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hyperrogue/hypgraph.cpp

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// Hyperbolic Rogue -- hyperbolic graphics
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file hypgraph.cpp
* \brief mapping hyperpoints to the screen, and related functions
*/
#include "hyper.h"
namespace hr {
ld ghx, ghy, ghgx, ghgy;
hyperpoint ghpm = C0;
#if HDR
inline bool sphereflipped() { return sphere && vid.alpha > 1.1 && GDIM == 3; }
#endif
void ghcheck(hyperpoint &ret, const hyperpoint &H) {
if(hypot(ret[0]-ghx, ret[1]-ghy) < hypot(ghgx-ghx, ghgy-ghy)) {
ghpm = H; ghgx = ret[0]; ghgy = ret[1];
}
}
EX void camrotate(ld& hx, ld& hy) {
ld cam = vid.camera_angle * degree;
GLfloat cc = cos(cam);
GLfloat ss = sin(cam);
ld ux = hx, uy = hy * cc + ss, uz = cc - ss * hy;
hx = ux / uz, hy = uy / uz;
}
hyperpoint perspective_to_space(hyperpoint h, ld alpha = vid.alpha, eGeometryClass geo = ginf[geometry].cclass);
EX bool non_spatial_model() {
if(among(pmodel, mdRotatedHyperboles, mdJoukowsky, mdJoukowskyInverted, mdPolygonal, mdPolynomial))
return true;
if(pmodel == mdSpiral && euclid)
return true;
return pmodel && vid.consider_shader_projection && (get_shader_flags() & SF_DIRECT);
}
EX hyperpoint perspective_to_space(hyperpoint h, ld alpha, eGeometryClass gc) {
ld hx = h[0], hy = h[1];
if(gc == gcEuclid)
return hpxy(hx * (1 + alpha), hy * (1 + alpha));
ld hr = hx*hx+hy*hy;
if(hr > .9999 && gc == gcHyperbolic) return Hypc;
ld A, B, C;
ld curv = gc == gcSphere ? 1 : -1;
A = 1+curv*hr;
B = 2*hr*vid.alpha*-curv;
C = 1 - curv*hr*vid.alpha*vid.alpha;
B /= A; C /= A;
ld rootsign = 1;
// if(gc == gcSphere && vid.alpha > 1) rootsign = -1;
ld hz = B / 2 + rootsign * sqrt(C + B*B/4);
hyperpoint H;
H[0] = hx * (hz+vid.alpha);
H[1] = hy * (hz+vid.alpha);
H[LDIM] = hz;
return H;
}
EX hyperpoint space_to_perspective(hyperpoint z, ld alpha IS(vid.alpha)) {
ld s = 1 / (alpha + z[LDIM]);
z[0] *= s;
z[1] *= s;
if(GDIM == 3) {
z[2] *= s;
z[3] = 0;
}
else
z[2] = 0;
return z;
}
EX hyperpoint gethyper(ld x, ld y) {
ld hx = (x - current_display->xcenter) / current_display->radius;
ld hy = (y - current_display->ycenter) / current_display->radius / vid.stretch;
if(pmodel) {
ghx = hx, ghy = hy;
return ghpm;
}
if(vid.camera_angle) camrotate(hx, hy);
return perspective_to_space(hpxyz(hx, hy, 0));
}
void ballmodel(hyperpoint& ret, double alpha, double d, double zl) {
hyperpoint H = ypush(vid.camera) * xpush(d) * ypush(zl) * C0;
ld tzh = vid.ballproj + H[LDIM];
ld ax = H[0] / tzh;
ld ay = H[1] / tzh;
ld ca = cos(alpha), sa = sin(alpha);
ret[0] = ax * ca;
ret[1] = ay;
ret[2] = ax * sa;
models::apply_ball(ret[2], ret[1]);
}
void apply_depth(hyperpoint &f, ld z) {
if(vid.usingGL)
f[2] = z;
else {
z = z * current_display->radius;
ld mul = current_display->radius / (current_display->radius + z);
f[0] = f[0] * mul;
f[1] = f[1] * mul;
f[2] = vid.xres * current_display->eyewidth() / 2 / current_display->radius + vid.ipd * mul / 2;
}
}
bool hypot_zlev(ld zlev, ld& d, ld& df, ld& zf) {
if(zlev == 1) {
df = 1; zf = 0;
return false;
}
else {
// (0,0,1) -> (0, sin z, cos z) -> (sin d cos z, sin z, cos d cos z)
ld z = geom3::factor_to_lev(zlev);
ld tz = sin_auto(z);
ld td = sin_auto(abs(d)) * cos_auto(z);
ld h = hypot(td, tz);
zf = tz / h, df = td / h;
if(d > 0)
d = hypot_auto(d, z);
else
d = -hypot_auto(d, z);
return true;
}
}
int twopoint_sphere_flips;
bool twopoint_do_flips;
ld find_zlev(hyperpoint& H) {
if(spatial_graphics) {
ld zlev = zlevel(H);
if(zlev > 1-1e-6 && zlev < 1+1e-6) return 1;
H /= zlev;
return zlev;
}
return 1;
}
ld get_tz(hyperpoint H) {
ld tz = euclid ? (1+vid.alpha) : vid.alpha+H[LDIM];
if(tz < BEHIND_LIMIT && tz > -BEHIND_LIMIT) tz = BEHIND_LIMIT;
return tz;
}
EX ld atan2(hyperpoint h) {
return atan2(h[1], h[0]);
}
pair<ld, ld> move_z_to_y(hyperpoint& H) {
if(GDIM == 2) return make_pair(0, 0);
ld R = hypot(H[1], H[2]);
pair<ld, ld> res = { H[1] / R, H[2] / R };
H[1] = R; H[2] = 0;
return res;
}
void move_y_to_z(hyperpoint& H, pair<ld, ld> coef) {
if(GDIM == 3) {
H[2] = H[1] * coef.second;
H[1] = H[1] * coef.first;
H[3] = 1;
}
}
template<class T> void makeband(hyperpoint H, hyperpoint& ret, const T& f) {
ld zlev = find_zlev(H);
models::apply_orientation_yz(H[1], H[2]);
models::apply_orientation(H[0], H[1]);
auto r = move_z_to_y(H);
ld x, y, yf, zf=0;
y = asin_auto(H[1]);
x = asin_auto_clamp(H[0] / cos_auto(y));
if(sphere) {
if(H[LDIM] < 0 && x > 0) x = M_PI - x;
else if(H[LDIM] < 0 && x <= 0) x = -M_PI - x;
}
x += band_shift;
hypot_zlev(zlev, y, yf, zf);
f(x, y);
ld yzf = y * zf; y *= yf;
ret = hpxyz(x / M_PI, y / M_PI, 0);
move_y_to_z(ret, r);
models::apply_orientation(ret[1], ret[0]);
models::apply_orientation_yz(ret[2], ret[1]);
if(zlev != 1 && current_display->stereo_active())
apply_depth(ret, yzf / M_PI);
return;
}
void band_conformal(ld& x, ld& y) {
switch(cgclass) {
case gcSphere:
y = atanh(sin(y));
x *= 2; y *= 2;
break;
case gcHyperbolic:
y = 2 * atan(tanh(y/2));
x *= 2; y *= 2;
break;
case gcEuclid:
default:
// y = y;
y *= 2; x *= 2;
break;
}
}
void make_twopoint(ld& x, ld& y) {
auto p = vid.twopoint_param;
ld dleft = hypot_auto(x-p, y);
ld dright = hypot_auto(x+p, y);
if(sphere) {
int tss = twopoint_sphere_flips;
if(tss&1) { tss--;
dleft = 2*M_PI - 2*p - dleft;
dright = 2*M_PI - 2*p - dright;
swap(dleft, dright);
y = -y;
}
while(tss) { tss -= 2;
dleft = 2*M_PI - 4*p + dleft;
dright = 2*M_PI - 4*p + dright;
}
}
x = (dright*dright-dleft*dleft) / 4 / p;
y = (y>0?1:-1) * sqrt(dleft * dleft - (x-p)*(x-p) + 1e-9);
}
hyperpoint mobius(hyperpoint h, ld angle, ld scale = 1) {
h = perspective_to_space(h * scale, 1, gcSphere);
h = cspin(1, 2, angle * degree) * h;
return space_to_perspective(h, 1) / scale;
}
hyperpoint compute_hybrid(hyperpoint H, int rootid) {
auto& t = vid.twopoint_param;
hyperpoint Hl = xpush(+t) * H;
hyperpoint Hr = xpush(-t) * H;
ld g = (Hl[0] + 1e-7) / (Hl[1] + 1e-8);
ld d = hdist0(Hr);
hyperpoint spinned = spintox(Hl) * xpush0(2*t);
if(Hl[0] < 0) spinned = pispin * spinned;
ld y = asin_auto(spinned[1]);
ld x = asin_auto_clamp(spinned[0] / cos_auto(y));
int sign = (Hl[0] > 0 ? 1 : -1) * hdist0(Hl) < x ? -1 : 1;
switch(rootid & 3) {
case 1: sign = -sign; break;
case 2: sign = 1; break;
case 3: sign = -1; break;
}
// (x + t) / g = y
