mirror of
https://github.com/zenorogue/hyperrogue.git
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2936 lines
94 KiB
C++
2936 lines
94 KiB
C++
// Hyperbolic Rogue -- nonisotropic spaces (Solv and Nil)
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// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details
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/** \file nonisotropic.cpp
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* \brief nonisotropic spaces (Solv and Nil)
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*/
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#include "hyper.h"
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namespace hr {
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EX namespace nisot {
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#if HDR
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inline bool local_perspective_used() { return nonisotropic || prod; }
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#endif
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EX bool geodesic_movement = true;
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EX transmatrix translate(hyperpoint h, ld co IS(1)) {
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if(sl2 || sphere)
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return co > 0 ? stretch::translate(h) : stretch::itranslate(h);
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transmatrix T = Id;
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for(int i=0; i<GDIM; i++) T[i][LDIM] = h[i];
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if(sol && nih) {
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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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else if(sol) {
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T[0][0] = exp(-h[2]);
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T[1][1] = exp(+h[2]);
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}
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else if(nih) {
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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(co < 0) return iso_inverse(T);
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return T;
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}
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EX }
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#if !CAP_SOLV
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EX namespace sn {
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EX always_false in() { return always_false(); }
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EX }
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#endif
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#if CAP_SOLV
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EX namespace sn {
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EX bool in() { return cgclass == gcSolNIH; }
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EX eGeometry geom() {
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if(asonov::in()) return gSol;
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else return geometry;
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}
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#if HDR
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typedef array<float, 3> compressed_point;
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inline hyperpoint decompress(compressed_point p) { return point3(p[0], p[1], p[2]); }
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inline compressed_point compress(hyperpoint h) { return make_array<float>(h[0], h[1], h[2]); }
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struct tabled_inverses {
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int PRECX, PRECY, PRECZ;
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vector<compressed_point> tab;
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string fname;
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bool loaded;
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void load();
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hyperpoint get(ld ix, ld iy, ld iz, bool lazy);
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compressed_point& get_int(int ix, int iy, int iz) { return tab[(iz*PRECY+iy)*PRECX+ix]; }
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GLuint texture_id;
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bool toload;
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GLuint get_texture_id();
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tabled_inverses(string s) : fname(s), texture_id(0), toload(true) {}
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};
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#endif
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void tabled_inverses::load() {
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if(loaded) return;
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FILE *f = fopen(fname.c_str(), "rb");
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if(!f) f = fopen((rsrcdir + fname).c_str(), "rb");
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if(!f) { addMessage(XLAT("geodesic table missing")); pmodel = mdPerspective; return; }
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ignore(fread(&PRECX, 4, 1, f));
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ignore(fread(&PRECY, 4, 1, f));
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ignore(fread(&PRECZ, 4, 1, f));
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tab.resize(PRECX * PRECY * PRECZ);
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ignore(fread(&tab[0], sizeof(compressed_point) * PRECX * PRECY * PRECZ, 1, f));
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fclose(f);
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loaded = true;
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}
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hyperpoint tabled_inverses::get(ld ix, ld iy, ld iz, bool lazy) {
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ix *= PRECX-1;
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iy *= PRECY-1;
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iz *= PRECZ-1;
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hyperpoint res;
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if(lazy) {
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return decompress(get_int(int(ix+.5), int(iy+.5), int(iz+.5)));
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}
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else {
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if(ix >= PRECX-1) ix = PRECX-2;
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if(iy >= PRECX-1) iy = PRECX-2;
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if(iz >= PRECZ-1) iz = PRECZ-2;
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int ax = ix, bx = ax+1;
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int ay = iy, by = ay+1;
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int az = iz, bz = az+1;
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#define S0(x,y,z) get_int(x, y, z)[t]
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#define S1(x,y) (S0(x,y,az) * (bz-iz) + S0(x,y,bz) * (iz-az))
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#define S2(x) (S1(x,ay) * (by-iy) + S1(x,by) * (iy-ay))
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for(int t=0; t<3; t++)
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res[t] = S2(ax) * (bx-ix) + S2(bx) * (ix-ax);
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res[3] = 0;
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}
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return res;
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}
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GLuint tabled_inverses::get_texture_id() {
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if(!toload) return texture_id;
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load();
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if(!loaded) return 0;
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println(hlog, "installing table");
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toload = false;
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if(texture_id == 0) glGenTextures(1, &texture_id);
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glBindTexture( GL_TEXTURE_3D, texture_id);
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glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
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glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
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glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
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glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
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glTexParameteri(GL_TEXTURE_3D, GL_TEXTURE_WRAP_R, GL_CLAMP_TO_EDGE);
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auto xbuffer = new glvertex[PRECZ*PRECY*PRECX];
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for(int z=0; z<PRECZ*PRECY*PRECX; z++) {
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auto& t = tab[z];
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xbuffer[z] = glhr::makevertex(t[0], t[1], t[2]);
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}
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#if !ISWEB
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glTexImage3D(GL_TEXTURE_3D, 0, 34836 /*GL_RGBA32F*/, PRECX, PRECX, PRECZ, 0, GL_RGBA, GL_FLOAT, xbuffer);
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#else
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// glTexStorage3D(GL_TEXTURE_3D, 1, 34836 /*GL_RGBA32F*/, PRECX, PRECX, PRECZ);
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// glTexSubImage3D(GL_TEXTURE_3D, 0, 0, 0, 0, PRECX, PRECY, PRECZ, GL_RGBA, GL_FLOAT, xbuffer);
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#endif
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delete[] xbuffer;
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return texture_id;
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}
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EX ld x_to_ix(ld u) {
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if(u == 0.) return 0.;
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ld diag = u*u/2.;
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ld x = diag;
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ld y = u;
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ld z = diag+1.;
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x /= (1.+z);
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y /= (1.+z);
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return 0.5 - atan((0.5-x) / y) / M_PI;
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}
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EX ld ix_to_x(ld ix) {
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ld minx = 0;
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while(x_to_ix(minx) <= ix) minx++;
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ld maxx = minx; minx--;
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for(int it=0; it<20; it++) {
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ld x = (minx + maxx) / 2;
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if(x_to_ix(x) < ix) minx = x;
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else maxx = x;
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}
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return minx;
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}
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EX ld z_to_iz(ld z) {
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z = sinh(z) / (1 + cosh(z));
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if(nih) z = (z+1) / 2;
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return z;
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}
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EX ld iz_to_z(ld iz) {
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ld minz = 0;
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while(z_to_iz(minz) <= iz) minz++;
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while(z_to_iz(minz) > iz) minz--;
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ld maxz = minz + 1;
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for(int it=0; it<20; it++) {
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ld z = (minz + maxz) / 2;
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if(z_to_iz(z) < iz) minz = z;
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else maxz = z;
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}
