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archimedean.cpp
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archimedean.cpp
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// Hyperbolic Rogue -- Archimedean Tilings
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file archimedean.cpp
* \brief Archimedean tilings
*
* These are tilings available in the 'Archimedean' option in Geometry Experiments; simpler Archimedean tilings are defined in other files.
*/
#include "hyper.h"
namespace hr {
EX namespace arcm {
EX bool in() { return cgflags & qARCHI; }
EX ld euclidean_edge_length = .5;
#if HDR
struct hr_archimedean_error : hr_exception {
hr_archimedean_error(string _s) : hr_exception(_s) {}
};
struct archimedean_tiling {
int coloring;
string symbol;
vector<int> faces;
vector<int> adj;
vector<bool> invert;
vector<int> nflags;
bool have_ph, have_line, have_symmetry;
int real_faces;
int real_face_type;
int repetition;
int N;
bool regular;
ld euclidean_angle_sum;
vector<int> flags;
vector<vector<pair<int, int>>> adjacent;
vector<vector<pair<ld, ld>>> triangles;
void make_match(int a, int i, int b, int j);
void prepare();
void compute_sum();
void compute_geometry();
void parse();
void parse(string s) { symbol = s; parse(); }
ld edgelength;
vector<ld> inradius, circumradius, alphas;
vector<vector<int>> matches;
vector<int> periods;
vector<int> tilegroup;
vector<int> groupoffset;
int tilegroups;
int errors;
string errormsg;
pair<int, int>& get_adj(heptagon *h, int cid);
pair<int, int>& get_adj(heptspin hs) { return get_adj(hs.at, hs.spin); }
pair<ld, ld>& get_triangle(heptagon *h, int cid);
pair<ld, ld>& get_triangle(heptspin hs) { return get_triangle(hs.at, hs.spin); }
pair<ld, ld>& get_triangle(const pair<int, int>& p, int delta = 0);
pair<int, int>& get_adj(const pair<int, int>& p, int delta = 0);
int support_threecolor();
int support_threecolor_bitruncated();
int support_football();
bool support_chessboard();
void regroup();
string world_size();
void get_nom_denom(int& anom, int& adenom);
geometryinfo1& get_geometry(ld mul = 1);
eGeometryClass get_class() { return get_geometry().kind; }
bool get_step_values(int& steps, int& single_step);
ld dual_tile_area();
transmatrix adjcell_matrix(heptagon *h, int d);
ld scale();
};
#endif
#if HDR
static constexpr int sfPH = 1;
static constexpr int sfLINE = 2;
static constexpr int sfCHESS = 4;
static constexpr int sfTHREE = 8;
static constexpr int sfSEMILINE = 16;
#endif
#if CAP_ARCM
EX archimedean_tiling current;
EX archimedean_tiling fake_current;
EX archimedean_tiling& current_or_fake() {
if(fake::in_ext()) return fake_current;
return current;
}
/** id of vertex in the archimedean tiling
* odd numbers = reflected tiles
* 0, 2, ..., 2(N-1) = as in the symbol
* 2N = bitruncated tile
*/
EX short& id_of(heptagon *h) {
return h->zebraval;
}
/** which index in id_of's neighbor list does h->move(0) have */
EX short& parent_index_of(heptagon *h) {
return h->emeraldval;
}
/** total number of neighbors */
EX int neighbors_of(heptagon *h) {
return isize(current.triangles[id_of(h)]);
}
EX int gcd(int x, int y) { return x ? gcd(y%x, x) : y < 0 ? -y : y; }
void archimedean_tiling::make_match(int a, int i, int b, int j) {
if(isize(adjacent[a]) != isize(adjacent[b])) {
DEBB(DF_GEOM, ("(error here)"));
