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hyperrogue/goldberg.cpp
Zeno Rogue bf0ce8d2f0 gp:: looks better on spheres
2018-05-01 19:32:55 +02:00

730 lines
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namespace gp {
bool on;
loc param(1, 0);
hyperpoint next;
ld scale;
ld alpha;
int area;
loc operator+(loc e1, loc e2) {
return make_pair(e1.first+e2.first, e1.second+e2.second);
}
loc operator-(loc e1, loc e2) {
return make_pair(e1.first-e2.first, e1.second-e2.second);
}
loc operator*(loc e1, loc e2) {
return make_pair(e1.first*e2.first-e1.second*e2.second,
e1.first*e2.second + e2.first*e1.second + e1.second*e2.second);
}
loc operator*(loc e1, int i) {
return loc(e1.first*i, e1.second*i);
}
struct goldberg_mapping_t {
cellwalker cw;
char rdir;
char mindir;
};
loc eudir(int d) {
d %= 6; if (d < 0) d += 6;
switch(d) {
case 0: return make_pair(1, 0);
case 1: return make_pair(0, 1);
case 2: return make_pair(-1, 1);
case 3: return make_pair(-1, 0);
case 4: return make_pair(0, -1);
case 5: return make_pair(1, -1);
default: return make_pair(0, 0);
}
}
int get_code(const local_info& li) {
return
((li.relative.first & 15) << 0) +
((li.relative.second & 15) << 4) +
((fix6(li.total_dir)) << 8) +
((li.last_dir & 15) << 12);
}
local_info get_local_info(cell *c) {
local_info li;
if(c == c->master->c7) {
li.relative = loc(0,0);
li.first_dir = -1;
li.last_dir = -1;
li.total_dir = -1;
}
else {
vector<int> dirs;
while(c != c->master->c7) {
dirs.push_back(c->spin(0));
c = c->mov[0];
}
li.first_dir = dirs[0];
li.last_dir = dirs.back();
loc at(0,0);
int dir = 0;
at = at + eudir(dir);
dirs.pop_back();
while(dirs.size()) {
dir += dirs.back() + 3;
dirs.pop_back();
at = at + eudir(dir);
}
li.relative = at;
li.total_dir = dir + 3;
}
return li;
}
int last_dir(cell *c) {
return get_local_info(c).last_dir;
}
loc get_coord(cell *c) {
return get_local_info(c).relative;
}
int pseudohept_val(cell *c) {
loc v = get_coord(c);
return (v.first - v.second + MODFIXER)%3;
}
// mapping of the local equilateral triangle
// goldberg_map[y][x].cw is the cellwalker in this triangle at position (x,y)
// facing local direction 0
goldberg_mapping_t goldberg_map[32][32];
void clear_mapping() {
for(int y=0; y<32; y++) for(int x=0; x<32; x++) {
goldberg_map[y][x].cw.c = NULL;
goldberg_map[y][x].rdir = -1;
goldberg_map[y][x].mindir = 0;
}
}
goldberg_mapping_t& get_mapping(loc c) {
return goldberg_map[c.second&31][c.first&31];
}
const char *disp(loc at) {
static char bufs[16][16];
static int bufid;
bufid++; bufid %= 16;
snprintf(bufs[bufid], 16, "[%2d,%2d]", at.first, at.second);
return bufs[bufid];
}
const char *dcw(cellwalker cw) {
static char bufs[16][32];
static int bufid;
bufid++; bufid %= 16;
snprintf(bufs[bufid], 32, "[%p/%2d:%d:%d]", cw.c, cw.c?cw.c->type:-1, cw.spin, cw.mirrored);
return bufs[bufid];
}
int spawn;
#define WHD(x) // x
