scitbx::math::r3_rotation Namespace Reference

Algorithms for R3 (i.e. 3-dimensional space) rotation matrices. More...

Classes
struct	axis_and_angle_from_matrix
	Numerically robust computation of rotation axis and angle. More...
Functions
template<typename FloatType>
mat3< FloatType >	axis_and_angle_as_matrix (vec3< FloatType > const &axis, FloatType angle, bool deg=false, FloatType const &min_axis_length=1.e-15)
	Conversion of axis and angle to a rotation matrix.
template<typename FloatType>
af::tiny< FloatType, 4 >	normalized_axis_and_angle_rad_as_unit_quaternion (const FloatType *axis, FloatType const &angle)
	Conversion without validation of inputs.
template<typename FloatType>
af::tiny< FloatType, 4 >	axis_and_angle_as_unit_quaternion (vec3< FloatType > const &axis, FloatType angle, bool deg=false, FloatType const &min_axis_length=1.e-15)
	Conversion with validation of inputs.
template<typename FloatType>
mat3< FloatType >	vector_to_vector (vec3< FloatType > const &given_unit_vector, vec3< FloatType > const &target_unit_vector, FloatType const &sin_angle_is_zero_threshold=1.e-10)
	Returns rotation matrix mapping given_unit_vector onto target_unit_vector.
template<typename FloatType>
mat3< FloatType >	vector_to_001 (vec3< FloatType > const &given_unit_vector, FloatType const &sin_angle_is_zero_threshold=1.e-10)
	Returns rotation matrix mapping given_unit_vector onto (0,0,1).
template<typename FloatType>
mat3< FloatType >	vector_to_010 (vec3< FloatType > const &given_unit_vector, FloatType const &sin_angle_is_zero_threshold=1.e-10)
	Returns rotation matrix mapping given_unit_vector onto (0,1,0).
template<typename FloatType>
mat3< FloatType >	vector_to_100 (vec3< FloatType > const &given_unit_vector, FloatType const &sin_angle_is_zero_threshold=1.e-10)
	Returns rotation matrix mapping given_unit_vector onto (1,0,0).
template<typename FloatType>
mat3< FloatType >	unit_quaternion_as_matrix (FloatType const &q0, FloatType const &q1, FloatType const &q2, FloatType const &q3)
	Unit quaternion (a.k.a. Euler parameters) as matrix.
template<typename FloatType>
mat3< FloatType >	unit_quaternion_as_matrix (af::tiny< FloatType, 4 > const &q)
template<typename FloatType>
af::tiny< FloatType, 4 >	matrix_as_unit_quaternion (mat3< FloatType > const &r)
	Matrix as unit quaternion (a.k.a. Euler parameters).

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Detailed Description

Algorithms for R3 (i.e. 3-dimensional space) rotation matrices.

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Function Documentation

mat3<FloatType> scitbx::math::r3_rotation::axis_and_angle_as_matrix	(	vec3< FloatType > const &	axis,
		FloatType	angle,
		bool	deg = false,
		FloatType const &	min_axis_length = 1.e-15
	)			[inline]

Conversion of axis and angle to a rotation matrix.

http://skal.planet-d.net/demo/matrixfaq.htm

References SCITBX_ASSERT.

Referenced by axis_and_angle_from_matrix::as_matrix().

af::tiny<FloatType, 4> scitbx::math::r3_rotation::matrix_as_unit_quaternion

(

mat3< FloatType > const &

r

)

[inline]

Matrix as unit quaternion (a.k.a. Euler parameters).

The matrix elements must satisfy the orthogonality condition r.transpose()*r = identity but this is not thoroughly checked.

Based on work by: Shepperd (1978), J. Guidance and Control, 1, 223-224. Sam Buss, http://math.ucsd.edu/~sbuss/MathCG Robert Hanson, jmol/Jmol/src/org/jmol/util/Quaternion.java

Also implemented in Python: scitbx/matrix.py

mat3<FloatType> scitbx::math::r3_rotation::unit_quaternion_as_matrix	(	FloatType const &	q0,
		FloatType const &	q1,
		FloatType const &	q2,
		FloatType const &	q3
	)			[inline]

Unit quaternion (a.k.a. Euler parameters) as matrix.

The unit quaternion elements must satisfy the normalization condition q0**2+q1**2+q2**2+q3**3 = 1 but this is not checked.

Also implemented in Python: scitbx/matrix.py

mat3<FloatType> scitbx::math::r3_rotation::vector_to_001	(	vec3< FloatType > const &	given_unit_vector,
		FloatType const &	sin_angle_is_zero_threshold = 1.e-10
	)			[inline]

Returns rotation matrix mapping given_unit_vector onto (0,0,1).

It is not checked if the input vector is a unit vector. The result is meaningless if this is not true.

The implementation is a simplification of vector_to_vector().

mat3<FloatType> scitbx::math::r3_rotation::vector_to_010	(	vec3< FloatType > const &	given_unit_vector,
		FloatType const &	sin_angle_is_zero_threshold = 1.e-10
	)			[inline]

Returns rotation matrix mapping given_unit_vector onto (0,1,0).

It is not checked if the input vector is a unit vector. The result is meaningless if this is not true.

The implementation is a simplification of vector_to_vector().

mat3<FloatType> scitbx::math::r3_rotation::vector_to_100	(	vec3< FloatType > const &	given_unit_vector,
		FloatType const &	sin_angle_is_zero_threshold = 1.e-10
	)			[inline]

Returns rotation matrix mapping given_unit_vector onto (1,0,0).

It is not checked if the input vector is a unit vector. The result is meaningless if this is not true.

The implementation is a simplification of vector_to_vector().

mat3<FloatType> scitbx::math::r3_rotation::vector_to_vector	(	vec3< FloatType > const &	given_unit_vector,
		vec3< FloatType > const &	target_unit_vector,
		FloatType const &	sin_angle_is_zero_threshold = 1.e-10
	)			[inline]

Returns rotation matrix mapping given_unit_vector onto target_unit_vector.

It is not checked if the input vectors are unit vectors. The result is meaningless if this is not true.

See also: axis_and_angle_as_matrix()

References vec3::cross(), vec3::length(), and vec3::ortho().