mirror of
https://github.com/zenorogue/hyperrogue.git
synced 2024-11-24 05:17:17 +00:00
303 lines
8.3 KiB
C++
303 lines
8.3 KiB
C++
#include "../hyper.h"
|
|
|
|
// Twisted S2xE.
|
|
|
|
// We use a model with coordinates (r,phi,z), where (r,phi) are the polar coordinates in S2.
|
|
|
|
// Metric: ds^2 = (dr)^2 + (sin r * dphi)^2 + (dz + K * (1-cos(r)) dphi)^2
|
|
|
|
// See https://youtu.be/lZCkEuud6aU and https://youtu.be/rfu6m_xGxWY
|
|
|
|
|
|
namespace hr {
|
|
|
|
EX namespace ts2 {
|
|
|
|
eGeometry ts2 = eGeometry(-1);
|
|
|
|
EX bool in() { return geometry == gTS; }
|
|
|
|
EX ld K = -.9;
|
|
|
|
EX hyperpoint at = point3(.5, 0, 0);
|
|
EX transmatrix camera;
|
|
|
|
void init() {
|
|
ld r = .5;
|
|
at = point3(r, 0, 0);
|
|
camera = build_matrix(
|
|
point3(1, 0, 0),
|
|
point3(0, 1/sin(r), K/sin(r)*(cos(r)-1)),
|
|
point3(0, 0, 1),
|
|
point31(0,0,0)
|
|
);
|
|
camera = camera * cspin(1, 2, 90*degree);
|
|
}
|
|
|
|
// a dummy map that does nothing
|
|
struct hrmap_ts2 : hrmap {
|
|
heptagon *origin;
|
|
heptagon *getOrigin() override { return origin; }
|
|
|
|
struct transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
|
|
return Id;
|
|
}
|
|
|
|
hrmap_ts2() {
|
|
init();
|
|
heptagon*& h =origin;
|
|
h = tailored_alloc<heptagon> (S7);
|
|
h->c7 = newCell(S7, h);
|
|
h->distance = 0;
|
|
h->dm4 = 0;
|
|
h->fieldval = 0;
|
|
h->cdata = NULL;
|
|
h->alt = NULL;
|
|
}
|
|
|
|
heptagon *create_step(heptagon *parent, int d) override {
|
|
parent->c.connect(d, parent, d, false);
|
|
return parent;
|
|
}
|
|
|
|
void draw() override {
|
|
println(hlog, "at = ", at);
|
|
for(int i=0; i<3; i++)
|
|
println(hlog, i, ": ", camera * point3(i==0, i==1, i==2));
|
|
}
|
|
};
|
|
|
|
EX hrmap* new_map() { return new hrmap_ts2; };
|
|
|
|
EX hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
|
|
const ld r = at[0];
|
|
|
|
hyperpoint c = point3(0,0,0);
|
|
// const ld r2 = r * r;
|
|
const ld K2 = K * K;
|
|
const ld sr = sin(r);
|
|
// const ld sr2 = sr * sr;
|
|
|
|
const ld cr = cos(r) - 1;
|
|
const ld cr2 = cr * cr;
|
|
|
|
c[ 0 ] = 0
|
|
+ velocity[ 1 ] * transported[ 1 ] * (-K2*(cr) + cos(r))*sr
|
|
+ velocity[ 1 ] * transported[ 2 ] * K*sr/2
|
|
+ velocity[ 2 ] * transported[ 1 ] * K*sr/2;
|
|
c[ 1 ] = 0
|
|
+ velocity[ 0 ] * transported[ 1 ] * (K2*cos(r) - K2 - 2*cos(r))/(2*sr)
|
|
+ velocity[ 0 ] * transported[ 2 ] * -K/(2*sr)
|
|
+ velocity[ 1 ] * transported[ 0 ] * (K2*cos(r) - K2 - 2*cos(r))/(2*sr)
|
|
+ velocity[ 2 ] * transported[ 0 ] * -K/(2*sr);
|
|
c[ 2 ] = 0
|
|
+ velocity[ 0 ] * transported[ 1 ] * K*(K2 - 1)*cr2/(2*sr)
|
|
+ velocity[ 0 ] * transported[ 2 ] * K2*(1 - cos(r))/(2*sr)
|
|
+ velocity[ 1 ] * transported[ 0 ] * K*(K2 - 1)*cr2/(2*sr)
|
|
+ velocity[ 2 ] * transported[ 0 ] * K2*(1 - cos(r))/(2*sr);
|
|
|
|
return c;
|
|
}
|
|
|
|
void geodesic_step(hyperpoint& at, hyperpoint& velocity) {