bool operator != (cellwalker cw1, cellwalker cw2) {
return cw1.c != cw2.c || cw1.spin != cw2.spin || cw1.mirrored != cw2.mirrored;
}
cell*& peek(cellwalker cw) {
return cw.c->mov[cw.spin];
}
cellwalker get_localwalk(const goldberg_mapping_t& wc, int dir) {
if(dir < wc.mindir) dir += 6;
if(dir >= wc.mindir + 6) dir -= 6;
return wc.cw + dir;
}
void set_localwalk(goldberg_mapping_t& wc, int dir, const cellwalker& cw) {
if(dir < wc.mindir) dir += 6;
if(dir >= wc.mindir + 6) dir -= 6;
wc.cw = cw - dir;
}
bool pull(loc at, int dir) {
auto& wc = get_mapping(at);
auto at1 = at + eudir(dir);
int dir1 = fix6(dir+3);
cellwalker wcw = get_localwalk(wc, dir);
auto& wc1= get_mapping(at1);
if(wc1.cw.c) {
if(peek(wcw)) {
auto wcw1 = get_localwalk(wc1, dir1);
if(wcw + wstep != wcw1) {
WHD( printf("%s : %s / %s (pull error from %s :: %s)\n", disp(at1), dcw(wcw+wstep), dcw(wcw1), disp(at), dcw(wcw)); )
exit(1);
}
}
return false;
}
if(peek(wcw)) {
set_localwalk(wc1, dir1, wcw + wstep);
WHD( printf("%s : %s (pulled from %s :: %s)\n", disp(at1), dcw(wcw + wstep), disp(at), dcw(wcw)); )
return true;
}
return false;
}
void conn1(loc at, int dir, int dir1) {
auto& wc = get_mapping(at);
auto wcw = get_localwalk(wc, dir);
auto& wc1 = get_mapping(at + eudir(dir));
WHD( printf(" connection %s/%d %s ~ %s/%d ", disp(at), dir, dcw(wc.cw+dir), disp(at+eudir(dir)), dir1); )
if(!wc1.cw.c) {
if(peek(wcw)) {
WHD( printf("(pulled) "); )
set_localwalk(wc1, dir1, wcw + wstep);
}
else {
peek(wcw) = newCell(6, wc.cw.c->master);
tsetspin(wcw.c->spintable, wcw.spin, 0);
set_localwalk(wc1, dir1, wcw + wstep);
spawn++;
WHD( printf("(created) "); )
}
}
WHD( printf("%s ", dcw(wc1.cw+dir1)); )
auto wcw1 = get_localwalk(wc1, dir1);
if(peek(wcw)) {
if(wcw+wstep != wcw1) {
WHD( printf("FAIL: %s / %s\n", dcw(wcw), dcw(wcw1)); exit(1); )
}
else {
WHD(printf("(was there)\n");)
}
}
else {
WHD(printf("ok\n"); )
peek(wcw) = wcw1.c;
tsetspin(wcw.c->spintable, wcw.spin, wcw1.spin + (wcw.mirrored != wcw1.mirrored ? 8 : 0));
if(wcw+wstep != wcw1) {
printf("assertion failed\n");
exit(1);
}
}
}
void conn(loc at, int dir) {
conn1(at, fix6(dir), fix6(dir+3));
conn1(at + eudir(dir), fix6(dir+3), fix6(dir));
}
goldberg_mapping_t& set_heptspin(loc at, heptspin hs) {
auto& ac0 = get_mapping(at);
ac0.cw = cellwalker(hs.h->c7, hs.spin, hs.mirrored);
WHD( printf("%s : %s\n", disp(at), dcw(ac0.cw)); )
return ac0;
}
void extend_map(cell *c, int d) {
WHD( printf("EXTEND %p %d\n", c, d); )
if(c->master->c7 != c) {
while(c->master->c7 != c) {
WHD( printf("%p direction 0 corresponds to %p direction %d\n", c, c->mov[0], c->spin(0)); )
d = c->spin(0);
c = c->mov[0];
}
// c move 0 equals c' move spin(0)
extend_map(c, d);
extend_map(c, fixdir(d-1, c));
extend_map(c, fixdir(d+1, c));
return;
}
clear_mapping();
// we generate a local map from an Euclidean grid to the
// hyperbolic grid we build.
