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models.cpp
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models.cpp
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// Hyperbolic Rogue -- models of hyperbolic geometry
// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
/** \file models.cpp
* \brief models of hyperbolic geometry: their properties, projection menu
*
* The actual models are implemented in hypgraph.cpp. Also shaders.cpp,
* drawing.cpp, and basegraph.cpp are important.
*/
#include "hyper.h"
namespace hr {
EX namespace polygonal {
#if ISMOBWEB
typedef double precise;
#else
typedef long double precise;
#endif
#if HDR
static constexpr int MSI = 120;
#endif
typedef long double xld;
typedef complex<xld> cxld;
EX int SI = 4;
EX ld STAR = 0;
EX int deg = ISMOBWEB ? 2 : 20;
precise matrix[MSI][MSI];
precise ans[MSI];
cxld coef[MSI];
EX ld coefr[MSI], coefi[MSI];
EX int maxcoef, coefid;
EX void solve() {
if(pmodel == mdPolynomial) {
for(int i=0; i<MSI; i++) coef[i] = cxld(coefr[i], coefi[i]);
return;
}
if(pmodel != mdPolygonal) return;
if(SI < 3) SI = 3;
for(int i=0; i<MSI; i++) ans[i] = cos(M_PI / SI);
for(int i=0; i<MSI; i++)
for(int j=0; j<MSI; j++) {
precise i0 = (i+0.) / (MSI-1);
// i0 *= i0;
// i0 = 1 - i0;
i0 *= M_PI;
matrix[i][j] =
cos(i0 * (j + 1./SI)) * (STAR > 0 ? (1+STAR) : 1)
- sin(i0 * (j + 1./SI)) * (STAR > 0 ? STAR : STAR/(1+STAR));
}
for(int i=0; i<MSI; i++) {
precise dby = matrix[i][i];
for(int k=0; k<MSI; k++) matrix[i][k] /= dby;
ans[i] /= dby;
for(int j=i+1; j<MSI; j++) {
precise sub = matrix[j][i];
ans[j] -= ans[i] * sub;
for(int k=0; k<MSI; k++)
matrix[j][k] -= sub * matrix[i][k];
}
}
for(int i=MSI-1; i>=0; i--) {
for(int j=0; j<i; j++) {
precise sub = matrix[j][i];
ans[j] -= ans[i] * sub;
for(int k=0; k<MSI; k++)
matrix[j][k] -= sub * matrix[i][k];
}
}
}
EX pair<ld, ld> compute(ld x, ld y, int prec) {
if(x*x+y*y > 1) {
xld r = hypot(x,y);
x /= r;
y /= r;
}
if(pmodel == mdPolynomial) {
cxld z(x,y);
cxld res (0,0);
for(int i=maxcoef; i>=0; i--) { res += coef[i]; if(i) res *= z; }
return make_pair(real(res), imag(res));
}
cxld z(x, y);
cxld res (0,0);
cxld zp = 1; for(int i=0; i<SI; i++) zp *= z;
for(int i=prec; i>0; i--) {
res += ans[i];
res *= zp;
}
res += ans[0]; res *= z;
return make_pair(real(res), imag(res));
}
EX pair<ld, ld> compute(ld x, ld y) { return compute(x,y,deg); }
EX }
#if HDR
inline bool mdAzimuthalEqui() { return (mdinf[pmodel].flags & mf::azimuthal) && (mdinf[pmodel].flags & (mf::equidistant | mf::equiarea | mf::equivolume) && !(mdinf[pmodel].flags & mf::twopoint)); }
inline bool mdBandAny() { return mdinf[pmodel].flags & mf::pseudocylindrical; }
inline bool mdPseudocylindrical() { return mdBandAny() && !(mdinf[pmodel].flags & mf::cylindrical); }
#endif
projection_configuration::projection_configuration() {
formula = "z^2"; top_z = 5; model_transition = 1; spiral_angle = 70; spiral_x = 10; spiral_y = 7;
rotational_nil = 1;
right_spiral_multiplier = 1;
any_spiral_multiplier = 1;
sphere_spiral_multiplier = 2;
spiral_cone = 360;
use_atan = false;
product_z_scale = 1;
aitoff_parameter = .5;
miller_parameter = .8;
loximuthal_parameter = 0;
winkel_parameter = .5;
show_hyperboloid_flat = true;
depth_scaling = 1;
vr_angle = 0;
hyperboloid_scaling = 1;
vr_zshift = 0;
vr_scale_factor = 1;
back_and_front = 0;
dualfocus_autoscale = false;
axial_angle = 90;
ptr_model_orientation = new trans23;
ptr_ball = new transmatrix;
*ptr_ball = cspin(2, 1, 20._deg);
ptr_camera = new transmatrix; *ptr_camera = Id;
offside = 0; offside2 = M_PI;
small_hyperboloid = false;
}
EX namespace models {
EX trans23 rotation;
EX int do_rotate = 1;
EX bool model_straight, model_straight_yz, camera_straight;
/** screen coordinates to orientation logical coordinates */
EX void ori_to_scr(hyperpoint& h) { if(!model_straight) h = pconf.mori().get() * h; }
EX void ori_to_scr(transmatrix& h) { if(!model_straight) h = pconf.mori().get() * h; }
/** orientation logical coordinates to screen coordinates */
EX void scr_to_ori(hyperpoint& h) { if(!model_straight) h = iso_inverse(pconf.mori().get()) * h; }
