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binary tiling in 3D works

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2019-02-21 18:47:32 +01:00
committed by Zeno Rogue
parent e73d2f2f22
commit 96e4ff6c9d
6 changed files with 197 additions and 9 deletions
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159
binary-tiling.cpp
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@@ -3,6 +3,8 @@ namespace hr {
namespace binary {
#if CAP_BT
#if DIM == 2
enum bindir {
bd_right = 0,
bd_up_right = 1,
@@ -13,16 +15,20 @@ namespace binary {
bd_down_left = 5, /* for cells of degree 7 */
bd_down_right = 6 /* for cells of degree 7 */
};
#endif
int type_of(heptagon *h) {
return h->c7->type;
}
#if DIM == 2
// 0 - central, -1 - left, +1 - right
int mapside(heptagon *h) {
return h->zebraval;
}
#endif
#if DIM == 2
#if DEBUG_BINARY_TILING
map<heptagon*, long long> xcode;
map<long long, heptagon*> rxcode;
@@ -40,6 +46,7 @@ namespace binary {
breakhere();
}
#endif
#endif
void breakhere() {
exit(1);
@@ -76,7 +83,12 @@ namespace binary {
return h1;
}
#if DIM == 2
heptagon *build(heptagon *parent, int d, int d1, int t, int side, int delta) {
#else
heptagon *build(heptagon *parent, int d, int d1, int delta) {
int t = 9; const int side = 0;
#endif
auto h = buildHeptagon1(tailored_alloc<heptagon> (t), parent, d, hsOrigin, d1);
h->distance = parent->distance + delta;
h->c7 = newCell(t, h);
@@ -93,6 +105,7 @@ namespace binary {
return h;
}
#if DIM == 2
heptagon *createStep(heptagon *parent, int d) {
auto h = parent;
switch(d) {
@@ -146,10 +159,120 @@ namespace binary {
breakhere();
return NULL;
}
#else
heptagon *createStep(heptagon *parent, int d) {
auto h = parent;
switch(d) {
case 0: case 1:
case 2: case 3:
return build(parent, d, 8, 1);
case 8:
return build(parent, 8, hrand(4), -1);
case 4:
parent->cmove(8);
if(parent->c.spin(8) & 1)
return path(h, 4, 5, {8, parent->c.spin(8) ^ 1});
else
return path(h, 4, 5, {8, 4, parent->c.spin(8) ^ 1});
case 5:
parent->cmove(8);
if(!(parent->c.spin(8) & 1))
return path(h, 5, 4, {8, parent->c.spin(8) ^ 1});
else
return path(h, 5, 4, {8, 5, parent->c.spin(8) ^ 1});
case 6:
parent->cmove(8);
if(parent->c.spin(8) & 2)
return path(h, 6, 7, {8, parent->c.spin(8) ^ 2});
else
return path(h, 6, 7, {8, 6, parent->c.spin(8) ^ 2});
case 7:
parent->cmove(8);
if(!(parent->c.spin(8) & 2))
return path(h, 7, 6, {8, parent->c.spin(8) ^ 2});
else
return path(h, 7, 6, {8, 7, parent->c.spin(8) ^ 2});
}
printf("error: case not handled in binary tiling\n");
breakhere();
return NULL;
}
#endif
transmatrix tmatrix(heptagon *h, int dir) {
switch(dir) {
case 0:
return xpush(-log(2)) * parabolic(-1, -1);
case 1:
return xpush(-log(2)) * parabolic(1, -1);
case 2:
return xpush(-log(2)) * parabolic(-1, 1);
case 3:
return xpush(-log(2)) * parabolic(1, 1);
case 4:
return parabolic(-2, 0);
case 5:
return parabolic(+2, 0);
case 6:
return parabolic(0, -2);
case 7:
return parabolic(0, +2);
case 8:
h->cmove(8);
return inverse(tmatrix(h->move(8), h->c.spin(8)));
}
printf("error: case not handled in binary tiling tmatrix\n");
breakhere();
return Id;
}
#if DIM == 3
void queuecube(const transmatrix& V, ld size, color_t linecolor, color_t facecolor) {
ld yy = log(2) / 2;
const int STEP=3;
const ld MUL = 1. / STEP;
