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mirror of https://github.com/zenorogue/hyperrogue.git synced 2024-12-25 17:40:36 +00:00

nilv:: the Nil model is now changeable

This commit is contained in:
Zeno Rogue 2023-01-30 00:02:13 +01:00
parent 80c0b4bb0c
commit 395cbf3668
5 changed files with 110 additions and 37 deletions

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@ -1137,7 +1137,7 @@ EX transmatrix iso_inverse(const transmatrix& T) {
return pseudo_ortho_inverse(T);
if(sphere)
return ortho_inverse(T);
if(nil) {
if(nil && nilv::model_used == 1) {
transmatrix U = Id;
U[2][LDIM] = T[0][LDIM] * T[1][LDIM] - T[2][LDIM];
U[1][LDIM] = -T[1][LDIM];

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@ -389,9 +389,9 @@ EX void apply_perspective(const hyperpoint& H, hyperpoint& ret) {
EX void apply_nil_rotation(hyperpoint& H) {
if(nil) {
H[2] -= H[0] * H[1] / 2;
nilv::convert_ref(H, nilv::model_used, nilv::nmSym);
models::apply_orientation(H[0], H[1]);
H[2] += H[0] * H[1] / 2 * pconf.rotational_nil;
nilv::convert_ref(H, nilv::nmSym, pconf.rotational_nil);
models::apply_orientation(H[1], H[0]);
}
}

