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ads tour added
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Zeno Rogue
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711
rogueviz/ads/tour.cpp
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711
rogueviz/ads/tour.cpp
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@ -0,0 +1,711 @@
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// TO DO
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// * knives in Asteroids sometimes do not hit rocks
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// * in Asteroids use the Relative Hell imagery
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// * visualize the 'Spherical symmetry' slide
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namespace hr {
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namespace ads_game {
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namespace ads_tour {
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using namespace rogueviz::pres;
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string defs =
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"\\def\\map{m}"
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"\\def\\VofH{V}"
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"\\def\\dist{\\delta}"
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"\\def\\ra{\\rightarrow}"
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"\\def\\bbH{\\mathbb{H}}"
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"\\def\\bbE{\\mathbb{E}}"
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"\\def\\bbR{\\mathbb{R}}"
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"\\def\\bbS{\\mathbb{S}}"
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"\\def\\dS#1{d\\bbS^#1}"
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"\\def\\wadS#1{ad\\bbS^#1}"
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"\\def\\uadS#1{\\widetilde{ad\\bbS^#1}}"
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"\\renewcommand{\\rmdefault}{\\sfdefault}\\sf"
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;
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int slv_mode;
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cell *slv;
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transmatrix at0, at1;
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int t0, t1;
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void straight_line_viz(presmode mode) {
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if(mode == pmKey) slv_mode = (slv_mode == 0 ? 1 : 0);
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if(mode == pmStart) rogueviz::rv_hook(hooks_markers, 100, [] {
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println(hlog, "slv_mode = ", slv_mode, " tick = ", ticks);
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if(slv_mode == 1) {
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t0 = ticks;
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slv = shmup::pc[0]->base;
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at0 = shmup::pc[0]->at;
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slv_mode++;
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return;
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}
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if(slv_mode == 2 && ticks >= t0 + 20) {
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println(hlog, "elapsed ", ticks - t0);
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t1 = ticks;
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if(slv != shmup::pc[0]->base) { slv_mode = 0; return; }
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at1 = shmup::pc[0]->at;
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slv_mode++;
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return;
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}
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if(slv_mode == 3) {
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ld t = (ticks - t0) * 1. / (t1 - t0);
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vector<vector<hyperpoint>> pts(6);
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vector<hpcshape*> shapes = { &cgi.shSpaceshipBase, &cgi.shSpaceshipCockpit, &cgi.shSpaceshipEngine, &cgi.shSpaceshipGun, &cgi.shSpaceshipEngine, &cgi.shSpaceshipGun };
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for(int si=0; si<6; si++) {
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auto& sh = *(shapes[si]);
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for(int i=sh.s; i<sh.e; i++) {
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hyperpoint h = cgi.hpc[i];
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if(si >= 4) h = MirrorY * h;
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hyperpoint a0 = at0 * h;
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hyperpoint a1 = at1 * h;
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ld d = geo_inner(a0, a1);
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if(hyperbolic) d = -d;
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ld di = acos_auto_clamp(d);
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hyperpoint diff = (a1 - a0 / d) / tan_auto(di);
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h = a0 * cos_auto(di*t) + diff * sin_auto(di*t);
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if(hdist0(h) < 5) pts[si].push_back(h);
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}
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}
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vid.linewidth *= 3;
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for (const shiftmatrix& V : hr::span_at(current_display->all_drawn_copies, slv)) for(auto& pts1: pts) {
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for(auto h: pts1) curvepoint(h);
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queuecurve(V, 0xFFFF80FF, 0, PPR::SUPERLINE);
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}
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vid.linewidth /= 3;
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}
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});
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}
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slide relhell_tour[] = {
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{"Intro", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
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"Relative Hell is a game taking place in relativistic analogs of spherical and hyperbolic geometries. "
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"Here is Space Rocks, a clone of the classic game Asteroids. It is based on Newtonian physics: "
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"if you accelerate, you move forever in that direction, unless you deaccelerate.",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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set_geometry(gEuclidSquare);
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set_variation(eVariation::pure);
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tour::slide_backup(land_structure, lsSingle);
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tour::slide_backup(specialland, laAsteroids);
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auto& ua = euc::eu_input;
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tour::slide_backup(ua, ua);
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for(int i=0; i<2; i++)
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for(int j=0; j<2; j++) ua.user_axes[i][j] = i == j ? 5 : 0;
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ua.twisted = false;
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euc::build_torus3();
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tour::slide_backup(shmup::on, true);
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tour::slide_backup(pconf.scale, 0.5);
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});
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}
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},
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{"Small Relativistic Effects", 10, LEGAL::ANY | QUICKGEO,
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"In our real world, the universe is expanding, and the spaceship would observe relativistic effects if it started to move very fast. "
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"Such effects can be also observed in this slide, although you still need to wait for a long time or move very fast. They will be more pronounced in Relative Hell, and in the later slides.",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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ads_game::run_ds_game_std();
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const ld sca = 100;
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tour::slide_backup(ds_simspeed, M_PI / 10 / sca * 5);
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tour::slide_backup(ds_missile_rapidity, 0.1);
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tour::slide_backup(ds_scale, 1 / sca);
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tour::slide_backup(pconf.scale, sca);
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tour::slide_backup(texture_off, true);
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dynamicval<ld> fs(future_shown, -10);
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ds_restart();
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rockgen.cshift = 0;
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if(1) {
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dynamicval<eGeometry> g(geometry, gSpace435);
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for(int x=-10; x<=10; x++)
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for(int y=-10; y<=10; y++) if(hypot(x+0.5, y) >= 2) {