// yy + (x-t)(x-t) = dd
// (x+t)*(x+t)/g*g + x*x + t*t - 2*x*t = dd
// x*x*(1+1/g*g) + t*t*(1+1/g*g) + 2xt (1/gg-1) = dd
// xx + 2xt (1/gg-1) / (1+1/gg) = dd / (1+1/gg) - tt
ld b = t*(1/g/g - 1) / (1+1/g/g);
ld c = d*d / (1+1/g/g) - t*t;
// xx + 2bx = c
// xx + 2bx + bb = c + bb
// (x+b)^2 = c+bb
// x = +/- sqrt(c+bb) - b
ld a = c+b*b;
hyperpoint ret;
ret[0] = (a > 0 ? sign * sqrt(a) : 0) - b;
ret[1] = (ret[0] + t) / g;
ret[2] = 0;
return ret;
}
EX ld signed_sqrt(ld x) { return x > 0 ? sqrt(x) : -sqrt(-x); };
EX void applymodel(hyperpoint H, hyperpoint& ret) {
hyperpoint H_orig = H;
if(models::product_model()) {
ld zlev = zlevel(H);
H /= exp(zlev);
hybrid::in_underlying_geometry([&] { applymodel(H, ret); });
ret[2] = zlev * models::product_z_scale;
ret = NLP * ret;
return;
}
switch(pmodel) {
case mdPerspective: {
ld ratio = vid.xres / current_display->tanfov / current_display->radius / 2;
if(prod) H = product::inverse_exp(H);
H = lp_apply(H);
if(H[2] == 0) { ret[0] = 1e6; ret[1] = 1e6; ret[2] = 1; return; }
ret[0] = H[0]/H[2] * ratio;
ret[1] = H[1]/H[2] * ratio;
ret[2] = 1;
return;
}
case mdGeodesic: {
auto S = lp_apply(inverse_exp(H, iTable));
ld ratio = vid.xres / current_display->tanfov / current_display->radius / 2;
ret[0] = S[0]/S[2] * ratio;
ret[1] = S[1]/S[2] * ratio;
ret[2] = 1;
return;
}
case mdPixel:
ret = H / current_display->radius;
return;
case mdBall: {
ld zlev = find_zlev(H);
ld zl = vid.depth-geom3::factor_to_lev(zlev);
ballmodel(ret, atan2(H), hdist0(H), zl);
break;
}
case mdDisk: {
if(nonisotropic) {
ret = lp_apply(inverse_exp(H, iTable, true));
ld w;
if(sn::in()) {
// w = 1 / sqrt(1 - sqhypot_d(3, ret));
// w = w / (vid.alpha + w);
w = 1 / (sqrt(1 - sqhypot_d(3, ret)) * vid.alpha + 1);
}
else {
w = hypot_d(3, ret);
w = sinh(w) / ((vid.alpha + cosh(w)) * w);
}
for(int i=0; i<3; i++) ret[i] *= w;
ret[3] = 1;
break;
}
ld tz = get_tz(H);
if(!vid.camera_angle) {
ret[0] = H[0] / tz;
ret[1] = H[1] / tz;
if(GDIM == 3) ret[2] = H[2] / tz;
else ret[2] = vid.xres * current_display->eyewidth() / 2 / current_display->radius - vid.ipd / tz / 2;
if(MAXMDIM == 4) ret[3] = 1;
}
else {
ld tx = H[0];
ld ty = H[1];
ld cam = vid.camera_angle * degree;
GLfloat cc = cos(cam);
GLfloat ss = sin(cam);
ld ux = tx, uy = ty * cc - ss * tz, uz = tz * cc + ss * ty;
ret[0] = ux / uz;
ret[1] = uy / uz;
ret[2] = vid.xres * current_display->eyewidth() / 2 / current_display->radius - vid.ipd / uz / 2;
}
return;
}
case mdCentralInversion: {
ld tz = get_tz(H);
for(int d=0; d<GDIM; d++) ret[d] = H[d] / tz;
ld r = 0;
for(int d=0; d<GDIM; d++) r += ret[d]*ret[d];
for(int d=0; d<GDIM; d++) ret[d] /= r;
return;
}
case mdHalfplane: {
// Poincare to half-plane
ld zlev = find_zlev(H);
H = space_to_perspective(H);
models::apply_orientation_yz(H[1], H[2]);
models::apply_orientation(H[0], H[1]);
H[1] += 1;
double rad = sqhypot_d(GDIM, H);
H /= -rad;
H[1] += .5;
if(GDIM == 3) {
// a bit simpler when we do not care about 3D
H *= models::halfplane_scale;
ret[0] = -H[0];
ret[1] = 1 + H[1];
ret[2] = H[2];
ret[3] = 1;
models::apply_orientation(ret[1], ret[0]);
models::apply_orientation_yz(ret[2], ret[1]);
break;
}
models::apply_orientation(H[0], H[1]);
H *= models::halfplane_scale;
ret[0] = -models::osin - H[0];
if(zlev != 1) {
if(abs(models::ocos) > 1e-5)
H[1] = H[1] * pow(zlev, models::ocos);
if(abs(models::ocos) > 1e-5 && models::osin)
H[1] += H[0] * models::osin * (pow(zlev, models::ocos) - 1) / models::ocos;
else if(models::osin)
H[1] += H[0] * models::osin * log(zlev);
}
ret[1] = models::ocos + H[1];
ret[2] = GDIM == 3 ? H[2] : 0;
if(MAXMDIM == 4) ret[3] = 1;
if(zlev != 1 && current_display->stereo_active())
apply_depth(ret, -H[1] * geom3::factor_to_lev(zlev));
break;
}
case mdHorocyclic: {
find_zlev(H);
models::apply_orientation_yz(H[1], H[2]);
models::apply_orientation(H[0], H[1]);
ret = hyperbolic ? deparabolic10(H) : H;
ret *= .5;
ret[LDIM] = 1;
models::apply_orientation(ret[1], ret[0]);
models::apply_orientation_yz(ret[2], ret[1]);
if(nonisotropic) ret = lp_apply(ret);
break;
}
case mdHemisphere: {
switch(cgclass) {
case gcHyperbolic: {
ld zl = zlevel(H);
ret = H / H[2];
ret[2] = sqrt(1 - sqhypot_d(2, ret));
ret = ret * (1 + (zl - 1) * ret[2]);
break;
}
case gcEuclid: default: {
// stereographic projection to a sphere
auto hd = hdist0(H) / vid.euclid_to_sphere;
if(hd == 0) ret = hpxyz(0, 0, -1);
else {
ld x = 2 * hd / (1 + hd * hd);
ld y = x / hd;
ret = H * x / hd / vid.euclid_to_sphere;
ret[2] = (1 - y);
ret = ret * (1 + (H[2]-1) * y / vid.euclid_to_sphere);
}
break;
}
case gcSphere: {
ret = H;
break;
}
}
swap(ret[1], ret[2]);
models::apply_ball(ret[2], ret[1]);
break;
}
case mdHyperboloidFlat:
case mdHyperboloid: {
if(nonisotropic) {
// if(nisot::local_perspective_used()) H = NLP * H;
ret = lp_apply(H);
break;
}
if(prod) {
ret = H;
break;
}
if(pmodel == mdHyperboloid) {
ld& topz = models::top_z;
if(H[2] > topz) {
ld scale = sqrt(topz*topz-1) / hypot_d(2, H);
H *= scale;
H[2] = topz;
}
}
else {
H = space_to_perspective(H, vid.alpha);
H[2] = 1 - vid.alpha;
}
ret[0] = H[0] / 3;
ret[1] = (1 - H[2]) / 3;
ret[2] = H[1] / 3;
models::apply_ball(ret[2], ret[1]);
break;
}
case mdFisheye: {
ld zlev;
if(nonisotropic) {
H = lp_apply(inverse_exp(H, iTable, false));
zlev = 1;
}
else {
zlev = find_zlev(H);
H = space_to_perspective(H);
}
H /= vid.fisheye_param;
H[LDIM] = zlev;
ret = H / sqrt(1 + sqhypot_d(GDIM+1, H));
if(GDIM == 3) ret[LDIM] = zlev;
break;
}
case mdSimulatedPerspective: {
models::apply_orientation_yz(H[1], H[2]);
models::apply_orientation(H[0], H[1]);
auto yz = move_z_to_y(H);
hyperpoint Hl = xpush(-vid.twopoint_param) * H;
hyperpoint Hr = xpush(+vid.twopoint_param) * H;
ld lyx = (Hl[1] + 1e-7) / (Hl[0] + 1e-8);
ld ryx = (Hr[1] + 1e-7) / (Hr[0] + 1e-8);
// (r.x + t) * lyx = (r.x - t) * ryx = r.y
// r.x * lyx + t * lyx = r.x * ryx - t * ryx
// r.x * (lyx-ryx) = - t * (ryx + lyx)
// r.x = -t * (ryx+lyx) / (lyx-ryx)
// r.x = - 2 * t * lyx * ryx / lyx / ryx
ret[0] = -vid.twopoint_param * (ryx + lyx) / (lyx - ryx);
ret[1] = (ret[0] + vid.twopoint_param) * lyx;
ret[2] = 0;
move_y_to_z(ret, yz);
models::apply_orientation(ret[0], ret[1]);
models::apply_orientation_yz(ret[2], ret[1]);
break;
}
case mdTwoHybrid: {
models::apply_orientation_yz(H[1], H[2]);
models::apply_orientation(H[0], H[1]);
