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hyperrogue/archimedean.cpp
? b25730d5c9 geometry flags part 1
2019-09-12 22:38:39 +02:00

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// Hyperbolic Rogue
// This file implements the 'Archimedean tilings' geometry.
// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details
namespace hr {
namespace arcm {
#if CAP_ARCM
#define SDEBUG(x) if(debug_geometry) { x; fflush(stdout); }
static const int sfPH = 1;
static const int sfLINE = 2;
static const int sfCHESS = 4;
static const int sfTHREE = 8;
static const int sfSEMILINE = 16;
archimedean_tiling current;
// id of vertex in the archimedean tiling
// odd numbers = reflected tiles
// 0, 2, ..., 2(N-1) = as in the symbol
// 2N = bitruncated tile
short& id_of(heptagon *h) {
return h->zebraval;
}
// which index in id_of's neighbor list does h->move[0] have
short& parent_index_of(heptagon *h) {
return h->emeraldval;
}
// total number of neighbors
int neighbors_of(heptagon *h) {
return isize(current.triangles[id_of(h)]);
}
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])) {
SDEBUG(printf("(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]);
}
void archimedean_tiling::prepare() {
euclidean_angle_sum = 0;
for(int f: faces) euclidean_angle_sum += (f-2.) / f;
for(int i: faces) if(i > MAX_EDGE) {
errormsg = XLAT("currently no more than %1 edges", its(MAX_EDGE));
errors++;
return;
}
if(isize(faces) > MAX_EDGE/2) {
errormsg = XLAT("currently no more than %1 faces in vertex", its(MAX_EDGE));
errors++;
return;
}
if(isize(faces) < 2) {
errormsg = XLAT("not enough faces");
errors++;
return;
}
for(int i: faces) if(i < 2) {
errormsg = XLAT("not enough edges");
errors++;
return;
}
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;
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 */
N = isize(faces);
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;
for(int i=0; i<M; i++) for(int j=0; j<M; j++) matches[i][j] = i==j ? 0 : -1;
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;
SDEBUG(printf("vertex ");)
for(int z=0; z<faces[i]; z++) {
SDEBUG(printf("[%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);
SDEBUG(printf("-> [%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;
}
}
SDEBUG(
for(int i=0; i<M; i++) {
printf("adjacent %2d:", i);
for(int j=0; j<isize(adjacent[i]); j++) {
auto p = adjacent[i][j];
printf(" (%d,%d)", p.first, p.second);
}
printf("\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;
SDEBUG( printf("triangle "); )
for(int s=0; s<3; s++) {
SDEBUG( printf("[%d %d] ", ai, aj); fflush(stdout); )
tie(ai, aj) = adjacent[ai][aj];
aj++; if(aj >= isize(adjacent[ai])) aj = 0;
}
SDEBUG( printf("-> [%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]));
}
for(int i=0; i<M; i++) tilegroup[i] = -1;
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);
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;
}
SDEBUG( for(int i=0; i<M; i+=(have_symmetry?1:2)) {
printf("tiling group of %2d: [%2d]%2d+Z%2d\n", i, tilegroup[i], groupoffset[i], periods[i]);
printf("\n");
} )
}
eGeometryClass archimedean_tiling::get_class() {
if(euclidean_angle_sum < 1.999999) return gcSphere;