errormsg = XLAT("polygons match incorrectly");
errors++;
}
if(matches[a][b] == -1)
matches[a][b] = j - i, matches[b][a] = i - j;
else
periods[a] = periods[b] = gcd(matches[a][b] - (j-i), periods[a]);
}
/** mostly to protect the user from entering too large numbers */
const int MAX_EDGE_ARCM = FULL_EDGE;
/** compute the edge length of an Archimedean tiling. Each element of facemul is (face sides, multiplicity) */
EX ld compute_edgelength(vector<pair<ld, ld>> facemul, ld halftotal IS(M_PI)) {
ld elmin = 0, elmax = hyperbolic ? 10 : sphere ? M_PI : 2 * euclidean_edge_length;
ld edgelength;
for(int p=0; p<100; p++) {
edgelength = (elmin + elmax) / 2;
ld alpha_total = 0;
for(auto fm: facemul) {
if(isinf(fm.first)) {
ld u = sqrt(cosh(edgelength) * 2 - 2);
ld a = atan2(1, u/2);
alpha_total += a * fm.second;
}
else {
ld gamma = M_PI / fm.first;
auto c = asin_auto(sin_auto(edgelength/2) / sin(gamma));
hyperpoint h = lxpush(c) * spin(M_PI - 2*gamma) * lxpush0(c);
ld a = atan2(h);
cyclefix(a, 0);
if(a < 0) a = -a;
alpha_total += a * fm.second;
}
}
if(isnan(alpha_total)) elmax = edgelength;
else if(sphere ^ (alpha_total > halftotal)) elmin = edgelength;
else elmax = edgelength;
}
return edgelength;
}
void archimedean_tiling::compute_sum() {
N = isize(faces);
euclidean_angle_sum = 0;
for(int f: faces) euclidean_angle_sum += (f-2.) / f;
real_faces = 0, real_face_type = 0;
for(int i=0; i<N; i++) if(faces[i] > 2) real_faces++, real_face_type += faces[i];
real_face_type /= 2;
}
void archimedean_tiling::prepare() {
compute_sum();
for(int i: faces) if(i > MAX_EDGE_ARCM) {
errormsg = XLAT("currently no more than %1 edges", its(MAX_EDGE_ARCM));
errors++;
return;
}
if(isize(faces) > MAX_EDGE_ARCM/2) {
errormsg = XLAT("currently no more than %1 faces in vertex", its(MAX_EDGE_ARCM/2));
errors++;
return;
}
for(int i: faces) if(i < 2) {
errormsg = XLAT("not enough edges");
errors++;
return;
}
vector<int> nondigonal;
for(int i: faces) if(i > 2) nondigonal.push_back(i);
if(isize(faces) < 2 || isize(nondigonal) == 1) {
errormsg = XLAT("not enough faces");
errors++;
return;
}
if(isize(nondigonal) == 2 && faces[0] != faces[1]) {
errormsg = XLAT("invalid dihedron");
errors++;
return;
}
for(int i=0; i<N; i++) {
bool forward = false;
int f = faces[i];
int i0 = i;
for(int k=0; k<f; k++) {
forward ^= invert[i0];
i0 = adj[i0];
if(forward) { if(faces[i0] != f) { errormsg = XLAT("face mismatch"); errors++; return; } i0++; if(i0 == N) i0 = 0; }
else { if(i0 == 0) i0 = N; i0--; if(faces[i0] != f) { errormsg = XLAT("face mismatch"); errors++; return; } }
}
for(int k=0; k<N; k++) {
f = faces[(i+N-k-1) % N];
if(forward) { if(faces[i0] != f) { errormsg = XLAT("face mismatch II "); errors++; return; } i0++; if(i0 == N) i0 = 0; }
else { if(i0 == 0) i0 = N; i0--; if(faces[i0] != f) { errormsg = XLAT("face mismatch II"); errors++; return; } }
}
}
if(real_faces) {
for(int i=1; i<isize(faces); i++) if(faces[i] == 2 && faces[i-1] == 2) {
errormsg = XLAT("Not implemented.");
errors++;
return;
}
if(faces[0] == 2 && faces[isize(faces)-1] == 2) {
errormsg = XLAT("Not implemented.");
errors++;
return;
}
}
if(real_faces == 2) {
for(int i: faces) if(i != real_face_type) {
errormsg = XLAT("polygons match incorrectly");
errors++;
}
}
errors = 0;
/* build the 'adjacent' table */
int M = 2 * N + 2;
adjacent.clear();
