n; i++) {
bool left = angles[i] == 0;
bool right = angles[gmod(i-1, isize(vertices))] == 0;
if(left && right) edges[i] = INFINITE_BOTH;
else if(left) edges[i] = INFINITE_LEFT;
else if(right) edges[i] = INFINITE_RIGHT;
}
}
EX bool correct_index(int index, int size) { return index >= 0 && index < size; }
template<class T> bool correct_index(int index, const T& v) { return correct_index(index, isize(v)); }
template<class T> void verify_index(int index, const T& v, exp_parser& ep) { if(!correct_index(index, v)) throw hr_parse_exception("bad index: " + its(index) + " at " + ep.where()); }
string unnamed = "unnamed";
EX void load_tile(exp_parser& ep, arbi_tiling& c, bool unit) {
c.shapes.emplace_back();
auto& cc = c.shapes.back();
cc.id = isize(c.shapes) - 1;
cc.orig_id = cc.id;
cc.is_mirrored = false;
cc.symmetric_value = 0;
cc.flags = 0;
cc.repeat_value = 1;
cc.apeirogonal = false;
bool is_symmetric = false;
while(ep.next() != ')') {
cld dist = 1;
ep.skip_white();
if(ep.eat("|")) {
cc.symmetric_value = ep.iparse();
is_symmetric = true;
ep.force_eat(")");
break;
}
if(ep.eat("*")) {
ld frep = ep.rparse(0);
if(isinf(frep)) {
cc.apeirogonal = true;
set_flag(ginf[gArbitrary].flags, qIDEAL, true);
if(ep.eat(",") && ep.eat("|")) {
is_symmetric = true;
if(isize(cc.in_edges) == 1 && ep.eat(")")) break;
cc.symmetric_value = ep.iparse();
}
ep.force_eat(")");
break;
}
int rep = int(frep+.5);
int repeat_from = 0;
int repeat_to = cc.in_edges.size();
if(rep == 0) {
cc.in_edges.resize(repeat_from);
cc.in_angles.resize(repeat_from);
cc.ideal_markers.resize(repeat_from);
}
else if(rep < 0) throw hr_parse_exception("don't know how to use a negative repeat in tile definition");
for(int i=1; i<rep; i++)
for(int j=repeat_from; j<repeat_to; j++) {
cc.in_edges.push_back(cc.in_edges[j]);
cc.in_angles.push_back(cc.in_angles[j]);
cc.ideal_markers.push_back(cc.ideal_markers[j]);
}
ep.skip_white();
if(ep.eat(",")) {
ep.force_eat("|");
is_symmetric = true;
if(repeat_to == 1 && ep.eat(")")) goto skip;
cc.symmetric_value = ep.iparse();
}
if(ep.eat(")")) {
skip:
if(repeat_from == 0) cc.repeat_value = rep;
break;
}
else throw hr_parse_exception("expecting ) after repeat");
}
if(!unit) {
dist = ep.parse(0);
ep.force_eat(",");
}
cld angle;
ep.skip_white();
if(ep.eat("[")) {
cc.in_edges.push_back(ep.validate_real(dist * ep.extra_params["distunit"]));
angle = ep.parse(0); ep.force_eat(",");
cc.in_angles.push_back(ep.validate_real(angle * ep.extra_params["angleunit"]));
cc.ideal_markers.push_back(true);
dist = ep.parse(0); ep.force_eat(",");
angle = ep.parse(0); ep.force_eat("]");
set_flag(ginf[gArbitrary].flags, qIDEAL, true);
}
else
angle = ep.parse(0);
cc.in_edges.push_back(ep.validate_real(dist * ep.extra_params["distunit"]));
cc.in_angles.push_back(ep.validate_real(angle * ep.extra_params["angleunit"]));
cc.ideal_markers.push_back(false);
if(ep.eat(",")) continue;
else if(ep.eat(")")) break;
else throw hr_parse_exception("expecting , or )");
}
try {
cc.build_from_angles_edges(c.is_combinatorial);
}
catch(hr_parse_exception& ex) {
throw hr_parse_exception(ex.s + ep.where());
}
catch(hr_polygon_error& poly) {
poly.params = ep.extra_params;
throw;
}
int n = cc.size();
if(is_symmetric && !cc.symmetric_value) cc.symmetric_value += n - (cc.apeirogonal ? 2 : 0);
cc.connections.resize(n);