else if(euclidean_angle_sum > 2.000001) return gcHyperbolic;
else return gcEuclid;
}
void archimedean_tiling::compute_geometry() {
ginf[gArchimedean].cclass = get_class();
set_flag(ginf[gArchimedean].flags, qBOUNDED, get_class() == gcSphere);
SDEBUG( printf("euclidean_angle_sum = %f\n", float(euclidean_angle_sum)); )
dynamicval<eGeometry> dv(geometry, gArchimedean);
/* compute the geometry */
inradius.resize(N);
circumradius.resize(N);
alphas.resize(N);
ld elmin = 0, elmax = hyperbolic ? 10 : sphere ? M_PI : 1;
if(real_faces == 2) {
/* standard methods fail for dihedra, but the answer is easy */
edgelength = 2 * M_PI / 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] = M_PI/2,
circumradius[i] = inradius[i] = M_PI/2;
}
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] = M_PI/2,
inradius[i] = 0;
}
else for(int p=0; p<100; p++) {
edgelength = (elmin + elmax) / 2;
ld alpha_total = 0;
for(int i=0; i<N; i++) {
ld crmin = 0, crmax = sphere ? M_PI/2 : 10;
ld el = 0;
for(int q=0; q<100; q++) {
circumradius[i] = (crmin + crmax) / 2;
hyperpoint p1 = xpush0(circumradius[i]);
hyperpoint p2 = spin(2 * M_PI / faces[i]) * p1;
inradius[i] = hdist0(mid(p1, p2));
el = hdist(p1, p2);
if(el > edgelength) crmax = circumradius[i];
else crmin = circumradius[i];
}
if(el < edgelength - 1e-3) alpha_total += 100; // could not make an edge that long
hyperpoint h = xpush(edgelength/2) * xspinpush0(M_PI/2, inradius[i]);
ld a = atan2(-h[1], h[0]);
if(a < 0) a += 2 * M_PI;
alphas[i] = a;
// printf(" H = %s alp = %f\n", display(h), (float) atan2(-h[1], h[0]));
alpha_total += alphas[i];
}
// printf("el = %f alpha = %f\n", float(edgelength), float(alpha_total));
if(sphere ^ (alpha_total > M_PI)) elmin = edgelength;
else elmax = edgelength;
if(euclid) break;
}
SDEBUG( printf("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(2*M_PI/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);
// printf("total = %lf\n", double(total));
}
SDEBUG( for(auto& ts: triangles) {
printf("T");
for(auto& t: ts) printf(" %f@%f", float(t.first), float(t.second));
printf("\n");
} )
}
ld archimedean_tiling::scale() {
if(real_faces == 0 && N == 2) return M_PI / 2;
if(real_faces == 2) return M_PI / 2;
if(real_faces == 0) return 2 * M_PI / N;
return edgelength;
}
map<heptagon*, vector<pair<heptagon*, transmatrix> > > altmap;
map<heptagon*, pair<heptagon*, transmatrix>> archimedean_gmatrix;
hrmap *current_altmap;
heptagon *build_child(heptspin p, pair<int, int> adj);
struct hrmap_archimedean : hrmap {
heptagon *origin;
heptagon *getOrigin() { return origin; }
hrmap_archimedean() {
int id = DUAL ? current.N * 2 : 0;;
int N0 = isize(current.adjacent[id]);
origin = tailored_alloc<heptagon> (N0);
origin->s = hsOrigin;
origin->emeraldval = 0;
origin->zebraval = 0;
origin->fiftyval = 0;
origin->fieldval = 0;
origin->rval0 = origin->rval1 = 0;
origin->cdata = NULL;
origin->alt = NULL;
origin->distance = 0;
parent_index_of(origin) = DUAL ? 1 : 0;
id_of(origin) = id;
origin->c7 = newCell(N0/DUALMUL, origin);
heptagon *alt = NULL;
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gNormal);
alt = tailored_alloc<heptagon> (S7);
alt->s = hsOrigin;
alt->emeraldval = 0;
alt->zebraval = 0;