auto yz = move_z_to_y(H);
ret = compute_hybrid(H, whateveri[0]);
move_y_to_z(ret, yz);
models::apply_orientation(ret[0], ret[1]);
models::apply_orientation_yz(ret[2], ret[1]);
break;
}
case mdJoukowsky:
case mdJoukowskyInverted: {
models::apply_orientation_yz(H[1], H[2]);
models::apply_orientation(H[0], H[1]);
// with equal speed skiprope: models::apply_orientation(H[1], H[0]);
if(vid.skiprope) {
static ld last_skiprope = 0;
static transmatrix lastmatrix;
if(vid.skiprope != last_skiprope) {
ret = mobius(C0, -vid.skiprope, 2);
const cld c1(1, 0);
const cld c2(2, 0);
const cld c4(4, 0);
cld w(ret[0], ret[1]);
cld z = sqrt(c4*w*w-c1) + c2*w;
if(abs(z) > 1) z = c1 / z;
hyperpoint zr = hpxyz(real(z), imag(z), 0);
hyperpoint inhyp = perspective_to_space(zr, 1, gcHyperbolic);
last_skiprope = vid.skiprope;
lastmatrix = rgpushxto0(inhyp);
}
H = lastmatrix * H;
}
H = space_to_perspective(H);
auto yz = move_z_to_y(H);
ld r = hypot_d(2, H);
ld c = H[0] / r;
ld s = H[1] / r;
ld& mt = models::model_transition;
ld a = 1 - .5 * mt, b = .5 * mt;
swap(a, b);
ret[0] = (a * r + b/r) * c / 2;
ret[1] = (a * r - b/r) * s / 2;
ret[2] = 0;
if(vid.skiprope)
ret = mobius(ret, vid.skiprope, 2);
if(pmodel == mdJoukowskyInverted) {
ld r2 = sqhypot_d(2, ret);
ret[0] = ret[0] / r2;
ret[1] = -ret[1] / r2;
move_y_to_z(ret, yz);
models::apply_orientation(ret[1], ret[0]);
/*
ret[0] += 1;
ld alpha = atan2(ret[1], ret[0]);
ld mod = hypot(ret[0], ret[1]);
// ret[0] = cos(alpha/2) * sqrt(mod);
// ret[1] = sin(alpha/2) * sqrt(mod);
ret[0] = alpha;
ret[1] = log(mod); */
}
else {
move_y_to_z(ret, yz);
models::apply_orientation(ret[0], ret[1]);
}
models::apply_orientation_yz(ret[2], ret[1]);
break;
}
case mdPolygonal: case mdPolynomial: {
H = space_to_perspective(H);
models::apply_orientation(H[0], H[1]);
pair<long double, long double> p = polygonal::compute(H[0], H[1]);
models::apply_orientation(p.second, p.first);
ret[0] = p.first;
ret[1] = p.second;
ret[2] = 0;
break;
}
case mdBand:
if(models::model_transition != 1) {
ld& mt = models::model_transition;
H = space_to_perspective(H);
models::apply_orientation(H[0], H[1]);
H[0] += 1;
double rad = H[0]*H[0] + H[1]*H[1];
H[1] /= rad;
H[0] /= rad;
H[0] -= .5;
ld phi = atan2(H);
ld r = hypot_d(2, H);
r = pow(r, 1 - mt);
phi *= (1 - mt);
ret[0] = r * cos(phi);
ret[1] = r * sin(phi);
ret[2] = 0;
ret[0] -= pow(0.5, 1-mt);
ret[0] /= -(1-mt) * M_PI / 2;
ret[1] /= (1-mt) * M_PI / 2;
models::apply_orientation(ret[1], ret[0]);
}
else
makeband(H, ret, band_conformal);
break;
case mdTwoPoint:
makeband(H, ret, make_twopoint);
break;
case mdMollweide:
makeband(H, ret, [] (ld& x, ld& y) {
ld theta =
hyperbolic ? min(y / 2 + 0.572365, y * 0.78509) :
euclid ? y :
y > 0 ? max(y * 0.012/0.015, M_PI/2 - (M_PI/2-y) * 0.066262/0.015708) :
min(y * 0.012/0.015, -M_PI/2 + (M_PI/2+y) * 0.066262/0.015708);
if(sphere && abs(theta) >= M_PI/2 - 1e-6) ;
else {
for(int it=0; it<4; it++) {
auto a = (sin_auto(2*theta) +2*theta - M_PI * sin_auto(y));
auto b = (2 + 2 * cos_auto(2*theta));
theta = theta - a / b;
} }
y = M_PI * sin_auto(theta) / 2;
x = x * cos_auto(theta);
});
break;
case mdCentralCyl:
makeband(H, ret, [] (ld& x, ld& y) { y = tan_auto(y); ld top = vid.yres * M_PI / current_display->radius; if(y>top) y=top; if(y<-top) y=-top; });
break;
case mdCollignon:
find_zlev(H);
makeband(H, ret, [] (ld& x, ld& y) {
ld sgn = 1;
if(vid.collignon_reflected && y > 0) y = -y, sgn = -1;
y = signed_sqrt(sin_auto(y) + vid.collignon_parameter);
x *= y / 1.2;
y -= signed_sqrt(vid.collignon_parameter);
y *= sgn;
y *= M_PI;
});
break;
case mdBandEquiarea:
makeband(H, ret, [] (ld& x, ld& y) { y = sin_auto(y); });
break;
case mdBandEquidistant:
makeband(H, ret, [] (ld& x, ld& y) { });
break;
case mdSinusoidal:
makeband(H, ret, [] (ld& x, ld& y) { x *= cos_auto(y); });
break;
case mdEquidistant: case mdEquiarea: case mdEquivolume: {
if(nonisotropic || prod) {
ret = lp_apply(inverse_exp(H, iTable, false));
ret[3] = 1;
break;
}
ld zlev = find_zlev(H);
ld rad = hypot_d(GDIM, H);
if(rad == 0) rad = 1;
ld d = hdist0(H);
ld df, zf;
hypot_zlev(zlev, d, df, zf);
// 4 pi / 2pi = M_PI
if(pmodel == mdEquivolume)
d = pow(volume_auto(d), 1/3.) * pow(M_PI / 2, 1/3.);
else if(pmodel == mdEquiarea && sphere)
d = sqrt(2*(1 - cos(d))) * M_PI / 2;
else if(pmodel == mdEquiarea && hyperbolic)
d = sqrt(2*(cosh(d) - 1)) / 1.5;
ret = H * (d * df / rad / M_PI);
if(GDIM == 2) ret[2] = 0;
if(MAXMDIM == 4) ret[3] = 1;
if(zlev != 1 && current_display->stereo_active())
apply_depth(ret, d * zf / M_PI);
break;
}
case mdRotatedHyperboles: {
// ld zlev = <- not implemented
find_zlev(H); // + vid.depth;
models::apply_orientation(H[0], H[1]);
ld y = asin_auto(H[1]);
ld x = asin_auto_clamp(H[0] / cos_auto(y));
// ld z = zlev == 1 ? 0 : geom3::factor_to_lev(zlev);
ld factor = geom3::lev_to_factor(y + vid.depth);
ret[0] = sinh(x) * factor;
ret[1] = cosh(x) * factor;
ret[2] = 0;
if(models::use_atan) {
ret[0] = atan(ret[0]);
ret[1] = atan(ret[1]);
}
break;
}
case mdFormula: {
dynamicval<eModel> m(pmodel, models::basic_model);
applymodel(H, ret);
exp_parser ep;
ep.extra_params["z"] = cld(ret[0], ret[1]);
ep.extra_params["cx"] = ret[0];
ep.extra_params["cy"] = ret[1];
ep.extra_params["cz"] = ret[2];
ep.extra_params["ux"] = H[0];
ep.extra_params["uy"] = H[1];
ep.extra_params["uz"] = H[2];
ep.s = models::formula;
cld res;
try {
res = ep.parse();
}
catch(hr_parse_exception&) {
res = 0;
}
ret[0] = real(res);
ret[1] = imag(res);
ret[2] = 0;
break;
}
case mdSpiral: {
cld z;
if(hyperbolic || sphere) makeband(H, ret, band_conformal);
else ret = H;
z = cld(ret[0], ret[1]) * models::spiral_multiplier;
if(models::spiral_cone < 360) {
ld alpha = imag(z) * 360 / models::spiral_cone;
ld r = real(z);
r = exp(r);
ret[0] = -sin(alpha) * r;
ret[1] = cos(alpha) * r;
if(euclid) ret = models::euclidean_spin * ret;
ret[2] = (r-1) * sqrt( pow(360/models::spiral_cone, 2) - 1);
models::apply_ball(ret[2], ret[1]);
}
else {
z = exp(z);
ret[0] = real(z);
ret[1] = imag(z);
if(euclid) ret = models::euclidean_spin * ret;
if(vid.skiprope)
ret = mobius(ret, vid.skiprope, 1);
}
}
case mdGUARD: case mdManual: break;
}
ghcheck(ret,H_orig);
}
// game-related graphics
EX transmatrix sphereflip; // on the sphere, flip
EX bool playerfound; // has player been found in the last drawing?