for(int i=0; i<isize(cc.connections); i++)
cc.connections[i] = connection_t{cc.id, i, false};
if(cc.apeirogonal) {
cc.connections[n-2].eid = n-1;
cc.connections[n-1].eid = n-2;
}
cc.stretch_shear.resize(n, make_pair(1, 0));
}
EX bool do_unmirror = true;
template<class T> void cycle(vector<T>& t) {
std::rotate(t.begin(), t.begin() + 2, t.end());
}
/** \brief for tessellations which contain mirror rules, remove them by taking the orientable double cover */
EX void unmirror(arbi_tiling& c) {
if(cgflags & qAFFINE) return;
auto& mirror_rules = c.mirror_rules;
mirror_rules = 0;
for(auto& s: c.shapes)
for(auto& t: s.connections)
if(t.mirror)
mirror_rules++;
if(!mirror_rules) return;
auto& sh = c.shapes;
int s = isize(sh);
vector<int> mirrored_id(s, -1);
for(int i=0; i<s; i++)
if(!sh[i].symmetric_value) {
mirrored_id[i] = isize(sh);
sh.push_back(sh[i]);
}
int ss = isize(sh);
for(int i=0; i<ss; i++) {
sh[i].id = i;
if(i >= s) sh[i].is_mirrored = true;
}
for(int i=s; i<ss; i++) {
for(auto& v: sh[i].vertices)
v[1] = -v[1];
reverse(sh[i].edges.begin(), sh[i].edges.end());
for(auto& e: sh[i].edges) {
if(e == INFINITE_LEFT) e = INFINITE_RIGHT;
else if(e == INFINITE_RIGHT) e = INFINITE_LEFT;
}
reverse(sh[i].vertices.begin()+1, sh[i].vertices.end());
reverse(sh[i].angles.begin(), sh[i].angles.end()-1);
reverse(sh[i].connections.begin(), sh[i].connections.end());
if(sh[i].apeirogonal) {
cycle(sh[i].edges);
cycle(sh[i].vertices);
if(debugflags & DF_GEOM) println(hlog, "angles before = ", sh[i].angles);
cycle(sh[i].angles);
if(debugflags & DF_GEOM) println(hlog, "angles now = ", sh[i].angles);
cycle(sh[i].connections);
}
}
if(true) for(int i=0; i<ss; i++) {
for(auto& co: sh[i].connections) {
bool mirr = co.mirror ^ (i >= s);
co.mirror = false;
if(mirr && mirrored_id[co.sid] == -1) {
if(sh[co.sid].reflectable(co.eid)) {
co.eid = sh[co.sid].reflect(co.eid);
}
}
else if(mirr) {
co.sid = mirrored_id[co.sid];
co.eid = isize(sh[co.sid].angles) - 1 - co.eid;
if(sh[co.sid].apeirogonal)
co.eid = gmod(co.eid - 2, isize(sh[co.sid].angles));
}
}
}
c.was_unmirrored = true;
}
static void reduce_gcd(int& a, int b) {
a = abs(gcd(a, b));
}
EX void mirror_connection(arb::arbi_tiling& ac, connection_t& co) {
if(co.mirror && ac.shapes[co.sid].reflectable(co.eid)) {
co.eid = ac.shapes[co.sid].reflect(co.eid);
co.mirror = !co.mirror;
}
}
EX void compute_vertex_valence_prepare(arb::arbi_tiling& ac) {
int tcl = -1;
while(true) {
for(auto& sh: ac.shapes) {
int i = sh.id;
int n = isize(sh.vertices);
for(int k=sh.cycle_length; k<n; k++) {
auto co = sh.connections[k];
auto co1 = sh.connections[k-sh.cycle_length];
if(co.sid != co1.sid) {
println(hlog, "ik = ", tie(i,k), " co=", co, " co1=", co1, " cl=", sh.cycle_length);
throw hr_parse_exception("connection error #2 in compute_vertex_valence");
}
mirror_connection(ac, co);
mirror_connection(ac, co1);
reduce_gcd(ac.shapes[co.sid].cycle_length, co.eid - co1.eid);
}
for(int k=0; k<n; k++) {
auto co = sh.connections[k];
auto co0 = co;
co = ac.shapes[co.sid].connections[co.eid];
if(co.sid != i) throw hr_parse_exception("connection error in compute_vertex_valence");
co.mirror ^= co0.mirror;
mirror_connection(ac, co);
reduce_gcd(sh.cycle_length, k-co.eid);
}
if(debugflags & DF_GEOM)
println(hlog, "tile ", i, " cycle_length = ", sh.cycle_length, " / ", n);
