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