alt->distance = 0;
alt->c7 = NULL;
alt->alt = alt;
alt->cdata = NULL;
current_altmap = newAltMap(alt);
}
transmatrix T = xpush(.01241) * spin(1.4117) * xpush(0.1241) * Id;
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) {
create_adjacent(origin, 0);
heptagon *o0 = origin->move(0);
create_adjacent(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) {
create_adjacent(origin, 0);
create_adjacent(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);
}
base_distlimit = 0;
celllister cl(origin->c7, 1000, 200, NULL);
base_distlimit = cl.dists.back();
if(sphere) base_distlimit = SEE_ALL;
}
~hrmap_archimedean() {
clearfrom(origin);
altmap.clear();
archimedean_gmatrix.clear();
if(current_altmap) {
dynamicval<eGeometry> g(geometry, gNormal);
delete current_altmap;
current_altmap = NULL;
}
}
void verify() { }
};
hrmap *new_map() { return new hrmap_archimedean; }
transmatrix adjcell_matrix(heptagon *h, int d);
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);
SDEBUG( printf("NEW %p.%d ~ %p.0\n", p.at, p.spin, h); )
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++;
SDEBUG( printf("OL2 %p.%d ~ %p.%d\n", h1.at, h1.spin, h2.at, h2.spin); )
h1.at->c.connect(h1.spin, h2);
}
}
void connectHeptagons(heptspin hi, heptspin hs) {
SDEBUG( printf("OLD %p.%d ~ %p.%d\n", hi.at, hi.spin, hs.at, hs.spin); )
if(hi.at->move(hi.spin) == hs.at && hi.at->c.spin(hi.spin) == hs.spin) {
SDEBUG( printf("WARNING: already connected\n"); )
return;
}
if(hi.peek()) {
SDEBUG( printf("ERROR: already connected left\n"); )
exit(1);
}
if(hs.peek()) {
SDEBUG( printf("ERROR: already connected right\n"); )
exit(1);
}
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<3; i++)
for(int j=0; j<3; 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);
}
void create_adjacent(heptagon *h, int d) {
SDEBUG( printf("%p.%d ~ ?\n", h, d); )
heptspin hi(h, d);
while(skip_digons(hi, 1)) hi++;
auto& t1 = current.get_triangle(hi);
// * spin(-tri[id][pi+i].first) * xpush(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) * xpush(t1.second);
transmatrix U = Id;
if(hyperbolic) {
dynamicval<eGeometry> g(geometry, gNormal);
U = T;
virtualRebaseSimple(alt, T);
U = U * inverse(T);
}
if(euclid)
alt = encodeId(pair_to_vec(int(T[0][2]), int(T[1][2])));
SDEBUG( println(hlog, "look for: ", alt, " / ", T * C0); )
for(auto& p2: altmap[alt]) if(intval(p2.second * C0, T * C0) < 1e-4) {
SDEBUG( println(hlog, "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);
SDEBUG( print(hlog, "compare: ", T1 * xpush0(1)); )
SDEBUG( println(hlog, ":: ", p2.second * xpush0(1)); )
if(intval(T1 * xpush0(1), p2.second * xpush0(1)) < 1e-4) {
// T1 = p2.second
// T * spin(pi+t2.first) == p2.second
// p1.second * spinm(-t1.first) * xpush(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) * xpush(-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;
}
}
SDEBUG( println(hlog, "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));
}
pair<ld, ld>& archimedean_tiling::get_triangle(heptagon *h, int cid) {
return triangles[id_of(h)][(parent_index_of(h) + cid + MODFIXER) % neighbors_of(h)];
}
pair<int, int>& archimedean_tiling::get_adj(heptagon *h, int cid) {