// we fill the equilateral triangle with the following vertices:
loc vc[3];
vc[0] = loc(0,0);
vc[1] = param;
vc[2] = param * loc(0,1);
heptspin hs(c->master, d, false);
auto& ac0 = set_heptspin(vc[0], hs);
ac0.mindir = -1;
auto& ac1 = set_heptspin(vc[1], hs + wstep - 3);
auto& ac2 = set_heptspin(vc[2], hs + 1 + wstep - 4);
ac2.mindir = 1;
if(elliptic && param.first == param.second) {
int x = param.first;
if(ac1.cw.mirrored != hs.mirrored) ac1.cw--;
if(ac2.cw.mirrored != hs.mirrored) ac2.cw--;
for(int d=0; d<3; d++) for(int k=0; k<3; k++)
for(int i=0; i<x; i++) {
int dd = (2*d+k);
loc cx = vc[d] + eudir(dd) * i;
if(!pull(cx, dd)) break;
}
for(int i=0; i<=2*x; i++)
for(int d=0; d<3; d++) {
loc cx = vc[d] + eudir(1+2*d) * i;
if(i < 2*x) conn(cx, 1+2*d);
int jmax = x-i, drev = 2*d;
if(jmax < 0) drev += 3, jmax = -jmax;
for(int j=0; j<jmax; j++) {
loc cy = cx + eudir(drev) * j;
conn(cy, drev);
conn(cy, drev+1);
conn(cy, drev+2);
}
}
return;
}
// then we set the edges of our big equilateral triangle (in a symmetric way)
for(int i=0; i<3; i++) {
loc start = vc[i];
loc end = vc[(i+1)%3];
WHD( printf("from %s to %s\n", disp(start), disp(end)); )
loc rel = param;
auto build = [&] (loc& at, int dx, bool forward) {
int dx1 = dx + 2*i;
WHD( printf("%s %d .. %s %d\n", disp(at), dx1, disp(at + eudir(dx1)), fix6(dx1+3)); )
conn(at, dx1);
if(forward) get_mapping(at).rdir = fix6(dx1);
else get_mapping(at+eudir(dx1)).rdir = fix6(dx1+3);
at = at + eudir(dx1);
};
while(rel.first >= 2 && rel.first >= 2 - rel.second) {
build(start, 0, true);
build(end, 3, false);
rel.first -= 2;
}
while(rel.second >= 2) {
build(start, 1, true);
build(end, 4, false);
rel.second -= 2;
}
while(rel.second <= -2) {
build(start, 5, true);
build(end, 2, false);
rel.second += 2;
rel.first -= 2;
}
while((rel.first>0 && rel.second > 0) | (rel.first > 1 && rel.second < 0)) {
build(start, 0, true);
build(end, 3, false);
rel.first -= 2;
}
for(int k=0; k<6; k++)
if(start + eudir(k+2*i) == end)
build(start, k, true);
if(start != end) { printf("assertion failed: start %s == end %s\n", disp(start), disp(end)); exit(1); }
}
// now we can fill the interior of our big equilateral triangle
loc at = vc[0];
while(true) {
auto& wc = get_mapping(at);
int dx = wc.rdir;
auto at1 = at + eudir(dx);
auto& wc1 = get_mapping(at1);
WHD( printf("%s (%d) %s (%d)\n", disp(at), dx, disp(at1), wc1.rdir); )
int df = wc1.rdir - dx;
if(df < 0) df += 6;
if(df == 3) break;
switch(df) {
case 0:
case 4:
case 5:
at = at1;
continue;
case 2: {
conn(at, dx+1);
wc.rdir = (dx+1) % 6;
break;
}
case 1: {
auto at2 = at + eudir(dx+1);
auto& wc2 = get_mapping(at2);
if(wc2.cw.c) { at = at1; continue; }
wc.rdir = (dx+1) % 6;
conn(at, (dx+1) % 6);
conn(at1, (dx+2) % 6);
conn(at2, (dx+0) % 6);
wc1.rdir = -1;
wc2.rdir = dx;
break;
}
default:
printf("case unhandled %d\n", df);
exit(1);
}
}
WHD( printf("DONE\n\n"); )
}
hyperpoint loctoh_ort(loc at) {