}
int new_tcl = 0;
for(auto& sh: ac.shapes) {
auto& len = sh.cycle_length;
if(len < 0) len = -len;
new_tcl += len;
}
if(new_tcl == tcl) break;
tcl = new_tcl;
}
}
/** returns true if we need to recompute */
EX bool compute_vertex_valence_flat(arb::arbi_tiling& ac) {
for(auto& sh: ac.shapes) {
int n = sh.size();
int i = sh.id;
sh.vertex_valence.resize(n);
sh.vertex_period.resize(n);
sh.vertex_angles.resize(n);
for(int k=0; k<n; k++) {
ld total = 0;
int qty = 0, pqty = 0;
connection_t at = {i, k, false};
connection_t at1 = at;
vector<ld> anglelist;
do {
if(at.sid == at1.sid && (at.eid-at1.eid) % ac.shapes[at.sid].cycle_length == 0) pqty = 0;
if(qty && pqty == 0 && !total) break;
ld a = ac.shapes[at.sid].angles[at.eid];
while(a < 0) a += TAU;
while(a > TAU) a -= TAU;
total += a;
anglelist.push_back(a);
qty++;
pqty++;
at.eid++;
if(at.eid == isize(ac.shapes[at.sid].angles)) at.eid = 0;
at = ac.shapes[at.sid].connections[at.eid];
}
while(total < TAU - 1e-6);
if(total == 0) qty = OINF;
if(total > TAU + 1e-6) throw hr_parse_exception("improper total in compute_stats");
if(at.sid != i) throw hr_parse_exception("ended at wrong type determining vertex_valence");
if((at.eid - k) % ac.shapes[i].cycle_length) {
reduce_gcd(ac.shapes[i].cycle_length, at.eid - k);
return true;
}
sh.vertex_valence[k] = qty;
sh.vertex_period[k] = pqty;
sh.vertex_angles[k] = std::move(anglelist);
}
if(debugflags & DF_GEOM)
println(hlog, "computed vertex_valence of ", i, " as ", ac.shapes[i].vertex_valence);
}
return false;
}
/** returns true if we need to recompute */
EX bool compute_vertex_valence_generic(arb::arbi_tiling& ac) {
for(auto& sh: ac.shapes) {
int n = sh.size();
int i = sh.id;
sh.vertex_valence.resize(n);
for(int k=0; k<n; k++) {
connection_t at = {i, k, false};
transmatrix T = Id;
int qty = 0;
do {
if(qty && at.sid == i) {
auto co1 = at;
bool found = find_connection(T, Id, co1);
if(found) {
mirror_connection(ac, co1);
if((co1.eid - k) % ac.shapes[i].cycle_length) {
reduce_gcd(ac.shapes[i].cycle_length, co1.eid - k);
return true;
}
break;
}
}
if(at.mirror) {
if(at.eid == 0) at.eid = isize(ac.shapes[at.sid].angles);
at.eid--;
}
else {
at.eid++;
if(at.eid == isize(ac.shapes[at.sid].angles)) at.eid = 0;
}
auto at0 = at;
at = ac.shapes[at.sid].connections[at.eid];
T = T * get_adj(ac, at0.sid, at0.eid, at.sid, at.eid, at.mirror);
at.mirror ^= at0.mirror;
qty++;
}
while(qty < OINF);
sh.vertex_valence[k] = qty;
}
if(debugflags & DF_GEOM)
println(hlog, "computed vertex_valence of ", i, " as ", ac.shapes[i].vertex_valence);
}
return false;
}
EX void compute_vertex_valence(arb::arbi_tiling& ac) {
for(auto& sh: ac.shapes)
sh.cycle_length = isize(sh.vertices) / sh.repeat_value;
bool generic = false;
if(!ac.was_unmirrored) for(auto& sh: ac.shapes) if(sh.symmetric_value) generic = true;
for(auto& sh: ac.shapes) for(auto& co: sh.connections) if(co.mirror) generic = true;
if(cgflags & qAFFINE) generic = true;
if(ac.is_star) generic = true;
recompute:
compute_vertex_valence_prepare(ac);
if(generic ? compute_vertex_valence_generic(ac) : compute_vertex_valence_flat(ac)) goto recompute;
ac.have_valence = true;
ac.min_valence = UNKNOWN; ac.max_valence = 0;
for(auto& sh: ac.shapes)
for(auto& val: sh.vertex_valence) {
if(val < ac.min_valence) ac.min_valence = val;