return adjacent[id_of(h)][(parent_index_of(h) + cid + MODFIXER) % neighbors_of(h)];
}
pair<int, int>& archimedean_tiling::get_adj(const pair<int, int>& p, int delta) {
return adjacent[p.first][(p.second + delta + MODFIXER) % isize(adjacent[p.first])];
}
pair<ld, ld>& archimedean_tiling::get_triangle(const pair<int, int>& p, int delta) {
return triangles[p.first][(p.second + delta + MODFIXER) % isize(adjacent[p.first])];
}
transmatrix adjcell_matrix(heptagon *h, int d) {
auto& t1 = current.get_triangle(h, d);
heptagon *h2 = h->move(d);
int d2 = h->c.spin(d);
auto& t2 = current.get_triangle(h2, d2);
return spin(-t1.first) * xpush(t1.second) * spin(M_PI + t2.first);
}
void draw() {
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));
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, 0, false);
}
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;
transmatrix V1 = V * adjcell_matrix(h, i);
bandfixer bf(V1);
dq::enqueue(h->move(i), V1);
}
}
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1) {
if(gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7))
return inverse(gmatrix0[h1->c7]) * gmatrix0[h2->c7];
transmatrix gm = Id, where = Id;
while(h1 != h2) {
for(int i=0; i<neighbors_of(h1); i++) {
if(h1->move(i) == h2) {
return gm * adjcell_matrix(h1, i) * where;
}
}
if(h1->distance > h2->distance) {
gm = gm * adjcell_matrix(h1, 0);
h1 = h1->move(0);
}
else {
where = inverse(adjcell_matrix(h2, 0)) * where;
h2 = h2->move(0);
}
}
return gm * where;
}
int fix(heptagon *h, int spin) {
int type = isize(current.adjacent[id_of(h)]);
spin %= type;
if(spin < 0) spin += type;
return spin;
}
void archimedean_tiling::parse() {
int at = 0;
auto peek = [&] () { if(at == isize(symbol)) return char(0); else return symbol[at]; };
auto is_number = [&] () { char p = peek(); return p >= '0' && p <= '9'; };
auto read_number = [&] () { int result = 0; while(is_number()) result = 10 * result + peek() - '0', at++; return result; };
faces.clear(); nflags.clear();
have_line = false;
have_ph = false;
int nflags0;
auto nfback = [this, &nflags0] () -> int& { if(nflags.empty()) return nflags0; else return nflags.back(); };
while(true) {
if(peek() == ')' || (peek() == '(' && isize(faces)) || peek() == 0) break;
else if((peek() == 'L') && faces.size()) {
if(!nflags.empty()) nfback() |= sfLINE;
have_line = true, at++;
}
else if((peek() == 'l') && faces.size()) {
if(!nflags.empty()) nfback() |= sfSEMILINE;
have_line = true, at++;
}
else if((peek() == 'H' || peek() == 'h') && faces.size()) {
if(!nflags.empty()) nfback() |= sfPH;
have_ph = true, at++;
}
else if(is_number()) faces.push_back(read_number()), nflags.push_back(0);
else if(peek() == '^' && !faces.empty()) {
at++;
int rep = read_number();
if(rep == 0) nflags.pop_back(), faces.pop_back();
for(int i=1; i<rep; i++) nflags.push_back(nfback()), faces.push_back(faces.back());
}
else at++;
}
nflags.push_back(nflags0);
repetition = 1;
N = isize(faces);
invert.clear(); invert.resize(N, true);
adj.clear(); adj.resize(N, 0); for(int i=0; i<N; i++) adj[i] = i;
while(peek() != 0) {
if(peek() == '^') at++, repetition = read_number();
else if(peek() == '(') {
at++; int a = read_number(); while(!is_number() && !among(peek(), '(', '[', ')',']', 0)) at++;