return hpxyz(at.first, at.second, 1);
}
hyperpoint corner_coords[7] = {
hpxyz(2, -1, 0),
hpxyz(1, 1, 0),
hpxyz(-1, 2, 0),
hpxyz(-2, 1, 0),
hpxyz(-1, -1, 0),
hpxyz(1, -2, 0),
hpxyz(0, 0, 0) // center, not a corner
};
hyperpoint cornmul(const transmatrix& corners, const hyperpoint& c) {
if(sphere) {
ld cmin = c[0] * c[1] * c[2] * (6 - S7);
return corners * hpxyz(c[0] + cmin, c[1] + cmin, c[2] + cmin);
}
else return corners * c;
}
hyperpoint atz(const transmatrix& T, const transmatrix& corners, loc at, int cornerid = 6, ld cf = 3) {
int sp = 0;
again:
auto corner = corners * hyperpoint_vec::operator+ (loctoh_ort(at), hyperpoint_vec::operator/ (corner_coords[cornerid], cf));
if(corner[1] < -1e-6 || corner[2] < -1e-6) {
at = at * eudir(1);
if(cornerid < 6) cornerid = (1 + cornerid) % 6;
sp++;
goto again;
}
if(sp>3) sp -= 6;
return normalize(spin(2*M_PI*sp/S7) * cornmul(T, corner));
}
transmatrix Tf[8][32][32][6];
transmatrix corners;
transmatrix dir_matrix(int i) {
cell cc; cc.type = S7;
return spin(-alpha) * build_matrix(
C0,
ddspin(&cc, i) * xpush(tessf) * C0,
ddspin(&cc, i+1) * xpush(tessf) * C0
);
}
void prepare_matrices() {
corners = inverse(build_matrix(
loctoh_ort(loc(0,0)),
loctoh_ort(param),
loctoh_ort(param * loc(0,1))
));
for(int i=0; i<S7; i++) {
transmatrix T = dir_matrix(i);
for(int x=-16; x<16; x++)
for(int y=-16; y<16; y++)
for(int d=0; d<6; d++) {
loc at = loc(x, y);
hyperpoint h = atz(T, corners, at, 6);
hyperpoint hl = atz(T, corners, at + eudir(d), 6);
Tf[i][x&31][y&31][d] = rgpushxto0(h) * rspintox(gpushxto0(h) * hl) * spin(M_PI);
}
}
}
hyperpoint get_corner_position(cell *c, int cid, ld cf = 3) {
auto li = get_local_info(c);
int i = li.last_dir;
if(i == -1)
return atz(dir_matrix(cid), corners, li.relative, 0, cf);
else {
auto& cellmatrix = Tf[i][li.relative.first&31][li.relative.second&31][fix6(li.total_dir)];
return inverse(cellmatrix) * atz(dir_matrix(i), corners, li.relative, fix6(cid + li.total_dir), cf);
}
}
map<pair<int, int>, loc> center_locs;
void compute_geometry() {
center_locs.clear();
if(on) {
int x = param.first;
int y = param.second;
area = ((2*x+y) * (2*x+y) + y*y*3) / 4;
next = hpxyz(x+y/2., -y * sqrt(3) / 2, 0);
scale = 1 / hypot2(next);
if(sphere) scale *= .7;
crossf *= scale;
hepvdist *= scale;
rhexf *= scale;
// spin = spintox(next);
// ispin = rspintox(next);
alpha = -atan2(next[1], next[0]);
base_distlimit = (base_distlimit + log(scale) / log(2.618)) / scale;
if(base_distlimit > 30)
base_distlimit = 30;
prepare_matrices();
}
else {
scale = 1;
alpha = 0;
}
}
loc config;
loc internal_representation(loc v) {
int& x = v.first, &y = v.second;
while(x < 0 || y < 0 || (x == 0 && y > 0))
v = v * loc(0, 1);
if(x > 8) x = 8;
if(y > 8) y = 8;
if(y > x) v = v * loc(1, -1);
return v;
}
loc human_representation(loc v) {
int& x = v.first, &y = v.second;
while(x < 0 || y < 0 || (x == 0 && y > 0))
v = v * loc(0, 1);