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@ -31,8 +31,10 @@ EX namespace nisot {
T[0][0] = pow(2, h[2]);
T[1][1] = pow(3, h[2]);
}
if(nil)
T[2][1] = h[0];
if(nil) {
T[2][1] = h[0] * (nilv::model_used + 1) / 2;
T[2][0] = h[1] * (nilv::model_used - 1) / 2;
}
if(co < 0) return iso_inverse(T);
return T;
}
@ -744,13 +746,68 @@ EX }
EX namespace nilv {
hyperpoint christoffel(const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported) {
ld x = Position[0];
return point3(
x * Velocity[1] * Transported[1] - 0.5 * (Velocity[1] * Transported[2] + Velocity[2] * Transported[1]),
-.5 * x * (Velocity[1] * Transported[0] + Velocity[0] * Transported[1]) + .5 * (Velocity[2] * Transported[0] + Velocity[0] * Transported[2]),
-.5 * (x*x-1) * (Velocity[1] * Transported[0] + Velocity[0] * Transported[1]) + .5 * x * (Velocity[2] * Transported[0] + Velocity[0] * Transported[2])
);
#if HDR
/** nmSym is the rotationally symmetric model of Nil, while nmHeis is the Heisenberg model. */
constexpr ld nmSym = 0, nmHeis = 1;
#endif
/** HyperRogue currently uses nmSym by default, but some parts are still written in nmHeis */
EX ld model_used = nmSym;
/** a helper function for model conversions */
EX ld sym_to_heis_bonus(const hyperpoint& H) {
return H[0] * H[1] / 2;
}
EX hyperpoint convert(hyperpoint H, ld from, ld to) {
H[2] += sym_to_heis_bonus(H) * (to - from);
return H;
}
EX void convert_ref(hyperpoint& H, ld from, ld to) {
H[2] += sym_to_heis_bonus(H) * (to - from);
}
EX void convert_tangent_ref(hyperpoint at, hyperpoint& v, ld from, ld to) {
v[2] += (at[0] * v[1] + at[1] * v[0]) * (to - from) / 2;
}
EX void convert_ref(transmatrix& T, ld from, ld to) {
auto T1 = transpose(T);
convert_ref(T1[3], from, to);
for(int i: {0, 1, 2})
convert_tangent_ref(T1[3], T1[i], from, to);
T = transpose(T1);
}
EX hyperpoint checked_convert(hyperpoint H, ld from, ld to) {
if(nil) return convert(H, from, to);
return H;
}
hyperpoint christoffel(const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported, ld model = model_used) {
/* to do: write these formulas in model */
if(model == nmHeis) {
ld x = Position[0];
return point3(
x * Velocity[1] * Transported[1] - 0.5 * (Velocity[1] * Transported[2] + Velocity[2] * Transported[1]),
-.5 * x * (Velocity[1] * Transported[0] + Velocity[0] * Transported[1]) + .5 * (Velocity[2] * Transported[0] + Velocity[0] * Transported[2]),
-.5 * (x*x-1) * (Velocity[1] * Transported[0] + Velocity[0] * Transported[1]) + .5 * x * (Velocity[2] * Transported[0] + Velocity[0] * Transported[2])
);
}
else {
hyperpoint P = Position;
hyperpoint V = Velocity;
hyperpoint T = Transported;
convert_ref(P, model_used, nmHeis);
convert_tangent_ref(P, V, model_used, nmHeis);
convert_tangent_ref(P, T, model_used, nmHeis);
auto res = christoffel(P, V, T, nmHeis);
convert_tangent_ref(P, res, nmHeis, model_used);
// this is acceleration, not tangent, so:
res[2] += (model_used-nmHeis) * V[0] * V[1];
return res;
}
}
EX hyperpoint formula_exp(hyperpoint v) {
@ -761,23 +818,25 @@ EX namespace nilv {
if(v[0] == 0 && v[1] == 0) return point31(v[0], v[1], v[2]);
if(v[2] == 0) return point31(v[0], v[1], v[0] * v[1] / 2);
if(v[2] == 0) return convert(point31(v[0], v[1], 0), nmSym, model_used);
ld alpha = atan2(v[1], v[0]);
ld w = v[2];
ld c = hypot(v[0], v[1]) / v[2];
return point31(
return convert(point31(
2 * c * sin(w/2) * cos(w/2 + alpha),
2 * c * sin(w/2) * sin(w/2 + alpha),
w * (1 + (c*c/2) * ((1 - sin(w)/w) + (1-cos(w))/w * sin(w + 2 * alpha)))
);
), nmHeis, model_used);
}
EX hyperpoint get_inverse_exp(hyperpoint h, flagtype prec IS(pNORMAL)) {
ld wmin, wmax;
ld side = h[2] - h[0] * h[1] / 2;
ld side = convert(h, model_used, nmSym)[2];
convert_ref(h, model_used, nmHeis);
if(hypot_d(2, h) < 1e-6) return point3(h[0], h[1], h[2]);
else if(side > 1e-6) {
@ -814,9 +873,10 @@ EX namespace nilv {
}
}
EX string nilshader =
"vec4 inverse_exp(vec4 h) {"
EX string nilshader() {
return "vec4 inverse_exp(vec4 h) {"
"float wmin, wmax;"
"h[2] += h[0] * h[1] / 2. * " + glhr::to_glsl(1-model_used) + ";"
"float side = h[2] - h[0] * h[1] / 2.;"
"if(h[0]*h[0] + h[1]*h[1] < 1e-12) return vec4(h[0], h[1], h[2], 1);"
"if(side > 1e-6) { wmin = 0.; wmax = 2.*PI; }"
@ -839,9 +899,11 @@ EX namespace nilv {
"float c = b / sin(w/2.);"
"return vec4(c*w*cos(alpha), c*w*sin(alpha), w, 1.);"
"}";
}
#if HDR
struct mvec : array<int, 3> {
/** these are in nmHeis */
mvec() { }
@ -864,7 +926,7 @@ EX namespace nilv {
EX ld nilwidth = 1;
hyperpoint mvec_to_point(mvec m) { return hpxy3(m[0] * nilwidth, m[1] * nilwidth, m[2] * nilwidth * nilwidth); }
hyperpoint mvec_to_point(mvec m) { return convert(hpxy3(m[0] * nilwidth, m[1] * nilwidth, m[2] * nilwidth * nilwidth), nmHeis, model_used); }
#if HDR
struct nilstructure {
@ -873,16 +935,18 @@ EX namespace nilv {
};
#endif