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rockgen.add(cspin(0, 2, (x + randd() - randd()) / sca) * cspin(1, 2, (y + randd() - randd()) / sca));
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}
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}
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rockgen.cshift = 10;
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});
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if(mode == pmStart) {
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add_ds_cleanup();
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rogueviz::on_cleanup_or_next([] { lps_enable(nullptr); });
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}
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}
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},
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{"Lorentz Contraction", 10, LEGAL::ANY | QUICKGEO,
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"Here we make the relativistic effects easier to observe. According to the principles of special relativity, fast moving objects are contracted. The closer their speed is to "
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"the speed of light, the more contracted they are. This can be "
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"seen when you look at the moving objects here.\n\n"
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"We mean objects moving fast relative to you -- if you accelerate, previously stationary objects will start moving fast relative to you. Your ship is able to accelerate much faster than in "
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"the previous slide.",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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ads_game::run_ds_game_std();
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const ld sca = 100;
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tour::slide_backup(ds_simspeed, M_PI / 10 / sca * 5);
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tour::slide_backup(ds_missile_rapidity, 0.5);
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tour::slide_backup(ds_accel, ds_accel * 10);
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tour::slide_backup(ds_scale, 1 / sca);
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tour::slide_backup(pconf.scale, sca);
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tour::slide_backup(texture_off, true);
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dynamicval<ld> fs(future_shown, -10);
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ds_restart();
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rockgen.cshift = 0;
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if(1) {
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dynamicval<eGeometry> g(geometry, gSpace435);
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for(int x=-10; x<=10; x++)
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for(int y=-10; y<=10; y++) if(hypot(x+0.5, y) >= 2) {
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rockgen.add(cspin(0, 2, (x + randd() - randd()) / sca) * cspin(1, 2, (y + randd() - randd()) / sca));
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}
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for(int x=0; x<=24; x++)
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for(int y=-10; y<=10; y++) if(y) {
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rockgen.cshift = (rand() % 1000) / 100. / sca;
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rockgen.add(cspin(0, 1, x * 15._deg) * cspin(1, 2, y / sca) * lorentz(0, 3, 1 + randd() * 3));
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}
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}
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rockgen.cshift = 10;
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});
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if(mode == pmStart) {
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add_ds_cleanup();
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rogueviz::on_cleanup_or_next([] { lps_enable(nullptr); });
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}
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}
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},
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{"Time Dilation", 10, LEGAL::ANY | QUICKGEO,
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"Another well-known relativistic effect is time dilation. Time passes differently for different objects.\n\n"
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"Try to accelerate, then return to the yellow star. Your clock will be different than the clock of the star.",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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ads_game::run_ds_game_std();
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const ld sca = 100;
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tour::slide_backup(ds_simspeed, M_PI / 10 / sca * 5);
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tour::slide_backup(ds_missile_rapidity, 0.5);
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tour::slide_backup(ds_accel, ds_accel * 10);
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tour::slide_backup(ds_scale, 5 / sca);
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tour::slide_backup(pconf.scale, sca);
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tour::slide_backup(texture_off, true);
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tour::slide_backup(view_proper_times, true);
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dynamicval<ld> fs(future_shown, -10);
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ds_restart();
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rockgen.cshift = 10;
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});
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if(mode == pmStart) {
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add_ds_cleanup();
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rogueviz::on_cleanup_or_next([] { lps_enable(nullptr); });
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}
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}
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},
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{"Spherical geometry", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
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"Relative Hell combines relativity with non-Euclidean geometry. "
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"Here is Space Rocks played in spherical geometry. It uses "
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"stereographic projection so that a big part of the sphere can be seen. (You can press '5' to switch to and from the orthogonal projection.)",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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set_geometry(gSphere);
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set_variation(eVariation::bitruncated);
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tour::slide_backup(land_structure, lsSingle);
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tour::slide_backup(specialland, laAsteroids);
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tour::slide_backup(shmup::on, true);
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tour::slide_backup(pconf.scale, 0.5);
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tour::slide_backup(pconf.alpha, 1);
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tour::slide_backup(vid.monmode, 2);
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});
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if(mode == pmKey) {
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if(pconf.alpha == 1) pconf.alpha = 1000, pconf.scale = 950;
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else pconf.alpha = 1, pconf.scale = 0.5;
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}
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}
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},
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{"Spherical symmetry", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
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"In the previous slide, time was implemented as in most games, and "
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"how Newton imagined it. It is assumed that objects move on geodesics "
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"(great circles) if no force is acting on them.\n\n"
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"Note that, in the world of Newton and Galileo, and also in the world of Einstein's special relativity, the spacetime is perfectly symmetric. "
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"You cannot really tell that you are moving (except by looking at landmarks); you can create a frame of reference and a system of coordinates "
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"in which the ship is not moving and the physics are the same.\n\n"
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"While the spherical space is perfectly symmetric, the spacetime as shown in this slide is not. "
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"The wings of our ship do not move in straight lines (instead they move in smaller circles, which are curved). "
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"If we had unchained items there, they would move towards the center of the ship, allowing the "
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"captain to tell that they are moving.\n\n"
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"Press 5 to see a visualization of how various parts of the ships would move if they actually moved in straight lines."
