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hyperrogue/geometry2.cpp
Zeno Rogue f355006b2b fixed virtualRebase for Nil
2020-05-01 11:32:12 +02:00

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// Hyperbolic Rogue -- advanced geometry
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file geometry2.cpp
* \brief Matrices to transform between coordinates of various cells, coordinates of cell corners, etc.
*/
#include "hyper.h"
namespace hr {
transmatrix &ggmatrix(cell *c);
EX void fixelliptic(transmatrix& at) {
if(elliptic && at[LDIM][LDIM] < 0) {
for(int i=0; i<MDIM; i++) for(int j=0; j<MDIM; j++)
at[i][j] = -at[i][j];
}
}
EX void fixelliptic(hyperpoint& h) {
if(elliptic && h[LDIM] < 0)
for(int i=0; i<MDIM; i++) h[i] = -h[i];
}
/** find relative_matrix via recursing the tree structure */
EX transmatrix relative_matrix_recursive(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<h1->type; i++) {
if(h1->move(i) == h2) {
return gm * currentmap->adj(h1, i) * where;
}
}
if(h1->distance > h2->distance) {
for(int i=0; i<h1->type; i++) if(h1->move(i) && h1->move(i)->distance < h1->distance) {
gm = gm * currentmap->adj(h1, i);
h1 = h1->move(i);
goto again;
}
}
else {
for(int i=0; i<h2->type; i++) if(h2->move(i) && h2->move(i)->distance < h2->distance) {
where = currentmap->iadj(h2, 0) * where;
h2 = h2->move(i);
goto again;
}
}
again: ;
}
return gm * where;
}
EX transmatrix master_relative(cell *c, bool get_inverse IS(false)) {
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()) * cgi.gpdata->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) {
if(c == c->master->c7)
return Id;
return (get_inverse?cgi.invhexmove:cgi.hexmove)[c->c.spin(0)];
}
else if(WDIM == 3)
return Id;
else
return pispin * Id;
}
EX transmatrix calc_relative_matrix(cell *c2, cell *c1, const hyperpoint& hint) {
return currentmap->relative_matrix(c2, c1, hint);
}
// target, source, direction from source to target
#if CAP_GP
namespace gp { extern gp::local_info draw_li; }
#endif
transmatrix hrmap_standard::adj(heptagon *h, int d) {
if(inforder::mixed()) {
int t0 = h->type;
int t1 = h->cmove(d)->type;
int sp = h->c.spin(d);
return spin(-d * 2 * M_PI / t0) * xpush(spacedist(h->c7, d)) * spin(M_PI + 2*M_PI*sp/t1);
}
transmatrix T = cgi.heptmove[d];
if(h->c.mirror(d)) T = T * Mirror;
int sp = h->c.spin(d);
if(sp) T = T * spin(2*M_PI*sp/S7);
return T;
}
transmatrix hrmap_standard::relative_matrix(cell *c2, cell *c1, const hyperpoint& hint) {
heptagon *h1 = c1->master;
transmatrix gm = master_relative(c1, true);
heptagon *h2 = c2->master;
transmatrix where = master_relative(c2);
transmatrix U = relative_matrix(h2, h1, hint);
return gm * U * where;
}
transmatrix hrmap_standard::relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) {
transmatrix gm = Id, where = Id;
// 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++) {
auto hm = h1->move(d);
if(!hm) continue;
transmatrix S = adj(h1, d);
if(hm == h2) {
transmatrix T1 = gm * S * where;
auto curdist = hdist(tC0(T1), hint);
if(curdist < bestdist) T = T1, bestdist = curdist;
}
if(geometry != gMinimal) for(int e=0; e<S7; e++) if(hm->move(e) == h2) {
transmatrix T1 = gm * S * adj(hm, e) * where;
auto curdist = hdist(tC0(T1), hint);
if(curdist < bestdist) T = T1, bestdist = curdist;
}
}
if(bestdist < 1e8) return T;
}
for(int d=0; d<h1->type; d++) if(h1->move(d) == h2) {
return gm * adj(h1, d) * where;
}
if(among(geometry, gFieldQuotient, gBring, gMacbeath)) {
int bestdist = 1000000, bestd = 0;
for(int d=0; d<S7; d++) {
int dist = celldistance(h1->cmove(d)->c7, h2->c7);
