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hyperrogue/geometry2.cpp
? fe174d8873 3D:: elliptic space
2019-09-12 22:38:40 +02:00

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// Hyperbolic Rogue
// advanced geometry
// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details
namespace hr {
transmatrix &ggmatrix(cell *c);
void fixelliptic(transmatrix& at) {
if(elliptic && at[DIM][DIM] < 0) {
for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++)
at[i][j] = -at[i][j];
}
}
void fixelliptic(hyperpoint& h) {
if(elliptic && h[DIM] < 0)
for(int i=0; i<MDIM; i++) h[i] = -h[i];
}
transmatrix master_relative(cell *c, bool get_inverse) {
if(0) ;
#if CAP_IRR
else if(IRREGULAR) {
int id = irr::cellindex[c];
ld alpha = 2 * M_PI / S7 * irr::periodmap[c->master].base.spin;
return get_inverse ? irr::cells[id].rpusher * spin(-alpha-master_to_c7_angle()): spin(alpha + master_to_c7_angle()) * irr::cells[id].pusher;
}
#endif
#if CAP_GP
else if(GOLDBERG) {
if(c == c->master->c7) {
return spin((get_inverse?-1:1) * master_to_c7_angle());
}
else {
auto li = gp::get_local_info(c);
transmatrix T = spin(master_to_c7_angle()) * gp::Tf[li.last_dir][li.relative.first&31][li.relative.second&31][gp::fixg6(li.total_dir)];
if(get_inverse) T = inverse(T);
return T;
}
}
#endif
else if(BITRUNCATED && !euclid) {
for(int d=0; d<S7; d++) if(c->master->c7->move(d) == c)
return (get_inverse?invhexmove:hexmove)[d];
return Id;
}
else
return pispin * Id;
}
transmatrix calc_relative_matrix(cell *c2, cell *c1, int direction_hint) {
return calc_relative_matrix(c2, c1, ddspin(c1, direction_hint) * xpush0(1e-2));
}
// target, source, direction from source to target
#if CAP_GP
namespace gp { extern gp::local_info draw_li; }
#endif
transmatrix calc_relative_matrix(cell *c2, cell *c1, const hyperpoint& point_hint) {
if(sphere_narcm && DIM == 2) {
if(!gmatrix0.count(c2) || !gmatrix0.count(c1)) {
printf("building gmatrix0 (size=%d)\n", isize(gmatrix0));
#if CAP_GP
auto bak = gp::draw_li;
#endif
swap(gmatrix, gmatrix0);
just_gmatrix = true;
drawStandard();
just_gmatrix = false;
swap(gmatrix, gmatrix0);
#if CAP_GP
gp::draw_li = bak;
#endif
}
if(gmatrix0.count(c2) && gmatrix0.count(c1)) {
transmatrix T = inverse(gmatrix0[c1]) * gmatrix0[c2];
if(elliptic && T[2][2] < 0)
T = centralsym * T;
return T;
}
else {
printf("error: gmatrix0 not known\n");
return Id;
}
}
#if CAP_BT
if(binarytiling) return binary::relative_matrix(c2->master, c1->master);
#endif
#if MAXDIM == 4
if(euclid && DIM == 3) return euclid3::relative_matrix(c2->master, c1->master);
if(sphere && DIM == 3) return sphere3::relative_matrix(c2->master, c1->master);
#endif
#if CAP_ARCM
if(archimedean) return arcm::relative_matrix(c2->master, c1->master);
#endif
if(euwrap) {
transmatrix t = Id;
// if(whateveri) printf("[%p,%d] ", c2, celldistance(c2, c1));
int d = celldistance(c2, c1);
while(d) {
forCellIdEx(cc, i, c1) {
int d1 = celldistance(cc, c2);
if(d1 < d) {
t = t * cellrelmatrix(c1, i);
c1 = cc;
d = d1;
goto again;
}
}
printf("ERROR not reached\n");
break;
again: ;
}
return t;
}
if(euclid)
return eumove(cell_to_vec(c2) - cell_to_vec(c1));
heptagon *h1 = c1->master;
transmatrix gm = master_relative(c1, true);
heptagon *h2 = c2->master;
transmatrix where = master_relative(c2);
// always add to last!
