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twisting fix

This commit is contained in:
Zeno Rogue 2019-04-16 03:22:52 +02:00
parent c0145c0d9c
commit 1cc26a7337
3 changed files with 138 additions and 9 deletions
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144
euclid.cpp
View File

@ -503,6 +503,8 @@ namespace euclid3 {
typedef long long coord;
static const long long COORDMAX = (1<<16);
typedef array<coord, 3> axes;
typedef array<array<int, 3>, 3> intmatrix;
static const axes main_axes = { 1, COORDMAX, COORDMAX * COORDMAX };
@ -524,7 +526,6 @@ namespace euclid3 {
static const coord D1 = main_axes[1];
static const coord D2 = main_axes[2];
vector<coord> shifttable;
vector<transmatrix> tmatrix;
switch(geometry) {
case gCubeTiling:
shifttable = { +D0, +D1, +D2 };
@ -551,6 +552,9 @@ namespace euclid3 {
coord canonicalize(coord x);
void build_torus3();
coord twist(coord x, transmatrix& M);
extern int twisted;
extern intmatrix T0;
struct hrmap_euclid3 : hrmap {
vector<coord> shifttable;
@ -615,6 +619,15 @@ namespace euclid3 {
return build(parent, d, canonicalize(ispacemap[parent] + shifttable[d]));
}
transmatrix get_move(cell *c, int i) {
if(!twisted) return tmatrix[i];
transmatrix res = tmatrix[i];
coord id = ispacemap[c->master];
id += shifttable[i];
twist(id, res);
return res;
}
void draw() {
dq::visited_by_matrix.clear();
dq::enqueue_by_matrix(viewctr.at, cview());
@ -632,13 +645,38 @@ namespace euclid3 {
drawcell(c, V, 0, false);
for(int i=0; i<S7; i++)
dq::enqueue_by_matrix(h->move(i), V * tmatrix[i]);
dq::enqueue_by_matrix(h->move(i), V * get_move(h->c7, i));
if(c == cwt.at) first_cell_to_draw = false;
}
first_cell_to_draw = true;
}
transmatrix warppush(coord dif) {
auto v = getcoord(dif);
for(int i: {0, 1})
v[i] = gmod(v[i] + T0[i][i] / 2, T0[i][i]) - T0[i][i] / 2;
return eupush3(v[0], v[1], v[2]);
}
transmatrix relative_matrix(heptagon *h2, heptagon *h1) {
if(twisted) {
coord c1 = ispacemap[h1];
coord c2 = ispacemap[h2];
transmatrix T = warppush(c2 - c1);
for(int d: {-1, 1}) {
transmatrix I = Id;
coord cs = c1;
for(int s=0; s<3; s++) {
cs += d * T0[2][2] * main_axes[2];
I = I * eupush3(0, 0, d * T0[2][2]);
cs = twist(cs, I);
transmatrix T1 = I * warppush(c2 - cs);
if(hdist0(tC0(T1)) < hdist0(tC0(T)))
T = T1;
}
}
return T;
}
auto d = ispacemap[h2] - ispacemap[h1];
d = canonicalize(d);
auto v = getcoord(d);
@ -678,9 +716,8 @@ namespace euclid3 {
return new hrmap_euclid3;
}
transmatrix move_matrix(int i) {
auto v = getcoord(cubemap()->shifttable[i]);
return eupush3(v[0], v[1], v[2]);
transmatrix move_matrix(cell *c, int i) {
return cubemap()->get_move(c, i);
}
bool pseudohept(cell *c) {
@ -786,8 +823,6 @@ namespace euclid3 {
/* quotient spaces */
typedef array<array<int, 3>, 3> intmatrix;
intmatrix make_intmatrix(axes a) {
intmatrix T;
T[0] = getcoord(a[0]);
@ -820,6 +855,7 @@ namespace euclid3 {
intmatrix T, T2, T0, T_edit;
int det;
int coords;
int twisted, twisted0, twisted_edit;
void clear_torus3() {
for(int i=0; i<3; i++) user_axes[i] = 0;
@ -903,13 +939,53 @@ namespace euclid3 {
canonical_index = 0;
add_canonical(0);
twisted = twisted0;
if(geometry != gCubeTiling && (T0[0][0] & 1)) twisted &=~ 1;
if(geometry != gCubeTiling && (T0[1][1] & 1)) twisted &=~ 2;
for(int i=0; i<3; i++) for(int j=0; j<3; j++)
if(i != j && T0[i][j]) twisted = 0;
if(T0[2][2] == 0) twisted = 0;
if(T0[0][0] != T0[1][1]) twisted &= 3;
for(eGeometry g: {gCubeTiling, gRhombic3, gBitrunc3}) {
set_flag(ginf[g].flags, qANYQ, coords);
set_flag(ginf[g].flags, qBOUNDED, coords == 3);
bool nonori = false;
if(twisted&1) nonori = !nonori;
if(twisted&2) nonori = !nonori;
if(twisted&4) nonori = !nonori;