EX void scr_to_ori(transmatrix& h) { if(!model_straight) h = iso_inverse(pconf.mori().get()) * h; }
EX transmatrix rotmatrix() {
if(gproduct) return rotation.v2;
return rotation.get();
}
int spiral_id = 7;
EX cld spiral_multiplier;
EX ld spiral_cone_rad;
EX bool ring_not_spiral;
/** the matrix to rotate the Euclidean view from the standard coordinates to the screen coordinates */
EX transmatrix euclidean_spin;
EX void configure() {
model_straight = (pconf.mori().get()[0][0] > 1 - 1e-9);
model_straight_yz = GDIM == 2 || (pconf.mori().get()[2][2] > 1-1e-9);
camera_straight = eqmatrix(pconf.cam(), Id);
if(history::on) history::apply();
if(!euclid) {
ld b = pconf.spiral_angle * degree;
ld cos_spiral = cos(b);
ld sin_spiral = sin(b);
spiral_cone_rad = pconf.spiral_cone * degree;
ring_not_spiral = abs(cos_spiral) < 1e-3;
ld mul = 1;
if(sphere) mul = .5 * pconf.sphere_spiral_multiplier;
else if(ring_not_spiral) mul = pconf.right_spiral_multiplier;
else mul = pconf.any_spiral_multiplier * cos_spiral;
spiral_multiplier = cld(cos_spiral, sin_spiral) * cld(spiral_cone_rad * mul / 2., 0);
}
if(euclid) {
euclidean_spin = pispin * iso_inverse(cview().T * currentmap->master_relative(centerover, true));
euclidean_spin = gpushxto0(euclidean_spin * C0) * euclidean_spin;
hyperpoint h = inverse(euclidean_spin) * (C0 + (euc::eumove(gp::loc{1,0})*C0 - C0) * vpconf.spiral_x + (euc::eumove(gp::loc{0,1})*C0 - C0) * vpconf.spiral_y);
spiral_multiplier = cld(0, TAU) / cld(h[0], h[1]);
}
if(centerover && !history::on)
if(isize(history::path_for_lineanimation) == 0 || ((quotient || arb::in()) && history::path_for_lineanimation.back() != centerover)) {
history::path_for_lineanimation.push_back(centerover);
}
}
/** mdRelPerspective and mdRelOrthogonal in hyperbolic space only make sense if it is actually a de Sitter visualization */
EX bool desitter_projections;
EX vector<bool_reaction_t> avail_checkers;
EX bool model_available(eModel pm) {
if(pm < isize(avail_checkers) && avail_checkers[pm]) return avail_checkers[pm]();
if(mdinf[pm].flags & mf::technical) return false;
if(gproduct) {
if(pm == mdPerspective) return true;
if(among(pm, mdBall, mdHemisphere)) return false;
return PIU(model_available(pm));
}
if(hyperbolic && desitter_projections && among(pm, mdRelPerspective, mdRelOrthogonal)) return true;
if(sl2) return among(pm, mdGeodesic, mdEquidistant, mdRelPerspective, mdRelOrthogonal, mdHorocyclic, mdPerspective);
if(among(pm, mdRelOrthogonal, mdRelPerspective)) return false;
if(nonisotropic) return among(pm, mdDisk, mdPerspective, mdHorocyclic, mdGeodesic, mdEquidistant, mdFisheye, mdLiePerspective, mdLieOrthogonal);
if(sphere && pm == mdBall) return false;
if(sphere && (mdinf[pm].flags & mf::horocyclic)) return false;
if(GDIM == 2 && is_perspective(pm)) return false;
if(pm == mdGeodesic && !nonisotropic) return false;
if(pm == mdLiePerspective && sphere) return false;
if(pm == mdLieOrthogonal && sphere) return false;
if(GDIM == 2 && pm == mdEquivolume) return false;
if(pm == mdThreePoint && !(GDIM == 3 && !nonisotropic && !gproduct)) return false;
if(GDIM == 3 && among(pm, mdBall, mdHyperboloid, mdFormula, mdPolygonal, mdRotatedHyperboles, mdSpiral, mdHemisphere)) return false;
if(pm == mdCentralInversion && !euclid) return false;
if(pm == mdPoorMan) return hyperbolic;
if(pm == mdRetroHammer) return hyperbolic;
return true;
}
EX bool has_orientation(eModel m) {
if(is_perspective(m) && vid.stereo_mode == sPanini) return true;
if(nonisotropic) return false;
return (mdinf[m].flags & mf::orientation);
}
/** @brief returns the broken coordinate, or zero */
EX int get_broken_coord(eModel m) {
if(mdinf[m].flags & mf::werner) return 1;
if(sphere) return (mdinf[m].flags & mf::broken) ? 2 : 0;
return 0;
}
EX bool is_hyperboloid(eModel m) {
return m == (sphere ? mdHemisphere : mdHyperboloid);
}
EX bool is_perspective(eModel m) {
return mdinf[m].flags & mf::perspective;
}
EX bool is_3d(const projection_configuration& p) {
if(GDIM == 3) return true;
return among(p.model, mdBall, mdHyperboloid, mdHemisphere) || (p.model == mdSpiral && p.spiral_cone != 360);
}
EX bool has_transition(eModel m) {