if(is_number()) { int b = read_number(); adj[a] = b; adj[b] = a; invert[a] = invert[b] = false; }
else { invert[a] = false; }
}
else if(peek() == '[') {
at++; int a = read_number(); while(!is_number() && !among(peek(), '(', '[', ')',']', 0)) at++;
if(is_number()) { int b = read_number(); adj[a] = b; adj[b] = a; invert[a] = invert[b] = true; }
else { invert[a] = true; }
}
else at++;
}
for(int i=0; i<N * (repetition-1); i++)
faces.push_back(faces[i]),
nflags.push_back(nflags[i]),
invert.push_back(invert[i]),
adj.push_back(adj[i] + N);
N *= repetition;
prepare();
}
#if CAP_COMMANDLINE
void show();
int readArgs() {
using namespace arg;
if(0) ;
else if(argis("-symbol")) {
PHASEFROM(2);
archimedean_tiling at;
shift(); at.parse(args());
if(at.errors) {
println(hlog, "error: ", at.errormsg);
}
else {
set_geometry(gArchimedean);
need_reset_geometry = true;
current = at;
showstartmenu = false;
}
}
else if(argis("-dgeom")) debug_geometry = true;
else if(argis("-dual")) { PHASEFROM(2); set_variation(eVariation::dual); }
else if(argis("-d:arcm"))
launch_dialog(show);
else return 1;
return 0;
}
#endif
#if CAP_COMMANDLINE
auto hook =
addHook(hooks_args, 100, readArgs);
#endif
int archimedean_tiling::support_threecolor() {
return (isize(faces) == 3 && invert[0] && invert[1] && invert[2] && faces[0] % 2 == 0 && faces[1] % 2 == 0 && faces[2] % 2 == 0) ? 2 :
tilegroup[N*2] > 1 ? 1 :
0;
return 2;
}
int archimedean_tiling::support_threecolor_bitruncated() {
for(int i: faces) if(i % 2) return 0;
return 2;
}
int archimedean_tiling::support_football() {
return
have_ph ? 1 :
(isize(faces) == 3 && invert[0] && invert[1] && invert[2] && faces[1] % 2 == 0 && faces[2] % 2 == 0) ? 2 :
0;
}
bool archimedean_tiling::support_chessboard() {
return N % 2 == 0;
}
bool pseudohept(cell *c) {
if(DUAL)
return !(c->master->rval0 & 3);
int id = id_of(c->master);
if(PURE)
return current.flags[id] & arcm::sfPH;
if(BITRUNCATED)
return id < current.N * 2;
return false;
}
bool chessvalue(cell *c) {
if(DUAL)
return c->master->rval1 - 1;
return c->master->fieldval & 1;
}
bool linespattern(cell *c) {
return current.flags[id_of(c->master)] & arcm::sfLINE;
}
int threecolor(cell *c) {
if(current.have_ph)
return !arcm::pseudohept(c);
else if(PURE)
return current.tilegroup[id_of(c->master)];
else {
int id = id_of(c->master);
if(current.support_threecolor() == 2) return id < current.N * 2 ? (id&1) : 2;
return current.tilegroup[id];
}
}
int cEucRegular = 0x008000;
int cEucSemiregular = 0x40C040;
int cPlatonic = 0x000080;
int cArchimedean = 0x4040C0;
int cPrism = 0x40A0A0;
int cAntiPrism = 0x80A0A0;
int cHyperRegular = 0x800000;
int cHyperSemi = 0xC04040;
int cWeird = 0xA000A0;
vector<pair<string, int> > samples = {
/* Euclidean */
{"(3,3,3,3,3,3)", cEucRegular},
{"(4,4,4,4)", cEucRegular},
{"(6,6,6)", cEucRegular},
{"(8,8,4)", cEucSemiregular},
{"(4,6,12)", cEucSemiregular},
{"(6,4,3,4)", cEucSemiregular},
{"(3,6,3,6)", cEucSemiregular},
{"(3,12,12)", cEucSemiregular},
{"(4,4,3L,3L,3L) [3,4]", cEucSemiregular},
{"(3,3,3,3,6) (1,2)(0,4)(3)", cEucSemiregular},
{"(3,3,4,3,4) (0,4)(1)(2,3)", cEucSemiregular},
/* Platonic */
{"(3,3,3)", cPlatonic},