if(dist < bestdist) bestdist = dist, bestd = d;
}
gm = gm * adj(h1, bestd);
h1 = h1->move(bestd);
}
#if CAP_CRYSTAL
else if(cryst) {
for(int d3=0; d3<S7; d3++) {
auto hm = h1->cmove(d3);
if(visited.count(hm)) continue;
visited.insert(hm);
ld dist = crystal::space_distance(hm->c7, h2->c7);
hbdist[dist].emplace_back(hm, gm * adj(h1, d3));
}
auto &bestv = hbdist.begin()->second;
tie(h1, gm) = bestv.back();
bestv.pop_back();
if(bestv.empty()) hbdist.erase(hbdist.begin());
}
#endif
else if(h1->distance < h2->distance) {
where = iadj(h2, 0) * where;
h2 = h2->move(0);
}
else {
gm = gm * adj(h1, 0);
h1 = h1->move(0);
}
}
return gm * where;
}
EX transmatrix &ggmatrix(cell *c) {
transmatrix& t = gmatrix[c];
if(t[LDIM][LDIM] == 0)
t = actual_view_transform * View * calc_relative_matrix(c, centerover, C0);
return t;
}
#if HDR
struct horo_distance {
ld a, b;
void become(hyperpoint h1);
horo_distance(hyperpoint h) { become(h); }
horo_distance(hyperpoint h1, const transmatrix& T);
bool operator < (const horo_distance z) const;
friend void print(hstream& hs, horo_distance x) { print(hs, "[", x.a, ":", x.b, "]"); }
};
#endif
void horo_distance::become(hyperpoint h1) {
if(sn::in()) {
a = abs(h1[2]);
if(asonov::in()) h1 = asonov::straighten * h1;
b = hypot_d(2, h1);
}
#if CAP_BT
else if(bt::in()) {
b = intval(h1, C0);
a = abs(bt::horo_level(h1));
}
#endif
else if(hybri)
a = 0, b = hdist(h1, C0);
else
a = 0, b = intval(h1, C0);
}
horo_distance::horo_distance(hyperpoint h1, const transmatrix& T) {
#if CAP_BT
if(bt::in()) become(inverse(T) * h1);
else
#endif
if(sn::in() || hybri || nil) become(inverse(T) * h1);
else
a = 0, b = intval(h1, tC0(T));
}
bool horo_distance::operator < (const horo_distance z) const {
#if CAP_BT
if(bt::in() || sn::in()) {
if(a < z.a-1e-6) return true;
if(a > z.a+1e-6) return false;
}
#endif
return b < z.b - 1e-4;
}
template<class T, class U>
void virtualRebase_cell(cell*& base, T& at, const U& check) {
horo_distance currz(check(at));
T best_at = at;
while(true) {
cell *newbase = NULL;
forCellIdCM(c2, i, base) {
transmatrix V2 = currentmap->iadj(base, i);
T cand_at = V2 * at;
horo_distance newz(check(cand_at));
if(newz < currz) {
currz = newz;
best_at = cand_at;
newbase = c2;
}
if(arb::in()) forCellIdCM(c3, j, c2) {
transmatrix V3 = currentmap->iadj(c2, j);
T cand_at3 = V3 * cand_at;
horo_distance newz3(check(cand_at3));
if(newz3 < currz) {
currz = newz3;
best_at = cand_at3;
newbase = c3;
}
}
}
if(!newbase) break;
base = newbase;
at = best_at;
}
}
template<class T, class U>
void virtualRebase(cell*& base, T& at, const U& check) {
if(nil) {
hyperpoint h = check(at);
auto step = [&] (int i) {
at = currentmap->iadj(base, i) * at;
base = base->cmove(i);
h = check(at);
};
while(h[1] < -0.5) step(1);
while(h[1] >= 0.5) step(4);
while(h[0] < -0.5) step(0);
while(h[0] >= 0.5) step(3);
while(h[2] < -0.5) step(2);
while(h[2] >= 0.5) step(5);
return;
}
if(prod) {
auto d = product_decompose(check(at)).first;
while(d > cgi.plevel / 2) {
at = currentmap->iadj(base, base->type-1) * at;
base = base->cmove(base->type-1); d -= cgi.plevel;
}
while(d < -cgi.plevel / 2) {
at = currentmap->iadj(base, base->type-2) * at;
base = base->cmove(base->type-2); d += cgi.plevel;
}
auto w = hybrid::get_where(base);
at = mscale(at, -d);
PIU( virtualRebase(w.first, at, check) );
at = mscale(at, +d);
base = hybrid::get_at(w.first, w.second);
return;
}
virtualRebase_cell(base, at, check);
}
EX void virtualRebase(cell*& base, transmatrix& at) {
virtualRebase(base, at, tC0);
}
EX void virtualRebase(cell*& base, hyperpoint& h) {
// we perform fixing in check, so that it works with larger range