auto at = [&] (ld x, ld y, ld z) { curvepoint(V * parabolic(size*x, size*y) * xpush(size*yy*z) * C0); };
for(int a:{-1,1}) {
for(ld t=-STEP; t<STEP; t++) at(a, 1,t*MUL);
for(ld t=-STEP; t<STEP; t++) at(a, -t*MUL,1);
for(ld t=-STEP; t<STEP; t++) at(a, -1,-t*MUL);
for(ld t=-STEP; t<STEP; t++) at(a, t*MUL,-1);
at(a, 1,-1);
queuecurve(linecolor, facecolor, PPR::LINE);
for(ld t=-STEP; t<STEP; t++) at(1,t*MUL,a);
for(ld t=-STEP; t<STEP; t++) at(-t*MUL,1,a);
for(ld t=-STEP; t<STEP; t++) at(-1,-t*MUL,a);
for(ld t=-STEP; t<STEP; t++) at(t*MUL,-1,a);
at(1,-1,a);
queuecurve(linecolor, facecolor, PPR::LINE);
for(ld t=-STEP; t<STEP; t++) at(1,a,t*MUL);
for(ld t=-STEP; t<STEP; t++) at(-t*MUL,a,1);
for(ld t=-STEP; t<STEP; t++) at(-1,a,-t*MUL);
for(ld t=-STEP; t<STEP; t++) at(t*MUL,a,-1);
at(1,a,-1);
queuecurve(linecolor, facecolor, PPR::LINE);
}
/*for(int a:{-1,1}) for(int b:{-1,1}) for(int c:{-1,1}) {
at(0,0,0); at(a,b,c); queuecurve(linecolor, facecolor, PPR::LINE);
}*/
}
#endif
#if DIM==2
transmatrix parabolic(ld u) {
return parabolic1(u * vid.binary_width / log(2) / 2);
}
#else
transmatrix parabolic(ld y, ld z) {
ld co = vid.binary_width / log(2) / 2;
return parabolic1(y * co, z * co);
}
#endif
ld btrange = 20;
void draw() {
dq::visited.clear();
@@ -163,20 +286,31 @@ namespace binary {
bandfixer bf(V);
dq::drawqueue.pop();
cell *c = h->c7;
#if DIM==2
if(!do_draw(c, V)) continue;
#endif
#if DIM==3
if(V[DIM][DIM] > btrange) continue;
setdist(c, 7, c);
#endif
drawcell(c, V, 0, false);
#if DIM==2
dq::enqueue(h->move(bd_up), V * xpush(-log(2)));
dq::enqueue(h->move(bd_right), V * parabolic(1));
dq::enqueue(h->move(bd_left), V * parabolic(-1));
if(c->type == 6)
dq::enqueue(h->move(bd_down), V * xpush(log(2)));
// down_left
if(c->type == 7) {
dq::enqueue(h->move(bd_down_left), V * parabolic(-1) * xpush(log(2)));
dq::enqueue(h->move(bd_down_right), V * parabolic(1) * xpush(log(2)));
}
#else
for(int i=0; i<9; i++)
dq::enqueue(h->move(i), V * tmatrix(h, i));
#endif
}
}
@@ -186,20 +320,28 @@ namespace binary {
transmatrix gm = Id, where = Id;
while(h1 != h2) {
if(h1->distance <= h2->distance) {
#if DIM==2
if(type_of(h2) == 6)
h2 = hr::createStep(h2, bd_down), where = xpush(-log(2)) * where;
else if(mapside(h2) == 1)
h2 = hr::createStep(h2, bd_left), where = parabolic(+1) * where;
else if(mapside(h2) == -1)
h2 = hr::createStep(h2, bd_right), where = parabolic(-1) * where;
#else
h2 = hr::createStep(h2, 8), where = inverse(tmatrix(h2, 8)) * where;
#endif
}
else {
#if DIM==2
if(type_of(h1) == 6)
h1 = hr::createStep(h1, bd_down), gm = gm * xpush(log(2));
else if(mapside(h1) == 1)
h1 = hr::createStep(h1, bd_left), gm = gm * parabolic(-1);
else if(mapside(h1) == -1)
h1 = hr::createStep(h1, bd_right), gm = gm * parabolic(+1);
#else
h1 = hr::createStep(h1, 8), where = where * tmatrix(h1, 8);
#endif
}
}
return gm * where;
@@ -212,9 +354,24 @@ auto bt_config = addHook(hooks_args, 0, [] () {
shift_arg_formula(vid.binary_width, delayed_geo_reset);
return 0;
}
else if(argis("-btrange")) {
shift_arg_formula(btrange);
return 0;
}
return 1;
});
#endif
#endif
int celldistance(cell *c1, cell *c2) {
int steps = 0;
while(c1 != c2) {
int d1 = celldistAlt(c1), d2 = celldistAlt(c2);
if(d1 >= d2) c1 = c1->cmove(8), steps++;
if(d2 >= d1) c2 = c2->cmove(8), steps++;
}
return steps;
}
}
}