//bool hsol = false;
//transmatrix sol;
set<heptagon*> visited;
map<ld, vector<pair<heptagon*, transmatrix>>> hbdist;
int steps = 0;
while(h1 != h2) {
steps++; if(steps > 10000) {
println(hlog, "not found"); return Id;
}
if(bounded) {
transmatrix T;
ld bestdist = 1e9;
for(int d=0; d<S7; d++) if(h2->move(d)) {
int sp = h2->c.spin(d);
transmatrix S = heptmove[sp] * spin(2*M_PI*d/S7);
if(h2->c.mirror(d)) S = heptmove[sp] * Mirror * spin(2*M_PI*d/S7);
if(h2->move(d) == h1) {
transmatrix T1 = gm * S * where;
auto curdist = hdist(tC0(T1), point_hint);
if(curdist < bestdist) T = T1, bestdist = curdist;
}
if(geometry != gMinimal) for(int e=0; e<S7; e++) if(h2->move(d)->move(e) == h1) {
int sp2 = h2->move(d)->c.spin(e);
transmatrix T1 = gm * heptmove[sp2] * spin(2*M_PI*e/S7) * S * where;
auto curdist = hdist(tC0(T1), point_hint);
if(curdist < bestdist) T = T1, bestdist = curdist;
}
}
if(bestdist < 1e8) return T;
}
for(int d=0; d<S7; d++) if(h2->move(d) == h1) {
int sp = h2->c.spin(d);
return gm * heptmove[sp] * spin(2*M_PI*d/S7) * where;
}
if(among(geometry, gFieldQuotient, gBring, gMacbeath)) {
int bestdist = 1000000, bestd = 0;
for(int d=0; d<S7; d++) {
int dist = celldistance(h2->cmove(d)->c7, c1);
if(dist < bestdist) bestdist = dist, bestd = d;
}
int sp = h2->c.spin(bestd);
where = heptmove[sp] * spin(2*M_PI*bestd/S7) * where;
h2 = h2->move(bestd);
}
#if CAP_CRYSTAL
else if(geometry == gCrystal) {
for(int d3=0; d3<S7; d3++) {
auto h3 = h2->cmove(d3);
if(visited.count(h3)) continue;
visited.insert(h3);
int sp3 = h2->c.spin(d3);
transmatrix where3 = heptmove[sp3] * spin(2*M_PI*d3/S7) * where;
ld dist = crystal::space_distance(h3->c7, c1);
hbdist[dist].emplace_back(h3, where3);
}
auto &bestv = hbdist.begin()->second;
tie(h2, where) = bestv.back();
bestv.pop_back();
if(bestv.empty()) hbdist.erase(hbdist.begin());
}
#endif
else if(h1->distance < h2->distance) {
int sp = h2->c.spin(0);
h2 = h2->move(0);
where = heptmove[sp] * where;
}
else {
int sp = h1->c.spin(0);
h1 = h1->move(0);
gm = gm * invheptmove[sp];
}
}
/*if(hsol) {
transmatrix sol2 = gm * where;
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
if(fabs(sol2[i][j]-sol[i][j] > 1e-3)) {
printf("ERROR\n");
display(sol);
display(sol2);
exit(1);
}
} */
return gm * where;
}
transmatrix &ggmatrix(cell *c) {
transmatrix& t = gmatrix[c];
if(t[2][2] == 0) {
if(euwrap && centerover.at)
t = calc_relative_matrix(c, centerover.at, C0);
else if(euclid && DIM == 2) {
if(!centerover.at) centerover = cwt;
t = View * eumove(cell_to_vec(c) - cellwalker_to_vec(centerover));
}
else
t = actualV(viewctr, cview()) * calc_relative_matrix(c, viewctr.at->c7, C0);
}
return t;
}
transmatrix calc_relative_matrix_help(cell *c, heptagon *h1) {
transmatrix gm = Id;
heptagon *h2 = c->master;
transmatrix where = Id;
if(0);
#if CAP_GP
else if(GOLDBERG && c != c->master->c7) {
auto li = gp::get_local_info(c);
where = gp::Tf[li.last_dir][li.relative.first&31][li.relative.second&31][fix6(li.total_dir)];
}
#endif
else if(BITRUNCATED) for(int d=0; d<S7; d++) if(h2->c7->move(d) == c)
where = hexmove[d];
// always add to last!
