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https://github.com/zenorogue/hyperrogue.git
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nilv:: the Nil model is now changeable
This commit is contained in:
Zeno Rogue
128
nonisotropic.cpp
128
nonisotropic.cpp
@@ -31,8 +31,10 @@ EX namespace nisot {
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T[0][0] = pow(2, h[2]);
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T[1][1] = pow(3, h[2]);
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}
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if(nil)
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T[2][1] = h[0];
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if(nil) {
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T[2][1] = h[0] * (nilv::model_used + 1) / 2;
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T[2][0] = h[1] * (nilv::model_used - 1) / 2;
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}
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if(co < 0) return iso_inverse(T);
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return T;
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}
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@@ -744,13 +746,68 @@ EX }
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EX namespace nilv {
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hyperpoint christoffel(const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported) {
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ld x = Position[0];
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return point3(
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x * Velocity[1] * Transported[1] - 0.5 * (Velocity[1] * Transported[2] + Velocity[2] * Transported[1]),
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-.5 * x * (Velocity[1] * Transported[0] + Velocity[0] * Transported[1]) + .5 * (Velocity[2] * Transported[0] + Velocity[0] * Transported[2]),
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-.5 * (x*x-1) * (Velocity[1] * Transported[0] + Velocity[0] * Transported[1]) + .5 * x * (Velocity[2] * Transported[0] + Velocity[0] * Transported[2])
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);
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#if HDR
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/** nmSym is the rotationally symmetric model of Nil, while nmHeis is the Heisenberg model. */
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constexpr ld nmSym = 0, nmHeis = 1;
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#endif
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/** HyperRogue currently uses nmSym by default, but some parts are still written in nmHeis */
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EX ld model_used = nmSym;
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/** a helper function for model conversions */
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EX ld sym_to_heis_bonus(const hyperpoint& H) {
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return H[0] * H[1] / 2;
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}
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EX hyperpoint convert(hyperpoint H, ld from, ld to) {
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H[2] += sym_to_heis_bonus(H) * (to - from);
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return H;
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}
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EX void convert_ref(hyperpoint& H, ld from, ld to) {
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H[2] += sym_to_heis_bonus(H) * (to - from);
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}
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EX void convert_tangent_ref(hyperpoint at, hyperpoint& v, ld from, ld to) {
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v[2] += (at[0] * v[1] + at[1] * v[0]) * (to - from) / 2;
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}
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EX void convert_ref(transmatrix& T, ld from, ld to) {
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auto T1 = transpose(T);
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convert_ref(T1[3], from, to);
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for(int i: {0, 1, 2})
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convert_tangent_ref(T1[3], T1[i], from, to);
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T = transpose(T1);
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}
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EX hyperpoint checked_convert(hyperpoint H, ld from, ld to) {
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if(nil) return convert(H, from, to);
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return H;
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}
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hyperpoint christoffel(const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported, ld model = model_used) {
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/* to do: write these formulas in model */
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if(model == nmHeis) {
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ld x = Position[0];
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return point3(
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x * Velocity[1] * Transported[1] - 0.5 * (Velocity[1] * Transported[2] + Velocity[2] * Transported[1]),
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-.5 * x * (Velocity[1] * Transported[0] + Velocity[0] * Transported[1]) + .5 * (Velocity[2] * Transported[0] + Velocity[0] * Transported[2]),
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-.5 * (x*x-1) * (Velocity[1] * Transported[0] + Velocity[0] * Transported[1]) + .5 * x * (Velocity[2] * Transported[0] + Velocity[0] * Transported[2])
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);
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}
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else {
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hyperpoint P = Position;
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hyperpoint V = Velocity;
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hyperpoint T = Transported;
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convert_ref(P, model_used, nmHeis);
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convert_tangent_ref(P, V, model_used, nmHeis);
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convert_tangent_ref(P, T, model_used, nmHeis);
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auto res = christoffel(P, V, T, nmHeis);
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convert_tangent_ref(P, res, nmHeis, model_used);
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// this is acceleration, not tangent, so:
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res[2] += (model_used-nmHeis) * V[0] * V[1];
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return res;
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}
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}
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EX hyperpoint formula_exp(hyperpoint v) {
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@@ -761,23 +818,25 @@ EX namespace nilv {
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if(v[0] == 0 && v[1] == 0) return point31(v[0], v[1], v[2]);
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if(v[2] == 0) return point31(v[0], v[1], v[0] * v[1] / 2);
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if(v[2] == 0) return convert(point31(v[0], v[1], 0), nmSym, model_used);
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ld alpha = atan2(v[1], v[0]);