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,
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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set_geometry(gSphere);
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set_variation(eVariation::bitruncated);
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tour::slide_backup(land_structure, lsSingle);
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tour::slide_backup(specialland, laAsteroids);
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tour::slide_backup(shmup::on, true);
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tour::slide_backup(pconf.scale, 0.5);
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tour::slide_backup(pconf.alpha, 1);
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tour::slide_backup(vid.monmode, 2);
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tour::slide_backup(vid.creature_scale, 3);
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tour::slide_backup(dont_gen_asteroids, true);
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});
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straight_line_viz(mode);
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}
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},
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{"de Sitter spacetime", 10, LEGAL::ANY | QUICKGEO,
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"The de Sitter spacetime is a way to add time to spherical geometry in a symmetric way. "
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"The space here feels to expand exponentially as the time passes, as in, nearby objects get farther and farther away. "
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"Still, the spacetime is symmetric -- if we are using an appropriate frame of reference, the 'totally geodesic' slice of spacetime at t=0 is "
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"always a sphere of the same size.\n\n"
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"If we fly too far away from the yellow star, we can never fly back to it, due to "
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"the expansion. For the same reason, we can also never actually reach the other side of the sphere.",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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ads_game::run_ds_game_std();
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tour::slide_backup(ds_simspeed, M_PI / 10);
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tour::slide_backup(ds_scale, 1);
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tour::slide_backup(pconf.scale, 1);
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dynamicval<ld> fs(future_shown, -10);
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ds_restart();
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rockgen.cshift = 10;
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});
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if(mode == pmStart) {
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add_ds_cleanup();
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rogueviz::on_cleanup_or_next([] { lps_enable(nullptr); });
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}
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}
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},
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{"de Sitter game", 10, LEGAL::ANY | QUICKGEO,
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"The de Sitter part of the Relative Hell game takes part in this spacetime. "
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"Try to stay close to the yellow star as long as possible! If required, you can "
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"shoot down stars with a limited number of missiles. For high score, you will also need to replenish your "
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"resources by capturing free-flying fuel, oxygen, health, and missiles.",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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ads_game::run_ds_game_std();
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});
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if(mode == pmStart) {
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add_ds_cleanup();
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rogueviz::on_cleanup_or_next([] { lps_enable(nullptr); });
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}
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}
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},
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{"Hyperbolic geometry", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
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"Hyperbolic geometry is the opposite of spherical geometry. "
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"Here is Space Rocks played in it. We use the Poincaré model to display the hyperbolic plane; "
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"you can press 5 to switch to the Beltrami-Klein model.\n\n",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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set_geometry(gKleinQuartic);
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set_variation(eVariation::bitruncated);
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tour::slide_backup(land_structure, lsSingle);
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tour::slide_backup(specialland, laAsteroids);
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tour::slide_backup(shmup::on, true);
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tour::slide_backup(pconf.scale, 0.95);
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tour::slide_backup(pconf.alpha, 1);
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tour::slide_backup(vid.monmode, 2);
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});
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if(mode == pmKey) {
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if(pconf.alpha == 1) pconf.alpha = 0;
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else pconf.alpha = 1;
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}
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}
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},
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{"Hyperbolic symmetry", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
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"Of course, just like in spherical space, this is not a symmetric spacetime.\n\n"
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"Press 5 to see a visualization of how various parts of the ships would move if they actually moved in straight lines.",
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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set_geometry(gKleinQuartic);
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set_variation(eVariation::bitruncated);
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tour::slide_backup(land_structure, lsSingle);
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tour::slide_backup(specialland, laAsteroids);
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tour::slide_backup(shmup::on, true);
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tour::slide_backup(pconf.scale, 0.95);
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tour::slide_backup(pconf.alpha, 1);
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tour::slide_backup(vid.monmode, 2);
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tour::slide_backup(dont_gen_asteroids, true);
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tour::slide_backup(vid.linequality, 3);
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});
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straight_line_viz(mode);
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}
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},
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{"anti-de Sitter spacetime", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
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"anti-de Sitter spacetime is a way to add time to this space in a symmetric way.\n\n"
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"Because of how the anti-de Sitter spacetime works, faraway objects are 'pulled' towards us. "
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"You can see this effect by shooting a missile -- it will eventually return to us!\n\n"
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"In the world of Relative Hell, this pull is countered by making the static objects rotate in a specific way -- this creates a centrifugal "
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"force which counterbalances this effect. As you can see, the heptagons further away are "
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"squashed -- this is again the Lorentz contraction\n\n."