{"(3,3,3,3)", cPlatonic},
{"(3,3,3,3,3)", cPlatonic},
{"(4,4,4)", cPlatonic},
{"(5,5,5)", cPlatonic},
/* Archimedean solids */
{"(3,6,6)", cArchimedean},
{"(3,4,3,4)", cArchimedean},
{"(3,8,8)", cArchimedean},
{"(4,6,6)", cArchimedean},
{"(3,4,4,4)", cArchimedean},
{"(4,6,8)", cArchimedean},
{"(3,3,3,3,4) (1,2)(0,4)(3)", cArchimedean},
{"(3,5,3,5)", cArchimedean},
{"(3,10,10)", cArchimedean},
{"(5,6,6)", cArchimedean},
{"(3,4,5,4)", cArchimedean},
{"(4,6,10)", cArchimedean},
{"(3,3,3,3,5) (1,2)(0,4)(3)", cArchimedean},
/* prisms */
{"(3,4,4)", cPrism},
{"(5,4,4)", cPrism},
{"(6,4,4)", cPrism},
{"(7,4,4)", cPrism},
/* sample antiprisms */
{"(3,3,3,4)(1)(2)", cAntiPrism},
{"(3,3,3,5)(1)(2)", cAntiPrism},
{"(3,3,3,6)(1)(2)", cAntiPrism},
{"(3,3,3,7)(1)(2)", cAntiPrism},
/* hyperbolic ones */
{"(3)^7", cHyperRegular},
{"(4)^5", cHyperRegular},
{"(4)^6", cHyperRegular},
{"(5,5,5,5)", cHyperRegular},
{"(7,7,7)", cHyperRegular},
{"(8,8,8)", cHyperRegular},
{"(7,6^2)", cHyperSemi},
{"(4,6,14)", cHyperSemi},
{"(3,4,7,4)", cHyperSemi},
{"(6,6,4L,4L)", cHyperSemi},
{"(8,8,4L,4L)", cHyperSemi},
{"(3,3,3,3,7) (1,2)(0,4)(3)", cHyperSemi},
{"(3H,6,6,6) (1,0)[2](3)", cHyperSemi},
{"(3,6,6,6) (0 1)(2)(3)", cHyperSemi},
{"(3,4,4L,4L,4)", cHyperSemi}, // buggy
{"(3l,4l,4,4,4) (0 1)[2 3](4)", cHyperSemi},
{"(3,4,4,4,4) (0 1)(2)(3)(4)", cHyperSemi},
{"(3,4,4L,4L,4L,4)", cHyperSemi},
{"(6,6,3L,3L,3L) (0 2)(1)(3)(4)", cHyperSemi},
{"(5,3,5,3,3) (0 1)(2 3)(4)", cHyperSemi},
{"(4,3,3,3,3,3) (0 1)(2 3)(4 5)", cHyperSemi},
{"(3l,5l,5,5,5,5) (0 1)[2 3](4)(5)", cHyperSemi},
{"(3,5,5,5,5,5) (0 1)(2 4)(3 5)", cHyperSemi},
{"(3l,5l,5,5,5,5) (0 1)(2 4)[3 5]", cHyperSemi},
{"(3l,5l,5,5,5,5) (0 1)[2 4](3)(5)", cHyperSemi},
{"(3,5,5,5,5,5) (0 1)(2)(3)(4)(5)", cHyperSemi},
/* interesting symmetry variants */
{"(3,3,3,3,3,3) (0,1)(2,3)(4,5)", cEucRegular},
{"(3,3H,3,3,3L,3L,3L) (0 4)(1 2)(3)(5)(6)", cHyperRegular},
{"(3,3H,3,3,3L,3L,3L) (0 4)(1 2)(3)[5 6]", cHyperRegular},
{"(3,3H,3,3L,3,3L,3L) [0 4](1 2)[3 5](6)", cHyperRegular},
/* with digons */
{"(2,3,3,3,3,3) (2,3)(4,5)", cWeird},
{"(6,6)", cWeird},
{"(2,2)", cWeird},
{"(2,2,2,2,2,2)", cWeird},
{"(6,6,2)", cWeird},
{"(6,2,6,2)", cWeird},
};
int lastsample = 0;
vector<archimedean_tiling> tilings;
int spos = 0;
archimedean_tiling edited;
bool symbol_editing;
void next_variation() {
set_variation(
PURE ? eVariation::dual :
DUAL ? eVariation::bitruncated :
eVariation::pure);
need_reset_geometry = true;
start_game();
}
void enable(archimedean_tiling& arct) {
stop_game();
if(!archimedean) set_variation(eVariation::pure);
set_geometry(gArchimedean);
patterns::whichPattern = patterns::PAT_NONE;
current = arct;
#if CAP_TEXTURE
if(texture::config.tstate == texture::tsActive && texture::cgroup == cpThree) {
patterns::whichPattern = patterns::PAT_COLORING;
if(geosupport_threecolor() < 2) {
if(arct.support_threecolor() == 2) set_variation(eVariation::pure);
else if(arct.support_threecolor_bitruncated() == 2) set_variation(eVariation::bitruncated);
}
}
if(texture::config.tstate == texture::tsActive && texture::cgroup == cpFootball) {
patterns::whichPattern = patterns::PAT_TYPES, patterns::subpattern_flags = patterns::SPF_FOOTBALL;