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return (minz+maxz) / 2;
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}
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EX hyperpoint azeq_to_table(hyperpoint x) {
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// azimuthal equidistant to Poincare
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ld r = hypot_d(3, x);
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if(r == 0) return point3(0,0,0);
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ld make_r = sinh(r) / (1 + cosh(r));
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ld d = make_r / r;
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return x * d;
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}
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EX hyperpoint table_to_azeq(hyperpoint x) {
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// Poincare to azimuthal equidistant
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ld hr = sqhypot_d(3, x);
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if(hr < 1e-5) return x * 2;
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if(hr >= 1) return x * 60;
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ld hz = (1 + hr) / (1 - hr);
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ld d = (hz+1) * acosh(hz) / sinh(acosh(hz));
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return x * d;
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}
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struct hrmap_solnih : hrmap {
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hrmap *binary_map;
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hrmap *ternary_map; /* nih only */
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unordered_map<pair<heptagon*, heptagon*>, heptagon*> at;
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unordered_map<heptagon*, pair<heptagon*, heptagon*>> coords;
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heptagon *origin;
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heptagon *getOrigin() override { return origin; }
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heptagon *get_at(heptagon *x, heptagon *y) {
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auto& h = at[make_pair(x, y)];
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if(h) return h;
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h = tailored_alloc<heptagon> (S7);
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h->c7 = newCell(S7, h);
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coords[h] = make_pair(x, y);
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h->distance = x->distance;
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h->dm4 = 0;
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h->zebraval = x->emeraldval;
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h->emeraldval = y->emeraldval;
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h->fieldval = 0;
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h->cdata = NULL;
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h->alt = NULL;
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return h;
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}
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hrmap_solnih() {
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heptagon *alt;
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heptagon *alt3;
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if(true) {
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dynamicval<eGeometry> g(geometry, gBinary4);
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alt = tailored_alloc<heptagon> (S7);
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alt->s = hsOrigin;
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alt->alt = alt;
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alt->cdata = NULL;
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alt->c7 = NULL;
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alt->zebraval = 0;
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alt->distance = 0;
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alt->emeraldval = 0;
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binary_map = bt::new_alt_map(alt);
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}
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if(nih) {
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dynamicval<eGeometry> g(geometry, gTernary);
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alt3 = tailored_alloc<heptagon> (S7);
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alt3->s = hsOrigin;
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alt3->alt = alt3;
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alt3->cdata = NULL;
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alt3->c7 = NULL;
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alt3->zebraval = 0;
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alt3->distance = 0;
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alt3->emeraldval = 0;
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ternary_map = bt::new_alt_map(alt3);
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}
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else {
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alt3 = alt;
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ternary_map = nullptr;
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}
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origin = get_at(alt, alt3);
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}
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heptagon *altstep(heptagon *h, int d) {
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dynamicval<eGeometry> g(geometry, gBinary4);
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dynamicval<hrmap*> cm(currentmap, binary_map);
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return h->cmove(d);
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}
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heptagon *altstep3(heptagon *h, int d) {
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dynamicval<eGeometry> g(geometry, gTernary);
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dynamicval<hrmap*> cm(currentmap, ternary_map);
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return h->cmove(d);
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}
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heptagon *create_step(heptagon *parent, int d) override {
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auto p = coords[parent];
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auto pf = p.first, ps = p.second;
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auto rule = [&] (heptagon *c1, heptagon *c2, int d1) {
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auto g = get_at(c1, c2);
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parent->c.connect(d, g, d1, false);
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return g;
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};
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switch(geometry){
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case gSol: switch(d) {
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case 0: // right
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return rule(altstep(pf, 2), ps, 4);
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case 1: // up
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return rule(pf, altstep(ps, 2), 5);
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case 2: // front left
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return rule(altstep(pf, 0), altstep(ps, 3), ps->zebraval ? 7 : 6);
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case 3: // front right
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return rule(altstep(pf, 1), altstep(ps, 3), ps->zebraval ? 7 : 6);
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case 4: // left
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return rule(altstep(pf, 4), ps, 0);
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case 5: // down
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return rule(pf, altstep(ps, 4), 1);
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case 6: // back down
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return rule(altstep(pf, 3), altstep(ps, 0), pf->zebraval ? 3 : 2);
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case 7: // back up
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return rule(altstep(pf, 3), altstep(ps, 1), pf->zebraval ? 3 : 2);
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default:
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return NULL;
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}
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case gNIH: switch(d) {
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case 0: // right
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return rule(altstep(pf, 2), ps, 2);
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case 1: // up
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return rule(pf, altstep3(ps, 3), 3);
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case 2: // left
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return rule(altstep(pf, 4), ps, 0);
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case 3: // down
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return rule(pf, altstep3(ps, 5), 1);
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case 4: // back
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return rule(altstep(pf, 3), altstep3(ps, 4), 5 + pf->zebraval + 2 * ps->zebraval);
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default:
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return rule(altstep(pf, (d-5) % 2), altstep3(ps, (d-5)/2), 4);
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}
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case gSolN: switch(d) {
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case 0: // right
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return rule(altstep(pf, 2), ps, 2);
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case 1: // up
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return rule(pf, altstep3(ps, 3), 3);
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case 2: // left
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return rule(altstep(pf, 4), ps, 0);
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case 3: // down
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return rule(pf, altstep3(ps, 5), 1);
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case 4: case 5:
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return rule(altstep(pf, d-4), altstep3(ps, 4), ps->zebraval + 6);
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case 6: case 7: case 8:
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return rule(altstep(pf, 3), altstep3(ps, d-6), pf->zebraval + 4);
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default:
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return NULL;
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}
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default: throw "not solnihv";
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}
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}
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~hrmap_solnih() {
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delete binary_map;
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if(ternary_map) delete ternary_map;
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for(auto& p: at) clear_heptagon(p.second);
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}
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transmatrix adjmatrix(int i, int j) {
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switch(geometry) {
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case gSol: {
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ld z = log(2);
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ld bw = vid.binary_width * z;
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switch(i) {
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case 0: return xpush(+bw);
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case 1: return ypush(+bw);
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case 2: case 3:
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return ypush(bw*(6.5-j)) * zpush(+z) * xpush(bw*(i-2.5));
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case 4: return xpush(-bw);
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case 5: return ypush(-bw);
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case 6: case 7:
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return xpush(bw*(2.5-j)) * zpush(-z) * ypush(bw*(i-6.5));
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default:return Id;
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}
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}
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case gNIH: {
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ld bw = vid.binary_width;
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switch(i) {
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case 0: return xpush(+bw);
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case 1: return ypush(+bw);
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case 2: return xpush(-bw);
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case 3: return ypush(-bw);
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case 4: return xpush(-((j-5)%2-.5)*bw) * ypush(-((j-5)/2-1)*bw) * zpush(1);
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default:
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return zpush(-1) * xpush(((i-5)%2-.5)*bw) * ypush(((i-5)/2-1)*bw);
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}
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}
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case gSolN: {
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ld bw = vid.binary_width;
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switch(i) {
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case 0: return xpush(+bw);
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case 1: return ypush(+bw);
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case 2: return xpush(-bw);
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case 3: return ypush(-bw);
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case 4:
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case 5:
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return ypush(bw*(7-j)) * zpush(+1) * xpush(bw*(i-4.5));
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case 6:
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case 7:
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case 8:
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return xpush(bw*(4.5-j)) * zpush(-1) * ypush(bw*(i-7));
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}
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}
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default: throw "not nihsolv";
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}
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}
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transmatrix adj(heptagon *h, int d) override {
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h->cmove(d); return adjmatrix(d, h->c.spin(d));
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}
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virtual transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
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for(int i=0; i<h1->type; i++) if(h1->move(i) == h2) return adjmatrix(i, h1->c.spin(i));
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if(gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7))
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return inverse_shift(gmatrix0[h1->c7], gmatrix0[h2->c7]);
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transmatrix front = Id, back = Id;
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int up, down;
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switch(geometry) {
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case gSol: up = 2; down = 6; break;
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case gSolN: up = 4; down = 7; break;
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case gNIH: up = 4; down = 4; break;
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default: throw "not nihsolv";
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}
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while(h1->distance > h2->distance) front = front * adj(h1, down), h1 = h1->cmove(down);
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while(h1->distance < h2->distance) back = iadj(h2, down) * back, h2 = h2->cmove(down);
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while(coords[h1].first != coords[h2].first) front = front * adj(h1, down), back = iadj(h2, down) * back, h1 = h1->cmove(down), h2 = h2->cmove(down);
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while(coords[h1].second != coords[h2].second) front = front * adj(h1, up), back = iadj(h2, up) * back, h1 = h1->cmove(up), h2 = h2->cmove(up);
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return front * back;
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}
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};
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EX pair<heptagon*,heptagon*> getcoord(heptagon *h) {
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return ((hrmap_solnih*)currentmap)->coords[h];
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}
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EX heptagon *get_at(heptagon *h1, heptagon *h2, bool gen) {
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auto m = ((hrmap_solnih*)currentmap);
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if(!gen && !m->at.count(make_pair(h1, h2))) return nullptr;
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return m->get_at(h1, h2);
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}
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EX string common =
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"uniform mediump sampler3D tInvExpTable;"
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|
"uniform mediump float PRECX, PRECY, PRECZ;"
|
|
|
|
"float x_to_ix(float u) {"
|
|
" if(u < 1e-6) return 0.;"
|
|
" float diag = u*u/2.;"
|
|
|
|
" float x = diag;"
|
|
" float y = u;"
|
|
" float z = diag+1.;"
|
|
|
|
" x /= (1.+z);"
|
|
" y /= (1.+z);"
|
|
|
|
" return 0.5 - atan((0.5-x) / y) / 3.1415926535897932384626433832795;"
|
|
" }"
|
|
|
|
"float z_to_iz_s(float z) {"
|
|
"return sinh(z) / (1. + cosh(z));"
|
|
"}"
|
|
|
|
"float z_to_iz_ns(float z) {"
|
|
"z = sinh(z) / (1. + cosh(z));"
|
|
"return (z+1.)/2.;"
|
|
"}";
|
|
|
|
hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
|
|
const ld l2 = log(2);
|
|
const ld l3 = log(3);
|
|
switch(geom()) {
|
|
case gSolN:
|
|
return hpxyz3(
|
|
-(velocity[2] * transported[0] + velocity[0] * transported[2]) * l2,
|
|
(velocity[2] * transported[1] + velocity[1] * transported[2]) * l3,
|
|
velocity[0] * transported[0] * exp(2*l2*at[2]) * l2 - velocity[1] * transported[1] * exp(-2*l3*at[2]) * l3,
|
|
0
|
|
);
|
|
case gSol:
|
|
return hpxyz3(
|
|
-velocity[2] * transported[0] - velocity[0] * transported[2],
|
|
velocity[2] * transported[1] + velocity[1] * transported[2],
|
|
velocity[0] * transported[0] * exp(2*at[2]) - velocity[1] * transported[1] * exp(-2*at[2]),
|
|
0
|
|
);
|
|
case gNIH:
|
|
return hpxyz3(
|
|
(velocity[2] * transported[0] + velocity[0] * transported[2]) * l2,
|
|
(velocity[2] * transported[1] + velocity[1] * transported[2]) * l3,
|
|
-(velocity[0] * transported[0] * exp(-2*l2*at[2]) * l2 + velocity[1] * transported[1] * exp(-2*l3*at[2]) * l3),
|
|
0
|
|
);
|
|
default:
|
|
throw "christoffel not in solnihv";
|
|
}
|
|
}
|
|
|
|
EX hyperpoint get_inverse_exp_symsol(hyperpoint h, flagtype flags) {
|
|
auto& s = get_tabled();
|
|
s.load();
|
|
|
|
ld ix = h[0] >= 0. ? sn::x_to_ix(h[0]) : sn::x_to_ix(-h[0]);
|
|
ld iy = h[1] >= 0. ? sn::x_to_ix(h[1]) : sn::x_to_ix(-h[1]);
|
|
ld iz = sn::z_to_iz(h[2]);
|
|
|
|
if(h[2] < 0.) { iz = -iz; swap(ix, iy); }
|
|
|
|
hyperpoint res = s.get(ix, iy, iz, flags & pfNO_INTERPOLATION);
|
|
|
|
if(h[2] < 0.) { swap(res[0], res[1]); res[2] = -res[2]; }
|
|
if(h[0] < 0.) res[0] = -res[0];
|
|
if(h[1] < 0.) res[1] = -res[1];
|
|
|
|
if(flags & pfNO_DISTANCE) return res;
|
|
return table_to_azeq(res);
|
|
}
|
|
|
|
EX hyperpoint get_inverse_exp_nsym(hyperpoint h, flagtype flags) {
|
|
auto& s = get_tabled();
|
|
s.load();
|
|
|
|
ld ix = h[0] >= 0. ? sn::x_to_ix(h[0]) : sn::x_to_ix(-h[0]);
|
|
ld iy = h[1] >= 0. ? sn::x_to_ix(h[1]) : sn::x_to_ix(-h[1]);
|
|
ld iz = sn::z_to_iz(h[2]);
|
|
|
|
hyperpoint res = s.get(ix, iy, iz, flags & pfNO_INTERPOLATION);
|
|
|
|
if(h[0] < 0.) res[0] = -res[0];
|
|
if(h[1] < 0.) res[1] = -res[1];
|
|
|
|
if(flags & pfNO_DISTANCE) return res;
|
|
return table_to_azeq(res);
|
|
}
|
|
|
|
EX string shader_symsol = sn::common +
|
|
|
|
"vec4 inverse_exp(vec4 h) {"
|
|
|
|
"float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);"
|
|
"float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);"
|
|
"float iz = z_to_iz_s(h[2]);"
|
|
|
|
"if(h[2] < 1e-6) { iz = -iz; float s = ix; ix = iy; iy = s; }"
|
|
"if(iz < 0.) iz = 0.;"
|
|
|
|
"vec4 res;"
|
|
|
|
"float cx = ix*(1.-1./PRECX) + .5/PRECX;"
|
|
"float cy = iy*(1.-1./PRECY) + .5/PRECY;"
|
|
"float cz = iz*(1.-1./PRECZ) + .5/PRECZ;"
|
|
|
|
// "if(ix > .5 && iy > .6 && ix < iy + .05 && iz < .2 && iz < (iy - 0.5) * 0.6)"
|
|
"\n#ifndef SOLV_ALL\n"
|
|
|
|
"bool ok = true;"
|
|
|
|
// hard to tell which triangles fall on the other sides
|
|
"if(iz < .03 && ix > .65 && iy > .65) ok = false;"
|
|
"if(iz < .013 && ix > .55 && iy > .55) ok = false;"
|
|
"if(iz < .0075 && ix > .45 && iy > .45) ok = false;"
|
|
"if(iz > 0.004 && ix > 0.4 && iy > 0.4 && ix < .6 && iy < .6) ok = true;"
|
|
"if(iz > 0.000004 && ix > 0.4 && ix < 0.7 && iy > 0.4 && iy < 0.7) ok = true;"
|
|
"if(iz < 0.04 && ix > 0.70 && ix < 0.8 && iy > 0.5 && iy < 0.7) ok = false;"
|
|
"if(iz < 0.05 && ix > .45 && iy > .75 && ix < .55 && iy < .95) ok = false;"
|
|
"if(iz < 0.05 && ix > .85 && iy > .45 && iy < .75) ok = false;"
|
|
"if(iz < 0.025 && ix > .65 && iy > .65 && ix < .8 && iy < .8) ok = false;"
|
|
|
|
"if(!ok) res = vec4(0,0,0,1);"
|
|
"else "
|
|
|
|
"\n#endif\n"
|
|
|
|
"res = texture3D(tInvExpTable, vec3(cx, cy, cz));"
|
|
|
|
"if(h[2] < 1e-6) { res.xy = res.yx; res[2] = -res[2]; }"
|
|
"if(h[0] < 0.) res[0] = -res[0];"
|
|
"if(h[1] < 0.) res[1] = -res[1];"
|
|
|
|
"return res;"
|
|
"}";
|
|
|
|
EX string shader_nsymsol = sn::common + R"*(
|
|
|
|
vec4 inverse_exp(vec4 h) {
|
|
|
|
float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);
|
|
float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);
|
|
float iz = z_to_iz_ns(h[2]);
|
|
|
|
vec4 res;
|
|
|
|
float cx = ix*(1.-1./PRECX) + .5/PRECX;
|
|
float cy = iy*(1.-1./PRECY) + .5/PRECY;
|
|
float cz = iz*(1.-1./PRECZ) + .5/PRECZ;
|
|
|
|
if(ix > .65 && iy > .5 && iz > .45 && iz < .55)
|
|
res = vec4(0.,0.,0.,1.);
|
|
else if(ix > .55 && iy > .75 && ix < .7 && iz > .45 && iz < .55)
|
|
res = vec4(0.,0.,0.,1.);
|
|
else if(ix > .45 && iy > .75 && ix < .7 && iz > .4 && iz < .5)
|
|
res = vec4(0.,0.,0.,1.);
|
|
else if(ix > .85 && iy > .5 && iz > .55 && iz < .75)
|
|
res = vec4(0.,0.,0.,1.);
|
|
else if(ix > .7 && iy > .55 && iz > .42 && iz < .58)
|
|
res = vec4(0.,0.,0.,1.);
|
|
else if(iz > 0.45 && ix > 0.8 && iy > 0.3 && iy < 0.6)
|
|
res = vec4(0.,0.,0.,1.);
|
|
else if(iz > 0.45 && ix > 0.8 && iy > 0.3 && iy < 0.6)
|
|
res = vec4(0.,0.,0.,1.);
|
|
else if(iz > .4 && iz < .55 && ix > .7 && iy > .36 && iy < .5 && ix < .8 && ix+iy > 1.2)
|
|
res = vec4(0.,0.,0.,1.);
|
|
else res = texture3D(tInvExpTable, vec3(cx, cy, cz));
|
|
|
|
if(h[0] < 0.) res[0] = -res[0];
|
|
if(h[1] < 0.) res[1] = -res[1];
|
|
|
|
return res;
|
|
})*";
|
|
|
|
EX string shader_nsym = sn::common +
|
|
|
|
"vec4 inverse_exp(vec4 h) {"
|
|
|
|
"float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);"
|
|
"float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);"
|
|
"float iz = z_to_iz_ns(h[2]);"
|
|
|
|
"vec4 res;"
|
|
|
|
"float cx = ix*(1.-1./PRECX) + .5/PRECX;"
|
|
"float cy = iy*(1.-1./PRECY) + .5/PRECY;"
|
|
"float cz = iz*(1.-1./PRECZ) + .5/PRECZ;"
|
|
|
|
"res = texture3D(tInvExpTable, vec3(cx, cy, cz));"
|
|
|
|
"if(h[0] < 0.) res[0] = -res[0];"
|
|
"if(h[1] < 0.) res[1] = -res[1];"
|
|
|
|
"return res;"
|
|
"}";
|
|
|
|
EX ld solrange_xy = 15;
|
|
EX ld solrange_z = 4;
|
|
|
|
EX bool in_table_range(hyperpoint h) {
|
|
return abs(h[0]) < solrange_xy && abs(h[1]) < solrange_xy && abs(h[2]) < solrange_z;
|
|
}
|
|
|
|
EX tabled_inverses solt = sn::tabled_inverses("solv-geodesics.dat");
|
|
EX tabled_inverses niht = sn::tabled_inverses("shyp-geodesics.dat");
|
|
EX tabled_inverses sont = sn::tabled_inverses("ssol-geodesics.dat");
|
|
|
|
EX tabled_inverses& get_tabled() {
|
|
switch(geom()) {
|
|
case gSol: return solt;
|
|
case gNIH: return niht;
|
|
case gSolN: return sont;
|
|
default: throw "not solnih";
|
|
}
|
|
}
|
|
|
|
EX int approx_distance(heptagon *h1, heptagon *h2) {
|
|
auto m = (sn::hrmap_solnih*) currentmap;
|
|
dynamicval<eGeometry> g(geometry, gBinary4);
|
|
dynamicval<hrmap*> cm(currentmap, m->binary_map);
|
|
int d1 = bt::celldistance3_approx(m->coords[h1].first, m->coords[h2].first);
|
|