return (mdinf[m].flags & mf::transition) && GDIM == 2;
}
EX bool product_model(eModel m) {
if(!gproduct) return false;
if(mdinf[m].flags & mf::product_special) return false;
return true;
}
int editpos = 0;
EX string get_model_name(eModel m) {
if(m == mdDisk && GDIM == 3 && (hyperbolic || nonisotropic)) return XLAT("ball model/Gans");
if(m == mdPerspective && gproduct) return XLAT("native perspective");
if(gproduct) return PIU(get_model_name(m));
if(nonisotropic) {
if(m == mdHorocyclic && sl2) return XLAT("layered equidistant");
if(m == mdHorocyclic && !sol) return XLAT("simple model: projection");
if(m == mdPerspective) return XLAT("simple model: perspective");
if(m == mdGeodesic) return XLAT("native perspective");
if(among(m, mdEquidistant, mdFisheye, mdHorocyclic, mdLiePerspective, mdLieOrthogonal, mdRelPerspective, mdRelOrthogonal)) return XLAT(mdinf[m].name_hyperbolic);
}
if(m == mdDisk && GDIM == 3) return XLAT("perspective in 4D");
if(m == mdHalfplane && GDIM == 3 && hyperbolic) return XLAT("half-space");
if(sphere)
return XLAT(mdinf[m].name_spherical);
if(euclid)
return XLAT(mdinf[m].name_euclidean);
if(hyperbolic)
return XLAT(mdinf[m].name_hyperbolic);
return "?";
}
vector<gp::loc> torus_zeros;
void match_torus_period() {
torus_zeros.clear();
for(int y=0; y<=200; y++)
for(int x=-200; x<=200; x++) {
if(y == 0 && x <= 0) continue;
transmatrix dummy = Id;
euc::coord v(x, y, 0);
bool mirr = false;
auto t = euc::eutester;
euc::eu.canonicalize(v, t, dummy, mirr);
if(v == euc::euzero && t == euc::eutester)
torus_zeros.emplace_back(x, y);
}
sort(torus_zeros.begin(), torus_zeros.end(), [] (const gp::loc p1, const gp::loc p2) {
ld d1 = hdist0(tC0(euc::eumove(p1)));
ld d2 = hdist0(tC0(euc::eumove(p2)));
if(d1 < d2 - 1e-6) return true;
if(d1 > d2 + 1e-6) return false;
return p1 < p2;
});
if(spiral_id > isize(torus_zeros)) spiral_id = 0;
dialog::editNumber(spiral_id, 0, isize(torus_zeros)-1, 1, 10, XLAT("match the period of the torus"), "");
dialog::get_di().reaction = [] () {
auto& co = torus_zeros[spiral_id];
vpconf.spiral_x = co.first;
vpconf.spiral_y = co.second;
};
dialog::bound_low(0);
dialog::bound_up(isize(torus_zeros)-1);
}
EX void edit_formula() {
if(vpconf.model != mdFormula) vpconf.basic_model = vpconf.model;
dialog::edit_string(vpconf.formula, "formula",
XLAT(
"This lets you specify the projection as a formula f. "
"The formula has access to the value 'z', which is a complex number corresponding to the (x,y) coordinates in the currently selected model; "
"the point z is mapped to f(z). You can also use the underlying coordinates ux, uy, uz."
)
);
#if CAP_QUEUE && CAP_CURVE
dialog::get_di().extra_options = [] () {
dialog::parser_help();
initquickqueue();
queuereset(mdPixel, PPR::LINE);
for(int a=-1; a<=1; a++) {
curvepoint(point2(-90._deg * current_display->radius, a*current_display->radius));
curvepoint(point2(+90._deg * current_display->radius, a*current_display->radius));
queuecurve(shiftless(Id), forecolor, 0, PPR::LINE);
curvepoint(point2(a*current_display->radius, -90._deg * current_display->radius));
curvepoint(point2(a*current_display->radius, +90._deg * current_display->radius));
queuecurve(shiftless(Id), forecolor, 0, PPR::LINE);
}
queuereset(vpconf.model, PPR::LINE);
quickqueue();
};
#endif
dialog::get_di().reaction_final = [] () {
vpconf.model = mdFormula;
};
}
EX void model_list() {
cmode = sm::SIDE | sm::MAYDARK | sm::CENTER;
gamescreen();
dialog::init(XLAT("models & projections"));
#if CAP_RUG
USING_NATIVE_GEOMETRY_IN_RUG;
#endif
dialog::start_list(2000, 2000, 'a');
for(int i=0; i<isize(mdinf); i++) {
eModel m = eModel(i);
if(m == mdFormula && ISMOBILE) continue;
if(model_available(m)) {
dialog::addBoolItem(get_model_name(m), vpconf.model == m, dialog::list_fake_key++);
dialog::add_action([m] () {
if(m == mdFormula) {
edit_formula();
return;
}
vpconf.model = m;
polygonal::solve();
vpconf.alpha = 1; vpconf.scale = 1;
if(pmodel == mdBand && sphere)
vpconf.scale = .3;
if(pmodel == mdDisk && sphere)
vpconf.scale = .4;
popScreen();
});
}
}
dialog::end_list();
dialog::addBreak(100);
dialog::addBack();
dialog::display();
