#include <nnm.hpp>

Public Member Functions
constexpr	Basis3 ()
template<typename Other>
constexpr	Basis3 (const Basis3< Other > &basis)
constexpr	Basis3 (const Matrix3< Real > &matrix)
constexpr Real	trace () const
constexpr Real	determinant () const
constexpr Basis3	unchecked_inverse () const
constexpr std::optional< Basis3 >	inverse () const
constexpr bool	valid () const
Basis3	rotate_axis_angle (const Vector3< Real > &axis, const Real angle) const
Basis3	rotate_axis_angle_local (const Vector3< Real > &axis, const Real angle) const
constexpr Basis3	rotate_quaternion (const Quaternion< Real > &quaternion) const
constexpr Basis3	rotate_quaternion_local (const Quaternion< Real > &quaternion) const
constexpr Basis3	scale (const Vector3< Real > &factor) const
constexpr Basis3	scale_local (const Vector3< Real > &factor) const
constexpr Basis3	shear_x (const Real factor_y, const Real factor_z) const
constexpr Basis3	shear_x_local (const Real factor_y, const Real factor_z) const
constexpr Basis3	shear_y (const Real factor_x, const Real factor_z) const
constexpr Basis3	shear_y_local (const Real factor_x, const Real factor_z) const
constexpr Basis3	shear_z (const Real factor_x, const Real factor_y) const
constexpr Basis3	shear_z_local (const Real factor_x, const Real factor_y) const
constexpr Basis3	transform (const Basis3 &by) const
constexpr Basis3	transform_local (const Basis3 &by) const
constexpr bool	approx_equal (const Basis3 &other) const
constexpr const Vector3< Real > &	at (const uint8_t column) const
constexpr Vector3< Real > &	at (const uint8_t column)
constexpr const Real &	at (const uint8_t column, const uint8_t row) const
constexpr Real &	at (const uint8_t column, const uint8_t row)
constexpr const Vector3< Real > &	operator[] (const uint8_t index) const
constexpr Vector3< Real > &	operator[] (const uint8_t index)
constexpr bool	operator== (const Basis3 &other) const
constexpr bool	operator!= (const Basis3 &other) const
constexpr bool	operator< (const Basis3 &other) const

Static Public Member Functions
static Basis3	from_rotation_axis_angle (const Vector3< Real > &axis, const Real angle)
static constexpr Basis3	from_rotation_quaternion (const Quaternion< Real > &quaternion)
static constexpr Basis3	from_scale (const Vector3< Real > &factor)
static constexpr Basis3	from_shear_x (const Real factor_y, const Real factor_z)
static constexpr Basis3	from_shear_y (const Real factor_x, const Real factor_z)
static constexpr Basis3	from_shear_z (const Real factor_x, const Real factor_y)

Public Attributes
Matrix3< Real >	matrix

Detailed Description

template<typename Real>
class nnm::Basis3< Real >

Three-dimensional basis matrix. Can represent three-dimensional scale, shear, and rotation.

Template Parameters

Real

Constructor & Destructor Documentation

◆ Basis3() [1/3]

template<typename Real>

nnm::Basis3< Real >::Basis3 ( )

inlineconstexpr

Initializes with identity.

◆ Basis3() [2/3]

template<typename Real>

template<typename Other>

nnm::Basis3< Real >::Basis3 ( const Basis3< Other > & basis )

inlineexplicitconstexpr

Casts from another basis type.

Template Parameters

Other Other basis type.

Parameters

basis Basis to cast from.

◆ Basis3() [3/3]

template<typename Real>

nnm::Basis3< Real >::Basis3 ( const Matrix3< Real > & matrix )

inlineexplicitconstexpr

Initialize from 3x3 matrix. No validation is done.

Parameters

matrix 3x3 matrix.

Member Function Documentation

◆ approx_equal()

template<typename Real>

bool nnm::Basis3< Real >::approx_equal ( const Basis3< Real > & other ) const

inlinenodiscardconstexpr

Determines if approximately equal to another basis.

Parameters

other Other basis.

Returns: True if approximately equal, false otherwise.

◆ at() [1/4]

template<typename Real>

Vector3< Real > & nnm::Basis3< Real >::at ( const uint8_t column )

inlineconstexpr

Reference to column at index.

Parameters

column Index of column.

Returns: Reference to column.

◆ at() [2/4]

template<typename Real>

const Vector3< Real > & nnm::Basis3< Real >::at ( const uint8_t column ) const

inlinenodiscardconstexpr

Constant reference to column at index.

Parameters

column Index of column.

Returns: Constant reference to column.

◆ at() [3/4]

template<typename Real>

Real & nnm::Basis3< Real >::at	(	const uint8_t	column,
		const uint8_t	row )

inlineconstexpr

Reference of element at index of column and row.

Parameters

column	Index of column.
row	Index of row.

Returns: Reference to element.

◆ at() [4/4]

template<typename Real>

const Real & nnm::Basis3< Real >::at	(	const uint8_t	column,
		const uint8_t	row ) const

inlinenodiscardconstexpr

Constant reference of element at index of column and row.