int d2 = bt::celldistance3_approx(m->coords[h1].second, m->coords[h2].second);
|
|
return d1 + d2 - abs(h1->distance - h2->distance);
|
|
}
|
|
EX }
|
|
#endif
|
|
|
|
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])
|
|
);
|
|
}
|
|
|
|
EX hyperpoint formula_exp(hyperpoint v) {
|
|
// copying Modelling Nil-geometry in Euclidean Space with Software Presentation
|
|
// v[0] = c cos alpha
|
|
// v[1] = c sin alpha
|
|
// v[2] = w
|
|
|
|
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);
|
|
|
|
ld alpha = atan2(v[1], v[0]);
|
|
ld w = v[2];
|
|
ld c = hypot(v[0], v[1]) / v[2];
|
|
|
|
return 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)))
|
|
);
|
|
}
|
|
|
|
EX hyperpoint get_inverse_exp(hyperpoint h, flagtype prec IS(pNORMAL)) {
|
|
ld wmin, wmax;
|
|
|
|
ld side = h[2] - h[0] * h[1] / 2;
|
|
|
|
if(hypot_d(2, h) < 1e-6) return point3(h[0], h[1], h[2]);
|
|
else if(side > 1e-6) {
|
|
wmin = 0, wmax = 2 * M_PI;
|
|
}
|
|
else if(side < -1e-6) {
|
|
wmin = - 2 * M_PI, wmax = 0;
|
|
}
|
|
else return point3(h[0], h[1], 0);
|
|
|
|
ld alpha_total = h[0] ? atan(h[1] / h[0]) : M_PI/2;
|
|
|
|
ld b;
|
|
if(abs(h[0]) > abs(h[1]))
|
|
b = h[0] / 2 / cos(alpha_total);
|
|
else
|
|
b = h[1] / 2 / sin(alpha_total);
|
|
|
|
ld s = sin(2 * alpha_total);
|
|
|
|
int max_iter = (prec & pfLOW_BS_ITER) ? 5 : 20;
|
|
|
|
for(int it=0;; it++) {
|
|
ld w = (wmin + wmax) / 2;
|
|
ld z = b * b * (s + (sin(w) - w)/(cos(w) - 1)) + w;
|
|
|
|
if(it == max_iter) {
|
|
ld alpha = alpha_total - w/2;
|
|
ld c = b / sin(w/2);
|
|
return point3(c * w * cos(alpha), c * w * sin(alpha), w);
|
|
}
|
|
if(h[2] > z) wmin = w;
|
|
else wmax = w;
|
|
}
|
|
}
|
|
|
|
EX string nilshader =
|
|
"vec4 inverse_exp(vec4 h) {"
|
|
"float wmin, wmax;"
|
|
"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; }"
|
|
"else if(side < -1e-6) { wmin = -2.*PI; wmax = 0.; }"
|
|
"else return vec4(h[0], h[1], 0., 1.);"
|
|
"float at = h[0] != 0. ? atan(h[1] / h[0]) : PI/2.;"
|
|
"float b = abs(h[0]) > abs(h[1]) ? h[0] / 2. / cos(at) : h[1] / 2. / sin(at);"
|
|
"float s = sin(2. * at);"
|
|
|
|
"for(int it=0; it<50; it++) {"
|
|
"float w = (wmin + wmax) / 2.;"
|
|
// the formula after ':' produces visible numerical artifacts for w~0
|
|
"float z = b * b * (s + (abs(w) < .1 ? w/3. + w*w*w/90. + w*w*w*w*w/2520.: (sin(w) - w)/(cos(w) - 1.))) + w;"
|
|
"if(h[2] > z) wmin = w;"
|
|
"else wmax = w;"
|
|
"}"
|
|
|
|
"float w = (wmin + wmax) / 2.;"
|
|
"float alpha = at - w/2.;"
|
|
"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> {
|
|
|
|
mvec() { }
|
|
|
|
mvec(int x, int y, int z) {
|
|
auto& a = *this;
|
|
a[0] = x; a[1] = y; a[2] = z;
|
|
}
|
|
mvec inverse() {
|
|
auto& a = *this;
|
|
return mvec(-a[0], -a[1], -a[2]+a[1] * a[0]);
|
|
}
|
|
mvec operator * (const mvec b) {
|
|
auto& a = *this;
|
|
return mvec(a[0] + b[0], a[1] + b[1], a[2] + b[2] + a[0] * b[1]);
|
|
}
|
|
};
|
|
#endif
|
|
|
|
static const mvec mvec_zero = mvec(0, 0, 0);
|
|
|
|
EX ld nilwidth = 1;
|
|
|
|
hyperpoint mvec_to_point(mvec m) { return hpxy3(m[0] * nilwidth, m[1] * nilwidth, m[2] * nilwidth * nilwidth); }
|
|
|
|
#if HDR
|
|
struct nilstructure {
|
|
vector<mvec> movevectors;
|
|
vector<vector<hyperpoint>> facevertices;
|
|
};
|
|
#endif
|
|
|
|
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), },
|
|
}}
|
|
};
|
|
|
|
nilstructure ns8 = {
|
|
{{ 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), },
|
|
}}
|
|
};
|
|
|
|
EX nilstructure& current_ns() { return S7 == 6 ? ns6 : ns8; }
|
|
|
|
EX array<int,3> nilperiod, nilperiod_edit;
|
|
int S7_edit;
|
|
|
|
EX transmatrix adjmatrix(int i) {
|
|
return nisot::translate(mvec_to_point(current_ns().movevectors[i]));
|
|
}
|
|
|
|
struct hrmap_nil : hrmap {
|
|
unordered_map<mvec, heptagon*> at;
|
|
unordered_map<heptagon*, mvec> coords;
|
|
|
|
heptagon *getOrigin() override { return get_at(mvec_zero); }
|
|
|
|
~hrmap_nil() {
|
|
for(auto& p: at) clear_heptagon(p.second);
|
|
}
|
|
|
|
heptagon *get_at(mvec c) {
|
|
auto& h = at[c];
|
|
if(h) return h;
|
|
h = tailored_alloc<heptagon> (S7);
|
|
h->c7 = newCell(S7, h);
|
|
coords[h] = c;
|
|
h->dm4 = 0;
|
|
h->zebraval = c[0];
|
|
h->emeraldval = c[1];
|
|
h->fieldval = c[2];
|
|
h->cdata = NULL;
|
|
h->alt = NULL;
|
|
return h;
|
|
}
|
|
|
|
heptagon *create_step(heptagon *parent, int d) override {
|
|
auto p = coords[parent];
|
|
auto q = p * current_ns().movevectors[d];
|
|
for(int a=0; a<3; a++) q[a] = zgmod(q[a], nilperiod[a]);
|
|
auto child = get_at(q);
|
|
parent->c.connect(d, child, (d + S7/2) % S7, false);
|
|
return child;
|
|
}
|
|
|
|
transmatrix adj(heptagon *h, int i) override { return adjmatrix(i); }
|
|
|
|
virtual transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
|
|
for(int a=0; a<S7; a++) if(h2 == h1->move(a)) return adjmatrix(a);
|
|
auto p = coords[h1].inverse() * coords[h2];
|
|
for(int a=0; a<3; a++) p[a] = szgmod(p[a], nilperiod[a]);
|
|
return nisot::translate(mvec_to_point(p));
|
|
}
|
|
};
|
|
|
|
EX mvec get_coord(heptagon *h) { return ((hrmap_nil*)currentmap)->coords[h]; }
|
|
|
|
EX heptagon *get_heptagon_at(mvec m) { return ((hrmap_nil*)currentmap)->get_at(m); }
|
|
|
|
EX void set_flags() {
|
|
int coords = 0;
|
|
for(int a=0; a<3; a++) if(nilperiod[a]) coords++;
|
|
set_flag(ginf[gNil].flags, qANYQ, coords);
|
|
set_flag(ginf[gNil].flags, qBOUNDED, coords == 3);
|
|
set_flag(ginf[gNil].flags, qSMALL, coords == 3 && nilperiod[0] * nilperiod[1] * nilperiod[2] <= 4096);
|
|
}
|
|
|
|
EX hyperpoint on_geodesic(hyperpoint s0, hyperpoint s1, ld x) {
|
|
hyperpoint local = nisot::translate(s0, -1) * s1;
|
|
hyperpoint h = get_inverse_exp(local);
|
|
return nisot::translate(s0) * formula_exp(h * x);
|
|
}
|
|
|
|
EX color_t colorize(cell *c, char whichCanvas) {
|
|
mvec at = ((hrmap_nil*)currentmap)->coords[c->master];
|
|
color_t res = 0;
|
|
|
|
auto setres = [&] (int z, color_t which) {
|
|
if(zgmod(at[2] - z, nilperiod[2]) == 0) res = which;
|
|
if(zgmod(at[2] - z-1, nilperiod[2]) == 0) res = which;
|
|
};
|
|
|
|
if(at[1] == 0 && at[0] >=0 && at[0] < 4)
|
|
setres(-at[0], gradient(0x1FF0000, 0x10000FF, 0, at[0], 4));
|
|
else if(at[0] == 4 && at[1] >= 0 && at[1] < 4)
|
|
setres(at[1]*3-4, gradient(0x10000FF, 0x100FF00, 0, at[1], 4));
|
|
else if(at[1] == 4 && at[0] >= 0 && at[0] <= 4)
|
|
setres(4+at[0], gradient(0x100FF00, 0x1FFFF00, 4, at[0], 0));
|
|
else if(at[0] == 0 && at[1] >= 0 && at[1] <= 4)
|
|
setres(at[1], gradient(0x1FFFF00, 0x1FF0000, 4, at[1], 0));
|
|
|
|
return res;
|
|
}
|
|
|
|
EX void prepare_niltorus3() {
|
|
nilperiod_edit = nilperiod;
|
|
S7_edit = ginf[gNil].sides;
|
|
}
|
|
|
|
EX void show_niltorus3() {
|
|
cmode = sm::SIDE | sm::MAYDARK;
|
|
gamescreen(1);
|
|
dialog::init(XLAT("Nil quotient spaces"));
|
|
for(int a=0; a<3; a++) {
|
|
string title = XLAT("%1 period", s0+char('X'+a));
|
|
dialog::addSelItem(title, its(nilperiod_edit[a]), 'x');
|
|
dialog::add_action([=] {
|
|
dialog::editNumber(nilperiod_edit[a], 0, 60, 1, 0, title,
|
|
XLAT("Set to 0 to make it non-periodic.")
|
|
);
|
|
dialog::bound_low(0);
|
|
});
|
|
}
|
|
dialog::addSelItem(XLAT("honeycomb"), its(S7_edit), 'h');
|
|
dialog::add_action([] { S7_edit = S7_edit ^ 6 ^ 8; });
|
|
|
|
bool ok = (!nilperiod_edit[1]) || (nilperiod_edit[2] && nilperiod_edit[1] % nilperiod_edit[2] == 0);
|
|
|
|
dialog::addBreak(50);
|
|
|
|
if(ok) {
|
|
dialog::addItem(XLAT("activate"), 'a');
|
|
dialog::add_action([] {
|
|
stop_game();
|
|
nilperiod = nilperiod_edit;
|
|
ginf[gNil].sides = S7_edit;
|
|
set_flags();
|
|
geometry = gNil;
|
|
start_game();
|
|
});
|
|
}
|
|
else dialog::addInfo(XLAT("Y period must be divisible by Z period"));
|
|
|
|
dialog::addBreak(50);
|
|
dialog::addBack();
|
|
dialog::display();
|
|
}
|
|
|
|
EX }
|
|
|
|
EX bool in_s2xe() { return prod && hybrid::under_class() == gcSphere; }
|
|
EX bool in_h2xe() { return prod && hybrid::under_class() == gcHyperbolic; }
|
|
EX bool in_e2xe() { return prod && hybrid::under_class() == gcEuclid; }
|
|
|
|
EX namespace hybrid {
|
|
|
|
EX eGeometry underlying;
|
|
EX geometry_information *underlying_cgip;
|
|
|
|
EX eGeometryClass under_class() { return ginf[hybrid::underlying].cclass; }
|
|
|
|
EX int csteps;
|
|
|
|
EX int disc_quotient = 0;
|
|
|
|
EX transmatrix ray_iadj(cell *c, int i) {
|
|
if(prod && i == c->type-2) return (mscale(Id, +cgi.plevel));
|
|
if(prod && i == c->type-1) return (mscale(Id, -cgi.plevel));
|
|
if(WDIM == 2) {
|
|
return to_other_side(get_corner_position(c, i), get_corner_position(c, (i+1)));
|
|
}
|
|
if(prod) {
|
|
transmatrix T;
|
|
cell *cw = hybrid::get_where(c).first;
|
|
hybrid::in_underlying_geometry([&] {
|
|
T = to_other_side(get_corner_position(cw, i), get_corner_position(cw, (i+1)));
|
|
});
|
|
return T;
|
|
}
|
|
if(rotspace) return rots::ray_iadj(c, i);
|
|
return currentmap->iadj(c, i);
|
|
}
|
|
|
|
EX void configure(eGeometry g) {
|
|
if(WDIM == 3) return;
|
|
ray::reset_raycaster();
|
|
check_cgi();
|
|
cgi.require_basics();
|
|
underlying = geometry;
|
|
underlying_cgip = cgip;
|
|
bool sph = sphere;
|
|
auto keep = ginf[g].menu_displayed_name;
|
|
ginf[g] = ginf[underlying];
|
|
ginf[g].menu_displayed_name = keep;
|
|
if(g == gRotSpace) {
|
|
ginf[g].g = sph ? giSphere3 : giSL2;
|
|
ginf[g].tiling_name = "Iso(" + ginf[g].tiling_name + ")";
|
|
string& qn = ginf[g].quotient_name;
|
|
if(csteps && csteps != (sph ? cgi.psl_steps*2 : 0)) {
|
|
string qplus;
|
|
if(csteps == cgi.psl_steps)
|
|
qplus = sph ? "elliptic" : "PSL";
|
|
else if(csteps == 2 * cgi.psl_steps && !sph)
|
|
qplus = "SL";
|
|
else qplus = its(csteps);
|
|
if(qn == "none") qn = qplus;
|
|
else qn = qn + "/" + qplus;
|
|
}
|
|
if(elliptic) ginf[g].flags |= qELLIPTIC;
|
|
if(csteps && csteps != cgi.psl_steps && csteps != 2*cgi.psl_steps)
|
|
ginf[g].flags |= qANYQ;
|
|
}
|
|
else {
|
|
ginf[g].cclass = g == gRotSpace ? gcSL2 : gcProduct;
|
|
ginf[g].g.gameplay_dimension++;
|
|
ginf[g].g.graphical_dimension++;
|
|
ginf[g].tiling_name += "xZ";
|
|
if(csteps) ginf[g].flags |= qANYQ, ginf[g].tiling_name += its(csteps);
|
|
}
|
|
ginf[g].flags |= qHYBRID;
|
|
}
|
|
|
|
EX void reconfigure() {
|
|
if(!hybri) return;
|
|
stop_game();
|
|
auto g = geometry;
|
|
geometry = underlying;
|
|
configure(g);
|
|
geometry = g;
|
|
}
|
|
|
|
EX hrmap *pmap;
|
|
EX geometry_information *pcgip;
|
|
EX eGeometry actual_geometry;
|
|
|
|
template<class T> auto in_actual(const T& t) -> decltype(t()) {
|
|
dynamicval<eGeometry> g(geometry, actual_geometry);
|
|
dynamicval<geometry_information*> gc(cgip, pcgip);
|
|
dynamicval<hrmap*> gu(currentmap, pmap);
|
|
dynamicval<hrmap*> gup(pmap, NULL);
|
|
return t();
|
|
}
|
|
|
|
struct hrmap_hybrid : hrmap {
|
|
|
|
hrmap *underlying_map;
|
|
|
|
bool twisted;
|
|
map<cell*, pair<cellwalker, cellwalker>> spins;
|
|
|
|
map<pair<cell*, int>, cell*> at;
|
|
map<cell*, pair<cell*, int>> where;
|
|
|
|
heptagon *getOrigin() override { return underlying_map->getOrigin(); }
|
|
|
|
const int SHIFT_UNKNOWN = 30000;
|
|
map<cell*, vector<int>> shifts;
|
|
|
|
EX vector<int>& make_shift(cell *c) {
|
|
auto& res = shifts[c];
|
|
if(res.empty()) res = vector<int> (c->type+1, SHIFT_UNKNOWN);
|
|
return res;
|
|
}
|
|
|
|
EX int& get_shift_current(cellwalker cw) {
|
|
return make_shift(cw.at)[cw.spin];
|
|
}
|
|
|
|
EX bool have_shift(cellwalker cw) {
|
|
return shifts.count(cw.at) && get_shift_current(cw) != SHIFT_UNKNOWN;
|
|
}
|
|
|
|
EX int get_shift(cellwalker cw0) {
|
|
if(S3 >= OINF) return 0;
|
|
auto& v = get_shift_current(cw0);
|
|
if(v != SHIFT_UNKNOWN) return v;
|
|
|
|
vector<int> candidates;
|
|
|
|
for(int a: {1, -1}) {
|
|
cellwalker cw = cw0;
|
|
cw += wstep; cw += a;
|
|
int s = 0;
|
|
while(cw != cw0) {
|
|
if(!have_shift(cw)) goto next;
|
|
s += shifts[cw.at][cw.spin];
|
|
cw += wstep;
|
|
cw += a;
|
|
}
|
|
candidates.push_back(-a * cgi.single_step * (sphere ? -1 : 1) - s);
|
|
next: ;
|
|
}
|
|
|
|
if(candidates.size() == 2 && candidates[0] != candidates[1]) {
|
|
int val = candidates[0] - candidates[1];
|
|
if(disc_quotient == 0) disc_quotient = val;
|
|
disc_quotient = gcd(val, disc_quotient);
|
|
if(disc_quotient < 0) disc_quotient = -disc_quotient;
|
|
}
|
|
|
|
int val = 0;
|
|
|
|
auto cw1 = cw0+wstep;
|
|
if(1) {
|
|
/* the value from PSL, helps to draw the underlying space correctly */
|
|
auto ps = cgi.psl_steps;
|
|
val = cw0.spin*ps / cw0.at->type - cw1.spin*ps / cw1.at->type + ps/2;
|
|
}
|
|
if(!candidates.empty()) val = candidates[0];
|
|
|
|
v = val;
|
|
get_shift_current(cw1) = -val;
|
|
|
|
return val;
|
|
}
|
|
|
|
EX void ensure_shifts(cell *c) {
|
|
if(S3 >= OINF) return;
|
|
if(!make_shift(c)[c->type]) return;
|
|
forCellEx(c1, c)
|
|
for(int a=0; a<c->type; a++) {
|
|
cellwalker cw0(c, a);
|
|
cellwalker cw = cw0;
|
|
while(cw != cw0) {
|
|
get_shift(cw);
|
|
cw += wstep;
|
|
cw += a;
|
|
}
|
|
}
|
|
make_shift(c)[c->type] = 0;
|
|
}
|
|
|
|
EX int cycle_discrepancy(cellwalker cw0) {
|
|
int total = 0;
|
|
auto cw = cw0;
|
|
do {
|
|
total += get_shift(cw);
|
|
