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289 lines
7.9 KiB
C++
289 lines
7.9 KiB
C++
// Hyperbolic Rogue
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// geometrical constants
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// Copyright (C) 2011-2012 Zeno Rogue, see 'hyper.cpp' for details
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ld tessf, crossf, hexf, hcrossf, hexhexdist;
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// tessf: distance from heptagon center to another heptagon center
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// hexf: distance from heptagon center to heptagon vertex
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// hcrossf: distance from heptagon center to big heptagon vertex
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// crossf: distance from heptagon center to adjacent hexagon center
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// hexhexdist: distance between adjacent hexagon vertices
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#define ALPHA (M_PI*2/S7)
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hyperpoint Crad[MAX_S84];
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transmatrix heptmove[MAX_EDGE], hexmove[MAX_EDGE];
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transmatrix invheptmove[MAX_EDGE], invhexmove[MAX_EDGE];
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transmatrix spinmatrix[MAX_S84];
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ld hexshift;
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const transmatrix& getspinmatrix(int id) {
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while(id>=S84) id -= S84;
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while(id<0) id += S84;
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return spinmatrix[id];
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}
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// the results are:
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// hexf = 0.378077 hcrossf = 0.620672 tessf = 1.090550
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// hexhexdist = 0.566256
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ld hcrossf7 = 0.620672;
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ld hexf7 = 0.378077;
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// the distance between two hexagon centers
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void precalc() {
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DEBB(DF_INIT, (debugfile,"precalc\n"));
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hexshift = 0;
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int vertexdegree = S6/2;
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ld fmin, fmax;
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if(euclid) {
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// dynamicval<eGeometry> g(geometry, gNormal);
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// precalc(); }
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// for(int i=0; i<S84; i++) spinmatrix[i] = spin(i * M_PI / S42);
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hcrossf = hexhexdist = hexf = hexf7;
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tessf = hexf * sqrt(3);
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goto finish;
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}
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fmin = 0, fmax = 3;
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for(int p=0; p<100; p++) {
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ld f = (fmin+fmax) / 2;
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ld v1, v2;
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if(vertexdegree == 3) {
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hyperpoint H = xpush(f) * C0;
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v1 = intval(H, C0), v2 = intval(H, spin(2*M_PI/S7)*H);
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}
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else if(vertexdegree == 4) {
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hyperpoint H = xpush(f) * C0;
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ld opposite = hdist(H, spin(2*M_PI/S7)*H);
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hyperpoint Hopposite = spin(M_PI/S7) * xpush(opposite) * C0;
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v2 = intval(H, Hopposite), v1 = intval(H, C0);
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}
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if(sphere ? v1 < v2 : v1 > v2) fmin = f; else fmax = f;
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}
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tessf = fmin;
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if(vertexdegree == 3) {
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fmin = 0, fmax = sphere ? M_PI / 2 : 2;
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for(int p=0; p<100; p++) {
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ld f = (fmin+fmax) / 2;
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hyperpoint H = spin(M_PI/S7) * xpush(f) * C0;
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ld v1 = intval(H, C0), v2 = intval(H, xpush(tessf) * C0);
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if(v1 < v2) fmin = f; else fmax = f;
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}
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hcrossf = fmin;
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}
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else {
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hcrossf = hdist(xpush(tessf) * C0, spin(2*M_PI/S7) * xpush(tessf) * C0) / 2;
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}
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crossf = purehepta ? tessf : hcrossf;
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fmin = 0, fmax = tessf;
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for(int p=0; p<100; p++) {
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ld f = (fmin+fmax) / 2;
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hyperpoint H = xpush(f) * C0;
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hyperpoint H1 = spin(2*M_PI/S7) * H;
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hyperpoint H2 = xpush(tessf-f) * C0;
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ld v1 = intval(H, H1), v2 = intval(H, H2);
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if(v1 < v2) fmin = f; else fmax = f;
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}
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hexf = fmin;
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if(!euclid && !purehepta && !(S7&1))
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hexshift = ALPHA/2 + ALPHA * ((S7-1)/2) + M_PI;
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finish:
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printf("S7=%d S6=%d hexf = " LDF" hcross = " LDF" tessf = " LDF" hexshift = " LDF "\n", S7, S6, hexf, hcrossf, tessf, hexshift);
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for(int i=0; i<S42; i++)
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Crad[i] = spin(2*M_PI*i/S42) * xpush(.4) * C0;
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for(int d=0; d<S7; d++)
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heptmove[d] = spin(-d * ALPHA) * xpush(tessf) * spin(M_PI);
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for(int d=0; d<S7; d++)
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hexmove[d] = spin(hexshift-d * ALPHA) * xpush(-crossf)* spin(M_PI);
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for(int d=0; d<S7; d++) invheptmove[d] = inverse(heptmove[d]);
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for(int d=0; d<S7; d++) invhexmove[d] = inverse(hexmove[d]);
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hexhexdist = hdist(xpush(crossf) * C0, spin(M_PI*2/S7) * xpush(crossf) * C0);
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for(int i=0; i<S84; i++) spinmatrix[i] = spin(i * M_PI / S42);
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}
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transmatrix ddi(ld dir, ld dist) {
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if(euclid)
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return eupush(cos(M_PI*dir/S42) * dist, -sin(M_PI*dir/S42) * dist);
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else
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return spin(M_PI*dir/S42) * xpush(dist) * spin(-M_PI*dir/S42);
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}
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hyperpoint ddi0(ld dir, ld dist) {
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if(euclid)
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return hpxy(cos(M_PI*dir/S42) * dist, -sin(M_PI*dir/S42) * dist);
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else
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return xspinpush0(M_PI*dir/S42, dist);
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}
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namespace geom3 {
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int tc_alpha=3, tc_depth=1, tc_camera=2;
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ld depth = 1; // world below the plane
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ld camera = 1; // camera above the plane
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ld wall_height = .3;
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ld slev = .08;