while(h1 != h2) {
for(int d=0; d<S7; d++) if(h1->move(d) == h2) printf("(adj) ");
if(h1->distance < h2->distance) {
int sp = h2->c.spin(0);
printf("A%d ", sp);
h2 = h2->move(0);
where = heptmove[sp] * where;
}
else {
int sp = h1->c.spin(0);
printf("B%d ", sp);
h1 = h1->move(0);
gm = gm * invheptmove[sp];
}
}
println(hlog, "OK");
println(hlog, gm * where);
return gm * where;
}
template<class T, class U>
void virtualRebase(cell*& base, T& at, bool tohex, const U& check) {
if((euclid || sphere) && DIM == 2) {
again:
if(euwrap) for(int i=0; i<6; i++) {
// fix cylinder and square grid
auto newat = eumovedir(3+i) * at;
if(hdist0(check(newat)) < hdist0(check(at))) {
at = newat;
base = createMov(base, i);
goto again;
}
}
else forCellCM(c2, base) {
auto newat = inverse(ggmatrix(c2)) * ggmatrix(base) * at;
if(hypot(check(newat)[0], check(newat)[1])
< hypot(check(at)[0], check(at)[1])) {
at = newat;
base = c2;
goto again;
}
}
fixelliptic(at);
return;
}
at = master_relative(base) * at;
base = base->master->c7;
while(true) {
double currz = check(at)[DIM];
heptagon *h = base->master;
cell *newbase = NULL;
transmatrix bestV;
if(DIM == 2 && !binarytiling) for(int d=0; d<S7; d++) {
heptspin hs(h, d, false);
heptspin hs2 = hs + wstep;
transmatrix V2 = spin(-hs2.spin*2*M_PI/S7) * invheptmove[d];
double newz = check(V2 * at) [DIM];
if(newz < currz) {
currz = newz;
bestV = V2;
newbase = hs2.at->c7;
}
}
if(newbase) {
base = newbase;
at = bestV * at;
}
else {
if(tohex && BITRUNCATED) for(int d=0; d<S7; d++) {
cell *c = createMov(base, d);
transmatrix V2 = spin(-base->c.spin(d)*2*M_PI/S6) * invhexmove[d];
double newz = check(V2 *at) [DIM];
if(newz < currz) {
currz = newz;
bestV = V2;
newbase = c;
}
}
if(newbase) {
base = newbase;
at = bestV * at;
}
else at = master_relative(base, true) * at;
if(binarytiling || (tohex && (GOLDBERG || IRREGULAR)) || DIM == 3) {
while(true) {
newbase = NULL;
forCellCM(c2, base) {
transmatrix V2 = calc_relative_matrix(base, c2, C0);
double newz = check(V2 * at) [DIM];
if(newz < currz) {
currz = newz;
bestV = V2;
newbase = c2;
}
}
if(!newbase) break;
base = newbase;
at = bestV * at;
}
}
break;
}
}
}
void virtualRebase(cell*& base, transmatrix& at, bool tohex) {
virtualRebase(base, at, tohex, tC0);
}
void virtualRebase(cell*& base, hyperpoint& h, bool tohex) {
// we perform fixing in check, so that it works with larger range
virtualRebase(base, h, tohex, [] (const hyperpoint& h) {
if(hyperbolic && DIM == 2) return hpxy(h[0], h[1]);
if(hyperbolic && DIM == 3) return hpxy3(h[0], h[1], h[2]);
return h;
});
}
// works only in geometries similar to the standard one, and only on heptagons
void virtualRebaseSimple(heptagon*& base, transmatrix& at) {
while(true) {
double currz = at[2][2];
heptagon *h = base;
heptagon *newbase = NULL;
transmatrix bestV {};
for(int d=0; d<S7; d++) {
heptspin hs(h, d, false);
heptspin hs2 = hs + wstep;
transmatrix V2 = spin(-hs2.spin*2*M_PI/S7) * invheptmove[d] * at;
double newz = V2[2][2];
if(newz < currz) {
currz = newz;
bestV = V2;
newbase = hs2.at;
}
}
if(newbase) {
base = newbase;
at = bestV;
continue;
}
return;
}
}
double cellgfxdist(cell *c, int i) {
if(euclid) {
if(c->type == 8 && (i&1)) return eurad * sqrt(2);
return eurad;
}
if(NONSTDVAR || archimedean) return hdist0(tC0(calc_relative_matrix(c->move(i), c, i)));
return !BITRUNCATED ? tessf : (c->type == 6 && (i&1)) ? hexhexdist : crossf;
}
transmatrix cellrelmatrix(cell *c, int i) {
if(NONSTDVAR || archimedean) return calc_relative_matrix(c->move(i), c, i);
double d = cellgfxdist(c, i);
transmatrix T = ddspin(c, i) * xpush(d);
if(c->c.mirror(i)) T = T * Mirror;
T = T * iddspin(c->move(i), c->c.spin(i), M_PI);
return T;
}
double randd() { return (rand() + .5) / (RAND_MAX + 1.); }
hyperpoint randomPointIn(int t) {
if(NONSTDVAR || archimedean) {
// Let these geometries be less confusing.