Parameters

column	Index of column.
row	Index of row.

Returns: Constant reference to element.

◆ determinant()

template<typename Real>

Real nnm::Basis3< Real >::determinant ( ) const

inlinenodiscardconstexpr

Determinant of the matrix.

Returns: Result.

◆ from_rotation_axis_angle()

template<typename Real>

Basis3 nnm::Basis3< Real >::from_rotation_axis_angle	(	const Vector3< Real > &	axis,
		const Real	angle )

inlinestatic

Basis rotated from normalized axis and angle.

Parameters

axis	Normalized axis.
angle	Angle in radians.

Returns: Result.

◆ from_rotation_quaternion()

template<typename Real>

constexpr Basis3 nnm::Basis3< Real >::from_rotation_quaternion ( const Quaternion< Real > & quaternion )

inlinestaticconstexpr

Basis rotated from quaternion.

Parameters

quaternion Quaternion.

Returns: Result.

◆ from_scale()

template<typename Real>

constexpr Basis3 nnm::Basis3< Real >::from_scale ( const Vector3< Real > & factor )

inlinestaticconstexpr

Basis scaled by factor.

Parameters

factor Scale factor.

Returns: Result.

◆ from_shear_x()

template<typename Real>

constexpr Basis3 nnm::Basis3< Real >::from_shear_x	(	const Real	factor_y,
		const Real	factor_z )

inlinestaticconstexpr

Basis sheared along the x-axis.

Parameters

factor_y	Y-Axis factor.
factor_z	Z-Axis factor.

Returns: Result.

◆ from_shear_y()

template<typename Real>

constexpr Basis3 nnm::Basis3< Real >::from_shear_y	(	const Real	factor_x,
		const Real	factor_z )

inlinestaticconstexpr

Basis sheared along the y-axis.

Parameters

factor_x	X-Axis factor.
factor_z	Z-Axis factor.

Returns: Result.

◆ from_shear_z()

template<typename Real>

constexpr Basis3 nnm::Basis3< Real >::from_shear_z	(	const Real	factor_x,
		const Real	factor_y )

inlinestaticconstexpr

Basis sheared along the z-axis.

Parameters

factor_x	X-Axis factor.
factor_y	Y-Axis factor.

Returns: Result.

◆ inverse()

template<typename Real>

std::optional< Basis3 > nnm::Basis3< Real >::inverse ( ) const

inlinenodiscardconstexpr

Inverse of the basis.

Returns: Inverse basis if the basis is valid or null otherwise.

◆ operator!=()

template<typename Real>

bool nnm::Basis3< Real >::operator!= ( const Basis3< Real > & other ) const

inlinenodiscardconstexpr

Element-wise inequality with another basis.

Parameters

other Other basis.

Returns: True if any elements are not equal, false otherwise.

◆ operator<()

template<typename Real>

bool nnm::Basis3< Real >::operator< ( const Basis3< Real > & other ) const

inlinenodiscardconstexpr

Lexicographical comparison between elements.

Parameters

other Other basis.

Returns: True if less than, false otherwise.

◆ operator==()

template<typename Real>

bool nnm::Basis3< Real >::operator== ( const Basis3< Real > & other ) const

inlinenodiscardconstexpr

Element-wise equality with another basis.

Parameters

other Other basis.

Returns: True if all elements are equal, false otherwise.

◆ operator[]() [1/2]

template<typename Real>

Vector3< Real > & nnm::Basis3< Real >::operator[] ( const uint8_t index )

inlineconstexpr

Reference to column at index.

Parameters

index Index of column.

Returns: Reference to column.

◆ operator[]() [2/2]

template<typename Real>

const Vector3< Real > & nnm::Basis3< Real >::operator[] ( const uint8_t index ) const

inlinenodiscardconstexpr

Constant reference to column at index.

Parameters

index Index of column.

Returns: Constant reference to column.

◆ rotate_axis_angle()

template<typename Real>

Basis3 nnm::Basis3< Real >::rotate_axis_angle	(	const Vector3< Real > &	axis,
		const Real	angle ) const

inlinenodiscard

Rotate about an axis by an angle.

Parameters

axis	Normalized axis vector.
angle	Angle in radians.

Returns: Result.

◆ rotate_axis_angle_local()

template<typename Real>

Basis3 nnm::Basis3< Real >::rotate_axis_angle_local	(	const Vector3< Real > &	axis,
		const Real	angle ) const

inlinenodiscard

Local rotate about an axis by an angle.

Parameters

axis	Normalize axis vector.
angle	Angle in radians.

Returns: Result.

◆ rotate_quaternion()

template<typename Real>

Basis3 nnm::Basis3< Real >::rotate_quaternion ( const Quaternion< Real > & quaternion ) const

inlinenodiscardconstexpr

Rotate by quaternion.

Parameters

quaternion Quaternion.

Returns: Result.

◆ rotate_quaternion_local()

template<typename Real>

Basis3 nnm::Basis3< Real >::rotate_quaternion_local ( const Quaternion< Real > & quaternion ) const

inlinenodiscardconstexpr

Local rotate by quaternion.

