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3d:: horohex geometry

This commit is contained in:
Zeno Rogue 2019-03-13 13:12:49 +01:00
parent 67ba896be9
commit cb9513dd0d
8 changed files with 123 additions and 16 deletions
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99
binary-tiling.cpp
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@ -79,8 +79,15 @@ namespace binary {
rec--;
return h1;
}
heptagon *pathc(heptagon *h, int d, int d1, std::vector<std::initializer_list<int>> p) {
h->cmove(S7-1);
int z = h->c.spin(S7-1);
return path(h, d, d1, p[z]);
}
ld hororec_scale = 0.25;
ld horohex_scale = 0.6;
heptagon *build(heptagon *parent, int d, int d1, int t, int side, int delta) {
auto h = buildHeptagon1(tailored_alloc<heptagon> (t), parent, d, hsOrigin, d1);
@ -120,8 +127,14 @@ namespace binary {
#if MAXMDIM==4
heptagon *build3(heptagon *parent, int d, int d1, int delta) {
int side = 0;
if(d < 4) side = (parent->zebraval * 2 + d) % 5;
if(d == 8) side = ((parent->zebraval-d1) * 3) % 5;
if(geometry == gBinary3) {
if(d < 4) side = (parent->zebraval * 2 + d) % 5;
if(d == S7-1) side = ((5+parent->zebraval-d1) * 3) % 5;
}
if(geometry == gHoroHex) {
if(d < 3) side = (parent->zebraval + d) % 3;
if(d == S7-1) side = (parent->zebraval + 3 - d1) % 3;
}
return build(parent, d, d1, S7, side, delta);
}
#endif
@ -260,6 +273,38 @@ namespace binary {
else return path(h, d, d, {7, d, 9-d-s});
}
}
case gHoroHex: {
// the comment is a picture...
// generated with the help of hexb.cpp
switch(d) {
case 0: case 1: case 2:
return build3(parent, d, 13, 1);
case 13:
return build3(parent, 13, hrand(3), -1);
case 3:
return pathc(h, 3, 12, {{13,4,2}, {13,5,2}, {13,3,2}});
case 4:
return pathc(h, 4, 12, {{13,6,2,0}, {13,7,0,0}, {13,8,1,0}});
case 5:
return pathc(h, 5, 12, {{13,1,1}, {13,2,1}, {13,0,1}});
case 6:
return pathc(h, 6, 10, {{13,5}, {13,3}, {13,4}});
case 7:
return pathc(h, 7, 11, {{13,2}, {13,0}, {13,1}});
case 8:
return pathc(h, 8, 9, {{13,6,0}, {13,7,1}, {13,8,2}});
case 9:
return pathc(h, 9, 8, {{13,4}, {13,5}, {13,3}});
case 10:
return pathc(h, 10, 6, {{13,6,2}, {13,7,0}, {13,8,1}});
case 11:
return pathc(h, 11, 7, {{13,1}, {13,2}, {13,0}});
case 12:
h->cmove(13);
int z = h->c.spin(13);
return path(h, 12, (z+1)%3+3, {13, z+6});
}
}
default: ;
}
@ -352,10 +397,15 @@ namespace binary {
hrmap *new_alt_map(heptagon *o) { return new hrmap_binary(o); }
transmatrix direct_tmatrix[8];
transmatrix inverse_tmatrix[8];
transmatrix direct_tmatrix[14];
transmatrix inverse_tmatrix[14];
int use_direct;
// directions below 'use_direct' are taken from direct_tmatrix;
// directions at/above are taken by checking spin and inverse_tmatrix based on that
void build_tmatrix() {
use_direct = S7-1;
if(geometry == gBinary3) {
direct_tmatrix[0] = xpush(-log(2)) * parabolic3(-1, -1);
direct_tmatrix[1] = xpush(-log(2)) * parabolic3(1, -1);
@ -387,23 +437,46 @@ namespace binary {
direct_tmatrix[4] = parabolic3(-2*r2*z, 0);
direct_tmatrix[5] = parabolic3(0, -4*z);
}
for(int i=0; i<S7-1; i++)
if(geometry == gHoroHex) {
// also generated with the help of hexb.cpp
ld l = log(3)/2;
auto& t = direct_tmatrix;
t[0] = parabolic3(horohex_scale, 0) * xpush(-l) * cspin(1, 2, M_PI/2);
t[1] = cspin(1, 2, 2*M_PI/3) * t[0];
t[2] = cspin(1, 2, 4*M_PI/3) * t[0];
auto it = inverse(t[0]);
t[5] = it * t[1] * t[1];
t[6] = it * t[5];
t[4] = it * t[6] * t[2] * t[0];
t[3] = it * t[4] * t[2];
t[7] = it * t[2];
t[8] = it * t[6] * t[0];
t[9] = it * t[4];
t[10] = it * t[6] * t[2];
t[11] = it * t[1];
for(int a=0; a<12; a++) println(hlog, t[a]);
use_direct--;
}
for(int i=0; i<use_direct; i++)
inverse_tmatrix[i] = inverse(direct_tmatrix[i]);
}
const transmatrix& tmatrix(heptagon *h, int dir) {
if(dir == S7-1) {
h->cmove(S7-1);
return inverse_tmatrix[h->c.spin(S7-1)];
if(dir >= use_direct) {
h->cmove(dir);
return inverse_tmatrix[h->c.spin(dir)];
}
else
return direct_tmatrix[dir];
}
const transmatrix& itmatrix(heptagon *h, int dir) {
if(dir == S7-1) {
h->cmove(S7-1);
return h->cmove(S7-1), direct_tmatrix[h->c.spin(S7-1)];
if(dir >= use_direct) {
h->cmove(dir);
return h->cmove(dir), direct_tmatrix[h->c.spin(dir)];
}
else
return inverse_tmatrix[dir];
@ -478,7 +551,7 @@ auto bt_config = addHook(hooks_args, 0, [] () {
bool pseudohept(cell *c) {
if(DIM == 2)
return c->type & c->master->distance & 1;
else if(geometry == gHoroTris)
else if(among(geometry, gHoroTris, gHoroRec))
return c->c.spin(S7-1) == 0 && (c->master->distance & 1);
else
return (c->master->zebraval == 1) && (c->master->distance & 1);

