Draft generators for finite axial qpms_pointgroup_t.
Former-commit-id: 0a9eba27d584038be532bb1590b7d5b6b98fba1b
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Marek Nečada
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1f8d146b13
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0530895f84
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#ifndef POINTGROUPS_H
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#define POINTGROUPS_H
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#include "qpms_error.h"
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#include "wigner.h"
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static inline _Bool qpms_pg_is_finite_axial(qpms_pointgroup_class cls) {
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switch(cls) {
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case QPMS_PGS_CN:
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case QPMS_PGS_S2N:
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case QPMS_PGS_CNH:
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case QPMS_PGS_CNV:
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case QPMS_PGS_DN:
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case QPMS_PGS_DND:
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case QPMS_PGS_DNH:
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return true;
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default:
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return false;
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}
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}
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/// Returns the order of a given 3D point group type.
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/** For infinite groups returns 0. */
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static inline size_t qpms_pg_order(qpms_pointgroup_class cls, ///< Point group class.
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size_t n ///< Number of rotations around main axis (only for finite axial groups).
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) {
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if (qpms_pg_is_finite_axial(cls))
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QPMS_ENSURE(n > 0, "n must be at least 1 for finite axial groups");
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switch(cls) {
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// Axial groups
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case QPMS_PGS_CN:
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return n;
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case QPMS_PGS_S2N:
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case QPMS_PGS_CNH:
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case QPMS_PGS_CNV:
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case QPMS_PGS_DN:
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return 2*n;
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case QPMS_PGS_DND:
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case QPMS_PGS_DNH:
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return 4*n;
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// Remaining polyhedral groups
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case QPMS_PGS_T:
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return 12;
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case QPMS_PGS_TD:
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case QPMS_PGS_TH:
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case QPMS_PGS_O:
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return 24;
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case QPMS_PGS_OH:
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return 48;
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case QPMS_PGS_I:
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return 60;
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case QPMS_PGS_IH:
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return 120;
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// Continuous axial groups
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case QPMS_PGS_CINF:
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case QPMS_PGS_CINFH:
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case QPMS_PGS_CINFV:
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case QPMS_PGS_DINF:
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case QPMS_PGS_DINFH:
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// Remaining continuous groups
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case QPMS_PGS_SO3:
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case QPMS_PGS_O3:
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return 0; // 0 is infinity :-)
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default:
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QPMS_WTF;
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}
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}
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/// Returns the number of canonical generators of a given 3D point group type.
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/** TODO what does it do for infinite (Lie) groups? */
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static inline size_t qpms_pg_genset_size(qpms_pointgroup_class cls, ///< Point group class.
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size_t n ///< Number of rotations around main axis (only for axial groups).
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) {
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if (qpms_pg_is_finite_axial(cls)) {
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QPMS_ENSURE(n > 0, "n must be at least 1 for finite axial groups");
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// n = 1 needs special care:
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if (n==1)
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switch(cls) {
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case QPMS_PGS_CN: return 0; // triv.
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case QPMS_PGS_S2N: return 1; // Z_2
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case QPMS_PGS_CNH: return 1; // Dih_1
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case QPMS_PGS_CNV: return 1; // Dih_1
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case QPMS_PGS_DN: return 1; // Dih_1
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case QPMS_PGS_DND: return 2; // Dih_2
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case QPMS_PGS_DNH: return 2; // Dih_1 x Dih_1
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default: QPMS_WTF;
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}
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}
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switch(cls) {
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// Axial groups
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case QPMS_PGS_CN: return 1; // Z_n
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case QPMS_PGS_S2N: return 1; // Z_{2n}
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case QPMS_PGS_CNH: return 2; // Z_n x Dih_1
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case QPMS_PGS_CNV: return 2; // Dih_n
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case QPMS_PGS_DN: return 2; // Dih_n
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case QPMS_PGS_DND: return 2; // Dih_2n
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case QPMS_PGS_DNH: return 3; // Dih_n x Dih_1
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// Remaining polyhedral groups
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case QPMS_PGS_T: // return ???; // A_4
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case QPMS_PGS_TD: // return 2; // S_4
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case QPMS_PGS_TH: // A_4 x Z_2
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case QPMS_PGS_O: // S_4
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case QPMS_PGS_OH: // return 3; // S_4 x Z_2
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case QPMS_PGS_I: // A_5
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case QPMS_PGS_IH: // A_5 x Z_2
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// Continuous axial groups
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case QPMS_PGS_CINF:
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case QPMS_PGS_CINFH:
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case QPMS_PGS_CINFV:
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case QPMS_PGS_DINF:
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case QPMS_PGS_DINFH:
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// Remaining continuous groups
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case QPMS_PGS_SO3:
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case QPMS_PGS_O3:
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QPMS_NOT_IMPLEMENTED("Not yet implemented for this point group class.");
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default:
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QPMS_WTF;
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}
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}
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/// Fills an array of canonical generators of a given 3D point group type.