// Also easier to implement ;)
return xspinpush0(2 * M_PI * randd(), asinh(randd() / 20));
}
while(true) {
hyperpoint h = xspinpush0(2*M_PI*(randd()-.5)/t, asinh(randd()));
double d =
PURE ? tessf : t == 6 ? hexhexdist : crossf;
if(hdist0(h) < hdist0(xpush(-d) * h))
return spin(2*M_PI/t * (rand() % t)) * h;
}
}
#if CAP_BT
hyperpoint get_horopoint(ld y, ld x) {
return xpush(-y) * binary::parabolic(x) * C0;
}
#endif
hyperpoint get_corner_position(cell *c, int cid, ld cf) {
#if CAP_GP
if(GOLDBERG) return gp::get_corner_position(c, cid, cf);
#endif
#if CAP_IRR
if(IRREGULAR) {
auto& vs = irr::cells[irr::cellindex[c]];
return mid_at_actual(vs.vertices[cid], 3/cf);
}
#endif
#if CAP_BT
if(binarytiling) {
if(DIM == 3) {
println(hlog, "get_corner_position called");
return C0;
}
ld yx = log(2) / 2;
ld yy = yx;
ld xx = 1 / sqrt(2)/2;
hyperpoint vertices[7];
vertices[0] = get_horopoint(-yy, xx);
vertices[1] = get_horopoint(yy, 2*xx);
vertices[2] = get_horopoint(yy, xx);
vertices[3] = get_horopoint(yy, -xx);
vertices[4] = get_horopoint(yy, -2*xx);
vertices[5] = get_horopoint(-yy, -xx);
vertices[6] = get_horopoint(-yy, 0);
return mid_at_actual(vertices[cid], 3/cf);
}
#endif
#if CAP_ARCM
if(archimedean) {
auto &ac = arcm::current;
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(C0, 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));
}
}
#endif
if(PURE) {
return ddspin(c,cid,M_PI/S7) * xpush0(hcrossf * 3 / cf);
}
if(BITRUNCATED) {
if(!ishept(c))
return ddspin(c,cid,M_PI/S6) * xpush0(hexvdist * 3 / cf);
else
return ddspin(c,cid,M_PI/S7) * xpush0(rhexf * 3 / cf);
}
return C0;
}
hyperpoint nearcorner(cell *c, int i) {
if(GOLDBERG) {
cellwalker cw(c, i);
cw += wstep;
transmatrix cwm = calc_relative_matrix(cw.at, c, i);
if(elliptic && cwm[2][2] < 0) cwm = centralsym * cwm;
return cwm * C0;
}
#if CAP_IRR
if(IRREGULAR) {
auto& vs = irr::cells[irr::cellindex[c]];
hyperpoint nc = vs.jpoints[vs.neid[i]];
return mid_at(C0, nc, .94);
}
#endif
#if CAP_ARCM
if(archimedean) {
if(PURE) {
auto &ac = arcm::current;
auto& t = ac.get_triangle(c->master, i-1);
int id = arcm::id_of(c->master);
int id1 = ac.get_adj(ac.get_adj(c->master, i-1), -2).first;
return xspinpush0(-t.first - M_PI / c->type, ac.inradius[id/2] + ac.inradius[id1/2] + (ac.real_faces == 0 ? 2 * M_PI / (ac.N == 2 ? 2.1 : ac.N) : 0));
}
if(BITRUNCATED) {
auto &ac = arcm::current;
auto& t = ac.get_triangle(c->master, i);
return xspinpush0(-t.first, t.second);
}
if(DUAL) {
auto &ac = arcm::current;
auto& t = ac.get_triangle(c->master, i * 2);
return xspinpush0(-t.first, t.second);
}
}
#endif
#if CAP_BT
if(binarytiling) {
if(DIM == 3) {
println(hlog, "nearcorner called");
return Hypc;
}
ld yx = log(2) / 2;
ld yy = yx;
// ld xx = 1 / sqrt(2)/2;
hyperpoint neis[7];