virtualRebase(base, h, [] (const hyperpoint& h) {
if(hyperbolic && GDIM == 2) return hpxy(h[0], h[1]);
if(hyperbolic && GDIM == 3) return hpxy3(h[0], h[1], h[2]);
return h;
});
}
void hrmap_hyperbolic::virtualRebase(heptagon*& base, transmatrix& at) {
while(true) {
double currz = at[LDIM][LDIM];
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 = iadj(h, d) * at;
double newz = V2[LDIM][LDIM];
if(newz < currz) {
currz = newz;
bestV = V2;
newbase = hs2.at;
}
}
if(newbase) {
base = newbase;
at = bestV;
continue;
}
return;
}
}
EX bool no_easy_spin() {
return NONSTDVAR || arcm::in() || WDIM == 3 || bt::in() || kite::in();
}
ld hrmap_standard::spin_angle(cell *c, int d) {
if(WDIM == 3) return SPIN_NOT_AVAILABLE;
ld hexshift = 0;
if(c == c->master->c7 && (S7 % 2 == 0) && BITRUNCATED) hexshift = cgi.hexshift + 2*M_PI/c->type;
else if(cgi.hexshift && c == c->master->c7) hexshift = cgi.hexshift;
if(IRREGULAR) {
auto id = irr::cellindex[c];
auto& vs = irr::cells[id];
if(d < 0 || d >= c->type) return 0;
auto& p = vs.jpoints[vs.neid[d]];
return -atan2(p[1], p[0]) - hexshift;
}
else
return M_PI - d * 2 * M_PI / c->type - hexshift;
}
EX transmatrix ddspin(cell *c, int d, ld bonus IS(0)) { return currentmap->spin_to(c, d, bonus); }
EX transmatrix iddspin(cell *c, int d, ld bonus IS(0)) { return currentmap->spin_from(c, d, bonus); }
EX ld cellgfxdist(cell *c, int d) { return currentmap->spacedist(c, d); }
EX transmatrix ddspin_side(cell *c, int d, ld bonus IS(0)) {
if(kite::in()) {
hyperpoint h1 = get_corner_position(c, gmod(d, c->type), 3);
hyperpoint h2 = get_corner_position(c, gmod(d+1, c->type) , 3);
hyperpoint hm = mid(h1, h2);
return rspintox(hm) * spin(bonus);
}
return currentmap->spin_to(c, d, bonus);
}
EX transmatrix iddspin_side(cell *c, int d, ld bonus IS(0)) {
if(kite::in()) {
hyperpoint h1 = get_corner_position(c, gmod(d, c->type), 3);
hyperpoint h2 = get_corner_position(c, gmod(d+1, c->type) , 3);
hyperpoint hm = mid(h1, h2);
return spintox(hm) * spin(bonus);
}
return currentmap->spin_from(c, d, bonus);
}
double hrmap_standard::spacedist(cell *c, int i) {
if(NONSTDVAR || WDIM == 3) return hrmap::spacedist(c, i);
if(inforder::mixed()) {
int t0 = c->type;
int t1 = c->cmove(i)->type;
auto halfmove = [] (int i) {
if(i == 1) return 0.0;
if(i == 2) return 0.1;
return edge_of_triangle_with_angles(0, M_PI/i, M_PI/i);
};
ld tessf0 = halfmove(t0);
ld tessf1 = halfmove(t1);
return (tessf0 + tessf1) / 2;
}
if(!BITRUNCATED) return cgi.tessf;
if(c->type == S6 && (i&1)) return cgi.hexhexdist;
return cgi.crossf;
}
int neighborId(heptagon *h1, heptagon *h2) {
for(int i=0; i<h1->type; i++) if(h1->move(i) == h2) return i;
return -1;
}
transmatrix hrmap_standard::adj(cell *c, int i) {
if(GOLDBERG && gp::do_adjm) {
transmatrix T = master_relative(c, true);
transmatrix U = master_relative(c->cmove(i), false);
if(gp::gp_adj.count(make_pair(c,i))) {
return T * gp::get_adj(c,i) * U;
}
else
println(hlog, "gpadj not found");
}
if(NONSTDVAR || WDIM == 3) {
return calc_relative_matrix(c->cmove(i), c, C0);
}
double d = cellgfxdist(c, i);
transmatrix T = ddspin(c, i) * xpush(d);
if(c->c.mirror(i)) T = T * Mirror;
cell *c1 = c->cmove(i);
T = T * iddspin(c1, c->c.spin(i), M_PI);
return T;
}
EX double randd() { return (rand() + .5) / (RAND_MAX + 1.); }
EX hyperpoint randomPointIn(int t) {
if(NONSTDVAR || arcm::in() || kite::in()) {
// 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 ? cgi.tessf : t == 6 ? cgi.hexhexdist : cgi.crossf;
if(hdist0(h) < hdist0(xpush(-d) * h))
return spin(2*M_PI/t * (rand() % t)) * h;
}
}