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"You can also press key '5' to switch to the Beltrami-Klein projection -- "
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"this counterbalances the squashing, making all the heptagons normal."
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,
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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ads_game::run_ads_game_std();
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/* disable everything */
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tour::slide_backup(pconf.alpha, 1);
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});
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if(mode == pmKey) {
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if(pconf.alpha == 1) pconf.alpha = 0;
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else pconf.alpha = 1;
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}
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}
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},
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{"auto-rotation", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
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"If the constantly spinning screen makes you feel dizzy, we can "
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"also automatically counter-rotate it. This makes the geometry harder to "
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"understand, but is also cool.\n\n."
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"You can also press key '5' to see how the spacetime behaves with auto-rotation on and off."
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,
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[] (presmode mode) {
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setCanvas(mode, &ccolor::plain, [] {
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ads_game::run_ads_game_std();
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/* disable everything */
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tour::slide_backup(pconf.alpha, 0);
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tour::slide_backup(auto_rotate, true);
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});
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if(mode == pmKey) {
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auto_rotate = !auto_rotate;
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}
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}
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},
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{"what you would see", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
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"One aspect we have not discussed so far: the game computed the "
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"coordinates of all objects in the ship's frame of reference "
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"(which puts the ship at the center and the current time at t=0), "
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"and displayed the slice t=0 of that spacetime.\n\n"
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"Due to the limited speed of light, this is not what the ship would "
|
||||
"actually see.\n\n"
|
||||
"In this slide, you can see the 'visible state' -- everything is seen at "
|
||||
"the moment that the ship would actually see.\n\n"
|
||||
|
||||
"You can press key '5' to see how the spacetime behaves with the 'visible state' and default.\n\n"
|
||||
