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hyperrogue/surface.cpp

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// Hyperbolic Rogue -- surfaces of constant negative curvature
// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details
/** \file surface.cpp
* \brief surfaces of constant negative curvature
*
* See http://webmath2.unito.it/paginepersonali/sergio.console/CurveSuperfici/AG15.pdf for a nice reference
*/
#include "hyper.h"
namespace hr {
#if CAP_SURFACE
EX namespace surface {
ld sech(ld d) { return 1 / cosh(d); }
#if HDR
enum eShape { dsNone, dsTractricoid, dsDini, dsKuen, dsHyperlike, dsHyperboloid, dsHemisphere, dsCrystal };
#endif
string shape_name[] = { "hypersian rug", "tractricoid", "Dini's surface", "Kuen surface", "concave barrel",
"hyperboloid", "hemisphere", "crystal" };
EX eShape sh;
hyperpoint unit_vector[3] = {point3(1,0,0), point3(0,1,0), point3(0,0,1)};
ld last_int_of = 0, last_int = 0;
EX ld dini_b = .15;
EX ld hyper_b = 1;
ld f(ld x) {
return sqrt(1 - pow(hyper_b * sinh(x), 2));
}
int kuen_branch(ld v, ld u);
ld integral(ld x) {
if(x == 0) {
last_int = last_int_of = 0;
}
else {
last_int += (x - last_int) * f((x + last_int)/2);
last_int_of = x;
}
return last_int;
}
hyperpoint coord(hyperpoint h) {
// return { cos(u)*sin(v), cos(u)*cos(v), sin(u) };
/*
ld t = h[0];
ld v = h[1];
ld r = 1 / cosh(t);
ld x = t - tanh(t);
return { x + v * .1, r * sin(v), r * cos(v) };
*/
switch(sh) {
case dsTractricoid: {
ld t = h[0];
ld v = h[1];
ld r = 1 / cosh(t);
ld x = t - tanh(t);
return point31( r * sin(v), r * cos(v), x );
break;
}
case dsDini: {
ld t = h[0];
ld v = h[1];
ld a = sqrt(1-dini_b*dini_b);
return point31( a * sin(v) * sin(t), a * cos(v) * sin(t), a * (cos(t) + log(tan(t/2))) + dini_b * v );
break;
}
case dsKuen: {
ld v = h[0];
ld u = h[1];
ld deno = 1 / (1 + u * u * sin(v) * sin(v));
return point31(
2 * (cos(u) + u * sin(u)) * sin(v) * deno,
2 * (sin(u) - u * cos(u)) * sin(v) * deno,
log(tan(v/2)) + 2 * cos(v) * deno
);
}
case dsHyperlike: {
ld u = h[0];
ld v = h[1];
ld phi = hyper_b * cosh(v);
ld psi = integral(v);
return point31( phi * cos(u), phi * sin(u), psi );
}
default:
return h;
}
}
ld det(hyperpoint h1, hyperpoint h2, hyperpoint h3) {
return det(build_matrix(h1, h2, h3,C03));
}
ld epsd = 1e-5;
hyperpoint coord_derivative(hyperpoint h, int cc) {
switch(sh) {
case dsHyperlike: {
ld u = h[0];
ld v = h[1];
if(cc == 0) {
ld phi = hyper_b * cosh(v);
return point3( phi * -sin(u), phi * cos(u), 0 );
}
else {
return point3( hyper_b * sinh(v) * cos(u), hyper_b * sinh(v) * sin(u), f(v) );
}
}
case dsKuen: {
ld v = h[0];
ld u = h[1];
ld denom = pow(sin(v),2)*(u*u)+1;
ld denom2 = denom * denom;
if(cc == 1)
return point3(
2*sin(v)/denom*u*cos(u)+-4*(sin(u)*u+cos(u))*pow(sin(v),3)/denom2*u,
-4*pow(sin(v),3)*(sin(u)-u*cos(u))/denom2*u+2*sin(u)*sin(v)/denom*u,
-4*pow(sin(v),2)/denom2*u*cos(v)
);
else return point3(
2*(sin(u)*u+cos(u))/denom*cos(v)+-4*(sin(u)*u+cos(u))*pow(sin(v),2)/denom2*(u*u)*cos(v),