cw += wstep;
|
|
cw++;
|
|
}
|
|
while(cw != cw0);
|
|
return total + cgi.single_step * (sphere ? -1 : 1);
|
|
}
|
|
|
|
EX void fix_bounded_cycles() {
|
|
if(!rotspace) return;
|
|
if(!bounded) return;
|
|
in_underlying([&] {
|
|
cellwalker final(currentmap->gamestart(), 0);
|
|
auto& ac = currentmap->allcells();
|
|
for(cell *c: ac) for(int i=0; i<c->type; i++) {
|
|
cellwalker cw(c, i);
|
|
int cd = cycle_discrepancy(cw);
|
|
if(!cd) continue;
|
|
while(cw != final) {
|
|
if(celldist(cw.peek()) < celldist(cw.at)) {
|
|
cw += wstep;
|
|
cw++;
|
|
}
|
|
else {
|
|
get_shift_current(cw) -= cd;
|
|
get_shift_current(cw+wstep) += cd;
|
|
cw++;
|
|
}
|
|
}
|
|
}
|
|
|
|
disc_quotient = abs(cycle_discrepancy(final));
|
|
|
|
if(debugflags & DF_GEOM) for(cell *c: ac) for(int i=0; i<c->type; i++) {
|
|
cellwalker cw(c, i);
|
|
if(cycle_discrepancy(cw)) println(hlog, cw, cycle_discrepancy(cw));
|
|
}
|
|
});
|
|
}
|
|
|
|
template<class T> auto in_underlying(const T& t) -> decltype(t()) {
|
|
pcgip = cgip;
|
|
dynamicval<hrmap*> gpm(pmap, this);
|
|
dynamicval<eGeometry> gag(actual_geometry, geometry);
|
|
dynamicval<eGeometry> g(geometry, underlying);
|
|
dynamicval<geometry_information*> gc(cgip, underlying_cgip);
|
|
dynamicval<hrmap*> gu(currentmap, underlying_map);
|
|
return t();
|
|
}
|
|
|
|
cell *getCell(cell *u, int h) {
|
|
if(twisted) {
|
|
if(!spins.count(u))
|
|
println(hlog, "link missing: ", u);
|
|
else {
|
|
while(h >= csteps) h -= csteps, u = spins[u].first.at;
|
|
while(h < 0) h += csteps, u = spins[u].second.at;
|
|
}
|
|
}
|
|
h = zgmod(h, csteps);
|
|
cell*& c = at[make_pair(u, h)];
|
|
if(!c) { c = newCell(u->type+2, u->master); where[c] = {u, h}; }
|
|
return c;
|
|
}
|
|
|
|
cell* gamestart() override { return getCell(underlying_map->gamestart(), 0); }
|
|
|
|
hrmap_hybrid() {
|
|
twisted = false;
|
|
disc_quotient = 0;
|
|
in_underlying([this] { initcells(); underlying_map = currentmap; });
|
|
for(hrmap*& m: allmaps) if(m == underlying_map) m = NULL;
|
|
fix_bounded_cycles();
|
|
}
|
|
|
|
~hrmap_hybrid() {
|
|
in_underlying([] { delete currentmap; });
|
|
for(auto& p: at) destroy_cell(p.second);
|
|
}
|
|
|
|
virtual transmatrix spin_to(cell *c, int d, ld bonus) override { if(d >= c->type-2) return Id; c = get_where(c).first; return in_underlying([&] { return currentmap->spin_to(c, d, bonus); }); }
|
|
virtual transmatrix spin_from(cell *c, int d, ld bonus) override { if(d >= c->type-2) return Id; c = get_where(c).first; return in_underlying([&] { return currentmap->spin_from(c, d, bonus); }); }
|
|
};
|
|
|
|
hrmap_hybrid* hmap() { return (hrmap_hybrid*) currentmap; }
|
|
|
|
EX cell *get_at(cell *base, int level) {
|
|
return hmap()->getCell(base, level);
|
|
}
|
|
|
|
EX pair<cell*, int> get_where(cell *c) { return hmap()->where[c]; }
|
|
|
|
EX void find_cell_connection(cell *c, int d) {
|
|
auto m = hmap();
|
|
if(d >= c->type - 2) {
|
|
int s = cgi.single_step;
|
|
int lev = m->where[c].second + (d == c->type-1 ? s : -s);
|
|
cell *c1 = get_at(m->where[c].first, lev);
|
|
c->c.connect(d, c1, c1->type - 3 + c->type - d, false);
|
|
}
|
|
else {
|
|
auto cu = m->where[c].first;
|
|
auto cu1 = m->in_underlying([&] { return cu->cmove(d); });
|
|
int d1 = cu->c.spin(d);
|
|
int s = 0;
|
|
if(geometry == gRotSpace) {
|
|
auto cm = (hrmap_hybrid*)currentmap;
|
|
m->in_underlying([&] { cm->ensure_shifts(cu); });
|
|
s = ((hrmap_hybrid*)currentmap)->get_shift(cellwalker(cu, d));
|
|
}
|
|
cell *c1 = get_at(cu1, m->where[c].second + s);
|
|
c->c.connect(d, c1, d1, cu->c.mirror(d));
|
|
}
|
|
}
|
|
|
|
EX hrmap* get_umap() { if(!dynamic_cast<hrmap_hybrid*>(currentmap)) return nullptr; else return ((hrmap_hybrid*)currentmap)->underlying_map; }
|
|
|
|
#if HDR
|
|
template<class T> auto in_underlying_geometry(const T& f) -> decltype(f()) {
|
|
if(!hybri) return f();
|
|
dynamicval<eGeometry> g(geometry, underlying);
|
|
dynamicval<eGeometry> gag(actual_geometry, geometry);
|
|
dynamicval<geometry_information*> gc(cgip, underlying_cgip);
|
|
dynamicval<hrmap*> gpm(pmap, currentmap);
|
|
dynamicval<hrmap*> gm(currentmap, get_umap());
|
|
return f();
|
|
}
|
|
|
|
#define PIU(x) hr::hybrid::in_underlying_geometry([&] { return (x); })
|
|
#endif
|
|
|
|
EX hyperpoint get_corner(cell *c, int i, int next, ld z) {
|
|
ld lev = cgi.plevel * z / 2;
|
|
if(WDIM == 2) {
|
|
ld zz = lerp(cgi.FLOOR, cgi.WALL, (1+z) / 2);
|
|
hyperpoint h = zshift(get_corner_position(c, i+next), zz);
|
|
return h;
|
|
}
|
|
if(prod) {
|
|
dynamicval<eGeometry> g(geometry, hybrid::underlying);
|
|
dynamicval<geometry_information*> gc(cgip, hybrid::underlying_cgip);
|
|
dynamicval<hrmap*> gm(currentmap, ((hrmap_hybrid*)currentmap)->underlying_map);
|
|
return mscale(get_corner_position(c, i+next), exp(lev));
|
|
}
|
|
else {
|
|
ld tf, he, alpha;
|
|
in_underlying_geometry([&] {
|
|
hyperpoint h1 = get_corner_position(c, i);
|
|
hyperpoint h2 = get_corner_position(c, i+1);
|
|
hyperpoint hm = mid(h1, h2);
|
|
tf = hdist0(hm)/2;
|
|
he = hdist(hm, h2)/2;
|
|
alpha = atan2(hm[1], hm[0]);
|
|
});
|
|
return spin(alpha) * rots::uxpush(tf) * rots::uypush(next?he:-he) * rots::uzpush(lev) * C0;
|
|
}
|
|
}
|
|
|
|
EX int wall_offset(cell *c) {
|
|
if(GOLDBERG) {
|
|
/* a bit slow... */
|
|
cell *c1 = WDIM == 2 ? c : get_where(c).first;
|
|
gp::draw_li = WDIM == 2 ? gp::get_local_info(c1) : PIU(gp::get_local_info(c1));
|
|
}
|
|
auto ugeometry = hybri ? hybrid::underlying : geometry;
|
|
int id = ugeometry == gArchimedean ? arcm::id_of(c->master) + 20 * arcm::parent_index_of(c->master) : shvid(c);
|
|
if(isize(cgi.walloffsets) <= id) cgi.walloffsets.resize(id+1, {-1, nullptr});
|
|
auto &wop = cgi.walloffsets[id];
|
|
int &wo = wop.first;
|
|
if(!wop.second) wop.second = c;
|
|
if(wo == -1) {
|
|
cell *c1 = hybri ? hybrid::get_where(c).first : c;
|
|
wo = isize(cgi.shWall3D);
|
|
int won = wo + c->type + (WDIM == 2 ? 2 : 0);
|
|
if(!cgi.wallstart.empty()) cgi.wallstart.pop_back();
|
|
cgi.reserve_wall3d(won);
|
|
|
|
if(prod || WDIM == 2) for(int i=0; i<c1->type; i++) {
|
|
hyperpoint w;
|
|
auto f = [&] {
|
|
/* mirror image of C0 in the axis h1-h2 */
|
|
hyperpoint h1 = get_corner_position(c1, i);
|
|
hyperpoint h2 = get_corner_position(c1, i+1);
|
|
transmatrix T = gpushxto0(h1);
|
|
T = spintox(T * h2) * T;
|
|
w = T * C0;
|
|
w[1] = -w[1];
|
|
w = iso_inverse(T) * w;
|
|
};
|
|
if(prod)
|
|
((hrmap_hybrid*)currentmap)->in_underlying(f);
|
|
else
|
|
f();
|
|
cgi.walltester[wo + i] = w;
|
|
}
|
|
|
|
for(int i=0; i<c1->type; i++)
|
|
cgi.make_wall(wo + i, {hybrid::get_corner(c1, i, 0, -1), hybrid::get_corner(c1, i, 0, +1), hybrid::get_corner(c1, i, 1, +1), hybrid::get_corner(c1, i, 1, -1)});
|
|
|
|
for(int a: {0,1}) {
|
|
vector<hyperpoint> l;
|
|
int z = a ? 1 : -1;
|
|
hyperpoint ctr = zpush0(z * cgi.plevel/2);
|
|
for(int i=0; i<c1->type; i++)
|
|
if(prod || WDIM == 2)
|
|
l.push_back(hybrid::get_corner(c1, i, 0, z));
|
|
else {
|
|
l.push_back(ctr);
|
|
l.push_back(hybrid::get_corner(c1, i, 0, z));
|
|
l.push_back(hybrid::get_corner(c1, i+1, 1, z));
|
|
l.push_back(ctr);
|
|
l.push_back(hybrid::get_corner(c1, i, 1, z));
|
|
l.push_back(hybrid::get_corner(c1, i, 0, z));
|
|
}
|
|
if(a == 0) std::reverse(l.begin()+1, l.end());
|
|
cgi.make_wall(won-2+a, l);
|
|
}
|
|
|
|
cgi.wallstart.push_back(isize(cgi.raywall));
|
|
cgi.compute_cornerbonus();
|
|
cgi.extra_vertices();
|
|
}
|
|
return wo;
|
|
}
|
|
|
|
auto clear_samples = addHook(hooks_clearmemory, 40, [] () {
|
|
for(auto& c: cgis) for(auto& v: c.second.walloffsets)
|
|
v.second = nullptr;
|
|
});
|
|
|
|
EX vector<pair<int, cell*>> gen_sample_list() {
|
|
if(!hybri && WDIM != 2) return {make_pair(0, centerover), make_pair(centerover->type, nullptr)};
|
|
vector<pair<int, cell*>> result;
|
|
for(auto& v: cgi.walloffsets) if(v.first >= 0) result.push_back(v);
|
|
sort(result.begin(), result.end());
|
|
result.emplace_back(isize(cgi.wallstart)-1, nullptr);
|
|
return result;
|
|
}
|
|
|
|
vector<cell*> to_link;
|
|
|
|
EX void will_link(cell *c) { if(pmap && ((hrmap_hybrid*) pmap)->twisted) to_link.push_back(c); }
|
|
|
|
EX bool in_link = false;
|
|
|
|
EX void link() {
|
|
if(in_link) return;
|
|
dynamicval<bool> b(in_link, true);
|
|
auto pm = (hrmap_hybrid*) pmap;
|
|
if(!pm) return;
|
|
auto& ss = pm->spins;
|
|
int success = -1;
|
|
while(success) {
|
|
vector<cell*> xlink = std::move(to_link);
|
|
success = 0;
|
|
for(cell *c: xlink) {
|
|
bool success_here = ss.count(c);
|
|
if(!success_here) forCellIdEx(c2, i, c) if(ss.count(c2)) {
|
|
ss[c].first = ss[c2].first + c->c.spin(i) + wstep - i;
|
|
ss[c].second = ss[c2].second + c->c.spin(i) + wstep - i;
|
|
success++;
|
|
success_here = true;
|
|
break;
|
|
}
|
|
if(!success_here) to_link.push_back(c);
|
|
}
|
|
}
|
|
}
|
|
|
|
EX int celldistance(cell *c1, cell *c2) {
|
|
if(sl2) {
|
|
auto w1 = hybrid::get_where(c1), w2 = hybrid::get_where(c2);
|
|
return PIU (hr::celldistance(w1.first, w2.first));
|
|
}
|
|
else if(csteps == 0) {
|
|
auto w1 = hybrid::get_where(c1), w2 = hybrid::get_where(c2);
|
|
return PIU (hr::celldistance(w1.first, w2.first)) + abs(w1.second - w2.second);
|
|
}
|
|
else {
|
|
int s = 0;
|
|
int a = 999999, b = -999999;
|
|
auto c = c1;
|
|
do {
|
|
auto w1 = hybrid::get_where(c), w2 = hybrid::get_where(c2);
|
|
if(w1.second == w2.second) {
|
|
int d = PIU(hr::celldistance(w1.first, w2.first));
|
|
a = min(s+d, a);
|
|
b = max(s-d, b);
|
|
}
|
|
c = c->cmove(c1->type-1); s++;
|
|
}
|
|
while(c != c1);
|
|
return min(a, s-b);
|
|
}
|
|
}
|
|
|
|
EX void configure_period() {
|
|
static int s;
|
|
s = csteps / cgi.single_step;
|
|
string str = "";
|
|
if(rotspace)
|
|
str = XLAT(
|
|
"If the 2D underlying manifold is bounded, the period should be a divisor of the 'rotation space' "
|
|
"value (PSL(2,R)) times the Euler characteristics of the underlying manifold. "
|
|
"For unbounded underlying manifold, any value should work (theoretically, "
|
|
"the current implementation in HyperRogue is not perfect).\n\n"
|
|
"We won't stop you from trying illegal numbers, but they won't work correctly.");
|
|
dialog::editNumber(s, 0, 16, 1, 0, XLAT("%1 period", "Z"), str);
|
|
dialog::bound_low(0);
|
|
auto set_s = [] (int s1, bool ret) {
|
|
return [s1,ret] {
|
|
if(ret) popScreen();
|
|
if(csteps == s1) return;
|
|
stop_game();
|
|
csteps = s1 * cgi.single_step;
|
|
hybrid::reconfigure();
|
|
start_game();
|
|
};
|
|
};
|
|
dialog::extra_options = [=] () {
|
|
if(rotspace) {
|
|
int e_steps = cgi.psl_steps / gcd(cgi.single_step, cgi.psl_steps);
|
|
bool ubounded = PIU(bounded);
|
|
dialog::addSelItem( XLAT(sphere ? "elliptic" : "PSL(2,R)"), its(e_steps), 'P');
|
|
dialog::add_action(set_s(e_steps, true));
|
|
dialog::addSelItem( XLAT(sphere ? "sphere" : "SL(2,R)"), its(2*e_steps), 'P');
|
|
dialog::add_action(set_s(2*e_steps, true));
|
|
if(sl2 && !ubounded) {
|
|
dialog::addSelItem( XLAT("universal cover"), its(0), 'P');
|
|
dialog::add_action(set_s(0, true));
|
|
}
|
|
dialog::addSelItem(ubounded ? XLAT("maximum") : XLAT("works correctly so far"), its(disc_quotient), 'Q');
|
|
dialog::add_action(set_s(disc_quotient, true));
|
|
}
|
|
else {
|
|
dialog::addSelItem( XLAT("non-periodic"), its(0), 'N');
|
|
dialog::add_action(set_s(0, true));
|
|
}
|
|
dialog::reaction_final = set_s(s, false);
|
|
};
|
|
}
|
|
|
|
EX }
|
|
|
|
EX namespace product {
|
|
|
|
int z0;
|
|
|
|
struct hrmap_product : hybrid::hrmap_hybrid {
|
|
transmatrix relative_matrix(cell *c2, cell *c1, const hyperpoint& hint) override {
|
|
return in_underlying([&] { return calc_relative_matrix(where[c2].first, where[c1].first, hint); }) * mscale(Id, cgi.plevel * szgmod(where[c2].second - where[c1].second, hybrid::csteps));
|
|
}
|
|
|
|
transmatrix adj(cell *c, int i) override {
|
|
if(twisted && i == c->type-1 && where[c].second == hybrid::csteps-1) {
|
|
auto b = spins[where[c].first].first;
|
|
transmatrix T = mscale(Id, cgi.plevel);
|
|
T = T * spin(2 * M_PI * b.spin / b.at->type);
|
|
if(b.mirrored) T = T * Mirror;
|
|
return T;
|
|
}
|
|
if(twisted && i == c->type-2 && where[c].second == 0) {
|
|
auto b = spins[where[c].first].second;
|
|
transmatrix T = mscale(Id, -cgi.plevel);
|
|
T = T * spin(2 * M_PI * b.spin / b.at->type);
|
|
if(b.mirrored) T = T * Mirror;
|
|
return T;
|
|
}
|
|
if(i == c->type-1) return mscale(Id, cgi.plevel);
|
|
else if(i == c->type-2) return mscale(Id, -cgi.plevel);
|
|
c = where[c].first;
|
|
return PIU(currentmap->adj(c, i));
|
|
}
|
|
|
|
hrmap_product() {
|
|
current_spin_invalid = false;
|
|
using hybrid::csteps;
|
|
if((cspin || cmirror) && csteps) {
|
|
in_underlying([&] {
|
|
twisted = validate_spin();
|
|
if(!twisted) { current_spin_invalid = true; return; }
|
|
auto ugs = currentmap->gamestart();
|
|
spins[ugs] = make_pair(
|
|
cellwalker(ugs, gmod(+cspin, ugs->type), cmirror),
|
|
cellwalker(ugs, gmod(-cspin, ugs->type), cmirror)
|
|
);
|
|
manual_celllister cl;
|
|
cl.add(ugs);
|
|
for(int i=0; i<isize(cl.lst); i++) {
|
|