1
classes.cpp
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@ -1789,6 +1789,7 @@ vector<geometryinfo> ginf = {
{"{3,3,5}","elliptic","{3,3,5} 600-cell (elliptic)", "e335", 4, 3, qsSMALLBE, gcSphere, 0x31800, {{SEE_ALL, SEE_ALL}}, eVariation::pure},
{"bin{3,6}", "none", "{3,6} on horospheres", "bin36", 8, 3, qBINARY, gcHyperbolic, 0x40000, {{7, 3}}, eVariation::pure},
{"bin-rect", "none", "rectangles on horospheres", "bin44/2", 7, 3, qBINARY, gcHyperbolic, 0x40200, {{7, 3}}, eVariation::pure},
{"bin{6,3}", "none", "{6,3} on horospheres", "bin63", 14, 3, qBINARY, gcHyperbolic, 0x40400, {{7, 3}}, eVariation::pure},
};
// bits: 9, 10, 15, 16, (reserved for later) 17, 18

2
classes.h
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@ -222,7 +222,7 @@ enum eGeometry {
gCell16, gECell16,
gCell24, gECell24,
gCell600, gECell600,
gHoroTris, gHoroRec,
gHoroTris, gHoroRec, gHoroHex,
gGUARD};
enum eGeometryClass { gcHyperbolic, gcEuclid, gcSphere };

1
config.cpp
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@ -384,6 +384,7 @@ void initConfig() {
addsaver(sightranges[gECell600], "sight-600cell-elliptic", M_PI);
addsaver(sightranges[gHoroTris], "sight-horotris", 3);
addsaver(sightranges[gHoroRec], "sight-hororec", 2);
addsaver(sightranges[gHoroHex], "sight-horohex", 2.5);
addsaver(smooth_scrolling, "smooth-scrolling", false);
addsaver(mouseaim_sensitivity, "mouseaim_sensitivity", 0.01);