EX bool outofmap(hyperpoint h) {
if(GDIM == 3)
return false;
else if(euclid)
return h[2] < .5; // false; // h[0] * h[0] + h[1] * h[1] > 15 * cgi.crossf;
else if(sphere)
return h[2] < .1 && h[2] > -.1 && h[1] > -.1 && h[1] < .1 && h[0] > -.1 && h[0] < .1;
else
return h[2] < .5;
}
EX hyperpoint mirrorif(const hyperpoint& V, bool b) {
if(b) return Mirror*V;
else return V;
}
EX transmatrix mirrorif(const transmatrix& V, bool b) {
if(b) return V*Mirror;
else return V;
}
// -1 if away, 0 if not away
EX int away(const transmatrix& V2) {
return (intval(C0, V2 * xpush0(.1)) > intval(C0, tC0(V2))) ? -1 : 0;
}
/* double zgrad(double f1, double f2, int nom, int den) {
using namespace geom3;
ld fo1 = factor_to_lev(f1);
ld fo2 = factor_to_lev(f2);
return lev_to_factor(fo1 + (fo2-fo1) * nom / den);
} */
EX double zgrad0(double l1, double l2, int nom, int den) {
using namespace geom3;
return lev_to_factor(l1 + (l2-l1) * nom / den);
}
EX bool behindsphere(const hyperpoint& h) {
if(!sphere) return false;
if(mdBandAny()) return false;
if(vid.alpha > 1) {
if(h[LDIM] > -1/vid.alpha) return true;
}
if(vid.alpha <= 1) {
if(h[LDIM] < .2-vid.alpha) return true;
}
return false;
}
ld to01(ld a0, ld a1, ld x) {
if(x < a0) return 0;
if(x > a1) return 1;
return (x-a0) / (a1-a0);
}
EX ld spherity(const hyperpoint& h) {
if(!sphere) return 1;
if(vid.alpha > 1) {
return to01(1/vid.alpha, 1, abs(h[2]));
}
if(vid.alpha <= 1) {
return to01(-1.5, 1, h[2]);
}
return 1;
}
EX bool behindsphere(const transmatrix& V) {
return behindsphere(tC0(V));
}
EX ld spherity(const transmatrix& V) {
return spherity(tC0(V));
}
EX bool confusingGeometry() {
return quotient;
}
EX ld master_to_c7_angle() {
if(hybri) return hybrid::in_underlying_geometry(master_to_c7_angle);
if(WDIM == 3) return 0;
ld alpha = 0;
#if CAP_GP
if(cgi.gpdata) alpha = cgi.gpdata->alpha;
#endif
return (!BITRUNCATED && !bt::in() && !arcm::in()) ? M_PI + alpha : 0;
}
EX transmatrix actualV(const heptspin& hs, const transmatrix& V) {
if(prod) return PIU(actualV(hs, V));
if(WDIM == 3) return V;
#if CAP_IRR
if(IRREGULAR)
return V * spin(M_PI + 2 * M_PI / S7 * (hs.spin + irr::periodmap[hs.at].base.spin));
#endif
#if CAP_ARCM
if(arcm::in()) return V * spin(-arcm::current.triangles[arcm::id_of(hs.at)][hs.spin].first);
#endif
#if CAP_BT
if(bt::in()) return V;
#endif
if(kite::in()) return V;
return (hs.spin || !BITRUNCATED) ? V * spin(hs.spin*2*M_PI/S7 + master_to_c7_angle()) : V;
}
EX bool point_behind(hyperpoint h) {
if(sphere) return false;
if(!in_perspective()) return false;
if(pmodel == mdGeodesic) h = inverse_exp(h, iLazy);
if(pmodel == mdPerspective && prod) h = product::inverse_exp(h);
h = lp_apply(h);
return h[2] < 1e-8;
}
void raise_error() {
println(hlog, "something wrong");
}
EX bool invalid_matrix(const transmatrix T) {
for(int i=0; i<GDIM; i++) for(int j=0; j<GDIM; j++)
if(std::isnan(T[i][j]) || T[i][j] > 1e8 || T[i][j] < -1e8 || std::isinf(T[i][j]))
return true;
if(prod) {
for(int i=0; i<GDIM; i++) for(int j=0; j<GDIM; j++) if(abs(T[i][j]) > 1e-60) return false;
}
else
for(int i=0; i<GDIM; i++) for(int j=0; j<GDIM; j++) if(T[i][j] > .5 || T[i][j] < -.5) return false;
return true;
}
EX bool invalid_point(const hyperpoint h) {
return std::isnan(h[LDIM]) || h[LDIM] > 1e8 || std::isinf(h[LDIM]);
}
EX bool in_smart_range(const transmatrix& T) {
hyperpoint h = tC0(T);
if(invalid_point(h)) return false;
if(nil || nih) return true;
#if CAP_SOLV
if(pmodel == mdGeodesic) return sn::in_table_range(h);
#endif
hyperpoint h1;
applymodel(h, h1);
if(invalid_point(h1)) return false;
ld x = current_display->xcenter + current_display->radius * h1[0];
ld y = current_display->ycenter + current_display->radius * h1[1] * vid.stretch;
if(x > current_display->xtop + current_display->xsize * 2) return false;
if(x < current_display->xtop - current_display->xsize * 1) return false;
if(y > current_display->ytop + current_display->ysize * 2) return false;
if(y < current_display->ytop - current_display->ysize * 1) return false;
if(GDIM == 3) {
if(-h1[2] < models::clip_min * 2 - models::clip_max) return false;
if(-h1[2] > models::clip_max * 2 - models::clip_min) return false;
}
ld epsilon = 0.01;
ld dx = 0, dy = 0, dz = 0, dh[MAXMDIM];
for(int i=0; i<GDIM; i++) {
hyperpoint h2;
applymodel(T * cpush0(i, epsilon), h2);
ld x1 = current_display->radius * abs(h2[0] - h1[0]) / epsilon;
ld y1 = current_display->radius * abs(h2[1] - h1[1]) * vid.stretch / epsilon;
dx = max(dx, x1); dy = max(dy, y1);
if(GDIM == 3) dz = max(dz, abs(h2[2] - h1[2]));
dh[i] = hypot(x1, y1);
}
if(GDIM == 3) {
if(-h1[2] + 2 * dz < models::clip_min || -h1[2] - 2 * dz > models::clip_max) return false;
sort(dh, dh+GDIM);
ld scale = sqrt(dh[1] * dh[2]) * cgi.scalefactor * hcrossf7;
if(scale <= (WDIM == 2 ? vid.smart_range_detail : vid.smart_range_detail_3)) return false;
}
else {
ld scale = sqrt(dh[0] * dh[1]) * cgi.scalefactor * hcrossf7;
if(scale <= vid.smart_range_detail) return false;
}
return
x - 2 * dx < current_display->xtop + current_display->xsize &&
x + 2 * dx > current_display->xtop &&
y - 2 * dy < current_display->ytop + current_display->ysize &&
y + 2 * dy > current_display->ytop;
}
#if CAP_GP
namespace gp {
/*
void drawrec(cell *c, const transmatrix& V) {
if(dodrawcell(c))
drawcell(c, V, 0, false);
for(int i=0; i<c->type; i++) {
cell *c2 = c->move(i);
if(!c2) continue;
if(c2->move(0) != c) continue;
if(c2 == c2->master->c7) continue;
transmatrix V1 = V * ddspin(c, i) * xpush(cgi.crossf) * iddspin(c2, 0) * spin(M_PI);
drawrec(c2, V1);
}
} */
bool drawrec(cell *c, const transmatrix& V, gp::loc at, int dir, int maindir) {
bool res = false;
transmatrix V1 = V * cgi.gpdata->Tf[draw_li.last_dir][at.first&31][at.second&31][fixg6(dir)];
if(do_draw(c, V1)) {
/* auto li = get_local_info(c);
if((dir - li.total_dir) % S6) printf("totaldir %d/%d\n", dir, li.total_dir);
if(at != li.relative) printf("at %s/%s\n", disp(at), disp(li.relative));
if(maindir != li.last_dir) printf("ld %d/%d\n", maindir, li.last_dir); */
draw_li.relative = at;
draw_li.total_dir = fixg6(dir);
drawcell(c, V1);
res = true;
}
for(int i=0; i<c->type; i++) {
cell *c2 = c->move(i);
if(!c2) continue;
if(c2->move(0) != c) continue;
if(c2 == c2->master->c7) continue;
res |= drawrec(c2, V, at + eudir(dir+i), dir + i + SG3, maindir);
}
return res;
}