adjacent.resize(M);
have_symmetry = false;
for(int i=0; i<N; i++) if(invert[i]) have_symmetry = true;
matches.resize(M);
for(int i=0; i<M; i++) {
matches[i].resize(M);
for(int j=0; j<M; j++) matches[i][j] = i==j ? 0 : -1;
}
periods.resize(M);
for(int i=0; i<M; i++) periods[i] = i<2*N ? faces[i/2] : N;
for(int i=0; i<N; i++) {
for(int oi=0; oi<1; oi++) {
int at = (i+oi)%N;
int inv = oi;
DEBB0(DF_GEOM, ("vertex "));
for(int z=0; z<faces[i]; z++) {
DEBB0(DF_GEOM, (hr::format("[%d %d] " , at, inv)));
adjacent[2*i+oi].emplace_back(2*N+int(inv), inv ? (2*at+2*N-2) % (2*N) : 2*at);
if(invert[at]) inv ^= 1;
at = adj[at];
if(inv) at = (at+1) % N;
else at = (at+N-1) % N;
}
if(!inv) make_match(2*i, 0, inv ? (2*at+2*N-1) % 2*N : 2*at, 0);
DEBB(DF_GEOM, (hr::format("-> [%d %d]\n", at, inv)));
}
}
for(int i=0; i<N; i++) {
adjacent[2*N].emplace_back(2*i, 0);
int ai = (i+1) % N;
adjacent[2*N].emplace_back(2*N+int(invert[ai]), (2*adj[ai]+2*N-1) % (2*N));
}
for(int d=0; d<=2*N; d+=2) {
int s = isize(adjacent[d]);
for(int i=0; i<s; i++) {
auto& orig = adjacent[d][s-1-i];
adjacent[d+1].emplace_back(orig.first ^ 1, orig.second);
}
}
for(int d=0; d<M; d++) {
int s = isize(adjacent[d]);
for(int i=0; i<s; i++) {
auto& orig = adjacent[d][i];
if(orig.first & 1) orig.second = isize(adjacent[orig.first]) - 1 - orig.second;
}
}
if(debugflags & DF_GEOM) {
for(int i=0; i<M; i++) {
DEBB0(DF_GEOM, ("adjacent ", i, ":"));
for(int j=0; j<isize(adjacent[i]); j++) {
auto p = adjacent[i][j];
DEBB0(DF_GEOM, (" ", p));
}
DEBB(DF_GEOM, ("\n"));
}
}
for(int i=0; i<M; i++) {
for(int j=0; j<isize(adjacent[i]); j++) {
auto p = adjacent[i][j];
auto q = adjacent[p.first][p.second];
make_match(i, j, q.first, q.second);
}
}
/* verify all the triangles */
for(int i=0; i<M; i++) {
for(int j=0; j<isize(adjacent[i]); j++) {
int ai = i, aj = j;
DEBB0(DF_GEOM, ("triangle "));
for(int s=0; s<3; s++) {
DEBB0(DF_GEOM, (hr::format("[%d %d] ", ai, aj)));
tie(ai, aj) = adjacent[ai][aj];
aj++; if(aj >= isize(adjacent[ai])) aj = 0;
}
DEBB(DF_GEOM, (hr::format("-> [%d %d]\n", ai, aj)));
make_match(i, j, ai, aj);
}
}
for(int i=0; i<2*N; i++) {
for(int j=0; j<isize(adjacent[i]); j++) {
auto aa = make_pair(i, j);
aa = get_adj(aa, 1);
aa = get_adj(aa, 2);
aa = get_adj(aa, 1);
aa = get_adj(aa, 2);
make_match(i, j, aa.first, aa.second);
}
}
regroup();
}
void archimedean_tiling::regroup() {
int M = 2 * N + 2;
for(int i=0; i<M; i++) for(int j=0; j<M; j++) if(matches[i][j] != -1)
for(int l=0; l<M; l++) for(int k=0; k<M; k++) if(matches[j][k] != -1) {
make_match(i, 0, k, matches[i][j] + matches[j][k]);
make_match(i, 0, k, matches[i][j] + matches[j][k] + gcd(periods[i], periods[j]));
}
tilegroup.clear();
tilegroup.resize(M, -1);
groupoffset.resize(M);
tilegroups = 0;
for(int i=0; i<M; i+=(have_symmetry?1:2)) if(tilegroup[i] == -1) {
if(periods[i] < 0) periods[i] = -periods[i];
for(int j=0; j<M; j++) if(matches[i][j] != -1)
tilegroup[j] = tilegroups, groupoffset[j] = matches[i][j] % periods[i];
tilegroups++;
}
flags.clear();
flags.resize(M, 0);
for(int i=0; i<M; i++)
for(int j=0; j<M; j++) {
if(tilegroup[i] == tilegroup[j]) {
flags[i] |= nflags[j/2];
if(j%2 == 1 && (nflags[j/2] & sfSEMILINE))
flags[i] |= sfLINE;
}
}
if(!have_ph) {
for(int i=0; i<M; i++) if(tilegroup[i] == 0) flags[i] |= sfPH;
}
if(debugflags & DF_GEOM) {