4
graph.cpp
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@ -3912,10 +3912,14 @@ int get_darkval(int d) {
const int darkval_e6[6] = {0,4,6,0,4,6};
const int darkval_e12[12] = {0,4,6,0,4,6,0,4,6,0,4,6};
const int darkval_e14[14] = {0,0,0,4,6,4,6,0,0,0,6,4,6,4};
const int darkval_hh[14] = {0,0,0,1,1,1,2,2,2,3,3,3,1,0};
const int darkval_hrec[7] = {0,0,2,4,2,4,0};
if(sphere) return darkval_s12[d];
if(euclid && S7 == 6) return darkval_e6[d];
if(euclid && S7 == 12) return darkval_e12[d];
if(euclid && S7 == 14) return darkval_e14[d];
if(geometry == gHoroHex) return darkval_hh[d];
if(geometry == gHoroRec) return darkval_hrec[d];
if(binarytiling) return darkval_hbt[d];
if(hyperbolic && S7 == 6) return darkval_e6[d];
if(hyperbolic && S7 == 12) return darkval_s12[d];

2
hyper.h
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@ -1524,7 +1524,7 @@ bool bearsCamelot(eLand l);
extern bool safety;
#define SAGEMELT .1
#define TEMPLE_EACH (geometry == gHoroRec ? 3 : (DIM == 3 && binarytiling) ? 2 : geometry == gSpace435 ? 4 : (DIM == 3 && hyperbolic) ? 3 : 6)
#define TEMPLE_EACH (among(geometry, gHoroRec, gHoroHex) ? 3 : (DIM == 3 && binarytiling) ? 2 : geometry == gSpace435 ? 4 : (DIM == 3 && hyperbolic) ? 3 : 6)
#define PT(x, y) ((tactic::on || quotient == 2 || daily::on) ? (y) : inv::on ? min(2*(y),x) : (x))
#define ROCKSNAKELENGTH 50
#define WORMLENGTH 15

1
landgen.cpp
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@ -2463,6 +2463,7 @@ void setdist(cell *c, int d, cell *from) {
ld z = vid.binary_width;
cell *cseek = c;
int step = 0;
if(geometry == gHoroHex) z *= 2;
while(z < 3.999 && step < 10) cseek = cseek->cmove(S7-1), z *= 2;
if(cseek->master->emeraldval) setland(c, eLand(cseek->master->emeraldval));
}

29
polygons.cpp
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@ -2448,7 +2448,7 @@ void create_wall3d() {
if(geometry == gHoroRec) {
ld r2 = sqrt(2);
ld z = hororec_scale;
ld z = binary::hororec_scale;
hyperpoint a00 = point3(-r2*z,-2*z,-.5);
hyperpoint a01 = point3(+r2*z,-2*z,-.5);
@ -2468,6 +2468,33 @@ void create_wall3d() {
make_wall(6, make4(a00+down, a01+down, a20+down));
}
if(geometry == gHoroHex) {
ld z = log(3) / log(2) / 2;
ld r3 = sqrt(3) / 2 * binary::horohex_scale;
ld h = binary::horohex_scale / 2;
hyperpoint down = point3(0,0,2*z);
for(int i=0; i<3; i++) {
transmatrix T = cspin(0, 1, 2*M_PI*i/3);
hyperpoint hcenter = point3(0,0,-z);
hyperpoint hu0 = T*point3(+h, +r3,-z);
hyperpoint hu1 = T*point3(+h*3,+r3,-z);
hyperpoint hd0 = T*point3(+h, -r3,-z);
hyperpoint hd1 = T*point3(+h*3,-r3,-z);
hyperpoint hcn = T*point3(-h*2,0, -z);
hyperpoint hun = T*point3(-h*3,+r3,-z);
hyperpoint hdn = T*point3(-h*3,-r3,-z);
make_wall(i, {hcenter, hu0, hu1, hd1, hd0});
make_wall(i+3, {hcn, hun, hdn});
make_wall(i+6, make4(hd1, hu1, hd1+down));
make_wall(i+9, make4(hun, hdn, hun+down));
}
make_wall(12, {point3(3*h,r3,z), point3(0,2*r3,z), point3(-3*h,r3,z)});
make_wall(13, {point3(3*h,r3,z), point3(3*h,-r3,z), point3(0,-2*r3,z), point3(-3*h,-r3,z), point3(-3*h,r3,z)}, true);
}
if(DIM == 3 && euclid && S7 == 6) {
for(int w=0; w<6; w++) {
vector<hyperpoint> vertices;