EX hyperpoint heis(ld x, ld y, ld z) { return convert(point31(x, y, z), nmHeis, model_used); }
nilstructure ns6 = {
{{ mvec(-1,0,0), mvec(0,-1,0), mvec(0,0,-1), mvec(1,0,0), mvec(0,1,0), mvec(0,0,1) }},
{{
{ point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,0.75), point31(-0.5,0.5,0.25), point31(-0.5,0.5,-0.75), },
{ point31(0.5,-0.5,-0.5), point31(0.5,-0.5,0.5), point31(-0.5,-0.5,0.5), point31(-0.5,-0.5,-0.5), },
{ point31(0,0,-0.5), point31(-0.5,0.5,-0.75), point31(-0.5,-0.5,-0.25), point31(0,0,-0.5), point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,-0.5), point31(0,0,-0.5), point31(-0.5,-0.5,-0.5), point31(0.5,-0.5,-0.5), point31(0,0,-0.5), point31(0.5,-0.5,-0.5), point31(0.5,-0.5,-0.75), point31(0,0,-0.5), point31(0.5,-0.5,-0.75), point31(0.5,0.5,-0.25), point31(0,0,-0.5), point31(0.5,0.5,-0.25), point31(0.5,0.5,-0.5), point31(0,0,-0.5), point31(0.5,0.5,-0.5), point31(-0.5,0.5,-0.5), point31(0,0,-0.5), point31(-0.5,0.5,-0.5), point31(-0.5,0.5,-0.75), },
{ point31(0.5,0.5,-0.25), point31(0.5,0.5,0.75), point31(0.5,-0.5,0.25), point31(0.5,-0.5,-0.75), },
{ point31(-0.5,0.5,-0.5), point31(-0.5,0.5,0.5), point31(0.5,0.5,0.5), point31(0.5,0.5,-0.5), },
{ point31(0,0,0.5), point31(-0.5,0.5,0.25), point31(-0.5,-0.5,0.75), point31(0,0,0.5), point31(-0.5,-0.5,0.75), point31(-0.5,-0.5,0.5), point31(0,0,0.5), point31(-0.5,-0.5,0.5), point31(0.5,-0.5,0.5), point31(0,0,0.5), point31(0.5,-0.5,0.5), point31(0.5,-0.5,0.25), point31(0,0,0.5), point31(0.5,-0.5,0.25), point31(0.5,0.5,0.75), point31(0,0,0.5), point31(0.5,0.5,0.75), point31(0.5,0.5,0.5), point31(0,0,0.5), point31(0.5,0.5,0.5), point31(-0.5,0.5,0.5), point31(0,0,0.5), point31(-0.5,0.5,0.5), point31(-0.5,0.5,0.25), },
{ heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,0.75), heis(-0.5,0.5,0.25), heis(-0.5,0.5,-0.75), },
{ heis(0.5,-0.5,-0.5), heis(0.5,-0.5,0.5), heis(-0.5,-0.5,0.5), heis(-0.5,-0.5,-0.5), },
{ heis(0,0,-0.5), heis(-0.5,0.5,-0.75), heis(-0.5,-0.5,-0.25), heis(0,0,-0.5), heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,-0.5), heis(0,0,-0.5), heis(-0.5,-0.5,-0.5), heis(0.5,-0.5,-0.5), heis(0,0,-0.5), heis(0.5,-0.5,-0.5), heis(0.5,-0.5,-0.75), heis(0,0,-0.5), heis(0.5,-0.5,-0.75), heis(0.5,0.5,-0.25), heis(0,0,-0.5), heis(0.5,0.5,-0.25), heis(0.5,0.5,-0.5), heis(0,0,-0.5), heis(0.5,0.5,-0.5), heis(-0.5,0.5,-0.5), heis(0,0,-0.5), heis(-0.5,0.5,-0.5), heis(-0.5,0.5,-0.75), },
{ heis(0.5,0.5,-0.25), heis(0.5,0.5,0.75), heis(0.5,-0.5,0.25), heis(0.5,-0.5,-0.75), },
{ heis(-0.5,0.5,-0.5), heis(-0.5,0.5,0.5), heis(0.5,0.5,0.5), heis(0.5,0.5,-0.5), },
{ heis(0,0,0.5), heis(-0.5,0.5,0.25), heis(-0.5,-0.5,0.75), heis(0,0,0.5), heis(-0.5,-0.5,0.75), heis(-0.5,-0.5,0.5), heis(0,0,0.5), heis(-0.5,-0.5,0.5), heis(0.5,-0.5,0.5), heis(0,0,0.5), heis(0.5,-0.5,0.5), heis(0.5,-0.5,0.25), heis(0,0,0.5), heis(0.5,-0.5,0.25), heis(0.5,0.5,0.75), heis(0,0,0.5), heis(0.5,0.5,0.75), heis(0.5,0.5,0.5), heis(0,0,0.5), heis(0.5,0.5,0.5), heis(-0.5,0.5,0.5), heis(0,0,0.5), heis(-0.5,0.5,0.5), heis(-0.5,0.5,0.25), },
}}
};
@ -890,14 +954,14 @@ EX namespace nilv {
{{ mvec(-1,0,0), mvec(-1,0,1), mvec(0,-1,0), mvec(0,0,-1), mvec(1,0,0), mvec(1,0,-1), mvec(0,1,0), mvec(0,0,1) }},
{{
{ point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,0.75), point31(-0.5,0.5,-0.25), },
{ point31(-0.5,-0.5,0.75), point31(-0.5,0.5,0.75), point31(-0.5,0.5,-0.25), },
{ point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,0.75), point31(0.5,-0.5,0.25), point31(0.5,-0.5,-0.75), },
{ point31(-0.5,-0.5,-0.25), point31(-0.5,0.5,-0.25), point31(0.5,0.5,-0.75), point31(0.5,-0.5,-0.75), },
{ point31(0.5,0.5,0.25), point31(0.5,-0.5,0.25), point31(0.5,-0.5,-0.75), },
{ point31(0.5,0.5,-0.75), point31(0.5,0.5,0.25), point31(0.5,-0.5,-0.75), },
{ point31(-0.5,0.5,0.75), point31(-0.5,0.5,-0.25), point31(0.5,0.5,-0.75), point31(0.5,0.5,0.25), },
{ point31(-0.5,-0.5,0.75), point31(-0.5,0.5,0.75), point31(0.5,0.5,0.25), point31(0.5,-0.5,0.25), },
{ heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,0.75), heis(-0.5,0.5,-0.25), },
{ heis(-0.5,-0.5,0.75), heis(-0.5,0.5,0.75), heis(-0.5,0.5,-0.25), },
{ heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,0.75), heis(0.5,-0.5,0.25), heis(0.5,-0.5,-0.75), },
{ heis(-0.5,-0.5,-0.25), heis(-0.5,0.5,-0.25), heis(0.5,0.5,-0.75), heis(0.5,-0.5,-0.75), },
{ heis(0.5,0.5,0.25), heis(0.5,-0.5,0.25), heis(0.5,-0.5,-0.75), },
{ heis(0.5,0.5,-0.75), heis(0.5,0.5,0.25), heis(0.5,-0.5,-0.75), },
{ heis(-0.5,0.5,0.75), heis(-0.5,0.5,-0.25), heis(0.5,0.5,-0.75), heis(0.5,0.5,0.25), },
{ heis(-0.5,-0.5,0.75), heis(-0.5,0.5,0.75), heis(0.5,0.5,0.25), heis(0.5,-0.5,0.25), },
}}
};
@ -3019,6 +3083,10 @@ EX namespace nisot {
shift(); product::cmirror = argi();
return 0;
}
else if(argis("-nil-model")) {
shift(); nilv::model_used = argf();
return 0;
}
return 1;
});
#endif

