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hyperrogue/geometry.cpp

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// Hyperbolic Rogue
// geometrical constants
// Copyright (C) 2011-2018 Zeno Rogue, see 'hyper.cpp' for details
namespace hr {
bool debug_geometry = false;
ld tessf, crossf, hexf, hcrossf, hexhexdist, hexvdist, hepvdist, rhexf;
// tessf: distance from heptagon center to another heptagon center
// hexf: distance from heptagon center to small heptagon vertex
// hcrossf: distance from heptagon center to big heptagon vertex
// crossf: distance from heptagon center to adjacent cell center (either hcrossf or tessf)
// hexhexdist: distance between adjacent hexagon vertices
// hexvdist: distance between hexagon vertex and hexagon center
// hepvdist: distance between heptagon vertex and hexagon center (either hcrossf or something else)
// rhexf: distance from heptagon center to heptagon vertex (either hexf or hcrossf)
int base_distlimit;
transmatrix heptmove[MAX_EDGE], hexmove[MAX_EDGE];
transmatrix invheptmove[MAX_EDGE], invhexmove[MAX_EDGE];
ld hexshift;
// the results are:
// hexf = 0.378077 hcrossf = 0.620672 tessf = 1.090550
// hexhexdist = 0.566256
ld hcrossf7 = 0.620672;
ld hexf7 = 0.378077;
ld scalefactor, orbsize, floorrad0, floorrad1, zhexf;
// the distance between two hexagon centers
void precalc() {
DEBB(DF_INIT, (debugfile,"precalc\n"));
hexshift = 0;
int vertexdegree = S6/2;
ld fmin, fmax;
if(archimedean)
ginf[gArchimedean].cclass = gcHyperbolic;
if(euclid) {
// dynamicval<eGeometry> g(geometry, gNormal);
// precalc(); }
// for(int i=0; i<S84; i++) spinmatrix[i] = spin(i * M_PI / S42);
if(a4 && !BITRUNCATED) {
crossf = .5;
hexf = .5;
hcrossf = crossf * sqrt(2) / 2;
hexhexdist = crossf;
hexvdist = hexf;
hepvdist = hexf;
rhexf = crossf * sqrt(2) / 2;
tessf = crossf;
}
else if(a4 && BITRUNCATED) {
ld s2 = sqrt(2);
ld xx = 1 - s2 / 2;
crossf = .5;
tessf = crossf * s2;
hexf = .5 * xx * s2;
hcrossf = crossf;
hexhexdist = crossf * s2;
hexvdist = crossf * hypot(1-xx, xx);
hepvdist = crossf;
rhexf = hexf;
tessf = crossf;
}
else {
crossf = .5;
tessf = crossf * sqrt(3);
hexf = tessf/3;
hcrossf = crossf;
hexhexdist = crossf;
hexvdist = hexf;
hepvdist = crossf;
rhexf = hexf;
}
goto finish;
}
if(sphere && DIM == 3) {
rhexf = hexf = 0.378077;
crossf = hcrossf = 0.620672;
tessf = 1.090550;
hexhexdist = 0.566256;
goto finish;
}
fmin = 0, fmax = hyperbolic ? 10 : 3;
for(int p=0; p<100; p++) {
ld f = (fmin+fmax) / 2;
ld v1=0, v2=0;
if(vertexdegree == 3) {
hyperpoint H = xpush0(f);
v1 = intval(H, C0), v2 = intval(H, spin(2*M_PI/S7)*H);
}
else if(vertexdegree == 4) {
hyperpoint H = xpush0(f);
ld opposite = hdist(H, spin(2*M_PI/S7)*H);
hyperpoint Hopposite = xspinpush0(M_PI/S7, opposite);
v2 = intval(H, Hopposite), v1 = intval(H, C0);
}
if(sphere ? v1 < v2 : v1 > v2) fmin = f; else fmax = f;
}
tessf = fmin;
if(elliptic && S7 == 4) tessf = M_PI/2;
if(vertexdegree == 3) {
fmin = 0, fmax = sphere ? M_PI / 2 : 2;
for(int p=0; p<100; p++) {
ld f = (fmin+fmax) / 2;
hyperpoint H = xspinpush0(M_PI/S7, f);
ld v1 = intval(H, C0), v2 = intval(H, xpush0(tessf));
if(v1 < v2) fmin = f; else fmax = f;
}
hcrossf = fmin;
}
else {
hcrossf = hdist(xpush0(tessf), xspinpush0(2*M_PI/S7, tessf)) / 2;
}
crossf = BITRUNCATED ? hcrossf : tessf;
fmin = 0, fmax = tessf;