if(val > ac.max_valence) ac.max_valence = val;
}
}
EX bool extended_football = true;
EX void check_football_colorability(arbi_tiling& c) {
if(!c.have_valence) return;
for(auto&sh: c.shapes) for(auto v: sh.vertex_valence)
if(v % 3) return;
for(int i=0; i<3; i++) {
for(auto&sh: c.shapes) sh.football_type = 3;
vector<int> aqueue;
c.shapes[0].football_type = i;
aqueue = {0};
bool bad = false;
for(int qi=0; qi<isize(aqueue); qi++) {
int sid = aqueue[qi];
auto& sh = c.shapes[sid];
for(int j=0; j<sh.size(); j++) {
auto &co = sh.connections[j];
auto t = sh.football_type;
if(c.have_ph && ((sh.flags & arcm::sfPH) != (t==2))) bad = true;
if(sh.apeirogonal && t < 2 && (isize(sh) & 1)) bad = true;
auto assign = [&] (int tt) {
auto& t1 = c.shapes[co.sid].football_type;
if(t1 == 3) {
t1 = tt;
aqueue.push_back(co.sid);
}
else {
if(t1 != tt) bad = true;
}
};
if(t < 2) {
if((j & 1) == t) assign(2); else assign((co.eid & 1) ? 0 : 1);
}
else {
assign((co.eid & 1) ? 1 : 0);
}
}
}
if(!bad) {
c.have_ph = 2;
for(auto& sh: c.shapes) if(sh.football_type == 2) sh.flags |= arcm::sfPH;
return;
}
}
if(extended_football && !c.have_tree) {
for(auto&sh: c.shapes)
sh.football_type = 0;
for(int i=0; i<3*isize(c.shapes); i++) {
for(auto&sh: c.shapes) {
int &res = sh.football_type;
int siz = sh.size();
if(sh.apeirogonal) siz -= 2;
else if(siz & 1) res |= 3;
if((sh.cycle_length & 1) && !sh.apeirogonal) {
if(res & 3) res |= 3;
}
if(sh.apeirogonal && (siz & 1)) {
if(res & 3) res |= 3;
}
if(sh.flags & arcm::sfPH) res |= 3;
for(int i=0; i<sh.size(); i++) {
auto co = sh.connections[i];
co.eid %= c.shapes[co.sid].cycle_length;
if(res & 1) {
if(i&1) {
if(co.eid & 1)
c.shapes[co.sid].football_type |= 1;
else
c.shapes[co.sid].football_type |= 2;
}
else
c.shapes[co.sid].football_type |= 4;
}
if(res & 2) {
if(!(i&1)) {
if(co.eid & 1)
c.shapes[co.sid].football_type |= 1;
else
c.shapes[co.sid].football_type |= 2;
}
else
c.shapes[co.sid].football_type |= 4;
}
if(res & 4) {
if(co.eid & 1)
c.shapes[co.sid].football_type |= 2;
else
c.shapes[co.sid].football_type |= 1;
}
}
}
}
c.is_football_colorable = true;
c.was_split_for_football = true;
for(auto&sh: c.shapes)
if(sh.football_type == 7)
c.is_football_colorable = false;
if(c.is_football_colorable) {
vector<array<int, 3> > new_indices(isize(c.shapes), make_array(-1, -1, -1));
auto oldshapes = c.shapes;
c.shapes.clear();
for(int i=0; i<isize(oldshapes); i++)
for(int t=0; t<3; t++)
if(!(oldshapes[i].football_type & (1<<t))) {
if(t == 1 && (oldshapes[i].cycle_length & 1) && !oldshapes[i].apeirogonal) continue;
new_indices[i][t] = isize(c.shapes);
c.shapes.push_back(oldshapes[i]);
c.shapes.back().football_type = t;
if(t == 2) c.shapes.back().flags |= arcm::sfPH;
}
for(int i=0; i<isize(oldshapes); i++)
for(int t=0; t<3; t++) {
int ni = new_indices[i][t];
if(ni == -1) continue;
auto& sh = c.shapes[ni];
sh.id = ni;
for(int j=0; j<isize(sh); j++) {
auto &co = sh.connections[j];
auto assign = [&] (int tt) {
auto ni1 = new_indices[co.sid][tt];
if(ni1 == -1 && tt == 1) {
ni1 = new_indices[co.sid][0];
co.eid += oldshapes[co.sid].cycle_length;
co.eid %= isize(oldshapes[co.sid]);
}
co.sid = ni1;
};
if(sh.apeirogonal && j >= isize(sh)-2) {
co.sid = ni;
if(t < 2 && (isize(sh) & 1)) co.sid = new_indices[i][t^1];
continue;
}
co.eid %= oldshapes[co.sid].cycle_length;