2*(sin(u)-u*cos(u))/denom*cos(v)+-4*pow(sin(v),2)*(sin(u)-u*cos(u))/denom2*(u*u)*cos(v),
-4*sin(v)/denom2*(u*u)*pow(cos(v),2)+1/tan(v/2)*(pow(tan(v/2),2)+1)/2+-2*sin(v)/denom
);
break;
}
default:
// too lazy do differentiate
return (coord(h + unit_vector[cc] * epsd) - coord(h)) / epsd;
}
}
ld compute_curvature(hyperpoint at) {
hyperpoint xu = coord_derivative(at, 0);
hyperpoint xv = coord_derivative(at, 1);
hyperpoint xuu = (coord_derivative(at + unit_vector[0] * epsd, 0) - xu) / epsd;
hyperpoint xuv = (coord_derivative(at + unit_vector[1] * epsd, 0) - xu) / epsd;
hyperpoint xvv = (coord_derivative(at + unit_vector[1] * epsd, 1) - xv) / epsd;
return
(det(xuu, xu, xv) * det(xvv, xu, xv) - pow(det(xuv, xu, xv), 2)) /
pow((xu|xu) * (xv|xv) - pow((xu|xv), 2), 2);
}
hyperpoint shape_origin() {
switch(sh) {
case dsDini:
return point31(A_PI * .82, 0, 0);
case dsTractricoid:
return point31(1, 0, 0);
case dsKuen:
return point31(90._deg * 1.000001, M_PI, 0);
case dsHyperlike:
return point31(0,0,0);
default:
return Hypc;
}
}
ld hyperlike_bound() { return asinh(1 / hyper_b); }
bool flag_clamp_min(ld& coord, ld minv) {
if(coord < minv) { coord = minv; return false; }
return true;
}
bool flag_clamp_max(ld& coord, ld maxv) {
if(coord > maxv) { coord = maxv; return false; }
return true;
}
bool flag_clamp(ld& coord, ld minv, ld maxv) {
return flag_clamp_min(coord, minv) && flag_clamp_max(coord, maxv);
}
bool flag_clamp_sym(ld& coord, ld v) {
return flag_clamp(coord, -v, v);
}
int surface_branch(hyperpoint p) {
if(sh == dsKuen) return kuen_branch(p[0], p[1]);
return 0;
}
bool inbound(ld& x, ld& y) {
switch(sh) {
case dsDini:
return flag_clamp(x, 90._deg, M_PI);
case dsTractricoid:
return flag_clamp_min(x, 0) && flag_clamp_sym(y, M_PI);
case dsKuen:
return flag_clamp(x, 0, M_PI) && flag_clamp(y, 0, TAU);
case dsHyperlike:
return flag_clamp_sym(x, M_PI) && flag_clamp_sym(y, hyperlike_bound());
default:
return true;
}
}
bool is_inbound(hyperpoint h) {
return inbound(h[0], h[1]);
}
int precision = 100;
using rug::dexp_data;
struct dexp_origin {
transmatrix H; // isometry of H2 moving zero to C0
transmatrix M; // local coordinates on H2 to local coordinates on surface
hyperpoint zero; // parameters of the zero point
};
dexp_data dexp(hyperpoint p, hyperpoint t) {
ld eps = 1. / precision;
int b = surface_branch(p);
for(ld u=0; u<1; u += eps) {
transmatrix T = build_matrix(coord_derivative(p, 0), coord_derivative(p, 1), Hypc, C03);
p += t * eps;
if(!is_inbound(p) || surface_branch(p) != b)
return { p - t * eps, t, hypot_d(3, t) * (1-u) / precision };
auto v0 = coord_derivative(p, 0);
auto v1 = coord_derivative(p, 1);
transmatrix T2 = build_matrix(v0, v1, v0 ^ v1, C03);
t = inverse(T2) * T * t;
t[2] = 0;
}
return { p, t, 0 };
}
dexp_data map_to_surface(hyperpoint p, const dexp_origin& dor) {
hyperpoint h = dor.H * p;
ld rad = hypot_d(2, h);
if(rad == 0) rad = 1;
ld d = hdist0(h);
hyperpoint direction;
direction[0] = d * h[0] / rad;
direction[1] = d * h[1] / rad;