set_flag(ginf[g].flags, qNONORIENTABLE, nonori);
}
}
void swap01(transmatrix& M) {
for(int i=0; i<4; i++) swap(M[i][0], M[i][1]);
}
coord twist(coord x, transmatrix& M) {
auto coo = getcoord(x);
while(coo[2] >= T0[2][2]) {
coo[2] -= T0[2][2];
if(twisted & 1) coo[0] *= -1, M = M * MirrorX;
if(twisted & 2) coo[1] *= -1, M = M * MirrorY;
if(twisted & 4) swap(coo[0], coo[1]), swap01(M);
}
while(coo[2] < 0) {
coo[2] += T0[2][2];
if(twisted & 4) swap(coo[0], coo[1]), swap01(M);
if(twisted & 1) coo[0] *= -1, M = M * MirrorX;
if(twisted & 2) coo[1] *= -1, M = M * MirrorY;
}
for(int i: {0,1})
if(T0[i][i]) coo[i] = gmod(coo[i], T0[i][i]);
return coo[0] * main_axes[0] + coo[1] * main_axes[1] + coo[2] * main_axes[2];
}
coord canonicalize(coord x) {
if(twisted) {
transmatrix M = Id;
return twist(x, M);
}
if(coords == 0) return x;
if(coords == 1) {
while(celldistance(x + optimal_axes[0]) <= celldistance(x)) x += optimal_axes[0];
@ -928,15 +1004,54 @@ namespace euclid3 {
void prepare_torus3() {
T_edit = T0;
twisted_edit = twisted0;
}
void show_torus3() {
cmode = sm::SIDE | sm::MAYDARK;
gamescreen(1);
dialog::init(XLAT("3D Euclidean spaces"));
for(int y=0; y<5; y++)
for(int y=0; y<4; y++)
dialog::addBreak(100);
dialog::addBreak(50);
bool nondiag = false;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++)
if(T_edit[i][j] && i != j) nondiag = true;
if(nondiag) {
dialog::addInfo(XLAT("twisting implemented only for diagonal matrices"));
dialog::addBreak(200);
}
else if(T_edit[2][2] == 0) {
dialog::addInfo(XLAT("nothing to twist"));
dialog::addInfo(XLAT("change the bottom left corner"));
dialog::addBreak(100);
}
else {
if(geometry == gCubeTiling || T0[0][0] % 2 == 0)
dialog::addBoolItem(XLAT("flip X coordinate"), twisted_edit & 1, 'x');
else
dialog::addBoolItem(XLAT("flipping X impossible"), twisted_edit & 1, 'x');
dialog::add_action([] { twisted_edit ^= 1; });
if(geometry == gCubeTiling || T0[1][1] % 2 == 0)
dialog::addBoolItem(XLAT("flip Y coordinate"), twisted_edit & 2, 'y');
else
dialog::addBoolItem(XLAT("flipping Y impossible"), twisted_edit & 2, 'y');
dialog::add_action([] { twisted_edit ^= 2; });
if(T_edit[0][0] == T_edit[1][1])
dialog::addBoolItem(XLAT("swap X and Y"), twisted_edit & 4, 'z');
else
dialog::addBoolItem(XLAT("swapping impossible"), twisted_edit & 4, 'z');
dialog::add_action([] { twisted_edit ^= 4; });
}
dialog::addBreak(50);
char xch = 'p';
for(eGeometry g: {gCubeTiling, gRhombic3, gBitrunc3}) {
dialog::addItem(XLAT(ginf[g].menu_displayed_name), xch++);
@ -944,6 +1059,7 @@ namespace euclid3 {
stop_game();
set_geometry(g);
T0 = T_edit;
twisted0 = twisted_edit;
start_game();
});
}
@ -982,6 +1098,18 @@ namespace euclid3 {
}
build_torus3();
}
else if(argis("-twist3")) {
PHASEFROM(2);
stop_game();
for(int i=0; i<3; i++)
for(int j=0; j<3; j++) T0[i][j] = 0;
for(int i=0; i<3; i++) {
shift(); T0[i][i] = argi();
}
shift(); twisted0 = argi();
build_torus3();
}
else return 1;
return 0;

1
hyper.h
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@ -249,6 +249,7 @@ const static transmatrix Zero = diag(0,0,0,0);
// mirror image
const static transmatrix Mirror = diag(1,-1,1,1);
const static transmatrix MirrorY = diag(1,-1,1,1);
// mirror image
const static transmatrix MirrorX = diag(-1,1,1,1);

2
hypgraph.cpp
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@ -1190,7 +1190,7 @@ void optimizeview() {
heptagon *h2 = createStep(viewctr.at, i1);
transmatrix T = currentmap->relative_matrix(h2, viewctr.at);
if(euclid && DIM == 3)
T = euclid3::move_matrix(i);
T = euclid3::move_matrix(viewctr.at->c7, i);
hyperpoint H = View * tC0(T);
ld quality = hdist0(H);
if(quality < best) best = quality, turn = i1, TB = T;