pointgroups.h File Reference

Quaternion-represented 3D point groups. More...

#include "qpms_error.h"
#include "quaternions.h"

Include dependency graph for pointgroups.h:

Go to the source code of this file.

Functions
static _Bool	qpms_pg_is_finite_axial (qpms_pointgroup_class cls)
	Returns true if the point group class belongs to one of the seven "axial" group series.
int	qpms_pg_irot3_approx_cmp (const qpms_irot3_t *, const qpms_irot3_t *, double atol)
	An ordering of qpms_irot3_t that considers close enough elements equal. More...
int	qpms_pg_irot3_approx_cmp_v (const void *, const void *)
	A search.h compatible ordering of qpms_irot3_t that considers close enough elements equal. More...
qpms_gmi_t	qpms_pg_order (qpms_pointgroup_class cls, qpms_gmi_t n)
	Returns the order of a given 3D point group type. More...
qpms_irot3_t *	qpms_pg_canonical_elems (qpms_irot3_t *target, qpms_pointgroup_class cls, qpms_gmi_t)
	Generates the canonical elements of a given 3D point group type. More...
qpms_gmi_t	qpms_pg_genset_size (qpms_pointgroup_class cls, qpms_gmi_t n)
	Returns the number of canonical generators of a given 3D point group type. More...
qpms_gmi_t	qpms_pg_genset (qpms_pointgroup_class cls, qpms_gmi_t n, qpms_irot3_t gen[])
	Fills an array of canonical generators of a given 3D point group type. More...
qpms_irot3_t *	qpms_pg_elems (qpms_irot3_t *target, qpms_pointgroup_t g)
	Generates all elements of a given point group. More...
_Bool	qpms_pg_is_subgroup (qpms_pointgroup_t a, qpms_pointgroup_t b)
	Checks whether a is subgroup of b (in a dirty general way).

Variables
double	qpms_pg_quat_cmp_atol
	Absolute tolerance threshold used internally to consider two different qpms_irot3_t instances equal. More...

Detailed Description

Quaternion-represented 3D point groups.

Function Documentation

qpms_pg_canonical_elems()

qpms_irot3_t* qpms_pg_canonical_elems	(	qpms_irot3_t *	target,
		qpms_pointgroup_class	cls,
		qpms_gmi_t	then
	)

Generates the canonical elements of a given 3D point group type.

Uses the canonical generators and DPS.

Parameters

target	Target array (optional; if NULL, a new one is allocated)
cls	Point group class.
then	Number of rotations around z axis (only for axial group classes).

qpms_pg_elems()

qpms_irot3_t* qpms_pg_elems	(	qpms_irot3_t *	target,
		qpms_pointgroup_t	g
	)

Generates all elements of a given point group.

The order of elements corresponds to the one obtained from qpms_pg_canonical_elems().

Parameters

target	Target array (optional; if NULL, a new one is allocated)
g	Specification of the point group.

qpms_pg_genset()

qpms_gmi_t qpms_pg_genset	(	qpms_pointgroup_class	cls,
		qpms_gmi_t	n,
		qpms_irot3_t	gen[]
	)

Fills an array of canonical generators of a given 3D point group type.

TODO what does it do for infinite (Lie) groups?

Parameters

cls	Point group class.
n	Number of rotations around main axis (only for axial groups).
gen	Target generator array

qpms_pg_genset_size()

qpms_gmi_t qpms_pg_genset_size	(	qpms_pointgroup_class	cls,
		qpms_gmi_t	n
	)

Returns the number of canonical generators of a given 3D point group type.

TODO what does it do for infinite (Lie) groups?

Parameters

cls	Point group class.
n	Number of rotations around main axis (only for axial groups).

qpms_pg_irot3_approx_cmp()

int qpms_pg_irot3_approx_cmp	(	const qpms_irot3_t *	p1,
		const qpms_irot3_t *	p2,
		double	atol
	)

An ordering of qpms_irot3_t that considers close enough elements equal.

Parameters

atol	Absolute tolerance for the quaternion part difference.

qpms_pg_irot3_approx_cmp_v()

int qpms_pg_irot3_approx_cmp_v	(	const void *	av,
		const void *	bv
	)

A search.h compatible ordering of qpms_irot3_t that considers close enough elements equal.

The tolerance is determined by global variable qpms_pg_quat_cmp_atol.

qpms_pg_order()

qpms_gmi_t qpms_pg_order	(	qpms_pointgroup_class	cls,
		qpms_gmi_t	n
	)

Returns the order of a given 3D point group type.

For infinite groups returns 0.

Parameters

cls	Point group class.
n	Number of rotations around main axis (only for finite axial groups).

Variable Documentation

qpms_pg_quat_cmp_atol

double qpms_pg_quat_cmp_atol

extern

Absolute tolerance threshold used internally to consider two different qpms_irot3_t instances equal.

Used by qpms_pg_irot3_approx_cmp_v. By default, set to QPMS_QUAT_ATOL. It should work fine if the point group orders stay reasonable (thousands or less). Do not touch if unsure what you are doing.