direction[2] = 0;
#if MAXMDIM == 4
direction[3] = 0;
#endif
return dexp(dor.zero, dor.M * direction);
}
transmatrix create_M_matrix(hyperpoint zero, hyperpoint v1) {
hyperpoint Te0 = coord_derivative(zero, 0);
hyperpoint Te1 = coord_derivative(zero, 1);
transmatrix T = build_matrix(Te0, Te1, Hypc, C03);
v1 = v1 / hypot_d(3, T*v1);
hyperpoint v2 = point3(1e-3, 1e-4, 0);
v2 = v2 - v1 * ((T*v1) | (T*v2)) / hypot_d(3, T*v1);
v2 = v2 / hypot_d(3, T*v2);
if((((T*v1) ^ (T*v2)) | ((T*unit_vector[0]) ^ (T*unit_vector[1]))) < 0)
v2 = v2 * -1;
transmatrix M = build_matrix(v1, v2, Hypc, C03);
println(hlog, M);
println(hlog, "M matrix test: ",
make_tuple(hypot_d(3, T*M*unit_vector[0]), hypot_d(3, T*M*unit_vector[1]), hypot_d(3, T*M*(unit_vector[0]+unit_vector[1])),
((T*M*unit_vector[0]) | (T*M*unit_vector[1]))));
return M;
}
dexp_origin at_zero(hyperpoint zero, transmatrix start) {
println(hlog, "zero = ", zero);
println(hlog, "curvature at zero = ", compute_curvature(zero));
println(hlog, "curvature at X1 = ", compute_curvature(zero + point3(.3, 0, 0)));
println(hlog, "curvature at X2 = ", compute_curvature(zero + point3(0, .3, 0)));
println(hlog, "curvature at X3 = ", compute_curvature(zero + point3(.4, .3, 0)));
return {start, create_M_matrix(zero, unit_vector[0]), zero};
}
dexp_origin at_other(dexp_origin& o1, hyperpoint h) {
println(hlog, "\n\nmapping ", h, "...");
println(hlog, o1.H, o1.M);
auto dd = map_to_surface(h, o1);
hyperpoint newzero = dd.params;
println(hlog, "error = ", dd.remaining_distance);
transmatrix Spin = spintox(o1.H * h);
transmatrix T = pushxto0(Spin * o1.H * h) * Spin;
println(hlog, "h is = ", h);
println(hlog, "T*c0 is = ", T * C0);
println(hlog, "T*h is = ", T * o1.H * h);
return {T * o1.H, create_M_matrix(newzero, dd.cont), newzero};
}
void addTriangleV(rug::rugpoint *t1, rug::rugpoint *t2, rug::rugpoint *t3, ld len = 1) {
if(t1 && t2 && t3)
rug::addTriangle(t1, t2, t3, len);
}
hyperpoint kuen_cross(ld v, ld u) {
auto du = coord_derivative(point3(v,u,0), 0);
auto dv = coord_derivative(point3(v,u,0), 1);
return du^dv;
}
ld kuen_hypot(ld v, ld u) {
auto du = coord_derivative(point3(v,u,0), 0);
auto dv = coord_derivative(point3(v,u,0), 1);
auto n = hypot_d(3, du^dv);
return n;
}
int kuen_branch(ld v, ld u) {
if(v > 90._deg)
return kuen_cross(v, u)[2] > 0 ? 1 : 2;
else
return kuen_cross(v, u)[2] < 0 ? 1 : 2;
}
int dexp_colors[16] = {
0xFF0000, 0x00FF00, 0x0000FF, 0xFFFF00 };
int dexp_comb_colors[16] = {
0x000000, 0x0000FF, 0x00FF00, 0x00FFFF,
0xFF0000, 0xFF00FF, 0xFFFF00, 0xFFFFFF,
0xFFD500,
0x123456, 0x123456, 0x123456, 0x123456, 0x123456, 0x123456, 0x123456
};
int coverage_style;
EX vector<pair<hyperpoint, int> > coverage;
#if CAP_KUEN_MAP
void draw_kuen_map() {
SDL_Surface *kuen_map = SDL_CreateRGBSurface(SDL_SWSURFACE,512,512,32,0,0,0,0);
ld nmax = 0;
for(int i=0; i<2; i++) {
for(int r=0; r<512; r++)
for(int h=0; h<512; h++) {
ld v = M_PI * (r+.5) / 512;
ld u = TAU * (h+.5) / 512;
auto du = coord_derivative(point3(v,u,0), 0);