for(int i=0; i<M; i+=(have_symmetry?1:2)) {
DEBB(DF_GEOM, (hr::format("tiling group of %2d: [%2d]%2d+Z%2d\n", i, tilegroup[i], groupoffset[i], periods[i])));
}
}
}
geometryinfo1& archimedean_tiling::get_geometry(ld mul) {
if(euclidean_angle_sum * mul < 1.999999) return giSphere2;
else if(euclidean_angle_sum * mul > 2.000001) return giHyperb2;
else return giEuclid2;
}
void archimedean_tiling::compute_geometry() {
if(embedded_plane && geometry != gArchimedean) return;
if(embedded_plane) return IPF(compute_geometry());
auto gg = get_geometry();
for(int a=0; a<2; a++) {
auto& arr = a ? geom3::ginf_backup : ginf;
if(arr.empty()) continue;
if(gg.kind == gcSphere) arr[gArchimedean].g = arr[gSphere].g;
if(gg.kind == gcEuclid) arr[gArchimedean].g = arr[gEuclid].g;
if(gg.kind == gcHyperbolic) arr[gArchimedean].g = arr[gNormal].g;
set_flag(arr[gArchimedean].flags, qCLOSED, gg.kind == gcSphere);
}
DEBB(DF_GEOM, (hr::format("euclidean_angle_sum = %f\n", float(euclidean_angle_sum))));
bool infake = fake::in_ext();
dynamicval<eGeometry> dv(geometry, gArchimedean);
/* compute the geometry */
inradius.resize(N+1); inradius[N] = 0;
circumradius.resize(N+1); circumradius[N] = 0;
alphas.resize(N);
ld total = M_PI;
dynamicval<geometryinfo1> dgi(ginf[geometry].g, ginf[geometry].g);
if(infake) {
total *= N / fake::around;
ginf[geometry].g = get_geometry(fake::around / N);
}
ld elmin = 0, elmax = hyperbolic ? 10 : sphere ? M_PI : 2 * euclidean_edge_length;
/* inradius[N] is used in farcorner and nearcorner. Probably a bug */
bool need_flip = embedded_plane;
if(need_flip) geom3::light_flip(true);
if(real_faces == 2) {
/* standard methods fail for dihedra, but the answer is easy */
edgelength = TAU / faces[0];
for(int i=0; i<N; i++)
if(faces[i] == 2)
alphas[i] = 0,
circumradius[i] = M_PI / real_face_type,
inradius[i] = 0;
else
alphas[i] = 90._deg,
circumradius[i] = inradius[i] = 90._deg;
}
else if(real_faces == 0) {
// these are called hosohedra
edgelength = M_PI;
for(int i=0; i<N; i++)
alphas[i] = M_PI / N,
circumradius[i] = 90._deg,
inradius[i] = 0;
}
else for(int p=0; p<100; p++) {
/* unfortunately we cannot just use compute_edgelength because we need to set other values */
edgelength = (elmin + elmax) / 2;
ld alpha_total = 0;
for(int i=0; i<N; i++) {
ld gamma = M_PI / faces[i];
auto& c = circumradius[i];
c = asin_auto(sin_auto(edgelength/2) / sin(gamma));
inradius[i] = hdist0(mid(xpush0(circumradius[i]), cspin(0, 1, 2*gamma) * xpush0(circumradius[i])));
hyperpoint h = xpush(c) * cspin(0, 1, M_PI - 2*gamma) * xpush0(c);
ld a = atan2(h);
cyclefix(a, 0);
if(a < 0) a = -a;
alphas[i] = a;
alpha_total += alphas[i];
}
if(debugflags & DF_GEOM)
if(p < 10 || p == 99)
println(hlog, "edgelength = ", edgelength, " angles = ", alphas, " inradius = ", inradius, " circumradius = ", circumradius);
if(isnan(alpha_total)) elmax = edgelength;
else if(sphere ^ (alpha_total > total)) elmin = edgelength;
else elmax = edgelength;
if(euclid) break;
}
if(need_flip) geom3::light_flip(false);
DEBB(DF_GEOM, (hr::format("computed edgelength = %f\n", float(edgelength))));
triangles.clear();
triangles.resize(2*N+2);
for(int i=0; i<N; i++) for(int j=0; j<2; j++)
for(int k=0; k<faces[i]; k++)
triangles[2*i+j].emplace_back(TAU/faces[i], circumradius[i]);
for(int k=0; k<N; k++) {