}
void stretch_extra() {
dialog::addBreak(100);
if(sphere && pmodel == mdBandEquiarea) {
dialog::addBoolItem("Gall-Peters", vpconf.stretch == 2, 'O');
dialog::add_action([] { vpconf.stretch = 2; dialog::get_ne().s = "2"; });
}
if(pmodel == mdBandEquiarea) {
// y = K * sin(phi)
// cos(phi) * cos(phi) = 1/K
if(sphere && vpconf.stretch >= 1) {
ld phi = acos(sqrt(1/vpconf.stretch));
dialog::addInfo(XLAT("The current value makes the map conformal at the latitude of %1 (%2°).", fts(phi), fts(phi / degree)));
}
else if(hyperbolic && abs(vpconf.stretch) <= 1 && abs(vpconf.stretch) >= 1e-9) {
ld phi = acosh(abs(sqrt(1/vpconf.stretch)));
dialog::addInfo(XLAT("The current value makes the map conformal %1 units from the main line.", fts(phi)));
}
else dialog::addInfo("");
}
}
bool set_vr_settings = true;
EX void model_menu() {
cmode = sm::SIDE | sm::MAYDARK | sm::CENTER;
gamescreen();
#if CAP_RUG
USING_NATIVE_GEOMETRY_IN_RUG;
#endif
dialog::init(XLAT("models & projections"));
mouseovers = XLAT("see http://www.roguetemple.com/z/hyper/models.php");
auto vpmodel = vpconf.model;
dialog::addSelItem(XLAT("projection type"), get_model_name(vpmodel), 'm');
dialog::add_action_push(model_list);
if(nonisotropic && !sl2)
dialog::addBoolItem_action(XLAT("geodesic movement in Sol/Nil"), nisot::geodesic_movement, 'G');
add_edit((GDIM == 2 || gproduct) ? rotation.v2 : rotation.v3);
if(do_rotate == 0) { dialog::lastItem().value = XLAT("NEVER"); dialog::lastItem().type = dialog::diItem; }
else { dialog::lastItem().value = ONOFF(do_rotate == 2); }
bool vr_settings = vrhr::active() && set_vr_settings;
if(vrhr::active()) {
dialog::addBoolItem_action(XLAT("edit VR or non-VR settings"), set_vr_settings, 'V');
if(set_vr_settings) dialog::items.back().value = "VR";
else dialog::items.back().value = "non-VR";
}
// if(vpmodel == mdBand && sphere)
if(!in_perspective_v() && !vr_settings) {
dialog::addSelItem(XLAT("scale factor"), fts(vpconf.scale), 'z');
dialog::add_action(editScale);
}
if(abs(vpconf.alpha-1) > 1e-3 && vpmodel != mdBall && vpmodel != mdHyperboloid && vpmodel != mdHemisphere && vpmodel != mdDisk) {
dialog::addBreak(50);
dialog::addInfo("NOTE: this works 'correctly' only if the Poincaré model/stereographic projection is used.");
dialog::addBreak(50);
}
if(among(vpmodel, mdDisk, mdBall, mdHyperboloid, mdRotatedHyperboles, mdPanini)) {
dynamicval<eModel> v(vpconf.model, vpconf.model);
if(vpmodel == mdHyperboloid) vpconf.model = mdDisk;
add_edit(vpconf.alpha);
}
if(has_orientation(vpmodel)) {
dialog::addMatrixItem(XLAT("model orientation"), vpconf.mori().get(), 'l');
dialog::add_action([] () {
dialog::editMatrix(vpconf.mori().get(), XLAT("model orientation"), "", GDIM);
});
}
if(among(vpmodel, mdPerspective, mdHorocyclic) && nil) {
dialog::addMatrixItem(XLAT("model orientation"), vpconf.mori().get(), 'l');
dialog::add_action([] () {
dialog::editMatrix(vpconf.mori().get(), XLAT("model orientation"), "", GDIM);
});
dialog::addSelItem(XLAT("rotational or Heisenberg"), fts(vpconf.rotational_nil), 'L');
dialog::add_action([] () {
dialog::editNumber(vpconf.rotational_nil, 0, 1, 1, 1, XLAT("1 = Heisenberg, 0 = rotational"), "");
});
}
if(GDIM == 3 && vpmodel != mdPerspective && !vr_settings) {
const string cliphelp = XLAT(
"Your view of the 3D model is naturally bounded from four directions by your window. "
"Here, you can also set up similar bounds in the Z direction. Radius of the ball/band "
"models, and the distance from the center to the plane in the halfspace model, are 1.\n\n");
dialog::addSelItem(XLAT("near clipping plane"), fts(vpconf.clip_max), 'c');
dialog::add_action([cliphelp] () {
dialog::editNumber(vpconf.clip_max, -10, 10, 0.2, 1, XLAT("near clipping plane"),
cliphelp + XLAT("Objects with Z coordinate "
"bigger than this parameter are not shown. This is useful with the models which "
"extend infinitely in the Z direction, or if you want things close to your character "
"to be not obscured by things closer to the camera."));
});
dialog::addSelItem(XLAT("far clipping plane"), fts(vpconf.clip_min), 'C');
dialog::add_action([cliphelp] () {