if(t < 2) {
if((j & 1) == t) assign(2); else assign((co.eid & 1) ? 0 : 1);
}
else {
assign((co.eid & 1) ? 1 : 0);
}
}
if((sh.cycle_length&1) && (t < 2) && !sh.apeirogonal) sh.cycle_length *= 2;
if(debugflags & DF_GEOM)
println(hlog, tie(i,t), " becomes ", ni, " with connections ", sh.connections, " and cycle length = ", sh.cycle_length);
}
c.have_ph = 2;
return;
}
}
for(auto&sh: c.shapes) sh.football_type = 3;
}
EX void add_connection_sub(arbi_tiling& c, int ai, int as, int bi, int bs, int m) {
int as0 = as, bs0 = bs;
auto& ash = c.shapes[ai];
auto& bsh = c.shapes[bi];
do {
ash.connections[as] = connection_t{bi, bs, m};
as = gmod(as + ash.size() / ash.repeat_value, ash.size());
}
while(as != as0);
do {
c.shapes[bi].connections[bs] = connection_t{ai, as, m};
bs = gmod(bs + bsh.size() / bsh.repeat_value, bsh.size());
}
while(bs != bs0);
}
EX void add_connection(arbi_tiling& c, int ai, int as, int bi, int bs, int m) {
auto& ash = c.shapes[ai];
auto& bsh = c.shapes[bi];
add_connection_sub(c, ai, as, bi, bs, m);
int as1, bs1;
if(ash.symmetric_value) {
as1 = ash.reflect(as);
add_connection_sub(c, ai, as1, bi, bs, !m);
}
if(bsh.symmetric_value) {
bs1 = bsh.reflect(bs);
add_connection_sub(c, ai, as, bi, bs1, !m);
}
if(ash.symmetric_value && bsh.symmetric_value)
add_connection_sub(c, ai, as1, bi, bs1, m);
}
EX void set_defaults(arb::arbi_tiling& c, bool keep_sliders, string fname) {
c.order++;
c.name = unnamed;
c.comment = "";
c.filename = fname;
c.cscale = 1;
c.range = 0;
c.boundary_ratio = 1;
c.floor_scale = .5;
c.have_ph = 0;
c.have_line = false;
c.is_football_colorable = false;
c.have_tree = false;
c.have_valence = false;
c.yendor_backsteps = 0;
c.is_star = false;
c.is_combinatorial = false;
c.was_unmirrored = false;
c.was_split_for_football = false;
c.shapes.clear();
if(!keep_sliders) {
c.sliders.clear();
c.intsliders.clear();
}
}
EX void load(const string& fname, bool load_as_slided IS(false), bool keep_sliders IS(false)) {
fhstream f(fname, "rt");
if(!f.f) throw hr_parse_exception("file " + fname + " does not exist");
string s;
while(true) {
int c = fgetc(f.f);
if(c < 0) break;
s += c;
}
auto& c = load_as_slided ? slided : current;
set_defaults(c, keep_sliders, fname);
int qsliders = 0, qintsliders = 0;
exp_parser ep;
ep.s = s;
ld angleunit = 1, distunit = 1;
auto addflag = [&] (int f) {
int ai;
if(ep.next() == ')') ai = isize(c.shapes)-1;
else ai = ep.iparse();
verify_index(ai, c.shapes, ep);
c.shapes[ai].flags |= f;
ep.force_eat(")");
};
while(true) {
ep.extra_params["distunit"] = distunit;
ep.extra_params["angleunit"] = angleunit;
ep.skip_white();
if(ep.next() == 0) break;
if(ep.eat("#")) {
bool doubled = ep.eat("#");
while(ep.eat(" ")) ;
string s = "";
while(ep.next() >= 32) s += ep.next(), ep.at++;
if(doubled) {
if(c.name == unnamed) c.name = s;
else {
c.comment += s;
c.comment += "\n";
}
}
}
else if(ep.eat("c2(")) {
ld curv = ep.rparse(0);
ep.force_eat(")");
ginf[gArbitrary].g = curv > 0 ? giSphere2 : curv < 0 ? giHyperb2 : giEuclid2;
ginf[gArbitrary].sides = 7;
set_flag(ginf[gArbitrary].flags, qCLOSED, curv > 0);
set_flag(ginf[gArbitrary].flags, qAFFINE, false);
geom3::apply_always3();
}
else if(ep.eat("e2.")) {
ginf[gArbitrary].g = giEuclid2;
ginf[gArbitrary].sides = 7;
set_flag(ginf[gArbitrary].flags, qCLOSED, false);