Parameters

quaternion Quaternion.

Returns: Result.

◆ scale()

template<typename Real>

Basis3 nnm::Basis3< Real >::scale ( const Vector3< Real > & factor ) const

inlinenodiscardconstexpr

Per-axis scale by factor.

Parameters

factor Vector scale factor.

Returns: Result.

◆ scale_local()

template<typename Real>

Basis3 nnm::Basis3< Real >::scale_local ( const Vector3< Real > & factor ) const

inlinenodiscardconstexpr

Local per-axis scale by factor.

Parameters

factor Vector scale factor.

Returns: Result.

◆ shear_x()

template<typename Real>

Basis3 nnm::Basis3< Real >::shear_x	(	const Real	factor_y,
		const Real	factor_z ) const

inlinenodiscardconstexpr

Shear about x-axis.

Parameters

factor_y	Y-Axis factor.
factor_z	Z-Axis factor.

Returns: Result.

◆ shear_x_local()

template<typename Real>

Basis3 nnm::Basis3< Real >::shear_x_local	(	const Real	factor_y,
		const Real	factor_z ) const

inlinenodiscardconstexpr

Local shear about x-axis

Parameters

factor_y	Y-Axis factor.
factor_z	Z-Axis factor.

Returns: Result.

◆ shear_y()

template<typename Real>

Basis3 nnm::Basis3< Real >::shear_y	(	const Real	factor_x,
		const Real	factor_z ) const

inlinenodiscardconstexpr

Shear about y-axis.

Parameters

factor_x	X-Axis factor.
factor_z	Z-Axis factor.

Returns: Result.

◆ shear_y_local()

template<typename Real>

Basis3 nnm::Basis3< Real >::shear_y_local	(	const Real	factor_x,
		const Real	factor_z ) const

inlinenodiscardconstexpr

Local shear about y-axis.

Parameters

factor_x	X-Axis factor.
factor_z	Z-Axis factor.

Returns: Result.

◆ shear_z()

template<typename Real>

Basis3 nnm::Basis3< Real >::shear_z	(	const Real	factor_x,
		const Real	factor_y ) const

inlinenodiscardconstexpr

Shear about z-axis.

Parameters

factor_x	X-Axis factor.
factor_y	Y-Axis factor.

Returns: Result.

◆ shear_z_local()

template<typename Real>

Basis3 nnm::Basis3< Real >::shear_z_local	(	const Real	factor_x,
		const Real	factor_y ) const

inlinenodiscardconstexpr

Local shear about z-axis.

Parameters

factor_x	X-Axis factor.
factor_y	Y-Axis factor.

Returns: Result.

◆ trace()

template<typename Real>

Real nnm::Basis3< Real >::trace ( ) const

inlinenodiscardconstexpr

Trace which is the sum of the matrix diagonal.

Returns: Result.

◆ transform()

template<typename Real>

Basis3 nnm::Basis3< Real >::transform ( const Basis3< Real > & by ) const

inlinenodiscardconstexpr

Transform by another basis.

Parameters

by Basis.

Returns: Result.

◆ transform_local()

template<typename Real>

Basis3 nnm::Basis3< Real >::transform_local ( const Basis3< Real > & by ) const

inlinenodiscardconstexpr

Local transform by another basis.

Parameters

by Basis.

Returns: Result.

◆ unchecked_inverse()

template<typename Real>

Basis3 nnm::Basis3< Real >::unchecked_inverse ( ) const

inlinenodiscardconstexpr

Inverse without checking if the basis is valid first.

Returns: Result.

◆ valid()

template<typename Real>

bool nnm::Basis3< Real >::valid ( ) const

inlinenodiscardconstexpr

Determines if the basis is valid.

Returns: True if valid, false otherwise.

Member Data Documentation

◆ matrix

template<typename Real>

Matrix3<Real> nnm::Basis3< Real >::matrix

The documentation for this class was generated from the following file:

include/nnm/nnm.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Basis3() [1/3]

◆ Basis3() [2/3]

◆ Basis3() [3/3]

Member Function Documentation

◆ approx_equal()

◆ at() [1/4]

◆ at() [2/4]

◆ at() [3/4]

◆ at() [4/4]

◆ determinant()

◆ from_rotation_axis_angle()

◆ from_rotation_quaternion()

◆ from_scale()

◆ from_shear_x()

◆ from_shear_y()

◆ from_shear_z()

◆ inverse()

◆ operator!=()

◆ operator<()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ rotate_axis_angle()

◆ rotate_axis_angle_local()

◆ rotate_quaternion()

◆ rotate_quaternion_local()

◆ scale()

◆ scale_local()

◆ shear_x()

◆ shear_x_local()

◆ shear_y()

◆ shear_y_local()

◆ shear_z()

◆ shear_z_local()

◆ trace()

◆ transform()

◆ transform_local()

◆ unchecked_inverse()

◆ valid()

Member Data Documentation

◆ matrix