dialog::editNumber(vpconf.clip_min, -10, 10, 0.2, -1, XLAT("far clipping plane"),
cliphelp + XLAT("Objects with Z coordinate "
"smaller than this parameter are not shown; it also affects the fog effect"
" (near clipping plane = 0% fog, far clipping plane = 100% fog)."));
});
}
if(vpmodel == mdPolynomial) {
dialog::addSelItem(XLAT("coefficient"),
fts(polygonal::coefr[polygonal::coefid]), 'x');
dialog::add_action([] () {
polygonal::maxcoef = max(polygonal::maxcoef, polygonal::coefid);
int ci = polygonal::coefid + 1;
dialog::editNumber(polygonal::coefr[polygonal::coefid], -10, 10, .01/ci/ci, 0, XLAT("coefficient"), "");
});
dialog::addSelItem(XLAT("coefficient (imaginary)"),
fts(polygonal::coefi[polygonal::coefid]), 'y');
dialog::add_action([] () {
polygonal::maxcoef = max(polygonal::maxcoef, polygonal::coefid);
int ci = polygonal::coefid + 1;
dialog::editNumber(polygonal::coefi[polygonal::coefid], -10, 10, .01/ci/ci, 0, XLAT("coefficient (imaginary)"), "");
});
dialog::addSelItem(XLAT("which coefficient"), its(polygonal::coefid), 'n');
dialog::add_action([] () {
dialog::editNumber(polygonal::coefid, 0, polygonal::MSI-1, 1, 0, XLAT("which coefficient"), "");
dialog::bound_low(0); dialog::bound_up(polygonal::MSI-1);
});
}
if(vpmodel == mdHalfplane) {
dialog::addSelItem(XLAT("half-plane scale"), fts(vpconf.halfplane_scale), 'b');
dialog::add_action([] () {
dialog::editNumber(vpconf.halfplane_scale, 0, 2, 0.25, 1, XLAT("half-plane scale"), "");
});
}
if(vpmodel == mdRotatedHyperboles) {
dialog::addBoolItem_action(XLAT("use atan to make it finite"), vpconf.use_atan, 'x');
}
if(among(vpmodel, mdLieOrthogonal, mdLiePerspective)) {
if(in_s2xe() || (sphere && GDIM == 2)) dialog::addInfo(XLAT("this is not a Lie group"), 0xC00000);
else if(!hyperbolic && !sol && !nih && !nil && !euclid && !in_h2xe() && !in_e2xe())
dialog::addInfo(XLAT("not implemented"));
}
if(vpmodel == mdBall && !vr_settings) {
dialog::addSelItem(XLAT("projection in ball model"), fts(vpconf.ballproj), 'x');
dialog::add_action([] () {
dialog::editNumber(vpconf.ballproj, 0, 100, .1, 0, XLAT("projection in ball model"),
"This parameter affects the ball model the same way as the projection parameter affects the disk model.");
});
}
if(vpmodel == mdPolygonal) {
dialog::addSelItem(XLAT("polygon sides"), its(polygonal::SI), 'x');
dialog::add_action([] () {
dialog::editNumber(polygonal::SI, 3, 10, 1, 4, XLAT("polygon sides"), "");
dialog::get_di().reaction = polygonal::solve;
});
dialog::addSelItem(XLAT("star factor"), fts(polygonal::STAR), 'y');
dialog::add_action([]() {
dialog::editNumber(polygonal::STAR, -1, 1, .1, 0, XLAT("star factor"), "");
dialog::get_di().reaction = polygonal::solve;
});
dialog::addSelItem(XLAT("degree of the approximation"), its(polygonal::deg), 'n');
dialog::add_action([](){
dialog::editNumber(polygonal::deg, 2, polygonal::MSI-1, 1, 2, XLAT("degree of the approximation"), "");
dialog::get_di().reaction = polygonal::solve;
dialog::bound_low(0); dialog::bound_up(polygonal::MSI-1);
});
}
if(is_3d(vpconf) && GDIM == 2 && !vr_settings)
add_edit(vpconf.ball());
if(vr_settings) {
dialog::addSelItem(XLAT("VR: rotate the 3D model"), fts(vpconf.vr_angle) + "°", 'B');
dialog::add_action([] {
dialog::editNumber(vpconf.vr_angle, 0, 90, 5, 0, XLAT("VR: rotate the 3D model"),
"How the VR model should be rotated."
);
});
dialog::addSelItem(XLAT("VR: shift the 3D model"), fts(vpconf.vr_zshift), 'Z');
dialog::add_action([] {
dialog::editNumber(vpconf.vr_zshift, 0, 5, 0.1, 1, XLAT("VR: shift the 3D model"),
"How the VR model should be shifted forward, in units. "
"The Poincaré disk has the size of 1 unit. You probably do not want this in perspective projections, but "
"it is useful to see e.g. the Poincaré ball not from the center."
);
});
dialog::addSelItem(XLAT("VR: scale the 3D model"), fts(vpconf.vr_scale_factor) + "m", 'S');
dialog::add_action([] {
dialog::editNumber(vpconf.vr_scale_factor, 0, 5, 0.1, 1, XLAT("VR: scale the 3D model"),
"How the VR model should be scaled. At scale 1, 1 unit = 1 meter. Does not affect perspective projections, "
"where the 'absolute unit' setting is used instead."