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ld lake_top = .25, lake_bottom = .9;
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ld rock_wall_ratio = .9;
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ld human_wall_ratio = .7;
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ld human_height;
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ld highdetail = 8, middetail = 8;
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// Here we convert between the following parameters:
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// abslev: level below the plane
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// lev: level above the world (abslev = depth-lev)
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// projection: projection parameter
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// factor: zoom factor
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ld abslev_to_projection(ld abslev) {
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if(sphere || euclid) return camera+abslev;
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return tanh(abslev) / tanh(camera);
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}
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ld projection_to_abslev(ld proj) {
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if(sphere || euclid) return proj-camera;
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// tanh(abslev) / tanh(camera) = proj
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return atanh(proj * tanh(camera));
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}
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ld lev_to_projection(ld lev) {
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return abslev_to_projection(depth - lev);
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}
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ld projection_to_factor(ld proj) {
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return lev_to_projection(0) / proj;
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}
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ld factor_to_projection(ld fac) {
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return lev_to_projection(0) / fac;
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}
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ld lev_to_factor(ld lev) {
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return projection_to_factor(lev_to_projection(lev));
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}
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ld factor_to_lev(ld fac) {
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return depth - projection_to_abslev(factor_to_projection(fac));
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}
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// how should we scale at level lev
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ld scale_at_lev(ld lev) {
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if(sphere || euclid) return 1;
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return cosh(depth - lev);
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}
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ld INFDEEP, BOTTOM, HELLSPIKE, LAKE, WALL,
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SLEV[4], FLATEYE,
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LEG1, LEG, LEG3, GROIN, GROIN1, GHOST,
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BODY, NECK1, NECK, NECK3, HEAD,
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ABODY, AHEAD, BIRD;
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string invalid;
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void compute() {
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// tanh(depth) / tanh(camera) == vid.alpha
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invalid = "";
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if(tc_alpha < tc_depth && tc_alpha < tc_camera)
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vid.alpha = tanh(depth) / tanh(camera);
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else if(tc_depth < tc_alpha && tc_depth < tc_camera) {
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ld v = vid.alpha * tanh(camera);
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if(v<-1 || v>1) invalid = "cannot adjust depth", depth = camera;
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else depth = atanh(v);
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}
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else {
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ld v = tanh(depth) / vid.alpha;
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if(v<-1 || v>1) invalid = "cannot adjust camera", camera = depth;
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else camera = atanh(v);
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}
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if(fabs(vid.alpha) < 1e-6) invalid = "does not work with perfect Klein";
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if(invalid != "") {
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INFDEEP = .7;
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BOTTOM = .8;
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HELLSPIKE = .85;
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LAKE = .9;
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WALL = 1.25;
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SLEV[0] = 1;
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SLEV[1] = 1.08;
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SLEV[2] = 1.16;
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SLEV[3] = 1.24;
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FLATEYE = 1.03;
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LEG1 = 1.025;
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LEG = 1.05;
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LEG3 = 1.075;
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GROIN = 1.09;
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GROIN1 = 1.105;
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GHOST = 1.1;
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BODY = 1.15;
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NECK1 = 1.16;
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NECK = 1.17;
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NECK3 = 1.18;
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HEAD = 1.19;
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ABODY = 1.08;
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AHEAD = 1.12;
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BIRD = 1.20;
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}
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else {
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INFDEEP = (euclid || sphere) ? 0.01 : lev_to_projection(0) * tanh(camera);
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WALL = lev_to_factor(wall_height);
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human_height = human_wall_ratio * wall_height;
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LEG1 = lev_to_factor(human_height * .1);
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LEG = lev_to_factor(human_height * .2);
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LEG3 = lev_to_factor(human_height * .3);
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GROIN = lev_to_factor(human_height * .4);
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GROIN1= lev_to_factor(human_height * .5);
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BODY = lev_to_factor(human_height * .6);
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NECK1 = lev_to_factor(human_height * .7);
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NECK = lev_to_factor(human_height * .8);
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NECK3 = lev_to_factor(human_height * .9);
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HEAD = lev_to_factor(human_height);
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ABODY = lev_to_factor(human_height * .4);
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AHEAD = lev_to_factor(human_height * .6);
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BIRD = lev_to_factor((human_wall_ratio+1)/2 * wall_height * .8);
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GHOST = lev_to_factor(human_height * .5);
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FLATEYE = lev_to_factor(human_height * .15);
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slev = rock_wall_ratio * wall_height / 3;
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for(int s=0; s<=3; s++)
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SLEV[s] = lev_to_factor(rock_wall_ratio * wall_height * s/3);
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LAKE = lev_to_factor(-lake_top);
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HELLSPIKE = lev_to_factor(-(lake_top+lake_bottom)/2);
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BOTTOM = lev_to_factor(-lake_bottom);
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}
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}
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}
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void initgeo() {
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// printf("%Lf\n", (ld) hdist0(xpush(-1)*ypush(0.01)*xpush(1)*C0));
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precalc();
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}
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