bool drawrec(cell *c, const transmatrix& V) {
draw_li.relative = loc(0,0);
draw_li.total_dir = 0;
draw_li.last_dir = -1;
bool res = false;
if(do_draw(c, V))
drawcell(c, V), res = true;
for(int i=0; i<c->type; i++) {
cell *c2 = c->move(i);
if(!c2) continue;
if(c2->move(0) != c) continue;
if(c2 == c2->master->c7) continue;
draw_li.last_dir = i;
res |= drawrec(c2, V, gp::loc(1,0), SG3, i);
}
return res;
}
}
#endif
vector<tuple<heptspin, hstate, transmatrix, ld> > drawn_cells;
bool in_multi = false;
EX bool drawcell_subs(cell *c, transmatrix V) {
#if CAP_GP
if(GOLDBERG) {
return gp::drawrec(c, V);
}
#endif
bool draw = false;
#if CAP_IRR
if(IRREGULAR) {
auto& hi = irr::periodmap[c->master];
auto& vc = irr::cells_of_heptagon[hi.base.at];
for(int i=0; i<isize(vc); i++) {
cell *c = hi.subcells[i];
transmatrix V1 = V * irr::cells[vc[i]].pusher;
if(do_draw(c, V1))
draw = true,
drawcell(hi.subcells[i], V * irr::cells[vc[i]].pusher);
}
return draw;
}
#endif
if(do_draw(c, V)) {
draw = true;
drawcell(c, V);
}
if(BITRUNCATED) forCellIdEx(c1, d, c) {
if(c->c.spin(d) == 0) {
transmatrix V2 = V * currentmap->adj(c, d);
if(do_draw(c1, V2))
draw = true,
drawcell(c1, V2);
}
}
return draw;
}
void hrmap_standard::draw() {
if(sphere && pmodel == mdSpiral && !in_multi) {
in_multi = true;
if(models::ring_not_spiral) {
int qty = ceil(1. / models::sphere_spiral_multiplier);
if(qty > 100) qty = 100;
for(int i=-qty; i < qty; i++) {
band_shift = 2 * M_PI * i;
draw();
}
}
else {
draw();
if(vid.use_smart_range) for(int i=1;; i++) {
int drawn = cells_drawn;
band_shift = 2 * M_PI * i;
draw();
band_shift = -2 * M_PI * i;
draw();
if(drawn == cells_drawn) break;
}
}
in_multi = false;
return;
}
drawn_cells.clear();
drawn_cells.emplace_back(centerover->master, hsOrigin, cview() * master_relative(centerover, true), band_shift);
for(int i=0; i<isize(drawn_cells); i++) {
// prevent reallocation due to insertion
if(drawn_cells.capacity() < drawn_cells.size() + 16)
drawn_cells.reserve(max<size_t>(2 * drawn_cells.size(), 128));
const auto& dc = drawn_cells[i];
auto& hs = get<0>(dc);
auto& s = get<1>(dc);
auto& V = get<2>(dc);
dynamicval<ld> bs(band_shift, get<3>(dc));
cell *c = hs.at->c7;
transmatrix V10;
const transmatrix& V1 = hs.mirrored ? (V10 = V * Mirror) : V;
bool draw = drawcell_subs(c, actualV(hs, V1));
if(sphere) draw = true;
if(draw) for(int d=0; d<S7; d++) {
hstate s2 = transition(s, d);
if(s2 == hsError) continue;
heptspin hs2 = hs + d + wstep;
transmatrix Vd = V * cgi.heptmove[d];
bandfixer bf(Vd);
drawn_cells.emplace_back(hs2, s2, Vd, band_shift);
}
}
}
EX void spinEdge(ld aspd) {
ld downspin = 0;
if(dual::state == 2 && dual::currently_loaded != dual::main_side) {
transmatrix our = dual::get_orientation();
transmatrix their = dual::player_orientation[dual::main_side];
fixmatrix(our);
fixmatrix(their);
if(GDIM == 2) {
transmatrix T = their * inverse(our);
hyperpoint H = T * xpush0(1);
downspin = -atan2(H[1], H[0]);
}
else rotate_view(their * inverse(our));
}
else if(playerfound && vid.fixed_facing) {
hyperpoint H = gpushxto0(playerV * C0) * playerV * xpush0(5);
downspin = atan2(H[1], H[0]);
downspin += vid.fixed_facing_dir * degree;
if(flipplayer) downspin += M_PI;
while(downspin < -M_PI) downspin += 2*M_PI;
while(downspin > +M_PI) downspin -= 2*M_PI;
aspd = (1 + 2 * abs(downspin)) * aspd;
}
else if((WDIM == 2 || prod) && GDIM == 3 && vid.fixed_yz && !CAP_ORIENTATION) {
aspd = 999999;
auto& vo = get_view_orientation();
// does not work well (also need change auto& to auto)
// if(hybri && !prod) vo = vo * inverse(nisot::translate(tC0(vo)));
if(straightDownSeek) {
auto sdp = straightDownPoint;
if(prod) sdp = vo * product::inverse_exp(sdp);
if(sdp[0])
downspin = models::rotation * degree - atan2(sdp[0], sdp[1]);
}
else {
if(vo[0][2])
downspin = -atan2(vo[0][2], vo[1][2]);
}
}
else if(straightDownSeek) {
downspin = atan2(straightDownPoint[1], straightDownPoint[0]);
downspin -= M_PI/2;
downspin += models::rotation * degree;
while(downspin < -M_PI) downspin += 2*M_PI;
while(downspin > +M_PI) downspin -= 2*M_PI;
downspin = downspin * min(straightDownSpeed, (double)1);
}
if(downspin > aspd) downspin = aspd;
if(downspin < -aspd) downspin = -aspd;
rotate_view(spin(downspin));
}
EX void centerpc(ld aspd) {
if(subscreens::split([=] () {centerpc(aspd);})) return;
if(dual::split([=] () { centerpc(aspd); })) return;
#if CAP_CRYSTAL
if(cryst)
crystal::centerrug(aspd);
#endif
#if CAP_RACING
if(racing::on && racing::set_view()) return;
#endif
#if MAXMDIM >= 4
if(shmup::on && vid.sspeed > -5 && GDIM == 3) {
int id = subscreens::in ? subscreens::current_player : 0;
auto& pc = shmup::pc[id];
centerover = pc->base;
transmatrix T = pc->at;
int sl = snakelevel(cwt.at);
if(sl && WDIM == 2) T = T * zpush(cgi.SLEV[sl] - cgi.FLOOR);
View = inverse(T);
if(prod) NLP = inverse(pc->ori);
if(WDIM == 2) rotate_view( cspin(0, 1, M_PI) * cspin(2, 1, M_PI/2 + shmup::playerturny[id]) * spin(-M_PI/2) );
return;
}
#endif
if(ors::mode == 2 && vid.sspeed < 5) return;
if(vid.sspeed >= 4.99) aspd = 1000;
DEBBI(DF_GRAPH, ("center pc"));
auto& W = current_display->which_copy;
ors::unrotate(W); ors::unrotate(View); ors::unrotate(cwtV);
/* what should we center? */
transmatrix T;
if(multi::players > 1)
T = cwtV; /* do not even try */
else {
T = W;
if(shmup::on)
T = T * shmup::pc[0]->at;
}
if(invalid_matrix(T)) return;
#if MAXMDIM >= 4
if(GDIM == 3 && WDIM == 2) {
geom3::do_auto_eye();
int sl = snakelevel(cwt.at);
if(isWorm(cwt.at->monst) && sl < 3) sl++;
if(sl || vid.eye) T = T * zpush(cgi.SLEV[sl] - cgi.FLOOR + vid.eye);
}
#endif
hyperpoint H = inverse(actual_view_transform) * tC0(T);
ld R = (zero_d(GDIM, H) && !prod) ? 0 : hdist0(H);
if(R < 1e-9) {
// either already centered or direction unknown
/* if(playerfoundL && playerfoundR) {
} */
spinEdge(aspd);
fixmatrix(View);
current_display->which_copy = gmatrix[cwt.at];
}
else {
aspd *= euclid ? (2+3*R*R) : (1+R+(shmup::on?1:0));
if(R < aspd)
shift_view_to(H);
else
shift_view_towards(H, aspd);
fixmatrix(View);
fixmatrix(current_display->which_copy);
spinEdge(aspd);
}
ors::rerotate(W); ors::rerotate(cwtV); ors::rerotate(View);
}
EX void optimizeview() {
if(subscreens::split(optimizeview)) return;
if(dual::split(optimizeview)) return;
transmatrix iView = inverse(View);
virtualRebase(centerover, iView);
View = inverse(iView);