);
});
}
if(is_hyperboloid(vpmodel))
add_edit(vpconf.top_z);
if(has_transition(vpmodel))
add_edit(vpconf.model_transition);
if(among(vpmodel, mdJoukowsky, mdJoukowskyInverted, mdSpiral) && GDIM == 2)
add_edit(vpconf.skiprope);
if(vpmodel == mdJoukowskyInverted)
add_edit(vpconf.dualfocus_autoscale);
if(vpmodel == mdHemisphere && euclid)
add_edit(vpconf.euclid_to_sphere);
if(mdinf[vpmodel].flags & mf::twopoint)
add_edit(vpconf.twopoint_param);
if(mdinf[vpmodel].flags & mf::axial)
add_edit(vpconf.axial_angle);
if(vpmodel == mdFisheye)
add_edit(vpconf.fisheye_param);
if(vpmodel == mdFisheye2) {
add_edit(vpconf.fisheye_param);
add_edit(vpconf.fisheye_alpha);
}
if(is_hyperboloid(vpmodel))
add_edit(pconf.show_hyperboloid_flat);
if(among(vpmodel, mdHyperboloid, mdHemisphere))
add_edit(pconf.small_hyperboloid);
if(vpmodel == mdCollignon)
add_edit(vpconf.collignon_parameter);
if(vpmodel == mdMiller) {
dialog::addSelItem(XLAT("parameter"), fts(vpconf.miller_parameter), 'b');
dialog::add_action([](){
dialog::editNumber(vpconf.miller_parameter, -1, 1, .1, 4/5., XLAT("parameter"),
"The Miller projection is obtained by multiplying the latitude by 4/5, using Mercator projection, and then multiplying Y by 5/4. "
"Here you can change this parameter."
);
});
}
if(among(vpmodel, mdLoximuthal, mdRetroHammer, mdRetroCraig))
add_edit(vpconf.loximuthal_parameter);
if(among(vpmodel, mdPolar)) {
add_edit(vpconf.offside);
add_edit(vpconf.offside2);
}
if(among(vpmodel, mdAitoff, mdHammer, mdWinkelTripel))
add_edit(vpconf.aitoff_parameter);
if(vpmodel == mdWinkelTripel)
add_edit(vpconf.winkel_parameter);
if(vpmodel == mdSpiral && !euclid) {
add_edit(vpconf.spiral_angle);
add_edit(
sphere ? vpconf.sphere_spiral_multiplier :
ring_not_spiral ? vpconf.right_spiral_multiplier :
vpconf.any_spiral_multiplier
);
add_edit(vpconf.spiral_cone);
}
if(vpmodel == mdSpiral && euclid) {
add_edit(vpconf.spiral_x);
add_edit(vpconf.spiral_y);
if(euclid && quotient) {
dialog::addSelItem(XLAT("match the period"), its(spiral_id), 'n');
dialog::add_action(match_torus_period);
}
}
add_edit(vpconf.stretch);
if(product_model(vpmodel))
add_edit(vpconf.product_z_scale);
#if CAP_GL
dialog::addBoolItem(XLAT("use GPU to compute projections"), vid.consider_shader_projection, 'G');
bool shaderside_projection = get_shader_flags() & SF_DIRECT;
if(vid.consider_shader_projection && !shaderside_projection)
dialog::lastItem().value = XLAT("N/A");
if(vid.consider_shader_projection && shaderside_projection && vpmodel)
dialog::lastItem().value += XLAT(" (2D only)");
dialog::add_action([] { vid.consider_shader_projection = !vid.consider_shader_projection; });
#endif
menuitem_sightrange('R');
dialog::addBreak(100);
dialog::addItem(XLAT("history mode"), 'a');
dialog::add_action_push(history::history_menu);
#if CAP_RUG
if(GDIM == 2 || rug::rugged) {
dialog::addItem(XLAT("hypersian rug mode"), 'u');
dialog::add_action_push(rug::show);
}
#endif
dialog::addBack();
dialog::display();
}
EX void quick_model() {
cmode = sm::CENTER | sm::SIDE | sm::MAYDARK;
gamescreen();
dialog::init("models & projections");
if(GDIM == 2 && !euclid) {
dialog::addItem(hyperbolic ? XLAT("Gans model") : XLAT("orthographic projection"), '1');
dialog::add_action([] { if(rug::rugged) rug::close(); pconf.alpha = 999; pconf.scale = 998; pconf.xposition = pconf.yposition = 0; popScreen(); });
dialog::addItem(hyperbolic ? XLAT("Poincaré model") : XLAT("stereographic projection"), '2');
dialog::add_action([] { if(rug::rugged) rug::close(); pconf.alpha = 1; pconf.scale = 1; pconf.xposition = pconf.yposition = 0; popScreen(); });
dialog::addItem(hyperbolic ? XLAT("Beltrami-Klein model") : XLAT("gnomonic projection"), '3');
dialog::add_action([] { if(rug::rugged) rug::close(); pconf.alpha = 0; pconf.scale = 1; pconf.xposition = pconf.yposition = 0; popScreen(); });
if(sphere) {
dialog::addItem(XLAT("stereographic projection") + " " + XLAT("(zoomed out)"), '4');
dialog::add_action([] { if(rug::rugged) rug::close(); pconf.alpha = 1; pconf.scale = 0.4; pconf.xposition = pconf.yposition = 0; popScreen(); });
}
if(hyperbolic) {
dialog::addItem(XLAT("Gans model") + " " + XLAT("(zoomed out)"), '4');
dialog::add_action([] { if(rug::rugged) rug::close(); pconf.alpha = 999; pconf.scale = 499; pconf.xposition = pconf.yposition = 0; popScreen(); });
#if CAP_RUG
dialog::addItem(XLAT("Hypersian Rug"), 'u');
dialog::add_action([] {