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@ -536,8 +536,13 @@ void raygen::move_forward() {
fsh +=
"mediump vec4 christoffel(mediump vec4 pos, mediump vec4 vel, mediump vec4 tra) {\n"
" mediump float x = pos.x;\n"
" return vec4(x*vel.y*tra.y - 0.5*dot(vel.yz,tra.zy), -.5*x*dot(vel.yx,tra.xy) + .5 * dot(vel.zx,tra.xz), -.5*(x*x-1.)*dot(vel.yx,tra.xy)+.5*x*dot(vel.zx,tra.xz), 0.);\n"
// " return vec4(0.,0.,0.,0.);\n"
" const float mu = " + to_glsl((1-nilv::model_used)/2) + ";\n"
" pos[2] += pos[0] * pos[1] * mu;\n"
" vel[2] += (pos[0] * vel[1] + pos[1] * vel[0]) * mu;\n"
" tra[2] += (pos[0] * tra[1] + pos[1] * tra[0]) * mu;\n"
" vec4 res = vec4(x*vel.y*tra.y - 0.5*dot(vel.yz,tra.zy), -.5*x*dot(vel.yx,tra.xy) + .5 * dot(vel.zx,tra.xz), -.5*(x*x-1.)*dot(vel.yx,tra.xy)+.5*x*dot(vel.zx,tra.xz), 0.);\n"
" res[2] -= (pos[0] * res[1] + vel[0] * vel[1] + pos[2] * res[0]) * mu;\n"
" return res;\n"
" }\n";
use_christoffel = false;
}

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@ -358,7 +358,7 @@ shared_ptr<glhr::GLprogram> write_shader(flagtype shader_flags) {
break;
#endif
case gcNil:
vsh += nilv::nilshader;
vsh += nilv::nilshader();
break;
case gcSL2:
vsh += slr::slshader;
@ -441,7 +441,7 @@ shared_ptr<glhr::GLprogram> write_shader(flagtype shader_flags) {
if(nil && pmodel == mdPerspective) {
vsh += "uniform mediump float uRotCos, uRotSin, uRotNil;\n";
coordinator +=
"t.z += (uRotCos * t.x + uRotSin * t.y) * (uRotCos * t.y - uRotSin * t.x) * uRotNil / 2. - t.x * t.y / 2.;\n";
"t.z += (uRotCos * t.x + uRotSin * t.y) * (uRotCos * t.y - uRotSin * t.x) * uRotNil / 2. - " + glhr::to_glsl(nilv::model_used) + " * t.x * t.y / 2.;\n";
}
if(!skip_t) {