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/** TODO what does it do for infinite (Lie) groups? */
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static inline size_t qpms_pg_genset(qpms_pointgroup_class cls, ///< Point group class.
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size_t n, ///< Number of rotations around main axis (only for axial groups).
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qpms_irot3_t gen[] ///< Target generator array
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) {
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if (qpms_pg_is_finite_axial(cls)) {
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QPMS_ENSURE(n > 0, "n must be at least 1 for finite axial groups");
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// n = 1 needs special care:
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if (n==1)
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switch(cls) {
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case QPMS_PGS_CN:
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return 0; // triv.
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case QPMS_PGS_S2N:
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gen[0] = QPMS_IROT3_INVERSION;
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return 1; // Z_2
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case QPMS_PGS_CNH:
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gen[0] = QPMS_IROT3_ZFLIP;
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return 1; // Dih_1
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case QPMS_PGS_CNV:
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gen[0] = QPMS_IROT3_XFLIP;
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return 1; // Dih_1
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case QPMS_PGS_DN:
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gen[0] = QPMS_IROT3_XROT_PI; // CHECKME
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return 1; // Dih_1
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case QPMS_PGS_DND:
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gen[0] = QPMS_IROT3_INVERSION;
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gen[1] = QPMS_IROT3_XFLIP;
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return 2; // Dih_2
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case QPMS_PGS_DNH: // CHECKME
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gen[0] = QPMS_IROT3_ZFLIP;
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gen[1] = QPMS_IROT3_XFLIP;
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return 2; // Dih_1 x Dih_1
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default: QPMS_WTF;
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}
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}
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switch(cls) {
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// Axial groups
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case QPMS_PGS_CN:
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gen[0] = qpms_irot3_zrot_Nk(n, 1);
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return 1; // Z_n
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case QPMS_PGS_S2N:
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gen[0].rot = qpms_quat_zrot_Nk(2*n, 1);
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gen[0].det = -1;
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return 1; // Z_{2n}
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case QPMS_PGS_CNH:
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gen[0] = qpms_irot3_zrot_Nk(n, 1);
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gen[1] = QPMS_IROT3_ZFLIP;
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return 2; // Z_n x Dih_1
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case QPMS_PGS_CNV:
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gen[0] = qpms_irot3_zrot_Nk(n, 1);
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gen[1] = QPMS_IROT3_XFLIP;
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return 2; // Dih_n
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case QPMS_PGS_DN:
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gen[0] = qpms_irot3_zrot_Nk(n, 1);
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gen[1] = QPMS_IROT3_XROT_PI;
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return 2; // Dih_n
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case QPMS_PGS_DND:
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gen[0].rot = qpms_quat_zrot_Nk(2*n, 1);
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gen[0].det = -1;
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gen[1] = QPMS_IROT3_XFLIP;
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return 2; // Dih_2n
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case QPMS_PGS_DNH:
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gen[0] = qpms_irot3_zrot_Nk(n, 1);
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gen[1] = QPMS_IROT3_ZFLIP;
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gen[2] = QPMS_IROT3_XFLIP;
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return 3; // Dih_n x Dih_1
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// Remaining polyhedral groups
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case QPMS_PGS_T: // return ???; // A_4
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case QPMS_PGS_TD: // return 2; // S_4
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case QPMS_PGS_TH: // A_4 x Z_2
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case QPMS_PGS_O: // S_4
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case QPMS_PGS_OH: // return 3; // S_4 x Z_2
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case QPMS_PGS_I: // A_5
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case QPMS_PGS_IH: // A_5 x Z_2
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// Continuous axial groups
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case QPMS_PGS_CINF:
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case QPMS_PGS_CINFH:
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case QPMS_PGS_CINFV:
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case QPMS_PGS_DINF:
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case QPMS_PGS_DINFH:
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// Remaining continuous groups
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case QPMS_PGS_SO3:
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case QPMS_PGS_O3:
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QPMS_NOT_IMPLEMENTED("Not yet implemented for this point group class.");
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default:
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QPMS_WTF;
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}
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}
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#endif //POINTGROUPS_H
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@ -227,6 +227,12 @@ static inline cart3_t qpms_irot3_apply_cart3(const qpms_irot3_t p, const cart3_t
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// Some basic transformations with irot3 type
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/// Identity
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static const qpms_irot3_t QPMS_IROT3_IDENTITY = {QPMS_QUAT_1, 1};
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/// \f$ \pi \f$ rotation around x axis.
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static const qpms_irot3_t QPMS_IROT3_XROT_PI = {QPMS_QUAT_I, 1};
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/// \f$ \pi \f$ rotation around y axis.
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static const qpms_irot3_t QPMS_IROT3_YROT_PI = {QPMS_QUAT_J, 1};
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/// \f$ \pi \f$ rotation around z axis.
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static const qpms_irot3_t QPMS_IROT3_ZROT_PI = {QPMS_QUAT_K, 1};
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/// Spatial inversion.
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static const qpms_irot3_t QPMS_IROT3_INVERSION = {QPMS_QUAT_1, -1};
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/// yz-plane mirror symmetry
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