"During the game, see the 'view mode' menu to change many options discussed in this tour, as well as some extra visualizations."
|
||||
,
|
||||
|
||||
[] (presmode mode) {
|
||||
setCanvas(mode, &ccolor::plain, [] {
|
||||
ads_game::run_ads_game_std();
|
||||
/* disable everything */
|
||||
tour::slide_backup(pconf.alpha, 0);
|
||||
tour::slide_backup(auto_rotate, false);
|
||||
tour::slide_backup(which_cross, -1);
|
||||
});
|
||||
if(mode == pmKey) {
|
||||
if(which_cross == -1) which_cross = 0;
|
||||
else which_cross = -1;
|
||||
}
|
||||
}
|
||||
},
|
||||
|
||||
{"turrets", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
|
||||
"Let us place some turrets in our anti-de Sitter world.\n\n"
|
||||
|
||||
"These turrets are as accurate as they could possibly be -- they see our ship, and compute the shooting angle so that the ship would be hit "
|
||||
"if it did not accelerate in the meantime. If you do not accelerate for some time, you should see that they indeed hit you.\n\n"
|
||||
|
||||
"As you can imagine from the previous parts, their information is rather outdated...\n\n"
|
||||
|
||||
"The world here is still displayed in the 'slice t=0' mode, rather than 'visible state'. The turrets are totally deterministic so let us assume the "
|
||||
"ship's AI helps us by computing the current state based on the visible past. The enemy bullets move at speed close to the speed of light, so it "
|
||||
"would hard to see them otherwise.\n\n"
|
||||
|
||||
"You may notice the \"wobbling\" of turrets, this is caused by the Lorentz transformations as the spaceship accelerates.",
|
||||
|
||||
[] (presmode mode) {
|
||||
setCanvas(mode, &ccolor::plain, [] {
|
||||
ads_game::run_ads_game_std();
|
||||
tour::slide_backup(pconf.alpha, 1);
|
||||
});
|
||||
}
|
||||
},
|
||||
|
||||
{"anti-de Sitter game", 10, LEGAL::ANY | QUICKGEO | NOTITLE,
|
||||
"So this is our anti-de Sitter game.\n\n"
|
||||
|
||||
"Shoot down the rocks to get gold and replenish resources. "
|
||||
"Similar to HyperRogue, collecting gold will allow you to find other parts of the spacetime, "
|
||||
"where you can find other treasures and challenges. Have fun!",
|
||||
|
||||
[] (presmode mode) {
|
||||
setCanvas(mode, &ccolor::plain, [] {
|
||||
ads_game::run_ads_game_std();
|
||||
});
|
||||
}
|
||||
},
|
||||
|
||||
{"MATH PART!", 123, LEGAL::ANY | NOTITLE, "",
|
||||
|
||||
[] (presmode mode) {
|
||||
empty_screen(mode);
|
||||
white_screen(mode);
|
||||
add_stat(mode, [] {
|
||||
dialog::init();
|
||||
dialog::addTitle("MATH PART!", 0x0, 200);
|
||||
dialog::addBreak(100);
|
||||
dialog::addHelp(
|
||||
"The rest of this guided tour is a lecture on mathematics of the things we have seen so far. "
|
||||
"If you just wanted an intuitive explanation of what is going on, read no further. "
|
||||
"But if math is fun for you, please go on!");
|
||||
dialog::display();
|
||||
return true;
|
||||
});
|
||||
}
|
||||
},
|
||||
|
||||
{"Euclidean geometry", 999, LEGAL::NONE | QUICKGEO | USE_SLIDE_NAME | NOTITLE,
|
||||
"explanation",
|
||||
[] (presmode mode) {
|
||||
setCanvas(mode, &ccolor::chessboard, [] { set_geometry(gEuclidSquare); set_variation(eVariation::pure); });
|
||||
latex_slide(mode, defs+R"=(
|
||||
{\color{remph}3-dimensional Euclidean space:}
|
||||
\begin{itemize}
|
||||
\item $\bbE^3 = \{(x,y,z): x,y,z \in \bbR\}$
|
||||
\item squared distance between \\ points $(x_1,y_1,z_1)$ and $(x_2, y_2, z_2)$ is \[(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2\]
|
||||
\item {\color{remph} isometries} (rotations, etc.) preserve this squared distance
|
||||
\end{itemize}