for(int p=0; p<100; p++) {
ld f = (fmin+fmax) / 2;
hyperpoint H = xpush0(f);
hyperpoint H1 = spin(2*M_PI/S7) * H;
hyperpoint H2 = xpush0(tessf-f);
ld v1 = intval(H, H1), v2 = intval(H, H2);
if(v1 < v2) fmin = f; else fmax = f;
}
hexf = fmin;
rhexf = BITRUNCATED ? hexf : hcrossf;
if(!euclid && BITRUNCATED && !(S7&1))
hexshift = ALPHA/2 + ALPHA * ((S7-1)/2) + M_PI;
finish:
for(int d=0; d<S7; d++)
heptmove[d] = spin(-d * ALPHA) * xpush(tessf) * spin(M_PI);
for(int d=0; d<S7; d++)
hexmove[d] = spin(hexshift-d * ALPHA) * xpush(-crossf)* spin(M_PI);
for(int d=0; d<S7; d++) invheptmove[d] = inverse(heptmove[d]);
for(int d=0; d<S7; d++) invhexmove[d] = inverse(hexmove[d]);
hexhexdist = hdist(xpush0(crossf), xspinpush0(M_PI*2/S7, crossf));
hexvdist = hdist(xpush0(hexf), xspinpush0(ALPHA/2, hcrossf));
if(debug_geometry)
printf("S7=%d S6=%d hexf = " LDF" hcross = " LDF" tessf = " LDF" hexshift = " LDF " hexhex = " LDF " hexv = " LDF "\n", S7, S6, hexf, hcrossf, tessf, hexshift,
hexhexdist, hexvdist);
base_distlimit = ginf[geometry].distlimit[!BITRUNCATED];
#if CAP_GP
gp::compute_geometry();
#endif
#if CAP_IRR
irr::compute_geometry();
#endif
#if CAP_ARCM
if(archimedean) {
arcm::current.compute_geometry();
crossf = hcrossf7 * arcm::current.scale();
hexvdist = arcm::current.scale() * .5;
rhexf = arcm::current.scale() * .5;
}
#endif
if(binarytiling) hexvdist = rhexf = 1, tessf = 1, scalefactor = 1, crossf = hcrossf7;
if(binarytiling && DIM == 3) binary::build_tmatrix();
scalefactor = crossf / hcrossf7;
orbsize = crossf;
zhexf = BITRUNCATED ? hexf : crossf* .55;
floorrad0 = hexvdist* 0.92;
floorrad1 = rhexf * 0.94;
if(euclid4) {
if(!BITRUNCATED)
floorrad0 = floorrad1 = rhexf * .94;
else
floorrad0 = hexvdist * .9,
floorrad1 = rhexf * .8;
}
set_sibling_limit();
}
transmatrix xspinpush(ld dir, ld dist) {
if(euclid)
return eupush(cos(dir) * dist, -sin(dir) * dist);
else
return spin(dir) * xpush(dist) * spin(-dir);
}
namespace geom3 {
int tc_alpha=3, tc_depth=1, tc_camera=2;
ld depth = 1; // world below the plane
ld camera = 1; // camera above the plane
ld wall_height = .3;
ld slev = .08;
ld lake_top = .25, lake_bottom = .9;
ld rock_wall_ratio = .9;
ld human_wall_ratio = .7;
ld human_height;
bool gp_autoscale_heights = true;
ld highdetail = 8, middetail = 8;
// Here we convert between the following parameters:
// abslev: level below the plane
// lev: level above the world (abslev = depth-lev)
// projection: projection parameter
// factor: zoom factor
ld abslev_to_projection(ld abslev) {
if(sphere || euclid) return camera+abslev;
return tanh(abslev) / tanh(camera);
}
ld projection_to_abslev(ld proj) {
if(sphere || euclid) return proj-camera;
// tanh(abslev) / tanh(camera) = proj
return atanh(proj * tanh(camera));
}
ld lev_to_projection(ld lev) {
return abslev_to_projection(depth - lev);
}
ld projection_to_factor(ld proj) {
return lev_to_projection(0) / proj;
}
ld factor_to_projection(ld fac) {
return lev_to_projection(0) / fac;
}
ld lev_to_factor(ld lev) {
if(DIM == 3) return lev;
return projection_to_factor(lev_to_projection(lev));
}
ld factor_to_lev(ld fac) {
if(DIM == 3) return fac;
return depth - projection_to_abslev(factor_to_projection(fac));
}
// how should we scale at level lev
ld scale_at_lev(ld lev) {
if(sphere || euclid) return 1;
return cosh(depth - lev);