triangles[2*N].emplace_back(alphas[k], circumradius[k]);
triangles[2*N].emplace_back(alphas[(k+1)%N], edgelength);
triangles[2*N+1].emplace_back(alphas[N-1-k], edgelength);
triangles[2*N+1].emplace_back(alphas[N-1-k], circumradius[N-1-k]);
}
for(auto& ts: triangles) {
ld total = 0;
for(auto& t: ts) tie(t.first, total) = make_pair(total, total + t.first);
}
if(debugflags & DF_GEOM) for(auto& ts: triangles) {
DEBB0(DF_GEOM, ("T"));
for(auto& t: ts) DEBB0(DF_GEOM, (hr::format(" %f@%f", float(t.first), float(t.second))));
DEBB(DF_GEOM, ());
}
regular = true;
for(int i: faces) if(i != faces[0]) regular = false;
}
ld archimedean_tiling::scale() {
if(real_faces == 0 && N == 2) return 90._deg;
if(real_faces == 2) return 90._deg;
if(real_faces == 0) return TAU / N;
return edgelength;
}
map<heptagon*, vector<pair<heptagon*, transmatrix> > > altmap;
EX map<heptagon*, pair<heptagon*, transmatrix>> archimedean_gmatrix;
EX hrmap *current_altmap;
heptagon *build_child(heptspin p, pair<int, int> adj);
bool skip_digons(heptspin hs, int step);
void connect_digons_too(heptspin h1, heptspin h2);
void fixup_matrix(transmatrix& T, const transmatrix& X, ld step);
void connectHeptagons(heptspin hi, heptspin hs);
/** @brief should we use gmatrix to compute relative_matrix faster? (not while in fake Archimedean) */
EX bool use_gmatrix = true;
/** @brief like adj, but in pure
* not used by arcm itself, but used in fake arcm
*/
EX geometry_information *alt_cgip[2];
EX geometry_information *find_alt_cgip() {
auto& galt_cgip = alt_cgip[embedded_plane];
if(galt_cgip) return galt_cgip;
check_cgi();
cgi.require_basics();
return galt_cgip = cgip;
}
struct hrmap_archimedean : hrmap {
map<gp::loc, struct cdata> eucdata;
heptagon *origin;
heptagon *getOrigin() override { return origin; }
hrmap_archimedean() {
dynamicval<hrmap*> curmap(currentmap, this);
int id = DUAL ? current.N * 2 : 0;;
int N0 = isize(current.adjacent[id]);
origin = init_heptagon(N0);
origin->s = hsOrigin;
parent_index_of(origin) = DUAL ? 1 : 0;
id_of(origin) = id;
origin->c7 = newCell(N0/DUALMUL, origin);
heptagon *alt = NULL;
if(hyperbolic) {
bool f = geom3::flipped;
if(f) geom3::light_flip(false);
if(1) {
dynamicval<eGeometry> g(geometry, gNormal);
dynamicval<eVariation> gv(variation, eVariation::pure);
dynamicval<geometry_information*> gi(cgip, find_alt_cgip());
alt = init_heptagon(S7);
alt->s = hsOrigin;
alt->alt = alt;
current_altmap = newAltMap(alt);
}
if(f) geom3::light_flip(true);
}
bool f = geom3::flipped;
if(f) geom3::light_flip(false);
transmatrix T = lxpush(.01241) * spin(1.4117) * lxpush(0.1241) * Id;
if(f) geom3::light_flip(true);
archimedean_gmatrix[origin] = make_pair(alt, T);
altmap[alt].emplace_back(origin, T);
if(current.real_faces == 0 && DUAL) {
heptspin hs(origin, 0);
heptagon *hnew = build_child(hs, current.get_adj(hs));
for(int s=1; s<2*current.N; s++)
origin->c.connect(s, hnew, s, false);
}
else if(current.real_faces == 0) {
may_create_step(origin, 0);
heptagon *o0 = origin->move(0);
may_create_step(origin, 1);
heptagon *o1 = origin->move(1);
for(int s=1; s<2*current.N; s+=2)
o0->c.connect(s, o1, 2*current.N-s, false);
for(int s=2; s<2*current.N; s+=2) {
heptspin hs(o0, s);
heptagon *hnew = build_child(hs, current.get_adj(hs));
// no need to specify archimedean_gmatrix and altmap
hnew->c.connect(1, heptspin(o1, 2*current.N-s));