if(geosupport_football() < 2) set_variation(eVariation::bitruncated);
}
if(texture::config.tstate == texture::tsActive && texture::cgroup == cpChess) {
patterns::whichPattern = patterns::PAT_CHESS;
if(!geosupport_chessboard()) {
if(arct.support_chessboard()) set_variation(eVariation::pure);
else if(arct.support_threecolor_bitruncated() == 2) set_variation(eVariation::dual);
}
}
#endif
need_reset_geometry = true;
start_game();
}
function<void()> setcanvas(char c) {
return [c] () {
stop_game();
firstland = specialland = laCanvas;
patterns::whichCanvas = c;
start_game();
};
};
void show() {
if(lastsample < isize(samples)) {
string s = samples[lastsample].first;
int col = samples[lastsample].second;
lastsample++;
archimedean_tiling tested;
tested.parse(s);
if(tested.errors) {
println(hlog, "WARNING: ", tested.errors, " errors on ", s, " '", tested.errormsg, "'");
}
else {
tested.coloring = col;
tilings.push_back(move(tested));
/* sort(tilings.begin(), tilings.end(), [] (archimedean_tiling& s1, archimedean_tiling& s2) {
if(s1.euclidean_angle_sum < s2.euclidean_angle_sum - 1e-6) return true;
if(s2.euclidean_angle_sum < s1.euclidean_angle_sum - 1e-6) return false;
return s1.symbol < s2.symbol;
}); */
}
}
cmode = sm::SIDE | sm::MAYDARK;
gamescreen(0);
dialog::init(XLAT("Archimedean tilings"));
if(symbol_editing) {
dialog::addSelItem("edit", dialog::view_edited_string(), '/');
dialog::add_action([] () {
symbol_editing = false;
if(!edited.errors) enable(edited);
});
dialog::addBreak(100);
if(edited.errors)
dialog::addInfo(edited.errormsg, 0xFF0000);
else
dialog::addInfo(XLAT("OK"), 0x00FF00);
dialog::addBreak(100);
dialog::addSelItem(XLAT("full angle"), fts(edited.euclidean_angle_sum * 180) + "°", 0);
dialog::addSelItem(XLAT("size of the world"), edited.world_size(), 0);
edited.compute_geometry();
dialog::addSelItem(XLAT("edge length"), fts(edited.edgelength) + (edited.get_class() == gcEuclid ? XLAT(" (arbitrary)") : ""), 0);
current.compute_geometry();
dialog::addBreak(100);
}
else {
string cs = archimedean ? current.symbol : XLAT("OFF");
dialog::addSelItem("edit", cs, '/');
dialog::add_action([] () {
symbol_editing = true;
edited = current;
dialog::start_editing(edited.symbol);
edited.parse();
});
dialog::addBreak(100);
int nextpos = spos;
int shown = 0;
while(nextpos < isize(tilings) && shown < 10) {
auto &ps = tilings[nextpos++];
bool valid = true;
string suffix = "";
#if CAP_TEXTURE
if(texture::config.tstate == texture::tsActive && texture::cgroup == cpThree) {
valid = false;
if(ps.support_threecolor() == 2) valid = true, suffix += bitruncnames[int(eVariation::pure)];
if(ps.support_threecolor_bitruncated() == 2) valid = true, suffix += bitruncnames[int(eVariation::bitruncated)];
}
if(texture::config.tstate == texture::tsActive && texture::cgroup == cpFootball) {
if(ps.support_football() == 2) suffix += bitruncnames[int(eVariation::pure)];
suffix += bitruncnames[int(eVariation::bitruncated)];
}
if(texture::config.tstate == texture::tsActive && texture::cgroup == cpChess && !ps.support_chessboard()) {
valid = false;
if(ps.support_chessboard()) valid = true, suffix += bitruncnames[int(eVariation::pure)];