|
||||
)=", sm::SIDE, 90);
|
||||
if(mode == pmStart) {
|
||||
tour::slide_backup(mapeditor::drawplayer, false);
|
||||
tour::slide_backup(vid.axes, 0);
|
||||
rogueviz::rv_hook(hooks_latex_slide, 100, [] { dialog::dwidth += 500; menu_darkening++; dialog::draw_side_shade(); dialog::dwidth -= 500; menu_darkening --; });
|
||||
}
|
||||
}},
|
||||
|
||||
{"Minkowski geometry", 999, LEGAL::NONE | QUICKGEO | USE_SLIDE_NAME | NOTITLE,
|
||||
"explanation",
|
||||
[] (presmode mode) {
|
||||
latex_slide(mode, defs+R"=(
|
||||
{\color{remph}Minkowski spacetime with 2 space and 1 time dimension:}
|
||||
\begin{itemize}
|
||||
\item $\bbE^{2,1} = \{(x,y,t): x,y,t \in \bbR\}$
|
||||
\item spacetime interval between \\ points $(x_1,y_1,t_1)$ and $(x_2, y_2, t_2)$ is \[(x_1-x_2)^2+(y_1-y_2)^2-(t_1-t_2)^2\]
|
||||
\item {\color{remph} Lorentz transformations} preserve this
|
||||
\end{itemize}
|
||||
)=", sm::SIDE, 90);
|
||||
setCanvas(mode, &ccolor::chessboard, [] { set_geometry(gEuclidSquare); set_variation(eVariation::pure); tour::slide_backup(vid.axes, 0); });
|
||||
static int start = -1;
|
||||
if(mode == pmKey) start = (start == -1) ? ticks : -1;
|
||||
if(mode == pmStart) {
|
||||
tour::slide_backup(anims::ma, anims::maTranslation);
|
||||
tour::slide_backup(pconf.stretch, 1);
|
||||
tour::slide_backup(anims::movement_angle.get(), spin(-90._deg));
|
||||
tour::slide_backup(anims::cycle_length, 0);
|
||||
tour::slide_backup(mapeditor::drawplayer, false);
|
||||
tour::slide_backup(vid.axes, 0);
|
||||
tour::slide_backup(vid.use_smart_range, 2);
|
||||
tour::slide_backup(vid.smart_range_detail, 1);
|
||||
rogueviz::rv_hook(hooks_frame, 101, [] {
|
||||
if(start == -1) { anims::cycle_length = 0; pconf.stretch = 1; return; }
|
||||
ld t = asinh((ticks - start) / 5000.);
|
||||
anims::cycle_length = sinh(t) * 10;
|
||||
pconf.stretch = sqrt(1 - tanh(t) * tanh(t));
|
||||
println(hlog, "t=", t, "sinh = ", anims::cycle_length, " stretch = ", pconf.stretch);
|
||||
});
|
||||
rogueviz::rv_hook(hooks_latex_slide, 100, [] {
|
||||
initquickqueue();
|
||||
dynamicval<ld> s(pconf.stretch, 1);
|
||||
drawMonsterType(moRunDog, nullptr, shiftless(spin(90._deg)), 0xFFFFFFFF, start >= 0 ? (ticks-start) / 500. : 0, 0xFFFFFFFF);
|
||||
sortquickqueue();
|
||||
quickqueue();
|
||||
dialog::dwidth += 500; menu_darkening++; dialog::draw_side_shade(); dialog::dwidth -= 500; menu_darkening --;
|
||||
});
|
||||
}
|
||||
}},
|
||||
|
||||
{"spherical geometry", 999, LEGAL::NONE | QUICKGEO | USE_SLIDE_NAME | NOTITLE,
|
||||
"explanation",
|
||||
[] (presmode mode) {
|
||||
setCanvas(mode, &ccolor::football, [] { set_geometry(gSphere); });
|
||||
if(mode == pmStart) {
|
||||
tour::slide_backup(pconf.scale, 500);
|
||||
tour::slide_backup(pconf.alpha, 1000);
|
||||
tour::slide_backup(mapeditor::drawplayer, false);
|
||||
tour::slide_backup(vid.axes, 0);
|
||||
}
|
||||
latex_slide(mode, defs+R"=(
|
||||
{\color{remph}2-dimensional sphere:}
|
||||
\begin{itemize}
|
||||
\item $\bbS^2 = \{(x,y,z) \in \bbE^3: x^2+y^2+z^2=1\}$
|
||||
\item distances measured as \\ the lengths of curves in Euclidean space
|
||||
\item {\color{remph} isometries} (rotations, etc.) keep this distance
|
||||
\end{itemize}
|
||||
)=", sm::SIDE, 90);
|
||||
}},
|
||||
|
||||
{"hyperbolic geometry", 999, LEGAL::NONE | QUICKGEO | USE_SLIDE_NAME | NOTITLE,
|
||||
"explanation",
|
||||
[] (presmode mode) {
|
||||
latex_slide(mode, defs+R"=(
|
||||
{\color{remph}2-dimensional hyperbolic space (Minkowski hyperboloid model):}
|
||||
\begin{itemize}
|
||||
\item $\bbH^2 = \{(x,y,t) \in \bbE^{2,1}: x^2+y^2-t^2=-1, t>0\}$