return v;
}
string operation_name() {
if(!gp::on) {
if(nonbitrunc) return XLAT("OFF");
else return XLAT("bitruncated");
}
else if(param == loc(1, 0))
return XLAT("OFF");
else if(param == loc(1, 1))
return XLAT("bitruncated");
else if(param == loc(2, 0))
return XLAT("chamfered");
else if(param == loc(3, 0))
return XLAT("2x bitruncated");
else {
auto p = human_representation(param);
return "GP(" + its(p.first) + "," + its(p.second) + ")";
}
}
void whirl_set(loc xy, bool texture_remap) {
#if CAP_TEXTURE
auto old_tstate = texture::config.tstate;
auto old_tstate_max = texture::config.tstate_max;
#endif
xy = internal_representation(xy);
if(xy.second && xy.second != xy.first && elliptic) {
addMessage("This does not work in elliptic geometry");
xy.second = 0;
}
config = human_representation(xy);
auto g = screens;
if(xy.first == 0 && xy.second == 0) xy.first = 1;
if(xy.first == 1 && xy.second == 0) {
if(gp::on) restartGame(rg::bitrunc);
if(!nonbitrunc) restartGame(rg::bitrunc);
}
else if(xy.first == 1 && xy.second == 1) {
if(gp::on) restartGame(rg::bitrunc);
if(nonbitrunc) restartGame(rg::bitrunc);
}
else {
if(nonbitrunc) restartGame(rg::bitrunc);
param = xy;
restartGame(rg::gp);
}
#if CAP_TEXTURE
if(texture_remap)
texture::config.remap(old_tstate, old_tstate_max);
#endif
screens = g;
}
string helptext() {
return
"Goldberg polyhedra are obtained by adding extra hexagons to a dodecahedron. "
"GP(x,y) means that, to get to a nearest non-hex from any non-hex, you should move x "
"cells in any direction, turn right 60 degrees, and move y cells. "
"HyperRogue generalizes this to any tesselation with 3 faces per vertex. "
"By default HyperRogue uses bitruncation, which corresponds to GP(1,1).";
}
void show(bool texture_remap) {
cmode = sm::SIDE;
gamescreen(0);
dialog::init(XLAT("Goldberg"));
bool show_nonthree = !(texture_remap && (S7&1));
if(show_nonthree) {
dialog::addBoolItem(XLAT("OFF"), param == loc(1,0), 'a');
dialog::lastItem().value = "GP(1,0)";
}
dialog::addBoolItem(XLAT("bitruncated"), param == loc(1,1), 'b');
dialog::lastItem().value = "GP(1,1)";
if(show_nonthree) {
dialog::addBoolItem(XLAT("chamfered"), param == loc(2,0), 'c');
dialog::lastItem().value = "GP(2,0)";
}
dialog::addBoolItem(XLAT("2x bitruncated"), param == loc(3,0), 'd');
dialog::lastItem().value = "GP(3,0)";
dialog::addBreak(100);
dialog::addSelItem("x", its(config.first), 'x');
dialog::addSelItem("y", its(config.second), 'y');
if((config.first-config.second)%3 && !show_nonthree)
dialog::addInfo("This pattern needs x-y divisible by 3");
else
dialog::addBoolItem(XLAT("select"), param == internal_representation(config), 'f');
dialog::addBreak(100);
dialog::addItem(XLAT("help"), SDLK_F1);
dialog::addItem(XLAT("back"), '0');
dialog::display();
keyhandler = [show_nonthree, texture_remap] (int sym, int uni) {
dialog::handleNavigation(sym, uni);
if(uni == 'a' && show_nonthree)
whirl_set(loc(1, 0), texture_remap);