fixmatrix(View);
#if CAP_ANIMATIONS
if(centerover && inmirror(centerover)) {
anims::reflect_view();
}
#endif
}
void addball(ld a, ld b, ld c) {
hyperpoint h;
ballmodel(h, a, b, c);
for(int i=0; i<3; i++) h[i] *= current_display->radius;
curvepoint(h);
}
void ballgeometry() {
queuereset(mdPixel, PPR::CIRCLE);
for(int i=0; i<60; i++)
addball(i * M_PI/30, 10, 0);
for(double d=10; d>=-10; d-=.2)
addball(0, d, 0);
for(double d=-10; d<=10; d+=.2)
addball(0, d, vid.depth);
addball(0, 0, -vid.camera);
addball(0, 0, vid.depth);
addball(0, 0, -vid.camera);
addball(0, -10, 0);
addball(0, 0, -vid.camera);
queuecurve(darkena(0xFF, 0, 0x80), 0, PPR::CIRCLE);
queuereset(pmodel, PPR::CIRCLE);
}
EX void resetview() {
DEBBI(DF_GRAPH, ("reset view"));
// EUCLIDEAN
NLP = Id;
if(cwt.at) {
centerover = cwt.at;
View = iddspin(cwt.at, cwt.spin);
if(!flipplayer) View = pispin * View;
if(cwt.mirrored) View = Mirror * View;
if(GDIM == 2) View = spin(M_PI + vid.fixed_facing_dir * degree) * View;
if(GDIM == 3 && !prod) View = cspin(0, 2, M_PI/2) * View;
if(prod) NLP = cspin(0, 2, M_PI/2);
}
else if(currentmap) {
centerover = currentmap->gamestart();
View = Id;
}
cwtV = View;
current_display->which_copy =
nonisotropic ? gpushxto0(tC0(inverse(View))) :
View;
// SDL_LockSurface(s);
// SDL_UnlockSurface(s);
}
EX void panning(hyperpoint hf, hyperpoint ht) {
View =
rgpushxto0(hf) * rgpushxto0(gpushxto0(hf) * ht) * gpushxto0(hf) * View;
playermoved = false;
}
EX int cells_drawn, cells_generated;
EX void fullcenter() {
history::path_for_lineanimation.clear();
if(playerfound && false) centerpc(INF);
else {
bfs();
resetview();
drawthemap();
centerpc(INF);
centerover = cwt.at;
}
playermoved = true;
}
transmatrix screenpos(ld x, ld y) {
transmatrix V = Id;
V[0][2] += (x - current_display->xcenter) / current_display->radius * (1+vid.alpha);
V[1][2] += (y - current_display->ycenter) / current_display->radius * (1+vid.alpha);
return V;
}
/**
In 3D, we use the standard translation matrices to place stuff on the screen.
In 2D, this does not work (as HyperRogue reduces matrices to 3x3) so we use the native disk projection
*/
EX eModel flat_model() { return MDIM == 4 ? mdPixel : mdDisk; }
EX transmatrix atscreenpos(ld x, ld y, ld size) {
transmatrix V = Id;
if(pmodel == mdPixel) {
V[0][3] += (x - current_display->xcenter);
V[1][3] += (y - current_display->ycenter);
V[0][0] = size * 2 * cgi.hcrossf / cgi.crossf;
V[1][1] = size * 2 * cgi.hcrossf / cgi.crossf;
if(WDIM == 3) V[2][2] = -1;
}
else {
V[0][2] += (x - current_display->xcenter);
V[1][2] += (y - current_display->ycenter);
V[0][0] = size * 2 * cgi.hcrossf / cgi.crossf;
V[1][1] = size * 2 * cgi.hcrossf / cgi.crossf;
V[2][2] = current_display->radius;
if(S3 == OINF) V[0][0] /= 5, V[1][1] /= 5;
}
return V;
}
void circle_around_center(ld radius, color_t linecol, color_t fillcol, PPR prio) {
#if CAP_QUEUE
if(among(pmodel, mdDisk, mdEquiarea, mdEquidistant, mdFisheye) && !(pmodel == mdDisk && hyperbolic && vid.alpha <= -1) && vid.camera_angle == 0) {
hyperpoint ret;
applymodel(xpush0(radius), ret);
ld r = hypot_d(2, ret);
queuecircle(current_display->xcenter, current_display->ycenter, r * current_display->radius, linecol, prio, fillcol);
return;
}
#endif
#if CAP_QUEUE
for(int i=0; i<=360; i++) curvepoint(xspinpush0(i * degree, 10));
auto& c = queuecurve(linecol, fillcol, prio);
if(pmodel == mdDisk && hyperbolic && vid.alpha <= -1)
c.flags |= POLY_FORCE_INVERTED;
if(pmodel == mdJoukowsky)
c.flags |= POLY_FORCE_INVERTED;
c.flags |= POLY_ALWAYS_IN;
#endif
}
EX color_t periodcolor = 0x00FF0080;
EX color_t ringcolor = darkena(0xFF, 0, 0xFF);
EX color_t modelcolor = 0;
#if CAP_QUEUE
EX void draw_model_elements() {
dynamicval<ld> lw(vid.linewidth, vid.linewidth * vid.multiplier_ring);
switch(pmodel) {
case mdRotatedHyperboles: {
queuestr(current_display->xcenter, current_display->ycenter + current_display->radius * vid.alpha, 0, vid.fsize, "X", ringcolor, 1, 8);
return;
}
case mdTwoHybrid: {
queuereset(mdPixel, PPR::CIRCLE);
for(int mode=0; mode<4; mode++) {
for(int s=-200; s<=200; s ++) {
ld p = tanh(s / 40.);
ld a = vid.twopoint_param * (1+p);
ld b = vid.twopoint_param * (1-p);
ld h = ((mode & 2) ? -1 : 1) * sqrt(asin_auto(tan_auto(a) * tan_auto(b)));
hyperpoint H = xpush(p * vid.twopoint_param) * ypush0(h);
hyperpoint res = compute_hybrid(H, 2 | mode);
models::apply_orientation(res[0], res[1]);
models::apply_orientation_yz(res[2], res[1]);
curvepoint(res * current_display->radius);
}
queuecurve(ringcolor, 0, PPR::CIRCLE);
}
queuereset(pmodel, PPR::CIRCLE);
/* fallthrough */
}
case mdTwoPoint: case mdSimulatedPerspective: {
ld a = -models::model_orientation * degree;
queuestr(xspinpush0(a, +vid.twopoint_param), vid.xres / 100, "X", ringcolor >> 8);
queuestr(xspinpush0(a, -vid.twopoint_param), vid.xres / 100, "X", ringcolor >> 8);
return;
}
case mdBall: {
queuecircle(current_display->xcenter, current_display->ycenter, current_display->radius, ringcolor, PPR::OUTCIRCLE, modelcolor);
ballgeometry();
return;
}
case mdHyperboloid: {
if(hyperbolic) {
#if CAP_QUEUE
curvepoint(point3(0,0,1));
curvepoint(point3(0,0,-vid.alpha));
queuecurve(ringcolor, 0, PPR::CIRCLE);
ld& tz = models::top_z;
ld z = acosh(tz);
hyperpoint a = xpush0(z);
ld cb = models::cos_ball;
ld sb = models::sin_ball;
a[1] = sb * a[2] / -cb;
a[0] = sqrt(-1 + a[2] * a[2] - a[1] * a[1]);
curvepoint(point3(0,0,-vid.alpha));
curvepoint(a);
curvepoint(point3(0,0,0));
a[0] = -a[0];
curvepoint(a);
curvepoint(point3(0,0,-vid.alpha));
queuecurve(ringcolor, 0, PPR::CIRCLE);
curvepoint(point3(-1,0,0));
curvepoint(point3(1,0,0));
queuecurve(ringcolor, 0, PPR::CIRCLE);
a[1] = sb * tz / -cb;
a[0] = sqrt(tz * tz - a[1] * a[1]);
a[2] = tz - vid.alpha;
curvepoint(a);
curvepoint(point3(0,0,-vid.alpha));
a[0] = -a[0];
curvepoint(a);
queuecurve(ringcolor, 0, PPR::CIRCLE);
#endif
}
return;
}
default: break;
}
}
void queuestraight(hyperpoint X, int style, color_t lc, color_t fc, PPR p) {
hyperpoint H0, H1;
applymodel(X, H0);
H0 *= current_display->radius;
ld mul0 = hypot(vid.xres, vid.yres) / hypot_d(2, H0);
if(style == 1) {
H1 = H0 * -mul0;
}
else {
applymodel(pispin * X, H1);
H1 *= current_display->radius;
}
ld mul1 = hypot(vid.xres, vid.yres) / hypot_d(2, H1);
queuereset(mdPixel, p);
curvepoint(H0 + spin(M_PI/2) * H0 * mul0);
curvepoint(H0 - spin(M_PI/2) * H0 * mul0);