|
||||
\item distances measured as \\ the lengths of curves in $\bbE^{2,1}$
|
||||
\item {\color{remph} isometries} (rotations, etc.) keep this distance
|
||||
\item we get the Poincaré model by projecting \\ $(x,y,t) \mapsto (\frac{x}{t+1}, \frac{y}{t+1})$
|
||||
\end{itemize}
|
||||
)=", sm::SIDE, 90);
|
||||
setCanvas(mode, &ccolor::football, [] {
|
||||
tour::slide_backup(pconf.model, mdHyperboloid);
|
||||
tour::slide_backup(pconf.scale, pconf.scale * 0.5);
|
||||
tour::slide_backup(pconf.ball(), cspin(1, 2, -20._deg));
|
||||
tour::slide_backup(mapeditor::drawplayer, false);
|
||||
tour::slide_backup(vid.axes, 0);
|
||||
rogueviz::rv_hook(hooks_latex_slide, 100, [] { dialog::dwidth += 500; menu_darkening++; dialog::draw_side_shade(); dialog::dwidth -= 500; menu_darkening --; });
|
||||
});
|
||||
}},
|
||||
|
||||
{"anti-de Sitter spacetime", 999, LEGAL::NONE | QUICKGEO | USE_SLIDE_NAME | NOTITLE,
|
||||
"explanation",
|
||||
[] (presmode mode) {
|
||||
latex_slide(mode, defs+R"=(
|
||||
{\color{remph}anti-de Sitter spacetime:}
|
||||
\begin{itemize}
|
||||
\item $\wadS{2} = \{(x,y,t,u) \in \bbE^{2,2}: \\ x^2+y^2-t^2-u^2=-1\}$
|
||||
\item take $u=0, t>0$ -- we get $\bbH^2$
|
||||
\item rotation in the $(t,u)$ plane \\ corresponds to the pass of time
|
||||
\item $\uadS{2}$ -- the {\color{remph}universal cover}: \\
|
||||
not a time loop of length $2\pi$, \\ but we ``unwrap'' it
|
||||
\end{itemize}
|
||||
)=", sm::SIDE | sm::NOSCR, 90);
|
||||
// if(mode == pmStart) slide_backup(nomap, true);
|
||||
static int phase = 0;
|
||||
static ld ctick;
|
||||
if(mode == pmStart) phase = 0;
|
||||
if(mode == pmKey) { phase = (1 + phase) % 3; ctick = ticks; }
|
||||
if(mode == pmStart) rogueviz::rv_hook(hooks_latex_slide, 100, [] {
|
||||
dynamicval<eGeometry> g(geometry, gCubeTiling);
|
||||
initquickqueue();
|
||||
dynamicval<ld> dw(vid.linewidth, 4);
|
||||
dynamicval<eModel> dm(pmodel, mdDisk);
|
||||
dynamicval<ld> dcmin(pconf.clip_min, -1000);
|
||||
dynamicval<ld> dcmax(pconf.clip_max, +100);
|
||||
transmatrix Rot = Id * cspin(0, 2, 5._deg) * cspin(1, 2, -15._deg);
|
||||
curvepoint(hyperpoint(2,0,0,1)); curvepoint(hyperpoint(-2,0,0,1)); queuecurve(shiftless(Rot), 0xFF, 0, PPR::LINE);
|
||||
curvepoint(hyperpoint(0,2,0,1)); curvepoint(hyperpoint(0,-2,0,1)); queuecurve(shiftless(Rot), 0xFF, 0, PPR::LINE);
|
||||
curvepoint(hyperpoint(0,0,2,1)); curvepoint(hyperpoint(0,0,-2,1)); queuecurve(shiftless(Rot), 0xFF, 0, PPR::LINE);
|
||||
// queuestr(shiftless(Rot * eupush(hyperpoint(1.75, 0.1, 0, 1))), 0.5, "t", 0);
|
||||
latex_in_space(shiftless(Rot * eupush(hyperpoint(1.75, 0.1, 0, 1))), 0.001, "$t$", 0xFF, 0);
|
||||
latex_in_space(shiftless(Rot * eupush(hyperpoint(0.15, 1.75, 0, 1))), 0.001, "$xy$", 0xFF, 0);
|
||||
latex_in_space(shiftless(Rot * eupush(hyperpoint(-0.1, 0, -1.75, 1))), 0.001, "$u$", 0xFF, 0);
|
||||
for(int y=0; y<=360; y+=15) {
|
||||
if(phase == 0 && y) continue;
|
||||
if(phase == 1 && y > (ticks - ctick) / 10.) continue;
|
||||
ld helix = min<ld>((ticks-ctick)/1000., 1); println(hlog, "helix = ", helix); helix = helix * helix * (3 - 2 * helix);
|
||||
for(int z=0; z<=360; z+=5) curvepoint(hyperpoint(1 + 0.5 * sin(z*1._deg), (phase == 2 ? -y/240. * helix :0 ) + 0.5 * cos(z*1._deg), 0, 1));
|
||||
queuecurve(shiftless(Rot * cspin(0, 2, y*1._deg)), 0xFF, 0xFFD500FF, PPR::LINE);
|
||||
}
|
||||
quickqueue();
|
||||
});
|
||||
}},
|
||||
|
||||
{"de Sitter spacetime", 999, LEGAL::NONE | QUICKGEO | USE_SLIDE_NAME | NOTITLE,
|
||||
"explanation",
|
||||
[] (presmode mode) {
|
||||
latex_slide(mode, defs+R"=(
|
||||