}
o1->c.connect(1, o0, 2*current.N-1, false);
}
else if(origin->degree() == 2) {
may_create_step(origin, 0);
may_create_step(origin, 1);
origin->move(0)->c.connect(1, origin->move(1), 2*current.N-1, false);
origin->move(1)->c.connect(1, origin->move(0), 2*current.N-1, false);
}
auto_compute_range(origin->c7);
}
~hrmap_archimedean() {
clearfrom(origin);
altmap.clear();
archimedean_gmatrix.clear();
if(current_altmap) {
dynamicval<eGeometry> g(geometry, gNormal);
dynamicval<eVariation> gv(variation, eVariation::pure);
dynamicval<geometry_information*> gi(cgip, find_alt_cgip());
delete current_altmap;
current_altmap = NULL;
}
}
void verify() override { }
heptagon *create_step(heptagon *h, int d) override {
bool f = geom3::flipped;
if(f) {
dynamicval<int> uc(cgip->use_count, cgip->use_count+1);
auto bcgip = cgip;
geom3::light_flip(false);
check_cgi();
cgi.require_basics();
auto h1 = create_step(h, d);
geom3::light_flip(true);
cgip = bcgip;
return h1;
}
DEBB(DF_GEOM, (heptspin(h,d), " ~ ?"));
dynamicval<geometryinfo1> gi(ginf[geometry].g, ginf[gArchimedean].g);
heptspin hi(h, d);
while(skip_digons(hi, 1)) hi++;
auto& t1 = current.get_triangle(hi);
// * spin(-tri[id][pi+i].first) * lxpush(t.second) * pispin * spin(tri[id'][p'+d'].first)
auto& p1 = archimedean_gmatrix[h];
heptagon *alt = p1.first;
transmatrix T = p1.second * spin(-t1.first) * lxpush(t1.second);
transmatrix U = Id;
if(hyperbolic) {
dynamicval<int> uc(cgip->use_count, cgip->use_count+1);
dynamicval<eGeometry> g(geometry, gNormal);
dynamicval<eVariation> gv(variation, eVariation::pure);
dynamicval<geometry_information*> gi(cgip, find_alt_cgip());
dynamicval<hrmap*> cm(currentmap, current_altmap);
U = T;
current_altmap->virtualRebase(alt, T);
U = U * iso_inverse(T);
}
if(euclid) {
/* hash the rough coordinates as heptagon* alt */
size_t s = size_t(T[0][LDIM]+.261) * 124101 + size_t(T[1][LDIM]+.261) * 82143;
alt = (heptagon*) s;
}
DEBB(DF_GEOM, ("look for: ", alt, " / ", kz(T * C0)));
for(auto& p2: altmap[alt]) if(same_point_may_warn(p2.second * tile_center(), T * tile_center())) {
DEBB(DF_GEOM, ("cell found: ", p2.first));
for(int d2=0; d2<p2.first->degree(); d2++) {
heptspin hs(p2.first, d2);
auto& t2 = current.get_triangle(p2.first, d2);
transmatrix T1 = T * spin(M_PI + t2.first);
DEBB(DF_GEOM, ("compare: ", kz(T1 * lxpush0(1)), ":: ", kz(p2.second * lxpush0(1))));
if(same_point_may_warn(T1 * lxpush0(1), p2.second * lxpush0(1))) {
// T1 = p2.second
// T * spin(pi+t2.first) == p2.second
// p1.second * spinm(-t1.first) * lxpush(t1.second) * spin(pi+t2.first) == p2.second
// bring p1 and p2 closer, to prevent floating point errors
if(hyperbolic) {
fixup_matrix(p1.second, U * p2.second * spin(-M_PI - t2.first) * lxpush(-t1.second) * spin(t1.first), 0.25);
fixup_matrix(p2.second, T1, 0.25);
}
while(skip_digons(hs, -1)) hs--;
connectHeptagons(hi, hs);
connect_digons_too(hi, hs);
return h->move(d);
}
}
DEBB(DF_GEOM, ("but rotation not found"));
}
auto& t2 = current.get_triangle(current.get_adj(hi));
transmatrix T1 = T * spin(M_PI + t2.first);
fixmatrix(T1);
heptagon *hnew = build_child(hi, current.get_adj(hi));
altmap[alt].emplace_back(hnew, T1);
archimedean_gmatrix[hnew] = make_pair(alt, T1);
connect_digons_too(hi, heptspin(hnew, 0));
return hnew;
}