cell *c = cl.lst[i];
|
|
hybrid::will_link(c);
|
|
forCellEx(c2, c) cl.add(c2);
|
|
}
|
|
hybrid::link();
|
|
});
|
|
}
|
|
}
|
|
};
|
|
|
|
EX bool current_spin_invalid, cmirror;
|
|
EX int cspin;
|
|
|
|
/* todo might need a shiftpoint version */
|
|
EX hyperpoint inverse_exp(hyperpoint h) {
|
|
hyperpoint res;
|
|
res[2] = zlevel(h);
|
|
h = zshift(h, -res[2]);
|
|
ld r = hypot_d(2, h);
|
|
if(hybrid::under_class() == gcEuclid) {
|
|
res[0] = h[0];
|
|
res[1] = h[1];
|
|
}
|
|
else if(r < 1e-6) {
|
|
res[0] = h[0];
|
|
res[1] = h[1];
|
|
}
|
|
else {
|
|
auto c = acos_auto_clamp(h[2]);
|
|
r = c / r;
|
|
res[0] = h[0] * r;
|
|
res[1] = h[1] * r;
|
|
}
|
|
return res;
|
|
}
|
|
|
|
EX hyperpoint direct_exp(hyperpoint h) {
|
|
hyperpoint res;
|
|
ld d = hypot_d(2, h);
|
|
ld cd = d == 0 ? 0 : sin_auto(d) / d;
|
|
res[0] = h[0] * cd;
|
|
res[1] = h[1] * cd;
|
|
res[2] = cos_auto(d);
|
|
return zshift(res, h[2]);
|
|
}
|
|
|
|
EX bool validate_spin() {
|
|
if(prod) return hybrid::in_underlying_geometry(validate_spin);
|
|
if(kite::in()) return false;
|
|
if(!quotient && !arcm::in()) return true;
|
|
map<cell*, cellwalker> cws;
|
|
manual_celllister cl;
|
|
cell *start = currentmap->gamestart();
|
|
cl.add(start);
|
|
cws[start] = cellwalker(start, gmod(cspin, start->type), cmirror);
|
|
for(int i=0; i<isize(cl.lst); i++) {
|
|
cell *c = cl.lst[i];
|
|
cellwalker cwc = cws.at(c);
|
|
forCellIdEx(c2, j, c) {
|
|
cellwalker cwc2 = cwc + j + wstep - c->c.spin(j);
|
|
if(!cws.count(c2)) cws[c2] = cwc2;
|
|
else if(cws[c2] != cwc2) return false;
|
|
cl.add(c2);
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
EX void show_config() {
|
|
cmode = sm::SIDE | sm::MAYDARK;
|
|
gamescreen(1);
|
|
dialog::init(XLAT("quotient product spaces"));
|
|
dialog::addSelItem(XLAT("%1 period", "Z"), its(hybrid::csteps), 'z');
|
|
dialog::add_action(hybrid::configure_period);
|
|
dialog::addSelItem(XLAT("rotation"), its(cspin), 'r');
|
|
dialog::add_action([] {
|
|
static int s;
|
|
dialog::editNumber(s, 0, 16, 1, 0, XLAT("rotation", "Z"),
|
|
XLAT("Works if the underlying space is symmetric.")
|
|
);
|
|
dialog::reaction_final = [] {
|
|
if(s == cspin) return;
|
|
stop_game();
|
|
cspin = s;
|
|
start_game();
|
|
};
|
|
});
|
|
dialog::addBoolItem(XLAT("reflect"), cmirror, 'f');
|
|
dialog::add_action([]{
|
|
stop_game();
|
|
cmirror = !cmirror;
|
|
start_game();
|
|
});
|
|
if(current_spin_invalid)
|
|
dialog::addInfo("the current rotation is invalid");
|
|
else
|
|
dialog::addBreak(100);
|
|
|
|
dialog::addBreak(50);
|
|
dialog::addBack();
|
|
dialog::display();
|
|
}
|
|
|
|
EX }
|
|
|
|
EX namespace slr {
|
|
|
|
EX ld range_xy = 2;
|
|
EX int steps = 15;
|
|
|
|
EX transmatrix translate(hyperpoint h) {
|
|
return matrix4(
|
|
h[3], -h[2], h[1], h[0],
|
|
h[2], h[3], -h[0], h[1],
|
|
h[1], -h[0], h[3], h[2],
|
|
h[0], h[1], -h[2], h[3]
|
|
);
|
|
}
|
|
|
|
EX hyperpoint polar(ld r, ld theta, ld phi) {
|
|
return hyperpoint(sinh(r) * cos(theta-phi), sinh(r) * sin(theta-phi), cosh(r) * sin(phi), cosh(r) * cos(phi));
|
|
}
|
|
|
|
EX hyperpoint xyz_point(ld x, ld y, ld z) {
|
|
ld r = hypot(x, y);
|
|
ld f = r ? sinh(r) / r : 1;
|
|
return hyperpoint(x * f * cos(z) + y * f * sin(z), y * f * cos(z) - x * f * sin(z), cosh(r) * sin(z), cosh(r) * cos(z));
|
|
}
|
|
|
|
EX hyperpoint get_inverse_exp(shiftpoint h) {
|
|
ld xy = hypot_d(2, h.h);
|
|
ld phi = atan2(h[2], h[3]) + h.shift;
|
|
|
|
if(xy < 1e-6) return point31(0.,0.,phi);
|
|
|
|
bool flipped = phi > 0;
|
|
if(flipped) phi = -phi;
|
|
|
|
ld SV = stretch::not_squared();
|
|
ld K = -1;
|
|
|
|
ld alpha = flipped ? atan2(h[1], h[0]) - h.shift : atan2(h[1], -h[0]) + h.shift;
|
|
|
|
hyperpoint res;
|
|
|
|
ld fiber_barrier = atan(1/SV);
|
|
|
|
ld flip_barrier = atan( 1 / tanh(asinh(xy)) / SV);
|
|
|
|
// test the side of the flip barrier
|
|
|
|
int part = -1;
|
|
|
|
if(1) {
|
|
ld kk = flip_barrier;
|
|
|
|
ld x_part = cos(kk);
|
|
ld z_part = sin(kk);
|
|
|
|
ld rparam = x_part / z_part / SV;
|
|
|
|
ld r = atanh(rparam);
|
|
|
|
ld cr = cosh(r);
|
|
ld sr = sinh(r);
|
|
|
|
// sinh(r) = xy
|
|
// r = tanh(sinh(xy))
|
|
|
|
|
|
ld z = cr * (K - 1/SV/SV);
|
|
|
|
ld k = M_PI/2;
|
|
ld a = k / K;
|
|
ld zw = xy * cr / sr;
|
|
ld u = z * a;
|
|
|
|
ld phi1 = atan2(zw, cos(k)) - u;
|
|
|
|
if(phi < phi1) part = 2;
|
|
}
|
|
|
|
if(part == -1) {
|
|
ld zw = xy;
|
|
|
|
ld u = xy * (K - 1/SV/SV) / K;
|
|
ld phi1 = atan2(zw, 1) - u;
|
|
|
|
if(phi > phi1) part = 0; else part = 1;
|
|
}
|
|
|
|
if(part == 2) {
|
|
ld min_k = fiber_barrier;
|
|
ld max_k = flip_barrier;
|
|
|
|
for(int it=0; it<30; it++) {
|
|
ld kk = (min_k + max_k) / 2;
|
|
|
|
ld x_part = cos(kk);
|
|
ld z_part = sin(kk);
|
|
|
|
ld rparam = x_part / z_part / SV;
|
|
|
|
assert(rparam <= 1);
|
|
|
|
ld r = atanh(rparam);
|
|
ld cr = cosh(r);
|
|
ld sr = sinh(r);
|
|
|
|
ld z = cr * (K - 1/SV/SV);
|
|
|
|
ld k = M_PI - asin(xy / sr);
|
|
ld a = k / K;
|
|
ld len = a * hypot(sr, cr/SV);
|
|
ld zw = xy * cr / sr;
|
|
ld u = z * a;
|
|
|
|
ld phi1 = atan2(zw, cos(k)) - u;
|
|
|
|
if(phi < phi1) max_k = kk;
|
|
else min_k = kk;
|
|
|
|
ld r_angle = alpha + u;
|
|
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
|
|
}
|
|
}
|
|
|
|
if(part == 0) {
|
|
ld min_k = 0;
|
|
ld max_k = fiber_barrier;
|
|
|
|
for(int it=0; it<30; it++) {
|
|
ld kk = (min_k + max_k) / 2;
|
|
|
|
ld x_part = cos(kk);
|
|
ld z_part = sin(kk);
|
|
|
|
ld rparam = x_part / z_part / SV;
|
|
|
|
ld cr = 1 / sqrt(rparam*rparam - 1);
|
|
ld sr = rparam * cr;
|
|
|
|
ld z = cr * (K - 1/SV/SV);
|
|
|
|
ld k = asinh(xy / sr);
|
|
ld a = k / K;
|
|
ld len = a * hypot(sr, cr/SV);
|
|
|
|
ld zw = xy * cr / sr;
|
|
|
|
ld u = z * a;
|
|
ld phi1 = atan2(zw, cosh(k)) - u;
|
|
|
|
if(phi > phi1) max_k = kk; else min_k = kk;
|
|
|
|
ld r_angle = alpha + u;
|
|
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
|
|
}
|
|
}
|
|
|
|
if(part == 1) {
|
|
ld min_k = fiber_barrier;
|
|
ld max_k = flip_barrier;
|
|
|
|
for(int it=0; it<30; it++) {
|
|
ld kk = (min_k + max_k) / 2;
|
|
|
|
ld x_part = cos(kk);
|
|
ld z_part = sin(kk);
|
|
|
|
ld rparam = x_part / z_part / SV;
|
|
|
|
ld r = atanh(rparam);
|
|
ld cr = cosh(r);
|
|
ld sr = sinh(r);
|
|
|
|
ld z = cr * (K - 1/SV/SV);
|
|
|
|
ld k = asin(xy / sr);
|
|
ld a = k / K;
|
|
ld len = a * hypot(sr, cr/SV);
|
|
ld zw = xy * cr / sr;
|
|
ld u = z * a;
|
|
|
|
ld phi1 = atan2(zw, cos(k)) - u;
|
|
|
|
if(isnan(phi1)) max_k = kk;
|
|
else if(phi > phi1) max_k = kk;
|
|
else min_k = kk;
|
|
|
|
ld r_angle = alpha + u;
|
|
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
|
|
}
|
|
}
|
|
|
|
if(flipped) res[0] *= -1, res[2] *= -1;
|
|
|
|
return res;
|
|
}
|
|
|
|
#if ISWEB
|
|
#define ITERATE " for(int it=0; it<50; it++) { if(it >= uIterations) break; "
|
|
#else
|
|
#define ITERATE " for(int it=0; it<uIterations; it++) {"
|
|
#endif
|
|
|
|
EX string slshader =
|
|
|
|
"uniform mediump float uIndexSL;"
|
|
"uniform mediump int uIterations;"
|
|
"uniform mediump float uSV;"
|
|
|
|
"vec4 inverse_exp(vec4 h) {"
|
|
|
|
"float xy = length(h.xy);"
|
|
"float phi = atan2(h[2], h[3]) + uIndexSL;"
|
|
|
|
"if(xy < 1e-6) return vec4(0.,0.,phi,1.);"
|
|
|
|
"vec4 res = vec4(sqrt(-1.),sqrt(-1.),sqrt(-1.),sqrt(-1.));"
|
|
|
|
"bool flipped = phi > 0.;"
|
|
|
|
"if(flipped) phi = -phi;"
|
|
|
|
"float alpha = flipped ? atan2(h[1], h[0]) - uIndexSL : atan2(h[1], -h[0]) + uIndexSL;"
|
|
|
|
"float fiber_barrier = atan(1./uSV);"
|
|
|
|
"float flip_barrier = atan(1. / tanh(asinh(xy)) / uSV);"
|
|
|
|
"int part = 0;"
|
|
|
|
"if(true) {"
|
|
"float x_part = cos(flip_barrier);"
|
|
"float z_part = sin(flip_barrier);"
|
|
"float rparam = x_part / z_part / uSV;"
|
|
"float r = atanh(rparam);"
|
|
"float cr = cosh(r);"
|
|
"float sr = sinh(r);"
|
|
"float z = cr * (-1.-1./uSV/uSV);"
|
|
"float k = PI/2.;"
|
|
"float a = -k;"
|
|
"float zw = xy * cr / sr;"
|
|
"float u = z * a;"
|
|
"float phi1 = atan2(zw, cos(k)) - u;"
|
|
"if(phi < phi1) part = 2;"
|
|
"}\n"
|
|
|
|
"if(part == 0) {"
|
|
"float zw = xy;"
|
|
"float u = xy * (1. + 1./uSV/uSV);"
|
|
"float phi1 = atan2(zw, 1.) - u;"
|
|
"if(phi > phi1) part = 0; else part = 1;"
|
|
"}\n"
|
|
|
|
"if(part == 2) {"
|
|
"float min_k = fiber_barrier;"
|
|
"float max_k = flip_barrier;"
|
|
|
|
ITERATE
|
|
"float kk = (min_k + max_k) / 2.;"
|
|
"float x_part = cos(kk);"
|
|
"float z_part = sin(kk);"
|
|
"float rparam = x_part / z_part / uSV;"
|
|
"float r = atanh(rparam);"
|
|
"float cr = cosh(r);"
|
|
"float sr = sinh(r);"
|
|
|
|
"float z = cr * (-1. - 1./uSV/uSV);"
|
|
"float k = PI - asin(xy / sr);"
|
|
"float a = -k;"
|
|
"float len = a * length(vec2(sr, cr/uSV));"
|
|
"float zw = xy * cr / sr;"
|
|
"float u = z * a;"
|
|
"float phi1 = atan2(zw, cos(k)) - u;"
|
|
"if(phi < phi1) max_k = kk; else min_k = kk;"
|
|
"float r_angle = alpha + u;"
|
|
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
|
|
"}"
|
|
"}\n"
|
|
|
|
"if(part == 0) {"
|
|
"float min_k = 0.;"
|
|
"float max_k = fiber_barrier;"
|
|
|
|
ITERATE
|
|
"float kk = (min_k + max_k) / 2.;"
|
|
"float x_part = cos(kk);"
|
|
"float z_part = sin(kk);"
|
|
"float rparam = x_part / z_part / uSV;"
|
|
"float cr = 1. / sqrt(rparam*rparam - 1.);"
|
|
"float sr = rparam * cr;"
|
|
"float z = cr * (-1. - 1./uSV/uSV);"
|
|
"float k = asinh(xy / sr);"
|
|
"float a = -k;"
|
|
"float len = a * length(vec2(sr, cr/uSV));"
|
|
"float zw = xy * cr / sr;"
|
|
"float u = z * a;"
|
|
"float phi1 = atan2(zw, cosh(k)) - u;"
|
|
|
|
"if(phi > phi1) max_k = kk; else min_k = kk;"
|
|
|
|
"float r_angle = alpha + u;"
|
|
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
|
|
"}"
|
|
"}\n"
|
|
|
|
"if(part == 1) {"
|
|
"float min_k = fiber_barrier;"
|
|
"float max_k = flip_barrier;"
|
|
|
|
ITERATE
|
|
"float kk = (min_k + max_k) / 2.;"
|
|
|
|
"float x_part = cos(kk);"
|
|
"float z_part = sin(kk);"
|
|
|
|
"float rparam = x_part / z_part / uSV;"
|
|
|
|
"float r = atanh(rparam);"
|
|
"float cr = cosh(r);"
|
|
"float sr = sinh(r);"
|
|
|
|
"float z = cr * (-1. - 1./uSV/uSV);"
|
|
|
|
"float k = asin(xy / sr);"
|
|
"float a = -k;"
|
|
"float len = a * length(vec2(sr, cr/uSV));"
|
|
"float zw = xy * cr / sr;"
|
|
"float u = z * a;"
|
|
|
|
"float phi1 = atan2(zw, cos(k)) - u;"
|
|
|
|
"if(phi > phi1) max_k = kk;"
|
|
"else min_k = kk;"
|
|
|
|
"float r_angle = alpha + u;"
|
|
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
|
|
"}"
|
|
"}\n"
|
|
|
|
"if(flipped) res[0] *= -1., res[2] *= -1.;"
|
|
|
|
"return res;"
|
|
"}";
|
|
|
|
EX }
|
|
|
|
EX namespace rots {
|
|
|
|
EX transmatrix uxpush(ld x) {
|
|
if(sl2) return xpush(x);
|
|
return cspin(1, 3, x) * cspin(0, 2, x);
|
|
}
|
|
|
|
EX transmatrix uypush(ld y) {
|
|
if(sl2) return ypush(y);
|
|
return cspin(0, 3, -y) * cspin(1, 2, y);
|
|
}
|
|
|
|
EX transmatrix uzpush(ld z) {
|
|
if(sl2) return zpush(z);
|
|
return cspin(3, 2, -z) * cspin(0, 1, -z);
|
|
}
|
|
|
|
EX transmatrix lift_matrix(const transmatrix& T) {
|
|
hyperpoint d;
|
|
ld alpha, beta, distance;
|
|
transmatrix Spin;
|
|
hybrid::in_underlying_geometry([&] {
|
|
hyperpoint h = tC0(T);
|
|
Spin = iso_inverse(gpushxto0(h) * T);
|
|
d = hr::inverse_exp(shiftless(h));
|
|
alpha = atan2(Spin[0][1], Spin[0][0]);
|
|
distance = hdist0(h);
|
|
beta = atan2(h[1], h[0]);
|
|
});
|
|
for(int k=0; k<3; k++) Spin[3][k] = Spin[k][3] = 0; Spin[3][3] = 1;
|
|
return spin(beta) * uxpush(distance/2) * spin(-beta+alpha);
|
|
}
|
|
|
|
std::unordered_map<int, transmatrix> saved_matrices_ray;
|
|
|
|
EX transmatrix ray_iadj(cell *c1, int i) {
|
|
if(i == c1->type-1) return uzpush(-cgi.plevel) * spin(-2*cgi.plevel);
|
|
if(i == c1->type-2) return uzpush(+cgi.plevel) * spin(+2*cgi.plevel);
|
|
cell *c2 = c1->cmove(i);
|
|
int id1 = hybrid::underlying == gArchimedean ? arcm::id_of(c1->master) + 20 * arcm::parent_index_of(c1->master) : shvid(c1);
|
|
int id2 = hybrid::underlying == gArchimedean ? arcm::id_of(c2->master) + 20 * arcm::parent_index_of(c2->master) : shvid(c2);
|
|
int j = c1->c.spin(i);
|
|
int id = id1 + (id2 << 10) + (i << 20) + (j << 26);
|
|
auto &M = saved_matrices_ray[id];
|
|
if(M[3][3]) return M;
|
|
|
|
cell *cw = hybrid::get_where(c1).first;
|
|
|
|
transmatrix T;
|
|
hybrid::in_underlying_geometry([&] {
|
|
hyperpoint h0 = get_corner_position(cw, i);
|
|
hyperpoint h1 = get_corner_position(cw, (i+1));
|
|
T = to_other_side(h0, h1);
|
|
});
|
|
|
|
return M = lift_matrix(T);
|
|
}
|
|
|
|
struct hrmap_rotation_space : hybrid::hrmap_hybrid {
|
|
|
|
std::unordered_map<int, transmatrix> saved_matrices;
|
|
|
|
transmatrix adj(cell *c1, int i) override {
|
|
if(i == c1->type-2) return uzpush(-cgi.plevel) * spin(-2*cgi.plevel);
|
|
if(i == c1->type-1) return uzpush(+cgi.plevel) * spin(+2*cgi.plevel);
|
|
cell *c2 = c1->cmove(i);
|
|
int id1 = hybrid::underlying == gArchimedean ? arcm::id_of(c1->master) + 20 * arcm::parent_index_of(c1->master) : shvid(c1);
|
|
int id2 = hybrid::underlying == gArchimedean ? arcm::id_of(c2->master) + 20 * arcm::parent_index_of(c2->master) : shvid(c2);