curvepoint(H1 + spin(M_PI/2) * H1 * mul1);
curvepoint(H1 - spin(M_PI/2) * H1 * mul1);
curvepoint(H0 + spin(M_PI/2) * H0 * mul0);
queuecurve(lc, fc, p).flags |= POLY_ALWAYS_IN | POLY_FORCEWIDE;
queuereset(pmodel, p);
/*
for(int i=0; i<1; i++) {
hyperpoint h = spin(i * 45 * degree) * X;
hyperpoint res;
applymodel(h, res);
if(hypot2(res) < 1000 && !std::isnan(res[0]) && !std::isnan(res[1]))
queuestr(h, 16, "X", 0xFF0000 + i * 0x20);
} */
}
EX void draw_boundary(int w) {
if(w == 1) return;
if(nonisotropic || euclid || prod) return;
dynamicval<ld> lw(vid.linewidth, vid.linewidth * vid.multiplier_ring);
color_t lc = ringcolor;
color_t fc = modelcolor;
PPR p = PPR::OUTCIRCLE;
if(haveaura()) lc = 0;
if(lc == 0 && fc == 0) return;
if(pmodel == mdRotatedHyperboles) return;
ld fakeinf = sphere ? M_PI-1e-5 : hyperbolic ? 10 : exp(10);
#if CAP_SVG
dynamicval<ld> dw(vid.linewidth, vid.linewidth * (svg::in ? svg::divby : 1));
#endif
if(elliptic && !among(pmodel, mdBand, mdBandEquidistant, mdBandEquiarea, mdSinusoidal, mdMollweide, mdCollignon))
circle_around_center(M_PI/2, periodcolor, 0, PPR::CIRCLE);
switch(pmodel) {
case mdTwoPoint: {
if(twopoint_do_flips || current_display->stereo_active() || !sphere) return;
queuereset(mdPixel, p);
for(int b=-1; b<=1; b+=2)
for(ld a=-90; a<=90+1e-6; a+=pow(.5, vid.linequality)) {
ld x = sin(a * vid.twopoint_param * b / 90);
ld y = 0;
ld z = -sqrt(1 - x*x);
models::apply_orientation(y, x);
hyperpoint h1;
applymodel(hpxyz(x,y,z), h1);
models::apply_orientation(h1[0], h1[1]);
h1[1] = abs(h1[1]) * b;
models::apply_orientation(h1[1], h1[0]);
curvepoint(h1);
}
queuecurve(lc, fc, p).flags |= POLY_FORCEWIDE;
queuereset(pmodel, p);
return;
}
case mdBand: case mdBandEquidistant: case mdBandEquiarea: case mdSinusoidal: case mdMollweide: case mdCentralCyl: case mdCollignon: {
if(GDIM == 3) return;
if(pmodel == mdBand && models::model_transition != 1) return;
bool bndband = (among(pmodel, mdBand, mdCentralCyl) ? hyperbolic : sphere);
transmatrix T = spin(-models::model_orientation * degree);
ld right = M_PI/2 - 1e-5;
if(bndband)
queuestraight(T * ypush0(hyperbolic ? 10 : right), 2, lc, fc, p);
ld xperiod = elliptic ? fakeinf/2 : fakeinf;
if(sphere && !bndband) {
queuestraight(T * xpush0(xperiod), 2, periodcolor, 0, PPR::CIRCLE);
}
if(sphere && bndband) {
ld adegree = degree-1e-6;
for(ld a=-90; a<90+1e-6; a+=pow(.5, vid.linequality)) {
curvepoint(T * xpush(xperiod) * ypush0(a * adegree));
}
for(ld a=-90; a<90+1e-6; a+=pow(.5, vid.linequality)) {
curvepoint(T * xpush(-xperiod) * ypush0(-a * adegree));
}
curvepoint(T * xpush(xperiod) * ypush0(-90 * adegree));
queuecurve(periodcolor, 0, PPR::CIRCLE).flags |= POLY_FORCEWIDE;
}
return;
}
case mdHalfplane:
if(hyperbolic && GDIM == 2) {
queuestraight(xspinpush0(-models::model_orientation * degree - M_PI/2, fakeinf), 1, lc, fc, p);
return;
}
break;
case mdHemisphere: {
if(hyperbolic) {
queuereset(mdPixel, p);
for(int i=0; i<=360; i++) {
ld s = sin(i * degree);
curvepoint(point3(current_display->radius * cos(i * degree), current_display->radius * s * (models::cos_ball * s >= 0 - 1e-6 ? 1 : abs(models::sin_ball)), 0));
}
queuecurve(lc, fc, p);
queuereset(pmodel, p);
p = PPR::CIRCLE; fc = 0;
queuereset(mdPixel, p);
for(int i=0; i<=360; i++) {
ld s = sin(i * degree);
curvepoint(point3(current_display->radius * cos(i * degree), current_display->radius * s * models::sin_ball, 0));
}
queuecurve(lc, fc, p);
queuereset(pmodel, p);
}
if(euclid || sphere) {
queuereset(mdPixel, p);
for(int i=0; i<=360; i++) {
curvepoint(point3(current_display->radius * cos(i * degree), current_display->radius * sin(i * degree), 0));
}
queuecurve(lc, fc, p);
queuereset(pmodel, p);
}
return;
}
case mdHyperboloid: {
if(hyperbolic) {
ld& tz = models::top_z;
ld mz = acosh(tz);
ld cb = models::cos_ball;
ld sb = models::sin_ball;
if(abs(sb) <= abs(cb) + 1e-5) {
ld step = .01 / (1 << vid.linequality);
hyperpoint a;
for(ld t=-1; t<=1; t += step) {
a = xpush0(t * mz);
if(t != 0) {
a[1] = sb * a[2] / -cb;
ld v = -1 + a[2] * a[2] - a[1] * a[1];
if(v < 0) continue;
a[0] = sqrt(v);
if(t < 0) a[0] = -a[0];
}
curvepoint(a);
}
if((sb > 0) ^ (cb < 0)) {
ld alpha = M_PI - atan2(a[0], -a[1]);
for(ld t=-1; t<=1; t += step)
curvepoint(xspinpush0(-M_PI/2 - t * alpha, mz));
}
else {
ld alpha = - atan2(a[0], -a[1]);
for(ld t=-1; t<=1; t += step)
curvepoint(xspinpush0(+M_PI/2 - t * alpha, mz));
}
queuecurve(lc, fc, p);
fc = 0; p = PPR::CIRCLE;
}
for(ld t=0; t<=360; t ++)
curvepoint(xspinpush0(t * degree, mz));
queuecurve(lc, fc, p);
}
return;
}
case mdSpiral: {
if(euclid) return;
if(models::ring_not_spiral) return;
// if(p == PPR::CIRCLE) p = PPR::OUTCIRCLE;
auto& sm = models::spiral_multiplier;
ld u = hypot(1, imag(sm) / real(sm));
if(real(sm)) {
queuereset(mdPixel, p);
for(ld a=-10; a<=10; a+=0.01 / (1 << vid.linequality) / u) {
cld z = exp(cld(a, a * imag(sm) / real(sm) + M_PI));
hyperpoint ret = point2(real(z), imag(z));
ret = mobius(ret, vid.skiprope, 1);
ret *= current_display->radius;
curvepoint(ret);
}
queuecurve(ringcolor, 0, p).flags |= POLY_ALWAYS_IN;
queuereset(pmodel, p);
}
return;
}
default: break;
}
if(sphere && pmodel == mdDisk && vid.alpha > 1) {
double rad = current_display->radius / sqrt(vid.alpha*vid.alpha - 1);
queuecircle(current_display->xcenter, current_display->ycenter, rad, lc, p, fc);
return;
}
if(sphere && !among(pmodel, mdEquidistant, mdEquiarea)) return;
circle_around_center(fakeinf, lc, fc, p);
}
#endif
EX ld band_shift = 0;
EX void fix_the_band(transmatrix& T) {
if(((mdinf[pmodel].flags & mf::uses_bandshift) && T[LDIM][LDIM] > 1e6) || (sphere && pmodel == mdSpiral)) {
T = spin(models::model_orientation * degree) * T;
hyperpoint H = tC0(T);
find_zlev(H);
ld y = asin_auto(H[1]);
ld x = asin_auto_clamp(H[0] / cos_auto(y));
if(sphere) {
if(H[LDIM] < 0 && x > 0) x = M_PI - x;
else if(H[LDIM] < 0 && x <= 0) x = -M_PI - x;
}
band_shift += x;
T = xpush(-x) * T;
fixmatrix(T);
T = spin(-models::model_orientation * degree) * T;
}
}
#if HDR
struct bandfixer {
dynamicval<ld> bw;
bandfixer(transmatrix& T) : bw(band_shift, band_shift) { fix_the_band(T); }
};
#endif
EX namespace dq {
EX queue<tuple<heptagon*, transmatrix, ld>> drawqueue;
EX set<heptagon*> visited;
EX void enqueue(heptagon *h, const transmatrix& T) {
if(!h || visited.count(h)) { return; }