void draw_at(cell *at, const shiftmatrix& where) override {
dq::clear_all();
dq::enqueue(at->master, where);
while(!dq::drawqueue.empty()) {
auto& p = dq::drawqueue.front();
heptagon *h = p.first;
shiftmatrix V = p.second;
dq::drawqueue.pop();
int id = id_of(h);
int S = isize(current.triangles[id]);
if(id < 2*current.N ? !DUAL : !PURE) {
if(!do_draw(h->c7, V)) continue;
drawcell(h->c7, V);
}
for(int i=0; i<S; i++) {
if(DUAL && (i&1)) continue;
h->cmove(i);
if(PURE && id >= 2*current.N && h->move(i) && id_of(h->move(i)) >= 2*current.N) continue;
shiftmatrix V1 = V * current.adjcell_matrix(h, i);
optimize_shift(V1);
dq::enqueue(h->move(i), V1);
}
}
}
transmatrix adj(cell *c, int dir) override {
return calc_relative_matrix(c->cmove(dir), c, C0);
}
transmatrix relative_matrixh(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
if(use_gmatrix && gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7))
return inverse_shift(gmatrix0[h1->c7], gmatrix0[h2->c7]);
transmatrix gm = Id, where = Id;
auto& cof = current_or_fake();
while(h1 != h2) {
for(int i=0; i<neighbors_of(h1); i++) {
if(h1->move(i) == h2) {
return gm * cof.adjcell_matrix(h1, i) * where;
}
}
if(h1->distance > h2->distance) {
gm = gm * cof.adjcell_matrix(h1, 0);
h1 = h1->move(0);
}
else {
where = iso_inverse(cof.adjcell_matrix(h2, 0)) * where;
h2 = h2->move(0);
}
}
return gm * where;
}
ld spin_angle(cell *c, int d) override {
auto &cof = current_or_fake();
if(PURE) {
auto& t1 = cof.get_triangle(c->master, d-1);
return -(t1.first + M_PI / c->type);
}
else if(DUAL) {
auto& t1 = cof.get_triangle(c->master, 2*d);
return -t1.first;
}
else { /* BITRUNCATED */
auto& t1 = cof.get_triangle(c->master, d);
return -t1.first;
}
}
void find_cell_connection(cell *c, int d) override {
if(PURE) {
if(arcm::id_of(c->master) < arcm::current.N * 2) {
heptspin hs = heptspin(c->master, d) + wstep + 2 + wstep + 1;
c->c.connect(d, hs.at->c7, hs.spin, hs.mirrored);
}
else c->c.connect(d, c, d, false);
}
else if(DUAL) {
if(arcm::id_of(c->master) >= arcm::current.N * 2) {
heptagon *h2 = createStep(c->master, d*2);
int d1 = c->master->c.spin(d*2);
c->c.connect(d, h2->c7, d1/2, false);
}
else {
printf("bad connection\n");
c->c.connect(d,c,d,false);
}
}
else hrmap::find_cell_connection(c, d);
}
int shvid(cell *c) override {
auto& ac = arcm::current;
int id = arcm::id_of(c->master);
if(ac.regular && id>=2 && id < 2*ac.N) id &= 1;
return id;
}
int full_shvid(cell *c) override {
return id_of(c->master) + 20 * parent_index_of(c->master);
}
hyperpoint get_corner(cell *c, int cid, ld cf) override {
auto &ac = arcm::current_or_fake();
if(PURE) {
if(arcm::id_of(c->master) >= ac.N*2) return C0;
auto& t = ac.get_triangle(c->master, cid-1);
return xspinpush0(-t.first, t.second * 3 / cf * (ac.real_faces == 0 ? 0.999 : 1));
}
if(BITRUNCATED) {
auto& t0 = ac.get_triangle(c->master, cid-1);
auto& t1 = ac.get_triangle(c->master, cid);
hyperpoint h0 = xspinpush0(-t0.first, t0.second * 3 / cf * (ac.real_faces == 0 ? 0.999 : 1));
hyperpoint h1 = xspinpush0(-t1.first, t1.second * 3 / cf * (ac.real_faces == 0 ? 0.999 : 1));
return mid3(tile_center(), h0, h1);
}
if(DUAL) {
auto& t0 = ac.get_triangle(c->master, 2*cid-1);
return xspinpush0(-t0.first, t0.second * 3 / cf * (ac.real_faces == 0 ? 0.999 : 1));
}
return C0;
}
int pattern_value(cell *c) override {