}
ld INFDEEP, BOTTOM, HELLSPIKE, LAKE, WALL,
SLEV[4], FLATEYE,
LEG0, LEG1, LEG, LEG3, GROIN, GROIN1, GHOST,
BODY, BODY1, BODY2, BODY3,
NECK1, NECK, NECK3, HEAD, HEAD1, HEAD2,
ALEG0, ALEG, ABODY, AHEAD, BIRD;
string invalid;
ld actual_wall_height() {
#if CAP_GP
if(GOLDBERG && gp_autoscale_heights)
return wall_height * min<ld>(4 / hypot2(gp::next), 1);
#endif
return wall_height;
}
void compute() {
// tanh(depth) / tanh(camera) == vid.alpha
invalid = "";
if(tc_alpha < tc_depth && tc_alpha < tc_camera)
vid.alpha = tan_auto(depth) / tan_auto(camera);
else if(tc_depth < tc_alpha && tc_depth < tc_camera) {
ld v = vid.alpha * tan_auto(camera);
if(hyperbolic && (v<1e-6-12 || v>1-1e-12)) invalid = "cannot adjust depth", depth = camera;
else depth = atan_auto(v);
}
else {
ld v = tan_auto(depth) / vid.alpha;
if(hyperbolic && (v<1e-12-1 || v>1-1e-12)) invalid = "cannot adjust camera", camera = depth;
else camera = atan_auto(v);
}
if(fabs(vid.alpha) < 1e-6) invalid = "does not work with perfect Klein";
if(invalid != "") {
INFDEEP = .7;
BOTTOM = .8;
HELLSPIKE = .85;
LAKE = .9;
WALL = 1.25;
SLEV[0] = 1;
SLEV[1] = 1.08;
SLEV[2] = 1.16;
SLEV[3] = 1.24;
FLATEYE = 1.03;
LEG1 = 1.025;
LEG = 1.05;
LEG3 = 1.075;
GROIN = 1.09;
GROIN1 = 1.105;
GHOST = 1.1;
BODY = 1.15;
BODY1 = 1.151;
BODY2 = 1.152;
BODY3 = 1.153;
NECK1 = 1.16;
NECK = 1.17;
NECK3 = 1.18;
HEAD = 1.188;
HEAD1= 1.189;
HEAD2= 1.190;
ABODY = 1.08;
AHEAD = 1.12;
BIRD = 1.20;
}
else {
INFDEEP = (euclid || sphere) ? 0.01 : lev_to_projection(0) * tanh(camera);
ld wh = actual_wall_height();
WALL = lev_to_factor(wh);
human_height = human_wall_ratio * wh;
if(DIM == 3) human_height *= 1.5;
ld reduce = (DIM == 3 ? human_height / 2 : 0);
LEG0 = lev_to_factor(human_height * .0 - reduce);
LEG1 = lev_to_factor(human_height * .1 - reduce);
LEG = lev_to_factor(human_height * .2 - reduce);
LEG3 = lev_to_factor(human_height * .3 - reduce);
GROIN = lev_to_factor(human_height * .4 - reduce);
GROIN1= lev_to_factor(human_height * .5 - reduce);
BODY = lev_to_factor(human_height * .6 - reduce);
BODY1 = lev_to_factor(human_height * .61 - reduce);
BODY2 = lev_to_factor(human_height * .62 - reduce);
BODY3 = lev_to_factor(human_height * .63 - reduce);
NECK1 = lev_to_factor(human_height * .7 - reduce);
NECK = lev_to_factor(human_height * .8 - reduce);
NECK3 = lev_to_factor(human_height * .9 - reduce);
HEAD = lev_to_factor(human_height * .98 - reduce);
HEAD1 = lev_to_factor(human_height * .99 - reduce);
HEAD2 = lev_to_factor(human_height);
reduce = (DIM == 3 ? human_height * .3 : 0);
ABODY = lev_to_factor(human_height * .4 - reduce);
ALEG0 = lev_to_factor(human_height * .0 - reduce);
ALEG = lev_to_factor(human_height * .2 - reduce);
AHEAD = lev_to_factor(human_height * .6 - reduce);
BIRD = lev_to_factor(DIM == 3 ? 0 : (human_wall_ratio+1)/2 * wh * .8);
GHOST = lev_to_factor(DIM == 3 ? 0 : human_height * .5);
FLATEYE = lev_to_factor(human_height * .15);
slev = rock_wall_ratio * wh / 3;
for(int s=0; s<=3; s++)
SLEV[s] = lev_to_factor(rock_wall_ratio * wh * s/3);
LAKE = lev_to_factor(-lake_top);
HELLSPIKE = lev_to_factor(-(lake_top+lake_bottom)/2);
BOTTOM = lev_to_factor(-lake_bottom);
}
}
}
void initgeo() {
// printf("%Lf\n", (ld) hdist0(xpush(-1)*ypush(0.01)*xpush(1)*C0));
precalc();
}
}
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