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euc:: Hantzsche-Wendt manifold

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Zeno Rogue 2020-06-16 01:31:41 +02:00
parent 2da94c3986
commit cbd0c1f934
1 changed files with 89 additions and 3 deletions
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92
euclid.cpp
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@ -77,7 +77,7 @@ EX namespace euc {
struct torus_config {
/** periods entered by the user */
intmatrix user_axes;
/** OR'ed flags: 1 -- flip X in 3D, 2 -- flip Y in 3D, 4 -- flip X/Y in 3D, 8 -- Klein bottle in 2D, 16 -- third turn in 3D */
/** OR'ed flags: 1 -- flip X in 3D, 2 -- flip Y in 3D, 4 -- flip X/Y in 3D, 8 -- Klein bottle in 2D, 16 -- third turn in 3D, 32 -- Hantzsche-Wendt in 3D */
int twisted;
torus_config() {}
@ -479,7 +479,24 @@ EX namespace euc {
if(m[2][0] != m[2][2]) return false;
return true;
}
EX torus_config make_hantzsche_wendt(int v) {
intmatrix im;
for(int i=0; i<3; i++)
for(int j=0; j<3; j++) im[i][j] = 0;
for(int i=0; i<3; i++) {
im[i][i] = v;
im[i][(i+1)%3] = v;
}
return {im, 32};
}
EX bool valid_hantzsche_wendt(const intmatrix& m) {
return m[0][0] > 0 && m == make_hantzsche_wendt(m[0][0]).user_axes;
}
EX torus_config make_third_turn(int a, int b, int c) {
intmatrix T0;
T0[0][0] = a;
@ -594,6 +611,10 @@ EX namespace euc {
if(g == gBitrunc3 && (T0[0][0]&1)) eu.twisted = 0;
if(g == gBitrunc3 && (T0[1][1]&1)) eu.twisted = 0;
}
else if(valid_hantzsche_wendt(eu.user_axes)) {
eu.twisted &= 32;
if(g == gBitrunc3 && (T0[0][0]&1)) eu.twisted = 0;
}
else {
eu.twisted &= 7;
if(g != gCubeTiling && ((T0[0][0]+T0[2][2]) & 1)) eu.twisted &=~ 1;
@ -654,6 +675,45 @@ EX namespace euc {
return;
}
auto& T0 = user_axes;
if(twisted & 32) {
int period = T0[0][0];
auto& coo = x;
while(true) {
restart:
/* These coordinates cause the algorithm below to go in circles. We simply break if they are detected */
if(coo[0] >= 0 && coo[1] == period - coo[0] && coo[2] == -coo[1] && coo[0]*2 > period && coo[0] < period) return;
if(coo[0]*2 <= -period && coo[0] >= -period && coo[2] == period+coo[0] && coo[2] == -coo[1]) return;
/* apply periods */
for(int i=0; i<3; i++) {
int j = (i+1) % 3;
int k = (i+2) % 3;
int v1 = coo[i] + coo[j];
int v2 = coo[i] - coo[j];
if(v1 >= period) {
coo[i] -= period; coo[j] -= period;
}
else if(v1 < -period) {
coo[i] += period; coo[j] += period;
}
else if(v2 >= period) {
coo[i] -= period; coo[j] += period;
}
else if(v2 < -period) {
coo[i] += period; coo[j] -= period;
}
else continue;
d[j] = -d[j]; d[k] = -d[k];
coo[j] = -coo[j]; coo[k] = -coo[k];
transmatrix S = Id;
S[j][j] = -1; S[k][k] = -1;
M = M * S;
goto restart;
}
return;
}
}
if(twisted & 16) {
int period = T0[2][2];
transmatrix RotYZX = Zero;
@ -813,6 +873,8 @@ EX namespace euc {
});
}
EX int quotient_size = 2;
EX void show_torus3() {
int dim = WDIM;
auto& T_edit = eu_edit.user_axes;
@ -847,6 +909,15 @@ EX namespace euc {
dialog::add_action([] { eu_edit.twisted ^= 16; });
}
if(valid_hantzsche_wendt(T_edit)) {
auto g = geometry;
if(g == gCubeTiling || g == gRhombic3 || (g == gBitrunc3 && T_edit[0][0] % 2 == 0))
dialog::addBoolItem(XLAT("Hantzsche-Wendt space"), twisted_edit & 32, 'x');
else
dialog::addBoolItem(XLAT("make it even"), twisted_edit & 32, 'x');
dialog::add_action([] { eu_edit.twisted ^= 32; });
}
if(nondiag) {
dialog::addInfo(XLAT("twisting implemented only for diagonal matrices"));
dialog::addInfo(XLAT("or for columns : (A,B,C), (B,C,A), (D,D,D) where A+B+C=0"));
@ -878,8 +949,16 @@ EX namespace euc {
dialog::add_action([] { eu_edit.twisted ^= 4; });
}
dialog::addBreak(50);
torus_config_option(XLAT("third-turn space"), 'A', make_third_turn(2,0,2));
torus_config_option(XLAT("quarter-turn space"), 'B', make_quarter_turn(2, 0, 2));
dialog::addItem("special manifolds", 'S');
dialog::add_action([] {
dialog::editNumber(quotient_size, 1, 12, 1, 2, "special manifold size", "");
dialog::extra_options = [] {
auto q = quotient_size;
torus_config_option(XLAT("third-turn space"), 'A', make_third_turn(q,0,q));
torus_config_option(XLAT("quarter-turn space"), 'B', make_quarter_turn(q,0,q));
torus_config_option(XLAT("Hantzsche-Wendt space"), 'C', make_hantzsche_wendt(q));
};
});
}
else {
if(T_edit[1][0] == 0 && T_edit[1][1] == 0)
@ -1012,6 +1091,13 @@ EX namespace euc {
shift(); eu_input.twisted = argi();
build_torus3();
}
else if(argis("-hw")) {
PHASEFROM(2);
stop_game();
shift();
eu_input = make_hantzsche_wendt(argi());
build_torus3();
}
else if(argis("-twisttest")) {
start_game();
celllister cl(cwt.at, 10000, 10000, NULL);