visited.insert(h);
drawqueue.emplace(h, T, band_shift);
}
EX set<int> visited_by_matrix;
EX void enqueue_by_matrix(heptagon *h, const transmatrix& T) {
if(!h) return;
if(sl2 && T[3][3] < 0) { enqueue_by_matrix(h, centralsym * T); return; }
int b = bucketer(tC0(T));
if(visited_by_matrix.count(b)) { return; }
visited_by_matrix.insert(b);
drawqueue.emplace(h, T, band_shift);
}
EX queue<tuple<cell*, transmatrix, ld>> drawqueue_c;
EX void enqueue_by_matrix_c(cell *c, const transmatrix& T) {
if(!c) return;
if(sl2 && T[3][3] < 0) { enqueue_by_matrix_c(c, centralsym * T); return; }
int b = bucketer(tC0(T));
if(visited_by_matrix.count(b)) { return; }
visited_by_matrix.insert(b);
drawqueue_c.emplace(c, T, band_shift);
}
EX }
EX bool do_draw(cell *c) {
// do not display out of range cells, unless on torus
if(c->pathdist == PINFD && !(euclid && quotient) && vid.use_smart_range == 0)
return false;
// do not display not fully generated cells, unless changing range allowed
if(c->mpdist > 7 && !allowChangeRange()) return false;
// in the Yendor Challenge, scrolling back is forbidden
if(c->cpdist > 7 && (yendor::on || isHaunted(cwt.at->land)) && !cheater && !autocheat) return false;
return true;
}
EX ld extra_generation_distance = 99;
// returns false if limited
bool limited_generation(cell *c) {
if(c->mpdist <= 7) return true;
if(cells_generated > vid.cells_generated_limit) return false;
setdist(c, 7, c);
cells_generated++;
return true;
}
EX bool do_draw(cell *c, const transmatrix& T) {
if(WDIM == 3) {
// do not care about cells outside of the track
if(GDIM == 3 && racing::on && c->land == laMemory && cells_drawn >= S7+1) return false;
if(cells_drawn > vid.cells_drawn_limit) return false;
if(cells_drawn < 50) { limited_generation(c); return true; }
if(nil && pmodel == mdGeodesic) {
ld dist = hypot_d(3, inverse_exp(tC0(T), iLazy));
if(dist > sightranges[geometry] + (vid.sloppy_3d ? 0 : 0.9)) return false;
if(dist <= extra_generation_distance && !limited_generation(c)) return false;
}
else if(pmodel == mdGeodesic && sol) {
if(!nisot::in_table_range(tC0(T))) return false;
if(!limited_generation(c)) return false;
}
else if(pmodel == mdGeodesic && nih) {
hyperpoint h = inverse_exp(tC0(T), iLazy, false);
ld dist = hypot_d(3, h);
if(dist > sightranges[geometry] + (vid.sloppy_3d ? 0 : cgi.corner_bonus)) return false;
if(dist <= extra_generation_distance && !limited_generation(c)) return false;
}
else if(pmodel == mdGeodesic && sl2) {
if(hypot(tC0(T)[2], tC0(T)[3]) > cosh(slr::range_xy)) return false;
if(!limited_generation(c)) return false;
}
else if(vid.use_smart_range) {
if(cells_drawn >= 50 && !in_smart_range(T)) return false;
if(!limited_generation(c)) return false;
}
else {
ld dist = hdist0(tC0(T));
if(dist > sightranges[geometry] + (vid.sloppy_3d ? 0 : cgi.corner_bonus)) return false;
if(dist <= extra_generation_distance && !limited_generation(c)) return false;
}
return true;
}
if(just_gmatrix && sphere) return true;
if(!do_draw(c)) return false;
if(euclid && pmodel == mdSpiral) {
hyperpoint h = tC0(T);
cld z(h[0], h[1]);
z = z * models::spiral_multiplier;
ld iz = imag(z) + 1.14279e-2; // make it never fall exactly on PI
if(iz < -M_PI || iz >= M_PI) return false;
}
if(pmodel == mdSpiral && models::ring_not_spiral) {
cld z;
hyperpoint H = tC0(T);
hyperpoint ret;
makeband(H, ret, band_conformal);
z = cld(ret[0], ret[1]) * models::spiral_multiplier;
if(imag(z) < -models::spiral_cone_rad/2-1e-5 || imag(z) >= models::spiral_cone_rad/2-1e-5) return false;
}
if(cells_drawn > vid.cells_drawn_limit) return false;
bool usr = vid.use_smart_range || quotient;
if(usr && cells_drawn >= 50 && !in_smart_range(T) && !(WDIM == 2 && GDIM == 3 && hdist0(tC0(T)) < 2.5)) return false;
if(vid.use_smart_range == 2 && !limited_generation(c)) return false;
return true;
}
EX int cone_side(const hyperpoint H) {
hyperpoint ret;
if(hyperbolic) makeband(H, ret, band_conformal);
else ret = H;
cld z = cld(ret[0], ret[1]) * models::spiral_multiplier;
auto zth = [&] (cld z) {
ld alpha = imag(z) * 360 / models::spiral_cone;
ld r = real(z);
r = exp(r);
hyperpoint ret;
ret[0] = -sin(alpha) * r;
ret[1] = cos(alpha) * r;
ret[2] = (r-1) * sqrt( pow(360/models::spiral_cone, 2) - 1);
models::apply_ball(ret[2], ret[1]);
return ret;
};
hyperpoint ret0 = zth(z);
hyperpoint ret1 = zth(z + cld(1e-3, 0));
hyperpoint ret2 = zth(z + cld(0, 1e-3));
return (ret1[1] - ret0[1]) * (ret2[0] - ret0[0]) < (ret2[1] - ret0[1]) * (ret1[0] - ret0[0]) ? 1 : -1;
}
/** get the current orientation of the view */
EX transmatrix& get_view_orientation() {
return prod ? NLP : View;
}
/** rotate the view using the given rotation matrix */
EX void rotate_view(transmatrix T) {
transmatrix& which = get_view_orientation();
which = T * which;
if(!prod && !nonisotropic) current_display->which_copy = T * current_display->which_copy;
}
/** shift the view according to the given tangent vector */
EX transmatrix get_shift_view_of(const hyperpoint H, const transmatrix V) {
if(!nonisotropic) {
return rgpushxto0(direct_exp(lp_iapply(H), 100)) * V;
}
else if(!nisot::geodesic_movement) {
transmatrix IV = inverse(V);
nisot::fixmatrix(IV);
const transmatrix V1 = inverse(IV);
return V1 * eupush(IV * eupush(H) * V1 * C0);
}
else {
return inverse(nisot::parallel_transport(inverse(V), -H));
}
}
/** shift the view according to the given tangent vector */
EX void shift_view(hyperpoint H) {
auto oView = View;
View = get_shift_view_of(H, View);
auto& wc = current_display->which_copy;
if(nonisotropic) {
transmatrix ioldv = eupush(tC0(inverse(oView)));
transmatrix newv = inverse(eupush(tC0(inverse(View))));
wc = newv * ioldv * wc;
}
else
wc = get_shift_view_of(H, wc);
}
void multiply_view(transmatrix T) {
View = T * View;
auto& wc = current_display->which_copy;
wc = T * wc;
}
EX void shift_view_to(hyperpoint H) {
if(!nonisotropic) multiply_view(gpushxto0(H));
else shift_view(-inverse_exp(H, iTable, false));
}
EX void shift_view_towards(hyperpoint H, ld l) {
if(!nonisotropic && !prod)
multiply_view(rspintox(H) * xpush(-l) * spintox(H));
else if(nonisotropic && !nisot::geodesic_movement)
shift_view(tangent_length(H-C0, -l));
else {
hyperpoint ie = inverse_exp(H, iTable, true);
if(prod) ie = lp_apply(ie);
shift_view(tangent_length(ie, -l));
}
}
}
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