auto dv = coord_derivative(point3(v,u,0), 1);
auto n = hypot_d(3, du^dv);
if(n > nmax) nmax = n;
if(i == 1) {
auto vv = kuen_cross(v, u);
auto& px = qpixel(kuen_map, r, h);
px |= 0xFF000000;
for(int k=0; k<3; k++)
part(px, k) = (vv[k] > 0 ? 0xFF : 0);
px = 0xFF000000 + (((int)(n*255/nmax)) * (kuen_branch(v,u) == 1 ? 0x10101 : 0x10001));
}
}
println(hlog, "nmax = ", nmax);
}
for(auto p: rug::points) {
auto hp = p->surface_point.params;
int x = int(512 * hp[0] / M_PI);
int y = int(512 * hp[1] / TAU);
qpixel(kuen_map, x, y) = 0xFF000000 | dexp_colors[p->dexp_id];
}
IMAGESAVE(kuen_map, "kuen.png");
}
#endif
void full_mesh() {
rug::clear_model();
rug::buildRug();
rug::qvalid = 0;
for(auto p: rug::points) p->valid = true, rug::qvalid++;
while(rug::subdivide_further()) rug::subdivide();
rug::sort_rug_points();
for(auto p: rug::points) p->valid = false;
rug::good_shape = true;
}
char rchar(int id) {
return 33 + id % 94;
}
void run_hyperlike() {
if(!rug::rugged) rug::reopen();
rug::clear_model();
int lim = (int) sqrt(rug::vertex_limit);
for(int r=0; r<lim; r++)
for(int h=0; h<lim; h++)
rug::addRugpoint(shiftless(xpush(TAU * hyper_b * (2*r-lim) / lim) * ypush(hyperlike_bound() * (2*h-lim) / lim) * C0), -1);
for(int r=0; r<lim-1; r++)
for(int h=0; h<lim-1; h++) {
addTriangle(rug::points[lim*r+h], rug::points[lim*r+h+1], rug::points[lim*r+h+lim]);
addTriangle(rug::points[lim*r+h+lim+1], rug::points[lim*r+h+lim], rug::points[lim*r+h+1]);
}
vector<ld> integral_table;
for(int i=0; i<=precision; i++)
integral_table.push_back(integral(hyperlike_bound() * i / precision));
int id = 0;
for(auto p: rug::points) {
auto h = unshift(p->h);
coverage.emplace_back(h, rchar(id++) + 7 * 256);
ld y = asinh(h[1]);
ld x = asinh(h[0] / cosh(y)) / hyper_b;
p->surface_point.remaining_distance = !inbound(x, y);
p->surface_point.params = hpxyz(x, y, 0);
int sgn = y > 0 ? 1 : -1;
ld phi = hyper_b * cosh(y);
int pt = y * precision * sgn / hyperlike_bound();
USING_NATIVE_GEOMETRY;
p->native = point31(phi * cos(x), phi * sin(x), sgn * integral_table[pt]);
p->valid = true;
}
}
void run_kuen() {
full_mesh();
auto H = Id;
auto Hi = inverse(H);
auto frontal_map = at_zero(hpxyz(90._deg * 1.000001, M_PI * 1, 0), Id);
auto back0 = at_zero(hpxyz(90._deg * 1.000001, .67, 0), H);
auto back1 = at_other(back0, Hi * spin(-90._deg) * hpxy(0.511, -0.5323));
auto back2 = at_other(back0, Hi * spin(-90._deg) * hpxy(0.511, 0.5323));
frontal_map.H = frontal_map.H * ypush(2.6);
back0.H = back0.H * ypush(.4);
back1.H = back1.H * ypush(.4);
back2.H = back2.H * ypush(.4);
int it = 0;
for(auto p: rug::points) p->dexp_id = it++;
vector<rug::rugpoint*> mesh = std::move(rug::points);
vector<rug::triangle> old_triangles = std::move(rug::triangles);
rug::clear_model();
int part = 0;
vector<int> coverages(isize(mesh), 0);
for(auto& m: { frontal_map, back0, back1, back2 } ) {
part++;
int pid[5] = {0, 8, 1, 2, 4};
string captions[5] = {"", "the upper component", "the lower center", "the lower left", "the lower right"};