EX hyperpoint get_corner_position(cell *c, int cid, ld cf IS(3)) {
#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(kite::in()) return kite::get_corner(c, cid, cf);
if(bt::in()) {
if(WDIM == 3) {
println(hlog, "get_corner_position called");
return C0;
}
return mid_at_actual(bt::get_horopoint(bt::get_corner_horo_coordinates(c, cid)), 3/cf);
}
#endif
#if CAP_ARCM
if(arcm::in()) {
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(arb::in()) {
auto& sh = arb::current.shapes[arb::id_of(c->master)];
return normalize(C0 + (sh.vertices[gmod(cid, c->type)] - C0) * 3 / cf);
}
if(PURE) {
return ddspin(c,cid,M_PI/S7) * xpush0(cgi.hcrossf * 3 / cf);
}
if(BITRUNCATED) {
if(!ishept(c))
return ddspin(c,cid,M_PI/S6) * xpush0(cgi.hexvdist * 3 / cf);
else
return ddspin(c,cid,M_PI/S7) * xpush0(cgi.rhexf * 3 / cf);
}
return C0;
}
EX bool approx_nearcorner = false;
EX hyperpoint nearcorner(cell *c, int i) {
if(GOLDBERG) {
cellwalker cw(c, i);
cw += wstep;
transmatrix cwm = currentmap->adj(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(arcm::in()) {
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(geometry == gBinary4) {
ld yx = log(2) / 2;
ld yy = yx;
hyperpoint neis[5];
neis[0] = bt::get_horopoint(2*yy, -0.5);
neis[1] = bt::get_horopoint(2*yy, +0.5);
neis[2] = bt::get_horopoint(0, 1);
neis[3] = bt::get_horopoint(-2*yy, c->master->zebraval ? -0.25 : +0.25);
neis[4] = bt::get_horopoint(0, -1);
return neis[i];
}
if(geometry == gTernary) {
ld yx = log(3) / 2;
ld yy = yx;
hyperpoint neis[6];
neis[0] = bt::get_horopoint(2*yy, -1);
neis[1] = bt::get_horopoint(2*yy, +0);
neis[2] = bt::get_horopoint(2*yy, +1);
neis[3] = bt::get_horopoint(0, 1);
neis[4] = bt::get_horopoint(-2*yy, c->master->zebraval / 3.);
neis[5] = bt::get_horopoint(0, -1);
return neis[i];
}
if(kite::in()) {
if(approx_nearcorner)
return kite::get_corner(c, i, 3) + kite::get_corner(c, i+1, 3) - C0;
else
return calc_relative_matrix(c->cmove(i), c, C0) * C0;
}
if(bt::in()) {
if(WDIM == 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] = bt::get_horopoint(0, 1);
neis[1] = bt::get_horopoint(yy*2, 1);
neis[2] = bt::get_horopoint(yy*2, 0);
neis[3] = bt::get_horopoint(yy*2, -1);
neis[4] = bt::get_horopoint(0, -1);
if(c->type == 7)
neis[5] = bt::get_horopoint(-yy*2, -.5),
neis[6] = bt::get_horopoint(-yy*2, +.5);
else
neis[5] = bt::get_horopoint(-yy*2, 0);
return neis[i];
}
#endif
double d = cellgfxdist(c, i);
return ddspin(c, i) * xpush0(d);
}
EX hyperpoint farcorner(cell *c, int i, int which) {
#if CAP_GP
if(GOLDBERG) {
cellwalker cw(c, i);
cw += wstep;
if(!cw.mirrored) cw.spin += (which?-1:2);
else cw.spin += (which?2:-1);
transmatrix cwm = currentmap->adj(c, i);
auto li1 = gp::get_local_info(cw.at);
return cwm * get_corner_position(li1, cw.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(bt::in() || kite::in())
return nearcorner(c, (i+which) % c->type); // lazy
#endif
#if CAP_ARCM
if(arcm::in()) {
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
cellwalker cw(c, i);
cw += wstep;
if(!cw.mirrored) cw.spin += (which?-1:2);
else cw.spin += (which?2:-1);
return currentmap->adj(c, i) * get_corner_position(c->move(i), cw.spin);
}
EX 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);
}
EX 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 || arcm::in()) return midcorner(c, cid, .5);
#endif
return ddspin(c,cid,M_PI/S7) * xpush0(cgi.tessf/2);
}
vector<hyperpoint> hrmap::get_vertices(cell* c) {
vector<hyperpoint> res;
for(int i=0; i<c->type; i++) res.push_back(get_corner_position(c, i, 3));
return res;
}
}
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