neis[0] = get_horopoint(0, 1);
neis[1] = get_horopoint(yy*2, 1);
neis[2] = get_horopoint(yy*2, 0);
neis[3] = get_horopoint(yy*2, -1);
neis[4] = get_horopoint(0, -1);
if(c->type == 7)
neis[5] = get_horopoint(-yy*2, -.5),
neis[6] = get_horopoint(-yy*2, +.5);
else
neis[5] = get_horopoint(-yy*2, 0);
return neis[i];
}
#endif
double d = cellgfxdist(c, i);
return ddspin(c, i) * xpush0(d);
}
hyperpoint farcorner(cell *c, int i, int which) {
#if CAP_GP
if(GOLDBERG) {
cellwalker cw(c, i);
int hint = cw.spin;
cw += wstep;
transmatrix cwm = calc_relative_matrix(cw.at, c, hint);
if(elliptic && cwm[2][2] < 0) cwm = centralsym * cwm;
// hyperpoint nfar = cwm*C0;
auto li1 = gp::get_local_info(cw.at);
if(which == 0)
return cwm * get_corner_position(li1, (cw+2).spin);
if(which == 1)
return cwm * get_corner_position(li1, (cw-1).spin);
}
#endif
#if CAP_IRR
if(IRREGULAR) {
auto& vs = irr::cells[irr::cellindex[c]];
int neid = vs.neid[i];
int spin = vs.spin[i];
auto &vs2 = irr::cells[neid];
int cor2 = isize(vs2.vertices);
transmatrix rel = vs.rpusher * vs.relmatrices[vs2.owner] * vs2.pusher;
if(which == 0) return rel * vs2.vertices[(spin+2)%cor2];
if(which == 1) return rel * vs2.vertices[(spin+cor2-1)%cor2];
}
#endif
#if CAP_BT
if(binarytiling)
return nearcorner(c, (i+which) % c->type); // lazy
#endif
#if CAP_ARCM
if(archimedean) {
if(PURE) {
auto &ac = arcm::current;
auto& t = ac.get_triangle(c->master, i-1);
int id = arcm::id_of(c->master);
auto id1 = ac.get_adj(ac.get_adj(c->master, i-1), -2).first;
int n1 = isize(ac.adjacent[id1]);
return spin(-t.first - M_PI / c->type) * xpush(ac.inradius[id/2] + ac.inradius[id1/2]) * xspinpush0(M_PI + M_PI/n1*(which?3:-3), ac.circumradius[id1/2]);
}
if(BITRUNCATED || DUAL) {
int mul = DUALMUL;
auto &ac = arcm::current;
auto adj = ac.get_adj(c->master, i * mul);
heptagon h; cell cx; cx.master = &h;
arcm::id_of(&h) = adj.first;
arcm::parent_index_of(&h) = adj.second;
auto& t1 = arcm::current.get_triangle(c->master, i);
auto& t2 = arcm::current.get_triangle(adj);
return spin(-t1.first) * xpush(t1.second) * spin(M_PI + t2.first) * get_corner_position(&cx, which ? -mul : 2*mul);
}
}
#endif
return cellrelmatrix(c, i) * get_corner_position(c->move(i), (cellwalker(c, i) + wstep + (which?-1:2)).spin);
}
hyperpoint midcorner(cell *c, int i, ld v) {
auto hcor = farcorner(c, i, 0);
auto tcor = get_corner_position(c, i, 3);
return mid_at(tcor, hcor, v);
}
hyperpoint get_warp_corner(cell *c, int cid) {
// midcorner(c, cid, .5) but sometimes easier versions exist
#if CAP_GP
if(GOLDBERG) return gp::get_corner_position(c, cid, 2);
#endif
#if CAP_IRR || CAP_ARCM
if(IRREGULAR || archimedean) return midcorner(c, cid, .5);
#endif
return ddspin(c,cid,M_PI/S7) * xpush0(tessf/2);
}
}
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