if(sphere) return c->master->fiftyval;
return hrmap::pattern_value(c);
}
};
EX hrmap *new_map() { return new hrmap_archimedean; }
heptagon *build_child(heptspin p, pair<int, int> adj) {
indenter ind;
auto h = buildHeptagon1(tailored_alloc<heptagon> (isize(current.adjacent[adj.first])), p.at, p.spin, hstate(1), 0);
DEBB(DF_GEOM, ("NEW ", p, " ~ ", heptspin(h, 0)));
id_of(h) = adj.first;
parent_index_of(h) = adj.second;
int nei = neighbors_of(h);
h->c7 = newCell(nei/DUALMUL, h);
h->distance = p.at->distance + 1;
if(adj.first < 2*current.N && !DUAL) {
int s = 0;
heptspin hs(p);
while(id_of(hs.at->move(0)) >= 2 * current.N) {
s += hs.spin / 2 - 1;
hs = hs - hs.spin + wstep - 1;
}
h->fieldval = hs.at->move(0)->fieldval + s + hs.spin/2;
}
else
h->fieldval = -100;
h->fiftyval = isize(archimedean_gmatrix);
if(p.at->s == hsOrigin)
h->rval1 = 1 + (p.spin % 2);
else {
if(p.spin % 2 == 0)
h->rval1 = p.at->move(0)->rval1;
else
h->rval1 = 3 - p.at->move(0)->rval1 - p.at->rval1;
}
h->rval0 = hrand(256);
heptspin hs(h, 0);
return h;
}
bool skip_digons(heptspin hs, int step) {
return
isize(current.adjacent[current.get_adj(hs).first]) == 2 ||
isize(current.adjacent[current.get_adj(hs+step).first]) == 2;
}
void connect_digons_too(heptspin h1, heptspin h2) {
if(skip_digons(h1, -1)) {
h1--, h2++;
heptagon *hnew = build_child(h1, current.get_adj(h1));
// no need to specify archimedean_gmatrix and altmap
hnew->c.connect(1, h2);
h1--, h2++;
DEBB(DF_GEOM, (hr::format("OL2 %p.%d ~ %p.%d\n", hr::voidp(h1.at), h1.spin, hr::voidp(h2.at), h2.spin)));
h1.at->c.connect(h1.spin, h2);
}
}
void connectHeptagons(heptspin hi, heptspin hs) {
DEBB(DF_GEOM, ("OLD ", hi, " ~ ", hs));
if(hi.at->move(hi.spin) == hs.at && hi.at->c.spin(hi.spin) == hs.spin) {
DEBB(DF_GEOM, (hr::format("WARNING: already connected\n")));
return;
}
if(hi.peek()) {
DEBB(DF_GEOM, (hr::format("ERROR: already connected left\n")));
throw hr_archimedean_error("Archimedean error: already connected left");
}
if(hs.peek()) {
DEBB(DF_GEOM, (hr::format("ERROR: already connected right\n")));
throw hr_archimedean_error("Archimedean error: already connected right");
}
hi.at->c.connect(hi.spin, hs);
auto p = current.get_adj(hi);
if(current.tilegroup[p.first] != current.tilegroup[id_of(hs.at)]) {
printf("should merge %d %d\n", p.first, id_of(hs.at));
current.make_match(p.first, p.second, id_of(hs.at), hs.spin + parent_index_of(hs.at));
current.regroup();
}
// heptagon *hnew = build_child(h, d, get_adj(h, d).first, get_adj(h, d).second);
}
/** T and X are supposed to be equal -- move T so that it is closer to X */
void fixup_matrix(transmatrix& T, const transmatrix& X, ld step) {
for(int i=0; i<MXDIM; i++)
for(int j=0; j<MXDIM; j++)
T[i][j] = (T[i][j] * (1-step) + X[i][j] * step);
/*
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
if(T[i][j] - X[i][j] > 1e-3) exit(1);
*/
fixmatrix(T);
}
pair<ld, ld>& archimedean_tiling::get_triangle(heptagon *h, int cid) {
return triangles[id_of(h)][gmod(parent_index_of(h) + cid, neighbors_of(h))];
}
pair<int, int>& archimedean_tiling::get_adj(heptagon *h, int cid) {
return adjacent[id_of(h)][gmod(parent_index_of(h) + cid, neighbors_of(h))];
}
pair<int, int>& archimedean_tiling::get_adj(const pair<int, int>& p, int delta) {
return adjacent[p.first][gmod(p.second + delta, isize(adjacent[p.first]))];