|
|
int j = c1->c.spin(i);
|
|
int id = id1 + (id2 << 10) + (i << 20) + (j << 26);
|
|
auto &M = saved_matrices[id];
|
|
if(M[3][3]) return M;
|
|
|
|
cell *cw = where[c1].first;
|
|
return M = lift_matrix(PIU(currentmap->adj(cw, i)));
|
|
}
|
|
|
|
virtual transmatrix relative_matrix(cell *c2, cell *c1, const hyperpoint& hint) override {
|
|
if(c1 == c2) return Id;
|
|
if(gmatrix0.count(c2) && gmatrix0.count(c1))
|
|
return inverse_shift(gmatrix0[c1], gmatrix0[c2]);
|
|
for(int i=0; i<c1->type; i++) if(c1->move(i) == c2) return adj(c1, i);
|
|
return Id; // not implemented yet
|
|
}
|
|
|
|
};
|
|
|
|
/** reinterpret the given point of rotspace as a rotation matrix in the underlying geometry (note: this is the inverse) */
|
|
EX transmatrix qtm(hyperpoint h) {
|
|
|
|
ld& x = h[0];
|
|
ld& y = h[1];
|
|
ld& z = h[2];
|
|
ld& w = h[3];
|
|
|
|
ld xx = x*x;
|
|
ld yy = y*y;
|
|
ld zz = z*z;
|
|
ld ww = w*w;
|
|
|
|
ld xy = x*y;
|
|
ld xz = x*z;
|
|
ld xw = x*w;
|
|
ld yz = y*z;
|
|
ld yw = y*w;
|
|
ld zw = z*w;
|
|
|
|
transmatrix M;
|
|
|
|
M[0][0] = +xx - yy - zz + ww;
|
|
M[1][1] = -xx + yy - zz + ww;
|
|
M[2][2] = -xx - yy + zz + ww;
|
|
|
|
M[0][1] = -2 * (xy + zw);
|
|
M[1][0] = -2 * (xy - zw);
|
|
|
|
M[0][2] = 2 * (xz - yw);
|
|
M[2][0] = 2 * (xz + yw);
|
|
|
|
M[1][2] = -2 * (yz + xw);
|
|
M[2][1] = -2 * (yz - xw);
|
|
|
|
if(hyperbolic) {
|
|
swap(M[0][2], M[1][2]);
|
|
swap(M[2][0], M[2][1]);
|
|
M[1][2] *= -1;
|
|
M[2][0] *= -1;
|
|
M[2][2] = xx + yy + zz + ww;
|
|
return M;
|
|
}
|
|
|
|
|
|
return M;
|
|
}
|
|
|
|
EX ld underlying_scale = 0;
|
|
|
|
EX void draw_underlying(bool cornermode) {
|
|
if(underlying_scale <= 0) return;
|
|
ld d = hybrid::get_where(centerover).second;
|
|
d *= cgi.plevel;
|
|
transmatrix T = rots::uzpush(-d) * spin(-2*d);
|
|
|
|
if(det(T) < 0) T = centralsym * T;
|
|
|
|
hyperpoint h = inverse(View * spin(master_to_c7_angle()) * T) * C0;
|
|
|
|
auto g = std::move(gmatrix);
|
|
auto g0 = std::move(gmatrix0);
|
|
|
|
ld alpha = atan2(ortho_inverse(NLP) * point3(1, 0, 0));
|
|
|
|
bool inprod = prod;
|
|
transmatrix pView = View;
|
|
if(inprod) {
|
|
pView = spin(alpha) * View;
|
|
ld z = zlevel(tC0(View));
|
|
for(int a=0; a<3; a++) pView[a] *= exp(-z);
|
|
}
|
|
|
|
cell *co = hybrid::get_where(centerover).first;
|
|
|
|
hybrid::in_underlying_geometry([&] {
|
|
cgi.require_shapes();
|
|
dynamicval<int> pcc(corner_centering, cornermode ? 1 : 2);
|
|
dynamicval<bool> pf(playerfound, true);
|
|
dynamicval<cell*> m5(centerover, co);
|
|
dynamicval<transmatrix> m2(View, inprod ? pView : ypush(0) * qtm(h));
|
|
if(PURE) View = View * pispin;
|
|
View = inverse(stretch::mstretch_matrix) * spin(2*d) * View;
|
|
dynamicval<shiftmatrix> m3(playerV, shiftless(Id));
|
|
dynamicval<transmatrix> m4(actual_view_transform, Id);
|
|
dynamicval<shiftmatrix> m6(cwtV, shiftless(Id));
|
|
dynamicval<eModel> pm(pmodel, mdDisk);
|
|
dynamicval<ld> pss(pconf.scale, (sphere ? 10 : 1) * underlying_scale);
|
|
dynamicval<ld> psa(pconf.alpha, sphere ? 10 : 1);
|
|
dynamicval<hrmap*> p(hybrid::pmap, NULL);
|
|
dynamicval<int> psr(sightrange_bonus, 0);
|
|
|
|
dynamicval<int> psx(vid.use_smart_range, 2);
|
|
dynamicval<ld> psy(vid.smart_range_detail, 1);
|
|
|
|
calcparam();
|
|
reset_projection(); current_display->set_all(0, 0);
|
|
ptds.clear();
|
|
drawthemap();
|
|
drawqueue();
|
|
displaychr(current_display->xcenter, current_display->ycenter, 0, 24, '+', 0xFFFFFFFF);
|
|
glflush();
|
|
});
|
|
gmatrix = std::move(g);
|
|
gmatrix0 = std::move(g0);
|
|
calcparam();
|
|
reset_projection(); current_display->set_all(0, 0);
|
|
}
|
|
|
|
/** @brief exponential function for both slr and Berger sphere */
|
|
|
|
EX hyperpoint formula_exp(hyperpoint vel) {
|
|
bool sp = sphere;
|
|
ld K = sp ? 1 : -1;
|
|
|
|
ld len = hypot_d(3, vel);
|
|
|
|
if(vel[2] < 0) len = -len;
|
|
|
|
ld z_part = vel[2]/len;
|
|
ld x_part = sqrt(max<ld>(1 - z_part * z_part, 0));
|
|
|
|
ld SV = stretch::not_squared();
|
|
|
|
ld rparam = x_part / z_part / SV;
|
|
|
|
ld beta = atan2(vel[1], vel[0]);
|
|
if(len < 0) beta += M_PI;
|
|
|
|
if(sl2 && rparam > 1) {
|
|
ld cr = 1 / sqrt(rparam*rparam - 1); // *i
|
|
ld sr = rparam * cr; // *i
|
|
|
|
if(z_part == 0) cr = 0, sr = 1;
|
|
|
|
ld z = cr * (K - 1/SV/SV); // *i
|
|
|
|
ld a = len / hypot(sr, cr/SV); // /i
|
|
|
|
ld k = K*a; // /i
|
|
ld u = z*a;
|
|
|
|
ld xy = sr * sinh(k);
|
|
ld zw = cr * sinh(k);
|
|
|
|
return hyperpoint(K*xy * cos(u+beta), K*xy * sin(u+beta), zw * cos(u) - cosh(k) * sin(u), zw * sin(u) + cosh(k)*cos(u));
|
|
}
|
|
|
|
else {
|
|
ld r = atan_auto(rparam);
|
|
ld cr = cos_auto(r);
|
|
ld sr = sin_auto(r);
|
|
|
|
ld z = cr * (K - 1/SV/SV);
|
|
|
|
ld a = len / hypot(sr, cr/SV);
|
|
|
|
ld k = K*a;
|
|
ld u = z*a;
|
|
|
|
ld xy = sr * sin(k);
|
|
ld zw = cr * sin(k);
|
|
|
|
return hyperpoint(K*xy * cos(u+beta), K*xy * sin(u+beta), zw * cos(u) - cos(k) * sin(u), zw * sin(u) + cos(k)*cos(u));
|
|
}
|
|
}
|
|
|
|
|
|
EX }
|
|
|
|
/** stretched rotation space (S3 or SLR) */
|
|
EX namespace stretch {
|
|
|
|
EX ld factor;
|
|
|
|
EX bool mstretch;
|
|
|
|
EX transmatrix m_itoa, m_atoi, m_pd;
|
|
EX ld ms_christoffel[3][3][3];
|
|
|
|
EX transmatrix mstretch_matrix;
|
|
|
|
EX void enable_mstretch() {
|
|
mstretch = true;
|
|
|
|
for(int a=0; a<4; a++)
|
|
for(int b=0; b<4; b++)
|
|
if(a==3 || b==3) m_atoi[a][b] = (a==b);
|
|
|
|
m_itoa = inverse3(m_atoi);
|
|
|
|
for(int a=0; a<4; a++)
|
|
for(int b=0; b<4; b++)
|
|
if(a==3 || b==3)
|
|
m_itoa[a][b] = m_atoi[a][b] = 0;
|
|
|
|
for(int j=0; j<3; j++)
|
|
for(int k=0; k<3; k++) {
|
|
m_pd[j][k] = 0;
|
|
for(int i=0; i<3; i++)
|
|
m_pd[j][k] += m_atoi[i][j] * m_atoi[i][k];
|
|
}
|
|
|
|
auto& c = ms_christoffel;
|
|
|
|
ld A00 = m_pd[0][0];
|
|
ld A11 = m_pd[1][1];
|
|
ld A22 = m_pd[2][2];
|
|
ld A01 = m_pd[0][1] + m_pd[1][0];
|
|
ld A02 = m_pd[0][2] + m_pd[2][0];
|
|
ld A12 = m_pd[2][1] + m_pd[1][2];
|
|
ld B01 = A01 * A01;
|
|
ld B02 = A02 * A02;
|
|
ld B12 = A12 * A12;
|
|
ld B00 = A00 * A00;
|
|
ld B11 = A11 * A11;
|
|
ld B22 = A22 * A22;
|
|
|
|
ld den = (-4*A00*A11*A22 + A00*B12 + B01*A22 - A01*A02*A12 + B02*A11);
|
|
|
|
if(sl2) {
|
|
c[ 0 ][ 0 ][ 0 ] = (A01*(A01*A12 - 2*A02*A11) - A02*(2*A01*A22 - A02*A12))/den;
|
|
c[ 0 ][ 0 ][ 1 ] = (A00*A01*A12 - 2*A00*A02*A11 - A01*A11*A12 + A01*A12*A22 + 2*A02*B11 + 2*A02*A11*A22 - A02*B12)/-den ;
|
|
c[ 0 ][ 0 ][ 2 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 + A22)*(2*A01*A22 - A02*A12))/den;
|
|
c[ 0 ][ 1 ][ 0 ] = (A00*A01*A12 - 2*A00*A02*A11 - A01*A11*A12 + A01*A12*A22 + 2*A02*B11 + 2*A02*A11*A22 - A02*B12)/-den ;
|
|
c[ 0 ][ 1 ][ 1 ] = -(A01*(A01*A12 - 2*A02*A11) + A12*(4*A11*A22 - B12))/den;
|
|
c[ 0 ][ 1 ][ 2 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 + 4*A11*B22 - B12*A22)/-den ;
|
|
c[ 0 ][ 2 ][ 0 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 + A22)*(2*A01*A22 - A02*A12))/den;
|
|
c[ 0 ][ 2 ][ 1 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 + 4*A11*B22 - B12*A22)/-den ;
|
|
c[ 0 ][ 2 ][ 2 ] = -(A02*(2*A01*A22 - A02*A12) + A12*(4*A11*A22 - B12))/den;
|
|
c[ 1 ][ 0 ][ 0 ] = (-A01*(2*A00*A12 - A01*A02) + A02*(4*A00*A22 - B02))/den;
|
|
c[ 1 ][ 0 ][ 1 ] = (A02*(2*A01*A22 - A02*A12)/2 + A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den;
|
|
c[ 1 ][ 0 ][ 2 ] = (-4*B00*A22 + A00*B02 + A00*B12 - 4*A00*B22 - B01*A22 + B02*A22)/-den ;
|
|
c[ 1 ][ 1 ][ 0 ] = (A02*(2*A01*A22 - A02*A12)/2 + A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den;
|
|
c[ 1 ][ 1 ][ 1 ] = (A01*(2*A00*A12 - A01*A02) + A12*(2*A01*A22 - A02*A12))/den;
|
|
c[ 1 ][ 1 ][ 2 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 + A22)*(2*A01*A22 - A02*A12))/den;
|
|
c[ 1 ][ 2 ][ 0 ] = (-4*B00*A22 + A00*B02 + A00*B12 - 4*A00*B22 - B01*A22 + B02*A22)/-den ;
|
|
c[ 1 ][ 2 ][ 1 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 + A22)*(2*A01*A22 - A02*A12))/den;
|
|
c[ 1 ][ 2 ][ 2 ] = (A02*(4*A00*A22 - B02) + A12*(2*A01*A22 - A02*A12))/den;
|
|
c[ 2 ][ 0 ][ 0 ] = (A01*(4*A00*A11 - B01) - A02*(2*A00*A12 - A01*A02))/den;
|
|
c[ 2 ][ 0 ][ 1 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 + A00*B12 + B01*A11 - B02*A11)/-den ;
|
|
c[ 2 ][ 0 ][ 2 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 + A22)*(2*A00*A12 - A01*A02))/den;
|
|
c[ 2 ][ 1 ][ 0 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 + A00*B12 + B01*A11 - B02*A11)/-den ;
|
|
c[ 2 ][ 1 ][ 1 ] = -(A01*(4*A00*A11 - B01) + A12*(A01*A12 - 2*A02*A11))/den;
|
|
c[ 2 ][ 1 ][ 2 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 + A01*A12*A22 - 2*A02*B11 - 2*A02*A11*A22)/-den ;
|
|
c[ 2 ][ 2 ][ 0 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 + A22)*(2*A00*A12 - A01*A02))/den;
|
|
c[ 2 ][ 2 ][ 1 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 + A01*A12*A22 - 2*A02*B11 - 2*A02*A11*A22)/-den ;
|
|
c[ 2 ][ 2 ][ 2 ] = -(A02*(2*A00*A12 - A01*A02) + A12*(A01*A12 - 2*A02*A11))/den;
|
|
}
|
|
else {
|
|
c[ 0 ][ 0 ][ 0 ] = (A01*(A01*A12 - 2*A02*A11) + A02*(2*A01*A22 - A02*A12))/den ;
|
|
c[ 0 ][ 0 ][ 1 ] = (A02*(4*A11*A22 - B12)/2 + A12*(2*A01*A22 - A02*A12)/2 - (A00 - A11)*(A01*A12 - 2*A02*A11))/den ;
|
|
c[ 0 ][ 0 ][ 2 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 - A22)*(2*A01*A22 - A02*A12))/den ;
|
|
c[ 0 ][ 1 ][ 0 ] = (A02*(4*A11*A22 - B12)/2 + A12*(2*A01*A22 - A02*A12)/2 - (A00 - A11)*(A01*A12 - 2*A02*A11))/den ;
|
|
c[ 0 ][ 1 ][ 1 ] = (-A01*(A01*A12 - 2*A02*A11) + A12*(4*A11*A22 - B12))/den ;
|
|
c[ 0 ][ 1 ][ 2 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 - 4*A11*B22 + B12*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
|
|
c[ 0 ][ 2 ][ 0 ] = (-A01*(4*A11*A22 - B12)/2 + A12*(A01*A12 - 2*A02*A11)/2 - (A00 - A22)*(2*A01*A22 - A02*A12))/den ;
|
|
c[ 0 ][ 2 ][ 1 ] = (B01*A22 - B02*A11 + 4*B11*A22 - A11*B12 - 4*A11*B22 + B12*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
|
|
c[ 0 ][ 2 ][ 2 ] = -(A02*(2*A01*A22 - A02*A12) + A12*(4*A11*A22 - B12))/den ;
|
|
c[ 1 ][ 0 ][ 0 ] = -(A01*(2*A00*A12 - A01*A02) + A02*(4*A00*A22 - B02))/den ;
|
|
c[ 1 ][ 0 ][ 1 ] = (-A02*(2*A01*A22 - A02*A12)/2 - A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den ;
|
|
c[ 1 ][ 0 ][ 2 ] = (-4*B00*A22 + A00*B02 + A00*B12 + 4*A00*B22 - B01*A22 - B02*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
|
|
c[ 1 ][ 1 ][ 0 ] = (-A02*(2*A01*A22 - A02*A12)/2 - A12*(4*A00*A22 - B02)/2 + (A00 - A11)*(2*A00*A12 - A01*A02))/den ;
|
|
c[ 1 ][ 1 ][ 1 ] = (A01*(2*A00*A12 - A01*A02) - A12*(2*A01*A22 - A02*A12))/den ;
|
|
c[ 1 ][ 1 ][ 2 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 - A22)*(2*A01*A22 - A02*A12))/den ;
|
|
c[ 1 ][ 2 ][ 0 ] = (-4*B00*A22 + A00*B02 + A00*B12 + 4*A00*B22 - B01*A22 - B02*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
|
|
c[ 1 ][ 2 ][ 1 ] = (A01*(4*A00*A22 - B02)/2 + A02*(2*A00*A12 - A01*A02)/2 + (A11 - A22)*(2*A01*A22 - A02*A12))/den ;
|
|
c[ 1 ][ 2 ][ 2 ] = (A02*(4*A00*A22 - B02) + A12*(2*A01*A22 - A02*A12))/den ;
|
|
c[ 2 ][ 0 ][ 0 ] = (A01*(4*A00*A11 - B01) + A02*(2*A00*A12 - A01*A02))/den ;
|
|
c[ 2 ][ 0 ][ 1 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 - A00*B12 + B01*A11 + B02*A11)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
|
|
c[ 2 ][ 0 ][ 2 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 - A22)*(2*A00*A12 - A01*A02))/den ;
|
|
c[ 2 ][ 1 ][ 0 ] = (4*B00*A11 - A00*B01 - 4*A00*B11 - A00*B12 + B01*A11 + B02*A11)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
|
|
c[ 2 ][ 1 ][ 1 ] = (-A01*(4*A00*A11 - B01) + A12*(A01*A12 - 2*A02*A11))/den ;
|
|
c[ 2 ][ 1 ][ 2 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 - A01*A12*A22 - 2*A02*B11 + 2*A02*A11*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
|
|
c[ 2 ][ 2 ][ 0 ] = (-A01*(A01*A12 - 2*A02*A11)/2 + A12*(4*A00*A11 - B01)/2 - (A00 - A22)*(2*A00*A12 - A01*A02))/den ;
|
|
c[ 2 ][ 2 ][ 1 ] = (A00*A01*A12 + 2*A00*A02*A11 - B01*A02 + A01*A11*A12 - A01*A12*A22 - 2*A02*B11 + 2*A02*A11*A22)/(4*A00*A11*A22 - A00*B12 - B01*A22 + A01*A02*A12 - B02*A11) ;
|
|
c[ 2 ][ 2 ][ 2 ] = -(A02*(2*A00*A12 - A01*A02) + A12*(A01*A12 - 2*A02*A11))/den ;
|
|
}
|
|
|
|
for(int i=0; i<3; i++)
|
|
for(int j=0; j<3; j++)
|
|
for(int k=0; k<3; k++)
|
|
if(c[i][j][k])
|
|
println(hlog, tie(i,j,k), " : ", c[i][j][k]);
|
|
|
|
|
|
println(hlog, "ATOI = ", m_atoi);
|
|
println(hlog, "ITOA = ", m_itoa, " vs ", 1/not_squared());
|
|
println(hlog, "PD = ", m_pd, " vs ", factor);
|
|
|
|
ray::reset_raycaster();
|
|
}
|
|
|
|
EX bool applicable() {
|
|
return rotspace || among(geometry, gCell120, gECell120, gCell24, gECell24, gCell8, gECell8);
|
|
}
|
|
|
|
EX bool in() {
|
|
return (factor || mstretch) && applicable();
|
|
}
|
|
|
|
EX transmatrix translate(hyperpoint h) {
|
|
if(!sphere) return slr::translate(h);
|
|
return matrix4(
|
|
h[3], -h[2], h[1], h[0],
|
|
h[2], h[3], -h[0], h[1],
|
|
-h[1], h[0], h[3], h[2],
|
|
-h[0], -h[1], -h[2], h[3]
|
|
);
|
|
}
|
|
|
|
EX transmatrix itranslate(hyperpoint h) {
|
|
h[0] = -h[0];
|
|
h[1] = -h[1];
|
|
h[2] = -h[2];
|
|
if(!sphere) return slr::translate(h);