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ld w = v[2];
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ld c = hypot(v[0], v[1]) / v[2];
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return point31(
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return convert(point31(
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2 * c * sin(w/2) * cos(w/2 + alpha),
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2 * c * sin(w/2) * sin(w/2 + alpha),
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w * (1 + (c*c/2) * ((1 - sin(w)/w) + (1-cos(w))/w * sin(w + 2 * alpha)))
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);
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), nmHeis, model_used);
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}
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EX hyperpoint get_inverse_exp(hyperpoint h, flagtype prec IS(pNORMAL)) {
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ld wmin, wmax;
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ld side = h[2] - h[0] * h[1] / 2;
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ld side = convert(h, model_used, nmSym)[2];
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convert_ref(h, model_used, nmHeis);
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if(hypot_d(2, h) < 1e-6) return point3(h[0], h[1], h[2]);
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else if(side > 1e-6) {
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@@ -814,9 +873,10 @@ EX namespace nilv {
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}
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}
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EX string nilshader =
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"vec4 inverse_exp(vec4 h) {"
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EX string nilshader() {
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return "vec4 inverse_exp(vec4 h) {"
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"float wmin, wmax;"
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"h[2] += h[0] * h[1] / 2. * " + glhr::to_glsl(1-model_used) + ";"
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"float side = h[2] - h[0] * h[1] / 2.;"
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"if(h[0]*h[0] + h[1]*h[1] < 1e-12) return vec4(h[0], h[1], h[2], 1);"
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"if(side > 1e-6) { wmin = 0.; wmax = 2.*PI; }"
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@@ -839,9 +899,11 @@ EX namespace nilv {
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"float c = b / sin(w/2.);"
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"return vec4(c*w*cos(alpha), c*w*sin(alpha), w, 1.);"
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"}";
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}
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#if HDR
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struct mvec : array<int, 3> {
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/** these are in nmHeis */
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mvec() { }
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@@ -864,7 +926,7 @@ EX namespace nilv {
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EX ld nilwidth = 1;
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hyperpoint mvec_to_point(mvec m) { return hpxy3(m[0] * nilwidth, m[1] * nilwidth, m[2] * nilwidth * nilwidth); }
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hyperpoint mvec_to_point(mvec m) { return convert(hpxy3(m[0] * nilwidth, m[1] * nilwidth, m[2] * nilwidth * nilwidth), nmHeis, model_used); }
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#if HDR
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struct nilstructure {
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@@ -873,16 +935,18 @@ EX namespace nilv {
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};
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#endif
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EX hyperpoint heis(ld x, ld y, ld z) { return convert(point31(x, y, z), nmHeis, model_used); }
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nilstructure ns6 = {
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{{ mvec(-1,0,0), mvec(0,-1,0), mvec(0,0,-1), mvec(1,0,0), mvec(0,1,0), mvec(0,0,1) }},
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{{
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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{ 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), },
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}}
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};
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@@ -890,14 +954,14 @@ EX namespace nilv {
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{{ 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) }},
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{{
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{ point31(-0.5,-0.5,-0.25), point31(-0.5,-0.5,0.75), point31(-0.5,0.5,-0.25), },
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{ point31(-0.5,-0.5,0.75), point31(-0.5,0.5,0.75), point31(-0.5,0.5,-0.25), },
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{ 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), },
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{ 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), },
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{ point31(0.5,0.5,0.25), point31(0.5,-0.5,0.25), point31(0.5,-0.5,-0.75), },
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{ point31(0.5,0.5,-0.75), point31(0.5,0.5,0.25), point31(0.5,-0.5,-0.75), },
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{ 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), },
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{ 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), },
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{ heis(-0.5,-0.5,-0.25), heis(-0.5,-0.5,0.75), heis(-0.5,0.5,-0.25), },
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{ heis(-0.5,-0.5,0.75), heis(-0.5,0.5,0.75), heis(-0.5,0.5,-0.25), },
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{ 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), },
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{ 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), },
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{ heis(0.5,0.5,0.25), heis(0.5,-0.5,0.25), heis(0.5,-0.5,-0.75), },
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{ heis(0.5,0.5,-0.75), heis(0.5,0.5,0.25), heis(0.5,-0.5,-0.75), },
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{ 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), },
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{ 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), },
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}}
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};
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@@ -3019,6 +3083,10 @@ EX namespace nisot {
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shift(); product::cmirror = argi();
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return 0;
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}
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else if(argis("-nil-model")) {
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shift(); nilv::model_used = argf();
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return 0;
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}
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return 1;
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});
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#endif
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