if(rug::rugged) pushScreen(rug::show);
else {
pconf.alpha = 1, pconf.scale = 1; if(!rug::rugged) rug::init(); popScreen();
}
});
#endif
}
}
else if(GDIM == 2 && euclid) {
auto zoom_to = [] (ld s) {
pconf.xposition = pconf.yposition = 0;
ld maxs = 0;
auto& cd = current_display;
for(auto& p: gmatrix) for(int i=0; i<p.first->type; i++) {
shiftpoint h = tC0(p.second * currentmap->adj(p.first, i));
hyperpoint onscreen;
applymodel(h, onscreen);
maxs = max(maxs, onscreen[0] / cd->xsize);
maxs = max(maxs, onscreen[1] / cd->ysize);
}
pconf.alpha = 1;
pconf.scale = s * pconf.scale / 2 / maxs / cd->radius;
popScreen();
};
dialog::addItem(XLAT("zoom 2x"), '1');
dialog::add_action([zoom_to] { zoom_to(2); });
dialog::addItem(XLAT("zoom 1x"), '2');
dialog::add_action([zoom_to] { zoom_to(1); });
dialog::addItem(XLAT("zoom 0.5x"), '3');
dialog::add_action([zoom_to] { zoom_to(.5); });
#if CAP_RUG
if(quotient) {
dialog::addItem(XLAT("cylinder/donut view"), 'u');
dialog::add_action([] {
if(rug::rugged) pushScreen(rug::show);
else {
pconf.alpha = 1, pconf.scale = 1; if(!rug::rugged) rug::init(); popScreen();
}
});
}
#endif
}
else if(GDIM == 3) {
auto& ysh = (WDIM == 2 ? vid.camera : vid.yshift);
dialog::addItem(XLAT("first-person perspective"), '1');
dialog::add_action([&ysh] { ysh = 0; vid.sspeed = 0; popScreen(); } );
dialog::addItem(XLAT("fixed point of view"), '2');
dialog::add_action([&ysh] { ysh = 0; vid.sspeed = -10; popScreen(); } );
dialog::addItem(XLAT("third-person perspective"), '3');
dialog::add_action([&ysh] { ysh = 1; vid.sspeed = 0; popScreen(); } );
}
if(WDIM == 2) {
dialog::addItem(XLAT("toggle full 3D graphics"), 'f');
dialog::add_action([] { geom3::switch_fpp(); popScreen(); });
}
dialog::addItem(XLAT("advanced projections"), 'a');
dialog::add_action_push(model_menu);
menuitem_sightrange('r');
dialog::addBack();
dialog::display();
}
#if CAP_COMMANDLINE
EX eModel read_model(const string& ss) {
for(int i=0; i<isize(mdinf); i++) {
if(hyperbolic && appears(mdinf[i].name_hyperbolic, ss)) return eModel(i);
if(euclid && appears(mdinf[i].name_euclidean, ss)) return eModel(i);
if(sphere && appears(mdinf[i].name_spherical, ss)) return eModel(i);
}
for(int i=0; i<isize(mdinf); i++) {
if(appears(mdinf[i].name_hyperbolic, ss)) return eModel(i);
if(appears(mdinf[i].name_euclidean, ss)) return eModel(i);
if(appears(mdinf[i].name_spherical, ss)) return eModel(i);
}
return eModel(atoi(ss.c_str()));
}
int readArgs() {
using namespace arg;
if(0) ;
else if(argis("-els")) {
shift_arg_formula(history::extra_line_steps);
}
else if(argis("-stretch")) {
PHASEFROM(2); shift_arg_formula(vpconf.stretch);
}
else if(argis("-PM")) {
PHASEFROM(2); shift(); vpconf.model = read_model(args());
if(vpconf.model == mdFormula) {
shift(); vpconf.basic_model = eModel(argi());
shift(); vpconf.formula = args();
}
}
else if(argis("-topz")) {
PHASEFROM(2);
shift_arg_formula(vpconf.top_z);
}
else if(argis("-twopoint")) {
PHASEFROM(2);
shift_arg_formula(vpconf.twopoint_param);
}
else if(argis("-hp")) {
PHASEFROM(2);
shift_arg_formula(vpconf.halfplane_scale);
}
else if(argis("-mets")) {
PHASEFROM(2);
shift_arg_formula(vpconf.euclid_to_sphere);
}
else if(argis("-mhyp")) {
PHASEFROM(2);
shift_arg_formula(vpconf.hyperboloid_scaling);
}
else if(argis("-mdepth")) {
PHASEFROM(2);
shift_arg_formula(vpconf.depth_scaling);
}
else if(argis("-mnil")) {
PHASEFROM(2);
shift_arg_formula(vpconf.rotational_nil);
}
else if(argis("-clip")) {
PHASEFROM(2);
shift_arg_formula(vpconf.clip_min);
shift_arg_formula(vpconf.clip_max);
}
else if(argis("-mtrans")) {
PHASEFROM(2);
shift_arg_formula(vpconf.model_transition);
}
else if(argis("-mparam")) {
PHASEFROM(2);
if(pmodel == mdCollignon) shift_arg_formula(vpconf.collignon_parameter);
else if(pmodel == mdMiller) shift_arg_formula(vpconf.miller_parameter);
else if(among(pmodel, mdLoximuthal, mdRetroCraig, mdRetroHammer)) shift_arg_formula(vpconf.loximuthal_parameter);
else if(among(pmodel, mdAitoff, mdHammer, mdWinkelTripel)) shift_arg_formula(vpconf.aitoff_parameter);
if(pmodel == mdWinkelTripel) shift_arg_formula(vpconf.winkel_parameter);
}
else if(argis("-sang")) {
PHASEFROM(2);
shift_arg_formula(vpconf.spiral_angle);
if(sphere)
shift_arg_formula(vpconf.sphere_spiral_multiplier);
else if(vpconf.spiral_angle == 90)
shift_arg_formula(vpconf.right_spiral_multiplier);
}
else if(argis("-ssm")) {
PHASEFROM(2);