|
|
auto acc = ts2::christoffel(at, velocity, velocity);
|
|
|
|
auto at2 = at + velocity / 2;
|
|
auto velocity2 = velocity + acc / 2;
|
|
|
|
auto acc2 = ts2::christoffel(at2, velocity2, velocity2);
|
|
|
|
at = at + velocity + acc2 / 2;
|
|
|
|
velocity = velocity + acc;
|
|
}
|
|
|
|
EX bool shift_view(hyperpoint dist) {
|
|
|
|
if(!in()) return false;
|
|
|
|
auto tPos = transpose(camera);
|
|
hyperpoint h = camera * dist;
|
|
|
|
int steps = 100;
|
|
h /= steps;
|
|
|
|
for(int i=0; i<steps; i++) {
|
|
for(int j=0; j<3; j++)
|
|
tPos[j] += christoffel(at, h, tPos[j]);
|
|
geodesic_step(at, h);
|
|
}
|
|
|
|
camera = transpose(tPos);
|
|
return true;
|
|
}
|
|
|
|
EX bool rotate_view(transmatrix T) {
|
|
if(!in()) return false;
|
|
camera = camera * inverse(T);
|
|
return true;
|
|
}
|
|
|
|
EX void radar() {
|
|
hyperpoint a = at;
|
|
hyperpoint v = camera * point3(0,0,1) / 100.;
|
|
|
|
int it;
|
|
for(it=0; it<1000; it++) {
|
|
geodesic_step(a, v);
|
|
// if(a[0] < .1) break;
|
|
|
|
if(a[0] > .5 && a[0] < .6 && cos(a[1]) > .9 && cos(a[2]) > .9) break;
|
|
}
|
|
|
|
println(hlog, "radar = ", it);
|
|
}
|
|
|
|
void twist() {
|
|
|
|
for(K = -2; K<=2; K += .1)
|
|
for(ld start: {0.5f, 1.f}) {
|
|
hyperpoint at = point3(start, 0, 0);
|
|
hyperpoint vel = point3(0, 1e-5, 0);
|
|
|
|
// println(hlog, "simulating");
|
|
|
|
hyperpoint at1 = at, at2 = at;
|
|
|
|
int it = 0;
|
|
for(; ; it++) {
|
|
at2 = at1; at1 = at;
|
|
// if(it % 1000 == 0) println(hlog, format("%6d. ", it), at, " vel = ", vel);
|
|
geodesic_step(at, vel);
|
|
|
|
if(at2[0] > at1[0] && at1[0] < at[0]) break;
|
|
}
|
|
|
|
println(hlog, format("%8d. ", it), lalign(40, kz(at)), " vel = ", lalign(40, kz(vel)), " K = ", K);
|
|
}
|
|
}
|
|
|
|
int readArgs() {
|
|
using namespace arg;
|
|
|
|
if(0) ;
|
|
else if(argis("-ts2")) {
|
|
if(ts2 == (eGeometry)(-1)) {
|
|
ts2 = (eGeometry) isize(ginf);
|
|
ginf.push_back(geometryinfo{
|
|
"TS", "none", "TS", "ts", 1, 1, qEXPERIMENTAL | qRAYONLY, giSphere3, 0x31400, {{7, 2}}, eVariation::pure
|
|
});
|
|
}
|
|
set_geometry(ts2);
|
|
}
|
|
else if(argis("-twist")) {
|
|
twist();
|
|
exit(1);
|
|
}
|
|
else return 1;
|
|
return 0;
|
|
}
|
|
|
|
auto fundamentalhook = addHook(hooks_args, 100, readArgs);
|
|
|
|
EX string fragmentshader() {
|
|
return
|
|
"varying mediump vec4 at;\n"
|
|
"uniform mediump vec4 uStart;\n"
|
|
"uniform mediump mat4 uLP;\n"
|
|
|
|
"const float K = float(" + fts(ts2::K) + ");\n"
|
|
"const float maxdist = 20.;\n"
|
|
|
|
"vec4 christoffel(vec4 at, vec4 vel) {\n"
|
|
"float r = at.x;\n"
|
|
|
|
"float K2 = K * K;\n"
|
|
"float sr = sin(r);\n"
|
|
"float cr = cos(r) - 1.;\n"
|
|
"float cr2 = cr * cr;\n"
|
|
|
|
"vec4 c;\n"
|
|
|
|
"c[ 0 ] = 0.\n"
|
|
"+ vel.y * vel.y * (-K2*(cr) + cos(r))*sr\n"
|
|
"+ vel.y * vel.z * K*sr/2.\n"
|
|
"+ vel.z * vel.y * K*sr/2.;\n"
|
|
"c[ 1 ] = 0."