vector<rug::rugpoint*> newmesh(isize(mesh), nullptr);
for(auto p: mesh) {
auto px = map_to_surface(unshift(p->h), m);
p->surface_point = px;
history::progress(XLAT("solving the geodesics on: %1, %2/%3", XLAT(captions[part]), its(p->dexp_id), its(isize(mesh))));
}
for(auto p: mesh) {
// make it a bit nicer by including the edges where only one endpoint is valid
auto& px = p->surface_point;
p->valid = px.remaining_distance == 0;
for(auto e: p->edges) if(e.target->surface_point.remaining_distance == 0)
p->valid = true;
if(p->valid) {
rug::rugpoint *np = new rug::rugpoint;
newmesh[p->dexp_id] = np;
rug::points.push_back(np);
np->x1 = p->x1;
np->y1 = p->y1;
np->valid = true;
np->inqueue = false;
np->dist = 0;
np->h = p->h;
USING_NATIVE_GEOMETRY;
np->native = coord(px.params);
np->surface_point = px;
np->dexp_id = p->dexp_id;
coverages[p->dexp_id] |= pid[part];
}
}
for(auto& t: old_triangles) {
rug::rugpoint* r[3];
for(int i=0; i<3; i++)
r[i] = newmesh[t.m[i]->dexp_id];
bool looks_good = true;
for(int i=0; i<3; i++)
if(!r[i]) looks_good = false;
if(!looks_good) continue;
for(int i=0; i<3; i++) {
USING_NATIVE_GEOMETRY;
if(hypot_d(3, r[i]->native - r[(i+1)%3]->native) > .2)
looks_good = false;
}
if(looks_good)
addTriangleV(r[0], r[1], r[2]);
}
}
for(auto t: mesh) {
int c = coverages[t->dexp_id];
coverage.emplace_back(unshift(t->h), rchar(t->dexp_id) + 256 * c);
}
// delete the old mesh
for(auto t: mesh) delete t;
#if CAP_KUEN_MAP
draw_kuen_map();
#endif
}
template<class T> void run_function(T f) {
full_mesh();
for(auto p: rug::points) {
USING_NATIVE_GEOMETRY;
p->native = f(unshift(p->h)),
p->valid = true;
}
}
void run_other() {
full_mesh();
auto dp = at_zero(shape_origin(), spin(90._deg));
int it = 0;
for(auto p: rug::points) {
it++;
auto h = unshift(p->h);
p->surface_point = map_to_surface(h, dp);
if(1) {
USING_NATIVE_GEOMETRY;
p->native = coord(p->surface_point.params);
}
history::progress(XLAT("solving the geodesics on: %1, %2/%3", XLAT(shape_name[sh]), its(it), its(isize(rug::points))));
if(p->surface_point.remaining_distance == 0)
coverage.emplace_back(h, rchar(it) + 256 * 7);
}
clearMessages();
for(auto p: rug::points) {
// make it a bit nicer by including the edges where only one endpoint is valid
p->valid = p->surface_point.remaining_distance == 0;
if(sh != dsKuen) {
for(auto e: p->edges) if(e.target->surface_point.remaining_distance == 0)
p->valid = true;
}
}
}
EX void run_shape(eShape s) {
coverage.clear();
need_mouseh = true;
sh = s;
if(rug::rugged) rug::close();
rug::gwhere = rug::rgEuclid;
rug::init();
// if(!rug::rugged) rug::reopen();
pushScreen(history::progress_screen);
if(sh != dsNone) rug::good_shape = true;
switch(sh) {
case dsNone:
break;
case dsKuen:
run_kuen();
break;
case dsHyperlike:
run_hyperlike();
break;
default:
run_other();
break;
case dsHyperboloid:
run_function([] (hyperpoint h) { return h; });
break;
case dsHemisphere:
run_function([] (hyperpoint h) { h = h / h[2]; h[2] = sqrt(1 - sqhypot_d(2, h)); return h; });