shift_arg_formula(vpconf.any_spiral_multiplier);
}
else if(argis("-scone")) {
PHASEFROM(2);
shift_arg_formula(vpconf.spiral_cone);
}
else if(argis("-sxy")) {
PHASEFROM(2);
shift_arg_formula(vpconf.spiral_x);
shift_arg_formula(vpconf.spiral_y);
}
else if(argis("-mob")) {
PHASEFROM(2);
shift_arg_formula(vpconf.skiprope);
}
else if(argis("-zoom")) {
PHASEFROM(2); shift_arg_formula(vpconf.scale);
}
else if(argis("-alpha")) {
PHASEFROM(2); shift_arg_formula(vpconf.alpha);
}
else if(argis("-d:model"))
launch_dialog(model_menu);
else if(argis("-d:formula")) {
launch_dialog();
edit_formula();
}
else if(argis("-d:match")) {
launch_dialog(match_torus_period);
edit_formula();
}
else return 1;
return 0;
}
auto hookArg = addHook(hooks_args, 100, readArgs);
#endif
void add_model_config() {
param_i(polygonal::SI, "polygon sides");
param_f(polygonal::STAR, parameter_names("star", "polygon star factor"));
param_i(polygonal::deg, "polygonal degree");
param_i(polygonal::maxcoef, "polynomial degree");
for(int i=0; i<polygonal::MSI; i++) {
param_f(polygonal::coefr[i], "polynomial "+its(i)+".real");
param_f(polygonal::coefi[i], "polynomial "+its(i)+".imag");
}
auto setrot = [] {
dialog::get_di().dialogflags |= sm::CENTER;
dialog::addBreak(100);
dialog::addBoolItem_choice("line animation only", models::do_rotate, 0, 'N');
dialog::addBoolItem_choice("gravity lands", models::do_rotate, 1, 'G');
dialog::addBoolItem_choice("all directional lands", models::do_rotate, 2, 'D');
};
param_matrix(models::rotation.v2, "rotation", 2)->editable("auto rotation", "", 'r')->set_extra(setrot);
param_matrix(models::rotation.v3, "rotation3", 3)->editable("auto rotation in 3D", "", 'r')->set_extra(setrot);
param_i(models::do_rotate, "auto_rotation_mode", 1);
param_f(pconf.halfplane_scale, parameter_names("hp", "halfplane scale"), 1);
auto add_all = [&] (projection_configuration& p, string pp, string sp) {
bool rug = pp != "";
dynamicval<function<bool()>> ds(auto_restrict);
auto_restrict = [&p] { return &vpconf == &p; };
if(&p.model == &pmodel) {
auto par = param_custom_int(pmodel, parameter_names(pp+"used_model", "used model"), menuitem_projection, '1');
par->help_text = "projection|Poincare|Klein|half-plane|perspective";
}
else param_enum(p.model, parameter_names(pp+"used_model", sp+"used model"), mdDisk);
param_matrix(p.mori().v2, pp+"mori", 2)
-> editable("model orientation", "", 'o');
param_matrix(p.mori().v3, pp+"mori3", 3)
-> editable("model orientation 3D", "", 'o');
param_f(p.top_z, sp+"topz", 3)
-> editable(1, 20, .25, "maximum z coordinate to show", "maximum z coordinate to show", 'l');
param_f(p.model_transition, parameter_names(pp+"mtrans", sp+"model transition"), 1)
-> editable(0, 1, .1, "model transition",
"You can change this parameter for a transition from another model to this one.", 't');
param_f(p.rotational_nil, sp+"rotnil", 1);
param_f(p.clip_min, parameter_names(pp+"clipmin", sp+"clip-min"), rug ? -100 : -1);
param_f(p.clip_max, parameter_names(pp+"clipmax", sp+"clip-max"), rug ? +10 : +1);
param_f(p.euclid_to_sphere, parameter_names(pp+"ets", sp+"euclid to sphere projection"), 1.5)
-> editable(1e-1, 10, .1, "ETS parameter", "Stereographic projection to a sphere. Choose the radius of the sphere.", 'l')
-> set_sets(dialog::scaleLog);
param_f(p.twopoint_param, parameter_names(pp+"twopoint", sp+"twopoint parameter"), 1)
-> editable(1e-3, 10, .1, "two-point parameter", "In two-point-based models, this parameter gives the distance from each of the two points to the center.", 'b')
-> set_sets(dialog::scaleLog);
param_f(p.axial_angle, parameter_names(pp+"axial", sp+"axial angle"), 90)
-> editable(1e-3, 10, .1, "angle between the axes", "In two-axe-based models, this parameter gives the angle between the two axes.", 'x')
-> set_sets(dialog::scaleLog);
param_f(p.fisheye_param, parameter_names(pp+"fisheye", sp+"fisheye parameter"), 1)
-> editable(1e-3, 10, .1, "fisheye parameter", "Size of the fish eye.", 'b')
-> set_sets(dialog::scaleLog);
param_f(p.fisheye_alpha, parameter_names(pp+"fishalpha", sp+"off-center parameter"), 0)
-> editable(1e-1, 10, .1, "off-center parameter",
"This projection is obtained by composing gnomonic projection and inverse stereographic projection. "
"This parameter changes the center of the first projection (0 = gnomonic, 1 = stereographic). Use a value closer to 1 "
"to make the projection more conformal.",