else if(uni == 'b')
whirl_set(loc(1, 1), texture_remap);
else if(uni == 'c' && show_nonthree)
whirl_set(loc(2, 0), texture_remap);
else if(uni == 'd')
whirl_set(loc(3, 0), texture_remap);
else if(uni == 'f' && (show_nonthree || (config.first-config.second)%3 == 0))
whirl_set(config, texture_remap);
else if(uni == 'x')
dialog::editNumber(config.first, 1, 10, 1, 1, "x", helptext());
else if(uni == 'y')
dialog::editNumber(config.second, 1, 10, 1, 1, "y", helptext());
else if(uni == 'z')
swap(config.first, config.second);
else if(uni == '?' || sym == SDLK_F1 || uni == 'h' || uni == '2')
gotoHelp(helptext());
else if(doexiton(sym, uni))
popScreen();
};
}
loc univ_param() {
if(on) return param;
else if(nonbitrunc) return loc(1,0);
else return loc(1,1);
}
void configure(bool texture_remap = false) {
auto l = univ_param();
param = l;
config = human_representation(l);
pushScreen([texture_remap] () { gp::show(texture_remap); });
}
void be_in_triangle(local_info& li) {
int sp = 0;
auto& at = li.relative;
again:
auto corner = corners * loctoh_ort(at);
if(corner[1] < -1e-6 || corner[2] < -1e-6) {
at = at * eudir(1);
sp++;
goto again;
}
if(sp>3) sp -= 6;
li.last_dir = fix7(li.last_dir - sp);
}
int length(loc p) {
return eudist(p.first, p.second);
}
// from some point X, (0,0) is in distance dmain, param is in distance d0, and param*z is in distance d1
// what is the distance of at from X?
int solve_triangle(int dmain, int d0, int d1, loc at) {
loc centerloc(0, 0);
auto rel = make_pair(d0-dmain, d1-dmain);
if(center_locs.count(rel))
centerloc = center_locs[rel];
else {
bool found = false;
for(int y=-20; y<=20; y++)
for(int x=-20; x<=20; x++) {
loc c(x, y);
int cc = length(c);
int c0 = length(c - param);
int c1 = length(c - param*loc(0,1));
if(c0-cc == d0-dmain && c1-cc == d1-dmain)
found = true, centerloc = c;
}
if(!found && !quotient)
printf("Warning: centerloc not found: %d,%d,%d\n", dmain, d0, d1);
center_locs[rel] = centerloc;
}
return dmain + length(centerloc-at) - length(centerloc);
}
array<cell*, 3> get_masters(cell *c) {
if(gp::on) {
auto li = get_local_info(c);
be_in_triangle(li);
auto cm = c->master;
int i = li.last_dir;
return make_array(cm->c7, createStep(cm, i)->c7, createStep(cm, fix7(i+1))->c7);
}
else
return make_array(c->mov[0], c->mov[2], c->mov[4]);
}
int compute_dist(cell *c, int master_function(cell*)) {
auto li = get_local_info(c);
be_in_triangle(li);
cell *cm = c->master->c7;
int i = li.last_dir;
auto at = li.relative;
auto dmain = master_function(cm);
auto d0 = master_function(createStep(cm->master, i)->c7);
auto d1 = master_function(createStep(cm->master, fixdir(i+1, cm))->c7);
return solve_triangle(dmain, d0, d1, at);
}
int dist_2() {
return length(univ_param());
}
int dist_3() {
return length(univ_param() * loc(1,1));
}
int dist_1() {
return dist_3() - dist_2();
}
}
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