{\color{remph}de Sitter spacetime:}
|
||||
\begin{itemize}
|
||||
\item $\dS{2} = \{(x,y,z,t) \in \bbE^{3,1}: \\ x^2+y^2+z^2-t^2=-1\}$
|
||||
\item take $t=0$ -- we get $\bbS^2$
|
||||
\item the universe is expanding with $t$ \\ (not if we apply Lorentz transformation)
|
||||
\end{itemize}
|
||||
)=", sm::NOSCR | sm::SIDE, 90);
|
||||
static int phase = 0;
|
||||
static ld ctick;
|
||||
if(mode == pmStart) phase = 0;
|
||||
if(mode == pmKey) { phase = (1 + phase) % 3; ctick = ticks; }
|
||||
if(mode == pmStart) rogueviz::rv_hook(hooks_latex_slide, 100, [] {
|
||||
dynamicval<eGeometry> g(geometry, gCubeTiling);
|
||||
initquickqueue();
|
||||
dynamicval<ld> dw(vid.linewidth, 4);
|
||||
dynamicval<eModel> dm(pmodel, mdDisk);
|
||||
dynamicval<ld> dcmin(pconf.clip_min, -1000);
|
||||
dynamicval<ld> dcmax(pconf.clip_max, +100);
|
||||
transmatrix Rot = Id * cspin(1, 2, -120._deg) * cspin(0, 1, 30._deg);
|
||||
curvepoint(hyperpoint(2,0,0,1)); curvepoint(hyperpoint(-2,0,0,1)); queuecurve(shiftless(Rot), 0xFF, 0, PPR::LINE);
|
||||
curvepoint(hyperpoint(0,2,0,1)); curvepoint(hyperpoint(0,-2,0,1)); queuecurve(shiftless(Rot), 0xFF, 0, PPR::LINE);
|
||||
curvepoint(hyperpoint(0,0,2,1)); curvepoint(hyperpoint(0,0,-2,1)); queuecurve(shiftless(Rot), 0xFF, 0, PPR::LINE);
|
||||
// queuestr(shiftless(Rot * eupush(hyperpoint(1.75, 0.1, 0, 1))), 0.5, "t", 0);
|
||||
latex_in_space(shiftless(Rot * eupush(hyperpoint(1.75, 0.1, 0, 1)) * inverse(Rot)), 0.001, "$x$", 0xFF, 0);
|
||||
latex_in_space(shiftless(Rot * eupush(hyperpoint(0.15, -1.75, 0, 1)) * inverse(Rot)), 0.001, "$y,z$", 0xFF, 0);
|
||||
latex_in_space(shiftless(Rot * eupush(hyperpoint(-0.1, 0, -1.75, 1)) * inverse(Rot)), 0.001, "$t$", 0xFF, 0);
|
||||
for(int y=0; y<=6; y+=1) {
|
||||
ld ay = y / 3.;
|
||||
if(phase == 0 && y) continue;
|
||||
if(phase == 1 && y > (ticks - ctick) / 250.) continue;
|
||||
for(int z=0; z<=360; z+=5) curvepoint(hyperpoint(cos(z*1._deg) * cosh(ay), sin(z*1._deg) * cosh(ay), sinh(ay), 1));
|
||||
queuecurve(shiftless(Rot), 0xFF, 0xFFD500FF, PPR::LINE);
|
||||
}
|
||||
quickqueue();
|
||||
if(phase > 0) {
|
||||
glClear(GL_DEPTH_BUFFER_BIT);
|
||||
initquickqueue();
|
||||
for(int s=-5; s<=5; s++) {
|
||||
for(ld y=0; y<=2; y+=0.01) curvepoint(hyperpoint(sin(s*18._deg)*cosh(y), -cos(s*18._deg)*cosh(y), sinh(y), 1));
|
||||
queuecurve(shiftless(Rot), 0xFF8080FF, 0, PPR::LINE);
|
||||
}
|
||||
quickqueue();
|
||||
}
|
||||
if(phase == 2) {
|
||||
glClear(GL_DEPTH_BUFFER_BIT);
|
||||
initquickqueue();
|
||||
for(int y=0; y<=6; y+=1) {
|
||||
ld ay = y / 3.;
|
||||
if(phase == 2 && y > (ticks - ctick) / 250.) continue;
|
||||
for(int z=0; z<=360; z+=5) curvepoint(hyperpoint(cos(z*1._deg) * cosh(ay), sin(z*1._deg) * cosh(ay), cos(z*1._deg)*sinh(ay), 1));
|
||||
}
|
||||
queuecurve(shiftless(Rot), 0x80FF80FF, 0, PPR::LINE);
|
||||
quickqueue();
|
||||
}
|
||||
});
|
||||
}},
|
||||
|
||||
{"THE END", 123, LEGAL::ANY | QUICKSKIP | NOTITLE | FINALSLIDE, "",
|
||||
|
||||
[] (presmode mode) {
|
||||
empty_screen(mode);
|
||||
white_screen(mode);
|
||||
add_stat(mode, [] {
|
||||
dialog::init();
|
||||
dialog::addTitle("THE END", 0x0, 200);
|
||||
dialog::addBreak(100);
|
||||
dialog::addInfo("That is all in the tour. Please play the game now!");
|
||||
dialog::display();
|
||||
return true;
|
||||
});
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
int pohooks =
|
||||
0 +
|
||||
addHook_slideshows(100, [] (tour::ss::slideshow_callback cb) {
|
||||
cb(XLAT("Relative Hell guided tour"), &relhell_tour[0], 'S');
|
||||
});
|
||||
|
||||
|
||||
}
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user