if(ps.support_threecolor_bitruncated() == 2) valid = true, suffix += bitruncnames[int(eVariation::dual)];
}
#endif
if(!valid) continue;
dialog::addSelItem(ps.symbol, fts(ps.euclidean_angle_sum * 180) + "°" + suffix, 'a' + shown);
dialog::lastItem().color = ps.coloring;
dialog::add_action([&] () { enable(ps); });
shown++;
}
dialog::addItem(XLAT("next page"), '-');
if(shown == 0) nextpos = 0;
dialog::add_action([nextpos] () {
if(nextpos >= isize(tilings))
spos = 0;
else spos = nextpos;
});
dialog::addItem(XLAT("previous page"), '=');
dialog::add_action([] () {
spos -= 10;
if(spos < 0) spos = 0;
});
if(archimedean) {
dialog::addSelItem(XLAT("size of the world"), current.world_size(), 0);
dialog::addSelItem(XLAT("edge length"), current.get_class() == gcEuclid ? (fts(current.edgelength) + XLAT(" (arbitrary)")) : fts6(current.edgelength), 0);
dialog::addItem(XLAT("color by symmetries"), 't');
dialog::add_action(setcanvas('A'));
}
else {
dialog::addBreak(100);
dialog::addBreak(100);
dialog::addBreak(100);
}
if(true) {
dialog::addItem(XLAT("color by sides"), 'u');
dialog::add_action(setcanvas('B'));
}
if(geosupport_threecolor() == 2) {
dialog::addItem(XLAT("three colors"), 'w');
dialog::add_action(setcanvas('T'));
}
else if(geosupport_football() == 2) {
dialog::addItem(XLAT("football"), 'w');
dialog::add_action(setcanvas('F'));
}
else if(geosupport_chessboard()) {
dialog::addItem(XLAT("chessboard"), 'w');
dialog::add_action(setcanvas('c'));
}
else dialog::addBreak(100);
if(archimedean) {
dialog::addSelItem(XLAT("variations"), gp::operation_name(), 'v');
dialog::add_action(next_variation);
}
else dialog::addBreak(100);
}
dialog::addHelp();
dialog::addBack();
dialog::display();
keyhandler = [] (int sym, int uni) {
if(symbol_editing && sym == SDLK_RETURN) sym = uni = '/';
dialog::handleNavigation(sym, uni);
if(symbol_editing && dialog::handle_edit_string(sym, uni)) {
edited.parse(edited.symbol);
return;
}
if(doexiton(sym, uni)) popScreen();
};
}
string archimedean_tiling::world_size() {
if(get_class() == gcEuclid) return "∞";
int nom = 2 - N, denom = 2;
for(int f: faces) {
int g = gcd(denom, f);
nom = (nom * f + denom) / g;
denom = denom / g * f;
}
int anom = 0, adenom = 1;
if(BITRUNCATED || DUAL) anom = 1, adenom = 1;
if(!DUAL) for(int f: faces) {
int g = gcd(adenom, f);
anom = (anom * f + adenom) / g;
adenom = adenom / g * f;
}
anom *= 2 * denom, adenom *= nom;
int g = gcd(anom, adenom);
if(g != 0) {
anom /= g; adenom /= g;
}
if(adenom < 0) anom = -anom, adenom = -adenom;
string s;
bool hyp = (anom < 0);
if(hyp) anom = -anom;
if(adenom != 1)
s += its(anom) + "/" + its(adenom);
else
s += its(anom);
if(hyp) s += " exp(∞)";
return s;
}
int degree(heptagon *h) {
return isize(current.adjacent[id_of(h)]);
}
bool is_vertex(heptagon *h) {
return id_of(h) >= 2 * current.N;
}
int valence() {
if(PURE) return arcm::current.N;
if(BITRUNCATED) return 3;
// in DUAL, usually valence would depend on the vertex.
// 3 is the most interesting, as it allows us to kill hedgehog warriors
int total = 0;
for(int i: current.faces) {
if(i == 3) return 3;
total += i;
}
return total / isize(current.faces);
}
#endif
}
}
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