break;
}
if(sh != dsNone) rug::good_shape = true;
rug::qvalid = 0;
popScreen();
if(sh != dsHyperboloid && sh != dsHemisphere && sh != dsNone) {
ld minx = 1e9, maxx = -1e9;
for(auto p: rug::points) if(p->valid) {
minx = min(p->native[2], minx);
maxx = max(p->native[2], maxx);
rug::qvalid++;
}
println(hlog, "minx = ", minx, " maxx = ", maxx);
ld shift = -(minx + maxx) / 2;
for(auto p: rug::points) if(p->valid)
p->native[2] += shift;
}
}
void cancel_shape() {
if(sh) {
sh = dsNone;
rug::good_shape = false;
rug::qvalid = 0;
for(auto p: rug::points)
p->valid = p->surface_point.remaining_distance == 0;
for(auto p: rug::points)
if(p->valid)
rug::qvalid++, rug::enqueue(p);
}
}
cell *coverage_center;
transmatrix coverage_matrix;
EX void show_surfaces() {
cmode = sm::SIDE;
gamescreen();
dialog::init(XLAT("constant curvature surfaces"), iinf[itPalace].color, 150, 0);
bool b = rug::rugged || coverage_style;
dialog::addBoolItem(XLAT("tractricoid"), b && sh == dsTractricoid, '1');
dialog::addBoolItem(XLAT("concave barrel"), b && sh == dsHyperlike, '2');
dialog::addSelItem(" " + XLAT("parameter"), fts(hyper_b), '@');
dialog::addBoolItem(XLAT("Dini's surface"), b && sh == dsDini, '3');
dialog::addSelItem(" " + XLAT("parameter") + " ", fts(dini_b), '#');
dialog::addBoolItem(XLAT("Kuen surface"), b && sh == dsKuen, '4');
dialog::addBreak(50);
dialog::addTitle(XLAT("other 3D models"), iinf[itPalace].color, 150);
dialog::addBoolItem(XLAT("Hypersian Rug"), b && sh == dsNone, '5');
dialog::addBoolItem(XLAT("Minkowski hyperboloid"), b && sh == dsHyperboloid, '6');
dialog::addBoolItem(XLAT("hemisphere"), b && sh == dsHemisphere, '7');
dialog::addBreak(100);
dialog::addSelItem(XLAT("precision"), its(precision), 'p');
string cstyles[4] = { "OFF", "on surface", "on H² (static)", "on H² (dynamic)" };
if((rug::rugged && sh && sh != dsHyperboloid && sh != dsHemisphere) || coverage_style)
dialog::addSelItem(XLAT("display coverage"), cstyles[coverage_style], 'c');
else dialog::addBreak(100);
#if CAP_FILES
if(rug::rugged)
dialog::addItem(XLAT("save the current embedding"), 's');
else
dialog::addItem(XLAT("load a saved embedding"), 's');
#endif
dialog::addHelp();
dialog::addBack();
dialog::display();
keyhandler = [] (int sym, int uni) {
dialog::handleNavigation(sym, uni);
if(uni == 'h' || uni == SDLK_F1)
gotoHelp(XLAT(
"In this menu you can choose from several known smooth surfaces of constant negative curvature. "
"Since the curvature of hyperbolic plane is also constant negative, these surfaces "
"are great to draw hyperbolic tesselations on. While they look great, only a small part "
"of the hyperbolic plane can be visibly represented in this way, so they are not "
"good for playing HyperRogue; however, the coverage extends far away in specific directions, "
"so first increasing sight range in graphics config and texture size in hypersian rug settings may improve the effect. "
"For convenience, you can also choose other 3D models from this menu."
