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3d:: HoroTris geometry

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Zeno Rogue
2019-03-06 16:31:10 +01:00
parent 9efa497b66
commit 105de56857
7 changed files with 88 additions and 33 deletions
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75
binary-tiling.cpp
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@@ -100,7 +100,7 @@ namespace binary {
int side = 0;
if(d < 4) side = (parent->zebraval * 2 + d) % 5;
if(d == 8) side = ((parent->zebraval-d1) * 3) % 5;
return build(parent, d, d1, 9, side, delta);
return build(parent, d, d1, S7, side, delta);
}
#endif
@@ -161,6 +161,7 @@ namespace binary {
#if MAXMDIM==4
heptagon *createStep3(heptagon *parent, int d) {
auto h = parent;
if(geometry == gBinary3)
switch(d) {
case 0: case 1:
case 2: case 3:
@@ -192,6 +193,18 @@ namespace binary {
else
return path(h, 7, 6, {8, 7, parent->c.spin(8) ^ 2});
}
if(geometry == gHoroTris) switch(d) {
case 0: case 1: case 2: case 3:
return build3(parent, d, 7, 1);
case 7:
return build3(parent, 7, hrand(3), -1);
case 4: case 5: case 6:
parent->cmove(7);
int s = parent->c.spin(7);
if(s == 0) return path(h, d, d, {7, d-3});
else if(s == d-3) return path(h, d, d, {7, 0});
else return path(h, d, d, {7, d, 9-d-s});
}
printf("error: case not handled in binary tiling\n");
breakhere();
return NULL;
@@ -202,31 +215,43 @@ namespace binary {
transmatrix inverse_tmatrix[8];
void build_tmatrix() {
direct_tmatrix[0] = xpush(-log(2)) * parabolic3(-1, -1);
direct_tmatrix[1] = xpush(-log(2)) * parabolic3(1, -1);
direct_tmatrix[2] = xpush(-log(2)) * parabolic3(-1, 1);
direct_tmatrix[3] = xpush(-log(2)) * parabolic3(1, 1);
direct_tmatrix[4] = parabolic3(-2, 0);
direct_tmatrix[5] = parabolic3(+2, 0);
direct_tmatrix[6] = parabolic3(0, -2);
direct_tmatrix[7] = parabolic3(0, +2);
for(int i=0; i<8; i++)
if(geometry == gBinary3) {
direct_tmatrix[0] = xpush(-log(2)) * parabolic3(-1, -1);
direct_tmatrix[1] = xpush(-log(2)) * parabolic3(1, -1);
direct_tmatrix[2] = xpush(-log(2)) * parabolic3(-1, 1);
direct_tmatrix[3] = xpush(-log(2)) * parabolic3(1, 1);
direct_tmatrix[4] = parabolic3(-2, 0);
direct_tmatrix[5] = parabolic3(+2, 0);
direct_tmatrix[6] = parabolic3(0, -2);
direct_tmatrix[7] = parabolic3(0, +2);
}
if(geometry == gHoroTris) {
ld r3 = sqrt(3);
direct_tmatrix[0] = xpush(-log(2)) * cspin(1,2, M_PI);
direct_tmatrix[1] = parabolic3(0, +r3/3) * xpush(-log(2));
direct_tmatrix[2] = parabolic3(-0.5, -r3/6) * xpush(-log(2));
direct_tmatrix[3] = parabolic3(+0.5, -r3/6) * xpush(-log(2));
direct_tmatrix[4] = parabolic3(0, -r3*2/3) * cspin(1,2, M_PI);
direct_tmatrix[5] = parabolic3(1, r3/3) * cspin(1,2,M_PI);
direct_tmatrix[6] = parabolic3(-1, r3/3) * cspin(1,2,M_PI);
}
for(int i=0; i<S7-1; i++)
inverse_tmatrix[i] = inverse(direct_tmatrix[i]);
}
const transmatrix& tmatrix(heptagon *h, int dir) {
if(dir == 8) {
h->cmove(8);
return inverse_tmatrix[h->c.spin(8)];
if(dir == S7-1) {
h->cmove(S7-1);
return inverse_tmatrix[h->c.spin(S7-1)];
}
else
return direct_tmatrix[dir];
}
const transmatrix& itmatrix(heptagon *h, int dir) {
if(dir == 8) {
h->cmove(8);
return h->cmove(8), direct_tmatrix[h->c.spin(8)];
if(dir == S7-1) {
h->cmove(S7-1);
return h->cmove(S7-1), direct_tmatrix[h->c.spin(S7-1)];
}
else
return inverse_tmatrix[dir];
@@ -316,7 +341,7 @@ namespace binary {
}
}
else {
for(int i=0; i<9; i++)
for(int i=0; i<S7; i++)
dq::enqueue(h->move(i), V * tmatrix(h, i));
}
}
@@ -329,7 +354,7 @@ namespace binary {
while(h1 != h2) {
if(h1->distance <= h2->distance) {
if(DIM == 3)
where = itmatrix(h2, 8) * where, h2 = hr::createStep(h2, 8);
where = itmatrix(h2, S7-1) * where, h2 = hr::createStep(h2, S7-1);
else {
if(type_of(h2) == 6)
h2 = hr::createStep(h2, bd_down), where = xpush(-log(2)) * where;
@@ -341,7 +366,7 @@ namespace binary {
}
else {
if(DIM == 3)
gm = gm * tmatrix(h1, 8), h1 = hr::createStep(h1, 8);
gm = gm * tmatrix(h1, S7-1), h1 = hr::createStep(h1, S7-1);
else {
if(type_of(h1) == 6)
h1 = hr::createStep(h1, bd_down), gm = gm * xpush(log(2));
@@ -377,14 +402,14 @@ int celldistance3(heptagon *c1, heptagon *c2) {
int steps = 0;
int d1 = c1->distance;
int d2 = c2->distance;
while(d1 > d2) c1 = c1->cmove(8), steps++, d1--;
while(d2 > d1) c2 = c2->cmove(8), steps++, d2--;
while(d1 > d2) c1 = c1->cmove(S7-1), steps++, d1--;
while(d2 > d1) c2 = c2->cmove(S7-1), steps++, d2--;
vector<int> dx, dy;
while(c1 != c2) {
dx.push_back((c1->c.spin(8) & 1) - (c2->c.spin(8) & 1));
dy.push_back((c1->c.spin(8) >> 1) - (c2->c.spin(8) >> 1));
c1 = c1->cmove(8);
c2 = c2->cmove(8);
dx.push_back((c1->c.spin(S7-1) & 1) - (c2->c.spin(S7-1) & 1));
dy.push_back((c1->c.spin(S7-1) >> 1) - (c2->c.spin(S7-1) >> 1));
c1 = c1->cmove(S7-1);
c2 = c2->cmove(S7-1);
steps += 2;
}
int xsteps = steps, sx = 0, sy = 0;