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ads:: future in AdS shown correctly (using light-like geodesics); show future for dS

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This commit is contained in:
Zeno Rogue 2022-09-25 22:20:18 +02:00
parent c49b320330
commit 4af232e9c1
3 changed files with 55 additions and 14 deletions
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31
rogueviz/ads/display.cpp
View File

@ -163,21 +163,24 @@ void draw_game_cell(const cell_to_draw& cd) {
}
if(paused && c == vctr_ship && !game_over) {
vector<hyperpoint> pts;
vector<ld> times;
int ok = 0, bad = 0;
for(int i=0; i<=360; i++) {
hybrid::in_actual([&]{
auto h = ads_inverse(current_ship * vctrV_ship) * spin(i*degree) * lorentz(0, 2, 6);
auto cr = cross0(current * V * h);
pts.push_back(cr.h);
times.push_back(cr.shift);
if(cr.shift > 0 && cr.shift < 90*degree) ok++; else bad++;
});
}
if(bad == 0) {
cross_result cr;
hybrid::in_actual([&]{
auto h = ads_inverse(current_ship * vctrV_ship);
cr = cross0(current * V * h);
// println(hlog, current * V * h);
println(hlog, "cr shift = ", cr.shift);
});
if(cr.shift > 0 && cr.shift < M_PI) {
vector<hyperpoint> pts;
for(int i=0; i<=360; i++) {
hybrid::in_actual([&]{
auto h = ads_inverse(current_ship * vctrV_ship) * spin(i*degree);
auto cr = cross0_light(current * V * h);
pts.push_back(cr.h);
});
}
for(auto h: pts) curvepoint(h);
queuecurve(shiftless(Id), 0x000000C0, 0x00000060, PPR::SUPERLINE);
queuecurve(shiftless(Id), 0xFF0000C0, 0x00000060, PPR::SUPERLINE);
}
}
}

25
rogueviz/ads/ds-game.cpp
View File

@ -190,6 +190,15 @@ cross_result ds_cross0(transmatrix T) {
return res;
}
cross_result ds_cross0_light(transmatrix T) {
// h = T * (t 0 1 t); h[3] == 0
ld t = T[3][2] / -(T[3][0] + T[3][3]);
cross_result res;
res.shift = t;
res.h = T * hyperpoint(t, 0, 1, t);
return res;
}
transmatrix tpt(ld x, ld y) {
return cspin(0, 2, x * scale) * cspin(1, 2, y * scale);
}
@ -292,6 +301,22 @@ void view_ds_game() {
string str = format(tformat, view_pt / time_unit);
queuestr(shiftless(Id), .1, str, 0xFFFF00, 8);
}
if(paused && !game_over) {
vector<hyperpoint> pts;
int ok = 0, bad = 0;
for(int i=0; i<=360; i++) {
dynamicval<eGeometry> g(geometry, gSpace435);
auto h = inverse(dscurrent_ship) * spin(i*degree);
auto cr = ds_cross0_light(dscurrent * h);
pts.push_back(cr.h);
if(cr.shift > 0) ok++; else bad++;
}
if(bad == 0) {
for(auto h: pts) curvepoint(h);
queuecurve(shiftless(Id), 0xFF0000C0, 0x00000060, PPR::SUPERLINE);
}
}
}
}

13
rogueviz/ads/math.cpp
View File

@ -145,6 +145,19 @@ cross_result cross0(ads_matrix hz) {
return cross_result{uhzt, t};
}
/** Similar as cross0_light but for light-like wordlines.
* The point returned by cross0_light(T) is the same as the limit of cross0(T * lorentz(0, 2, v)).
**/
cross_result cross0_light(ads_matrix hz) {
transmatrix uhz = unshift(hz);
ld t = uhz[2][3] / -(uhz[2][2] + uhz[2][0]);
hyperpoint uhzt = uhz * hyperpoint(t, 0, t, 1);
tie(uhzt[2], uhzt[3]) = make_pair(uhzt[3], -uhzt[2]);
if(uhzt[2] < 0) uhzt = -uhzt;
return cross_result{uhzt, t};
}
/** sample from Poisson distribution */
int rpoisson(ld lambda) {
ld prob = randd();