|
|
"+ vel.x * vel.y * (K2*cos(r) - K2 - 2.*cos(r))/(2.*sr)\n"
|
|
"+ vel.x * vel.z * -K/(2.*sr)\n"
|
|
"+ vel.y * vel.x * (K2*cos(r) - K2 - 2.*cos(r))/(2.*sr)\n"
|
|
"+ vel.z * vel.x * -K/(2.*sr);\n"
|
|
"c[ 2 ] = 0."
|
|
"+ vel.x * vel.y * K*(K2 - 1.)*cr2/(2.*sr)\n"
|
|
"+ vel.x * vel.z * K2*(1. - cos(r))/(2.*sr)\n"
|
|
"+ vel.y * vel.x * K*(K2 - 1.)*cr2/(2.*sr)\n"
|
|
"+ vel.z * vel.x * K2*(1. - cos(r))/(2.*sr);\n"
|
|
|
|
"return c;}\n"
|
|
|
|
"void main() {\n"
|
|
|
|
" mediump vec4 at0 = at;\n"
|
|
" at0.y = -at.y;\n"
|
|
" at0.xyz = at0.xyz / length(at0.xyz);\n"
|
|
|
|
" mediump vec4 position = uStart;\n"
|
|
" mediump vec4 tangent = uLP * at0;\n"
|
|
|
|
" tangent = tangent;\n"
|
|
" float dist = 0.;\n"
|
|
" int iter = 0;"
|
|
|
|
" while(dist < maxdist && iter < 10000) {"
|
|
|
|
// we make smaller steps if we are close to the singularities at the poles
|
|
|
|
" float step = sin(position.x) * .05;"
|
|
" dist = dist + step;\n"
|
|
" iter++;\n"
|
|
" tangent = tangent * step;\n"
|
|
|
|
" vec4 acc = christoffel(position, tangent);"
|
|
" vec4 at2 = position + tangent / 2.;"
|
|
" vec4 tangent2 = tangent + acc / 2.;"
|
|
" vec4 acc2 = christoffel(at2, tangent2);"
|
|
" position = position + tangent + acc2 / 2.;"
|
|
" tangent = tangent + acc;\n"
|
|
" tangent = tangent / step;\n"
|
|
" if(position.x > .5 && position.x < .6 && cos(position.y) > .9 && cos(position.z/2./K) > .9) {\n"
|
|
" float bri = float(1. - dist / maxdist);\n"
|
|
" int e = 0;\n"
|
|
" if(position.x < .51 || position.x > .59) e++;\n"
|
|
" if(cos(position.y) < .91) e++;\n"
|
|
" if(cos(position.z/2./K) < .91) e++;\n"
|
|
" if(e >= 2) bri /= 2.;\n"
|
|
" gl_FragColor = vec4(bri, bri, bri, 1.);\n"
|
|
" return;"
|
|
" }"
|
|
" }\n"
|
|
|
|
" gl_FragColor = vec4(0.,0.,0.,1.);\n"
|
|
|
|
" }";
|
|
}
|
|
|
|
int ah2 = addHook(ray::hooks_rayshader, 100, [] (string &vsh, string &fsh) { fsh = ts2::fragmentshader(); })
|
|
+ addHook(ray::hooks_rayset, 100, [] (shared_ptr<ray::raycaster> o) {
|
|
if(!in()) return false;
|
|
glUniformMatrix4fv(o->uLP, 1, 0, glhr::tmtogl_transpose3(ts2::camera).as_array());
|
|
auto pg = glhr::pointtogl(ts2::at);
|
|
glUniform4f(o->uStart, pg[0], pg[1], pg[2], pg[3]);
|
|
return true;
|
|
})
|
|
+ addHook(hooks_newmap, 100, [] () { if(in()) return ts2::new_map(); return (hrmap*) nullptr; })
|
|
+ addHook(hooks_rotate_view, 100, rotate_view)
|
|
+ addHook(hooks_shift_view, 100, shift_view)
|
|
;
|
|
|
|
|
|
EX }
|
|
|
|
}
|
|
|