));
#if CAP_FILES
else if(uni == 's') {
static string rugname = "saved.rug";
if(rug::rugged)
dialog::openFileDialog(rugname, XLAT("save embedding to:"), ".rug", [] () { rug::rug_save(rugname); return true; });
else
dialog::openFileDialog(rugname, XLAT("load embedding from:"), ".rug", [] () { rug::init(); rug::rug_load(rugname); return true; });
}
#endif
else if(uni == '1')
run_shape(dsTractricoid);
else if(uni == '2')
run_shape(dsHyperlike);
else if(uni == '3')
run_shape(dsDini);
else if(uni == '4')
run_shape(dsKuen);
else if(uni == '5')
run_shape(dsNone);
else if(uni == '6')
run_shape(dsHyperboloid);
else if(uni == '7')
run_shape(dsHemisphere);
else if(uni == '@') {
dialog::editNumber(hyper_b, -1, 1, .05, 1, XLAT("parameter"),
XLAT("Controls the inner radius.")
);
dialog::get_ne().reaction = [] () {
if(sh == dsHyperlike) run_shape(sh);
};
}
else if(uni == 'x')
for(auto p: rug::points)
p->native = p->surface_point.params;
else if(uni == '#')
dialog::editNumber(dini_b, -1, 1, .05, .15, XLAT("parameter"),
XLAT("The larger the number, the more twisted it is.")
);
else if(uni == 'p') {
dialog::editNumber(precision, 1, 10000, 0, 100, XLAT("precision"),
XLAT("Computing these models involves integrals and differential equations, which are currently solved numerically. This controls the precision.")
);
dialog::get_ne().step = .1;
dialog::scaleLog();
}
else if(uni == 'c') {
coverage_style = (1 + coverage_style) % 4;
if(coverage_style == 0) {
rug::reopen();
}
if(coverage_style == 2) {
if(rug::rugged) rug::close();
}
coverage_matrix = inverse(unshift(ggmatrix(coverage_center = cwt.at)));
}
else if(rug::handlekeys(sym, uni)) ;
else if(doexiton(sym, uni)) popScreen();
};
}
#if CAP_COMMANDLINE
int surface_args() {
using namespace arg;
if(0) ;
else if(argis("-kuen")) {
PHASE(3);
calcparam();
run_shape(dsKuen);
}
else if(argis("-dini")) {
PHASE(3);
calcparam();
shift();
dini_b = argf();
run_shape(dsDini);
}
else if(argis("-barrel")) {
PHASE(3);
calcparam();
shift();
hyper_b = argf();
run_shape(dsHyperlike);
}
else if(argis("-tractricoid")) {
PHASE(3);
calcparam();
run_shape(dsTractricoid);
}
else if(argis("-hemi")) {
PHASE(3);
calcparam();
run_shape(dsHemisphere);
}
else if(argis("-hyperb")) {
PHASE(3);
calcparam();
run_shape(dsHyperboloid);
}
else if(argis("-d:surface"))
launch_dialog(show_surfaces);
else return 1;
return 0;
}
#endif
#if CAP_COMMANDLINE
auto surface_hook = addHook(hooks_args, 100, surface_args);
#endif
void display_coverage() {
shiftmatrix M =
coverage_style == 3 ? ggmatrix(coverage_center) * coverage_matrix
: shiftless(Id);
if(coverage_style)
for(auto p : coverage)
queuestr(M * p.first, 10, s0+char(p.second), dexp_comb_colors[(p.second >> 8) & 15]);
/* if(p->valid && p->surface_point.remaining_distance == 0)
queuestr(p->h, 10, "x", dexp_colors[p->dexp_id]); */
}
auto surface_hook2 = addHook(hooks_frame, 0, display_coverage);
EX }
#endif
}
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