|
|
return translate(h);
|
|
}
|
|
|
|
hyperpoint mulz(const hyperpoint at, const hyperpoint velocity, ld zf) {
|
|
auto vel = itranslate(at) * velocity;
|
|
vel[2] *= zf;
|
|
return translate(at) * vel;
|
|
}
|
|
|
|
EX ld squared() {
|
|
return abs(1 + factor);
|
|
}
|
|
|
|
EX ld not_squared() {
|
|
return sqrt(squared());
|
|
}
|
|
|
|
EX hyperpoint isometric_to_actual(const hyperpoint at, const hyperpoint velocity) {
|
|
if(mstretch)
|
|
return translate(at) * m_itoa * itranslate(at) * velocity;
|
|
else
|
|
return mulz(at, velocity, 1/not_squared());
|
|
}
|
|
|
|
EX hyperpoint actual_to_isometric(const hyperpoint at, const hyperpoint velocity) {
|
|
if(mstretch)
|
|
return translate(at) * m_atoi * itranslate(at) * velocity;
|
|
else
|
|
return mulz(at, velocity, not_squared());
|
|
}
|
|
|
|
EX hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
|
|
|
|
auto vel = itranslate(at) * velocity;
|
|
auto tra = itranslate(at) * transported;
|
|
|
|
hyperpoint c;
|
|
|
|
if(mstretch) {
|
|
c = Hypc;
|
|
for(int i=0; i<3; i++)
|
|
for(int j=0; j<3; j++)
|
|
for(int k=0; k<3; k++)
|
|
c[i] += vel[j] * tra[k] * ms_christoffel[i][j][k];
|
|
}
|
|
|
|
else {
|
|
auto K = factor;
|
|
c[0] = (sphere ? -K : K+2) * (vel[1] * tra[2] + vel[2] * tra[1]);
|
|
c[1] = (sphere ? K : -(K+2)) * (vel[0] * tra[2] + vel[2] * tra[0]);
|
|
c[2] = 0;
|
|
c[3] = 0;
|
|
}
|
|
|
|
return translate(at) * c;
|
|
}
|
|
|
|
EX ld sqnorm(hyperpoint at, hyperpoint h) {
|
|
if(sphere)
|
|
return sqhypot_d(4, h);
|
|
h = itranslate(at) * h;
|
|
return h[0] * h[0] + h[1] * h[1] + h[2] * h[2];
|
|
}
|
|
|
|
EX vector<hyperpoint> inverse_exp_all(hyperpoint h, int generations) {
|
|
|
|
vector<hyperpoint> res;
|
|
|
|
ld SV = stretch::not_squared();
|
|
|
|
if(stretch::factor == 0) {
|
|
ld d = hypot_d(3, h);
|
|
if(h[3] >= 1 || h[3] <= -1|| d == 0) return res;
|
|
ld a = acos(h[3]);
|
|
|
|
res.push_back(point31(h[0] * a / d, h[1] * a / d, h[2] * a / d));
|
|
|
|
a = a - 2 * M_PI;
|
|
|
|
res.push_back(point31(h[0] * a / d, h[1] * a / d, h[2] * a / d));
|
|
|
|
return res;
|
|
}
|
|
|
|
if(h[0] == 0 && h[1] == 0) {
|
|
ld a = atan2(h[2], h[3]);
|
|
|
|
for(int it=-generations; it<generations; it++) {
|
|
res.push_back(point31(0, 0, (a + 2 * M_PI * it) * SV));
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
ld xy = hypot_d(2, h);
|
|
|
|
ld base_min_a = asin(xy);
|
|
ld base_max_a = M_PI - base_min_a;
|
|
|
|
ld seek = M_PI/2-atan2(h[3], h[2]);
|
|
|
|
auto ang = [&] (ld a) {
|
|
ld rp = xy / sin(a);
|
|
ld co = abs(rp) >= 1 ? 0 : sqrt(1-rp*rp);
|
|
|
|
return atan2(co * sin(a), cos(a)) - co * (1 - 1/SV/SV) * a;
|
|
|
|
// while(a0 > M_PI) a0 -= 2 * M_PI;
|
|
// while(a0 < -M_PI) a0 += 2 * M_PI;
|
|
};
|
|
|
|
for(int shift=-generations; shift<generations; shift++) {
|
|
ld min_a = base_min_a + M_PI * shift;
|
|
ld max_a = base_max_a + M_PI * shift;
|
|
|
|
ld ang_min = ang(min_a);
|
|
ld ang_max = ang(max_a);
|
|
|
|
for(int mi=0; mi<2; mi++) {
|
|
// 0 : minimum, 1 : maximum
|
|
ld tl = min_a, tr = max_a;
|
|
for(int it=0; it<20; it++) {
|
|
ld t1 = tl * .51 + tr * .49;
|
|
ld t2 = tl * .49 + tr * .51;
|
|
if((ang(t1) < ang(t2)) == mi)
|
|
tr = t1;
|
|
else
|
|
tl = t2;
|
|
}
|
|
ld extreme = (tl + tr) / 2;
|
|
ld ang_extreme = ang(extreme);
|
|
for(int t=0; t<2; t++) {
|
|
ld mmin = t == 0 ? min_a : extreme;
|
|
ld mmax = t == 0 ? extreme : max_a;
|
|
ld vmin = t == 0 ? ang_min : ang_extreme;
|
|
ld vmax = t == 0 ? ang_extreme : ang_max;
|
|
|
|
// make it increasing
|
|
if(t != mi) swap(mmin, mmax), swap(vmin, vmax);
|
|
|
|
// println(hlog, "*** ", mi, t, " ** ", tie(min_a, ang_min), tie(extreme, ang_extreme), tie(max_a, ang_max), " -> ", vmin, " to ", vmax);
|
|
|
|
int cmin = ceil((vmin - seek) / 2 / M_PI);
|
|
int cmax = floor((vmax - seek) / 2 / M_PI);
|
|
for(int c = cmin; c <= cmax; c++) {
|
|
ld cseek = seek + c * 2 * M_PI;
|
|
|
|
for(int it=0; it<40; it++) {
|
|
|
|
ld a = (mmin + mmax) / 2;
|
|
|
|
ld cros = ang(a);
|
|
if(cros > cseek) mmax = a; else mmin = a;
|
|
}
|
|
|
|
ld a = (mmin + mmax) / 2;
|
|
|
|
ld r = asin_clamp( xy / sin(a) );
|
|
|
|
ld z_part = 1;
|
|
ld x_part = SV * tan(r);
|
|
|
|
ld db = hypot(x_part, z_part);
|
|
x_part /= db;
|
|
z_part /= db;
|
|
|
|
ld alpha = atan2(-h[1], h[0]);
|
|
|
|
ld z = cos(r) * (1 - 1/SV/SV);
|
|
ld u = z * a;
|
|
|
|
ld r_angle = alpha + u;
|
|
|
|
ld len = a * hypot(sin_auto(r), cos_auto(r)/SV);
|
|
|
|
auto answer = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
|
|
|
|
// int id = (shift << 10) + (mi << 9) + (t << 8) + c;
|
|
|
|
/*
|
|
auto f = formula_exp(answer);
|
|
|
|
ld err = sqhypot_d(4, f - h);
|
|
|
|
println(hlog, "************************* ", answer, ": error = ", err, " id = ", id, " params = ", tie(shift, mi, t, c));
|
|
*/
|
|
|
|
res.emplace_back(answer);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
|
|
EX }
|
|
|
|
EX namespace nisot {
|
|
|
|
EX hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
|
|
if(nil) return nilv::christoffel(at, velocity, transported);
|
|
#if CAP_SOLV
|
|
else if(sn::in()) return sn::christoffel(at, velocity, transported);
|
|
#endif
|
|
else if(stretch::in() || sl2) return stretch::christoffel(at, velocity, transported);
|
|
else return point3(0, 0, 0);
|
|
}
|
|
|
|
EX bool in_table_range(hyperpoint h) {
|
|
#if CAP_SOLV
|
|
if(sol) return sn::in_table_range(h);
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
EX hyperpoint get_acceleration(const hyperpoint& at, const hyperpoint& vel) {
|
|
return christoffel(at, vel, vel);
|
|
}
|
|
|
|
EX void geodesic_step(hyperpoint& at, hyperpoint& vel) {
|
|
/* RK4 method */
|
|
auto acc1 = get_acceleration(at, vel);
|
|
auto acc2 = get_acceleration(at + vel/2, vel + acc1/2);
|
|
auto acc3 = get_acceleration(at + vel/2 + acc1/4, vel + acc2/2);
|
|
auto acc4 = get_acceleration(at + vel + acc2/2, vel + acc3);
|
|
|
|
at += vel + (acc1+acc2+acc3)/6;
|
|
vel += (acc1+2*acc2+2*acc3+acc4)/6;
|
|
}
|
|
|
|
EX int rk_steps = 20;
|
|
|
|
EX hyperpoint numerical_exp(hyperpoint v) {
|
|
hyperpoint at = point31(0, 0, 0);
|
|
v /= rk_steps;
|
|
v[3] = 0;
|
|
for(int i=0; i<rk_steps; i++) geodesic_step(at, v);
|
|
return at;
|
|
}
|
|
|
|
EX transmatrix parallel_transport_bare(transmatrix Pos, hyperpoint h) {
|
|
|
|
bool stretch = stretch::in() || sl2;
|
|
|
|
h[3] = 0;
|
|
|
|
if(stretch::in() && stretch::mstretch)
|
|
Pos = stretch::mstretch_matrix * Pos;
|
|
|
|
auto tPos = transpose(Pos);
|
|
|
|
h = Pos * h;
|
|
|
|
int steps = rk_steps;
|
|
h /= steps;
|
|
|
|
auto& at = tPos[3];
|
|
auto& vel = h;
|
|
|
|
array<ld, 4> ms;
|
|
|
|
if(stretch) {
|
|
for(int i=0; i<3; i++) {
|
|
ms[i] = stretch::sqnorm(at, tPos[i]);
|
|
tPos[i] = stretch::isometric_to_actual(at, tPos[i]);
|
|
}
|
|
ms[3] = stretch::sqnorm(at, vel);
|
|
if(!ms[3]) return Pos;
|
|
vel = stretch::isometric_to_actual(at, vel);
|
|
}
|
|
|
|
for(int i=0; i<steps; i++) {
|
|
auto acc1 = get_acceleration(at, vel);
|
|
auto at1 = at + vel/2; auto vel1 = vel + acc1/2;
|
|
auto acc2 = get_acceleration(at1, vel1);
|
|
auto at2 = at1 + acc1/4; auto vel2 = vel + acc2/2;
|
|
auto acc3 = get_acceleration(at2, vel2);
|
|
auto at3 = at + vel + acc2/2; auto vel3 = vel + acc3;
|
|
auto acc4 = get_acceleration(at3, vel3);
|
|
|
|
for(int j=0; j<3; j++) {
|
|
auto& tra = tPos[j];
|
|
|
|
auto tacc1 = christoffel(at, vel, tra);
|
|
auto tacc2 = christoffel(at1, vel1, tra + tacc1/2);
|
|
auto tacc3 = christoffel(at2, vel2, tra + tacc2/2);
|
|
auto tacc4 = christoffel(at3, vel3, tra + tacc3);
|
|
|
|
tra += (tacc1+tacc2*2+tacc3*2+tacc4) / 6;
|
|
}
|
|
|
|
at += vel + (acc1+acc2+acc3)/6;
|
|
vel += (acc1+2*acc2+2*acc3+acc4)/6;
|
|
|
|
if(stretch) {
|
|
at = normalize(at);
|
|
|
|
auto fix = [&] (hyperpoint& h, ld& m) {
|
|
h = stretch::itranslate(at) * h;
|
|
h[3] = 0;
|
|
ld m1;
|
|
if(stretch::mstretch) {
|
|
m1 = 0;
|
|
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
|
|
m1 += h[i] * stretch::m_pd[i][j] * h[j];
|
|
}
|
|
else
|
|
m1 = h[0] * h[0] + h[1] * h[1] + h[2] * h[2] * stretch::squared();
|
|
h /= sqrt(m1/m);
|
|
h = stretch::translate(at) * h;
|
|
};
|
|
|
|
for(int i=0; i<3; i++) fix(tPos[i], ms[i]);
|
|
fix(vel, ms[3]);
|
|
}
|
|
|
|
}
|
|
|
|
if(stretch) {
|
|
vel = stretch::actual_to_isometric(at, vel);
|
|
for(int i=0; i<3; i++) tPos[i] = stretch::actual_to_isometric(at, tPos[i]);
|
|
}
|
|
|
|
Pos = transpose(tPos);
|
|
|
|
if(stretch::in() && stretch::mstretch)
|
|
Pos = inverse(stretch::mstretch_matrix) * Pos;
|
|
|
|
return Pos;
|
|
}
|
|
|
|
EX void fixmatrix(transmatrix& T) {
|
|
if(sphere) return hr::fixmatrix(T);
|
|
transmatrix push = eupush( tC0(T) );
|
|
transmatrix push_back = eupush(tC0(T), -1);
|
|
transmatrix gtl = push_back * T;
|
|
{ dynamicval<eGeometry> g(geometry, gSphere); hr::fixmatrix(gtl); }
|
|
T = push * gtl;
|
|
}
|
|
|
|
EX transmatrix parallel_transport(const transmatrix Position, const hyperpoint direction) {
|
|
auto P = Position;
|
|
nisot::fixmatrix(P);
|
|
if(!geodesic_movement) return eupush(Position * translate(-direction) * inverse(Position) * C0, -1) * Position;
|
|
return parallel_transport_bare(P, direction);
|
|
}
|
|
|
|
EX transmatrix spin_towards(const transmatrix Position, const hyperpoint goal, flagtype prec IS(pNORMAL)) {
|
|
|
|
hyperpoint at = tC0(Position);
|
|
transmatrix push_back = translate(at, -1);
|
|
hyperpoint back_goal = push_back * goal;
|
|
back_goal = inverse_exp(shiftless(back_goal), prec);
|
|
|
|
transmatrix back_Position = push_back * Position;
|
|
|
|
return rspintox(inverse(back_Position) * back_goal);
|
|
}
|
|
|
|
EX hrmap *new_map() {
|
|
#if CAP_SOLV
|
|
if(sn::in()) return new sn::hrmap_solnih;
|
|
#endif
|
|
if(nil) return new nilv::hrmap_nil;
|
|
if(prod) return new product::hrmap_product;
|
|
if(hybri) return new rots::hrmap_rotation_space;
|
|
return NULL;
|
|
}
|
|
|
|
#if CAP_COMMANDLINE
|
|
auto config = addHook(hooks_args, 0, [] () {
|
|
using namespace arg;
|
|
#if CAP_SOLV
|
|
if(argis("-solrange")) {
|
|
shift_arg_formula(sn::solrange_xy);
|
|
shift_arg_formula(sn::solrange_z);
|
|
return 0;
|
|
}
|
|
#endif
|
|
if(argis("-slrange")) {
|
|
shift_arg_formula(slr::range_xy);
|
|
return 0;
|
|
}
|
|
#if CAP_SOLV
|
|
else if(argis("-fsol")) {
|
|
shift(); sn::solt.fname = args();
|
|
return 0;
|
|
}
|
|
else if(argis("-nihsol")) {
|
|
shift(); sn::niht.fname = args();
|
|
return 0;
|
|
}
|
|
#endif
|
|
else if(argis("-solgeo")) {
|
|
geodesic_movement = true;
|
|
pmodel = mdGeodesic;
|
|
return 0;
|
|
}
|
|
else if(argis("-solnogeo")) {
|
|
geodesic_movement = false;
|
|
pmodel = mdPerspective;
|
|
return 0;
|
|
}
|
|
else if(argis("-product")) {
|
|
PHASEFROM(2);
|
|
set_geometry(gProduct);
|
|
return 0;
|
|
}
|
|
else if(argis("-s2xe")) {
|
|
PHASEFROM(2);
|
|
shift(); s2xe::qrings = argi();
|
|
return 0;
|
|
}
|
|
else if(argis("-rotspace")) {
|
|
PHASEFROM(2);
|
|
set_geometry(gRotSpace);
|
|
return 0;
|
|
}
|
|
else if(argis("-rot_uscale")) {
|
|
PHASEFROM(2);
|
|
shift_arg_formula(rots::underlying_scale);
|
|
return 0;
|
|
}
|
|
else if(argis("-nilperiod")) {
|
|
PHASEFROM(2);
|
|
if(nil) stop_game();
|
|
for(int a=0; a<3; a++) { shift(); nilv::nilperiod[a] = argi(); }
|
|
nilv::set_flags();
|
|
return 0;
|
|
}
|
|
else if(argis("-nilwidth")) {
|
|
PHASEFROM(2);
|
|
shift_arg_formula(nilv::nilwidth);
|
|
return 0;
|
|
}
|
|
else if(argis("-rk-steps")) {
|
|
PHASEFROM(2);
|
|
shift(); rk_steps = argi();
|
|
return 0;
|
|
}
|
|
else if(argis("-nilv")) {
|
|
PHASEFROM(2);
|
|
if(nil) stop_game();
|
|
shift();
|
|
ginf[gNil].sides = argi();
|
|
return 0;
|
|
}
|
|
else if(argis("-catperiod")) {
|
|
PHASEFROM(2);
|
|
if(sol) stop_game();
|
|
shift(); asonov::period_xy = argi();
|
|
shift(); asonov::period_z = argi();
|
|
asonov::set_flags();
|
|
return 0;
|
|
}
|
|
else if(argis("-prodperiod")) {
|
|
PHASEFROM(2);
|
|
if(prod) stop_game();
|
|
shift(); hybrid::csteps = argi();
|
|
hybrid::reconfigure();
|
|
return 0;
|
|
}
|
|
else if(argis("-rot-stretch")) {
|
|
PHASEFROM(2);
|
|
shift_arg_formula(stretch::factor, ray::reset_raycaster);
|
|
return 0;
|
|
}
|
|
else if(argis("-mstretch")) {
|
|
PHASEFROM(2);
|
|
auto& M = stretch::m_atoi;
|
|
M = Id;
|
|
stretch::enable_mstretch();
|
|
while(true) {
|
|
shift();
|
|
string s = args();
|
|
if(isize(s) == 2 && among(s[0], 'a', 'b','c') && among(s[1], 'a', 'b', 'c'))
|
|
shift_arg_formula(M[s[0]-'a'][s[1]-'a'], stretch::enable_mstretch);
|
|
else break;
|
|
}
|
|
// shift_arg_formula(stretch::yfactor, ray::reset_raycaster);
|
|
return 0;
|
|
}
|
|
else if(argis("-mstretch1")) {
|
|
PHASEFROM(2);
|
|
auto& M = stretch::m_atoi;
|
|
M = Id;
|
|
M[2][2] = stretch::not_squared();
|
|
stretch::enable_mstretch();
|
|
// shift_arg_formula(stretch::yfactor, ray::reset_raycaster);
|
|
return 0;
|
|
}
|
|
else if(argis("-prodturn")) {
|
|
PHASEFROM(2);
|
|
if(prod) stop_game();
|
|
shift(); product::cspin = argi();
|
|
shift(); product::cmirror = argi();
|
|
return 0;
|
|
}
|
|
return 1;
|
|
});
|
|
#endif
|
|
}
|
|
|
|
}
|