5
cell.cpp
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@@ -73,7 +73,7 @@ hrmap_hyperbolic::hrmap_hyperbolic() {
binary::rxcode[1<<16] = &h;
#endif
h.zebraval = 0,
h.c7 = newCell(6, origin);
h.c7 = newCell(DIM == 3 ? 9 : 6, origin);
}
#endif
#if CAP_IRR
@@ -1868,6 +1868,9 @@ int celldistance(cell *c1, cell *c2) {
return 64;
}
#if DIM == 3
if(binarytiling) return binary::celldistance(c1, c2);
#endif
return hyperbolic_celldistance(c1, c2);
}

4
classes.cpp
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@@ -1757,7 +1757,11 @@ vector<geometryinfo> ginf = {
{"{8,3}", "Bolza", "Bolza Surface", "Bolza", 8, 3, qsDOCKS, gcHyperbolic, 0x18200, {{6, 4}}, eVariation::bitruncated},
{"{8,3}", "Bolza2", "Bolza Surface x2", "Bolza2", 8, 3, qsDOCKS, gcHyperbolic, 0x18400, {{6, 4}}, eVariation::bitruncated},
{"{7,3}", "minimal", "minimal quotient", "minimal", 7, 3, qsSMALLN, gcHyperbolic, 0x18600, {{7, 5}}, eVariation::bitruncated},
#if DIM == 2
{"binary","none", "variant of the binary tiling", "binary", 7, 3, 0,gcHyperbolic, 0, {{7, 5}}, eVariation::pure},
#else
{"binary","none", "variant of the binary tiling", "binary", 9, 3, 0,gcHyperbolic, 0, {{7, 3}}, eVariation::pure},
#endif
{"Arch", "none", "Archimedean", "A", 7, 3, 0, gcHyperbolic, 0, {{7, 5}}, eVariation::pure},
{"{7,3}", "Macbeath", "Macbeath Surface", "Macbeath", 7, 3, qsSMALL, gcHyperbolic, 0x20000, {{7, 5}}, eVariation::bitruncated},
{"{5,4}", "Bring", "Bring's Surface", "Bring", 5, 4, qsSMALL, gcHyperbolic, 0x20200, {{6, 4}}, eVariation::bitruncated},

14
geometry2.cpp
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@@ -436,8 +436,8 @@ hyperpoint randomPointIn(int t) {
}
#if CAP_BT
hyperpoint get_horopoint(ld y, ld x) {
return xpush(-y) * binary::parabolic(x) * C0;
hyperpoint get_horopoint(ld y, ld x DC(,ld z)) {
return xpush(-y) * binary::parabolic(x,z) * C0;
}
#endif
@@ -453,6 +453,7 @@ hyperpoint get_corner_position(cell *c, int cid, ld cf) {
#endif
#if CAP_BT
if(binarytiling) {
#if DIM == 2
ld yx = log(2) / 2;
ld yy = yx;
ld xx = 1 / sqrt(2)/2;
@@ -465,6 +466,10 @@ hyperpoint get_corner_position(cell *c, int cid, ld cf) {
vertices[5] = get_horopoint(-yy, -xx);
vertices[6] = get_horopoint(-yy, 0);
return mid_at_actual(vertices[cid], 3/cf);
#else
println(hlog, "get_corner_position called");
return C0;
#endif
}
#endif
#if CAP_ARCM
@@ -538,6 +543,7 @@ hyperpoint nearcorner(cell *c, int i) {
#endif
#if CAP_BT
if(binarytiling) {
#if DIM == 2
ld yx = log(2) / 2;
ld yy = yx;
// ld xx = 1 / sqrt(2)/2;
@@ -553,6 +559,10 @@ hyperpoint nearcorner(cell *c, int i) {
else
neis[5] = get_horopoint(-yy*2, 0);
return neis[i];
#else
println(hlog, "nearcorner called");
return Hypc;
#endif
}
#endif
double d = cellgfxdist(c, i);

8
graph.cpp
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@@ -5078,6 +5078,10 @@ void drawcell(cell *c, transmatrix V, int spinv, bool mirrored) {
#if CAP_QUEUE
if(error) {
if(ch == '#')
binary::queuecube(V, 1, 0xFF, darkena(asciicol, 0, 0xFF));
else if(ch == '.') ;
else
queuechr(V, 1, ch, darkenedby(asciicol, darken), 2);
}
@@ -5100,6 +5104,7 @@ void drawcell(cell *c, transmatrix V, int spinv, bool mirrored) {
if(0);
#if CAP_BT
else if(binarytiling) {
#if DIM == 2
ld yx = log(2) / 2;
ld yy = yx;
ld xx = 1 / sqrt(2)/2;
@@ -5113,6 +5118,9 @@ void drawcell(cell *c, transmatrix V, int spinv, bool mirrored) {
horizontal(yy, 2*xx, xx, 4, binary::bd_up_right);
horizontal(yy, xx, -xx, 8, binary::bd_up);
horizontal(yy, -xx, -2*xx, 4, binary::bd_up_left);
#else
binary::queuecube(V, 1, 0xC0C0C080, 0);
#endif
}
#endif
else if(isWarped(c) && has_nice_dual()) {

6
hyperpoint.cpp
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@@ -4,8 +4,14 @@
namespace hr {
#if DIM == 3
eGeometry geometry = gBinaryTiling;
eVariation variation = eVariation::pure;
#else
eGeometry geometry;
eVariation variation;
#endif
// hyperbolic points and matrices