math namespace, contains some math functions 更多...

类
class	Tensor
	Tensor class, used to store tensor data 更多...

class	Tensor< bool, Dims... >
	Bool Tensor class, used to store bool type tensor data 更多...

class	TensorBase
	TensorBase class, base class for tensor 更多...

struct	TensorShape
	TensorShape struct, used to store tensor shape information 更多...

class	Vector
	Vector class, support some vector operations, like dot, cross, normalize, etc. 更多...

class	Vector< bool, N >
	Vector class for bool type, support some vector logical operations etc. 更多...

函数
template<typename Scalar>
z::math::Vector< Scalar, 3 >	cross (const z::math::Vector< Scalar, 3 > &a, const z::math::Vector< Scalar, 3 > &b)
	cross product of two 3D vectors.

template<typename Scalar>
z::math::Vector< Scalar, 4 >	quat_conjugate (const z::math::Vector< Scalar, 4 > &quat)
	Compute the conjugate of a quaternion.

template<typename Scalar>
z::math::Vector< Scalar, 4 >	quat_unit (const z::math::Vector< Scalar, 4 > &quat)
	Normalize a quaternion to unit length.

template<typename Scalar>
z::math::Vector< Scalar, 4 >	quat_mul (const z::math::Vector< Scalar, 4 > &a, const z::math::Vector< Scalar, 4 > &b)
	Multiply two quaternions.

template<typename Scalar>
z::math::Vector< Scalar, 3 >	quat_rotate (const z::math::Vector< Scalar, 4 > &q, const z::math::Vector< Scalar, 3 > &v)
	Rotate a 3D vector by a quaternion.

template<typename Scalar>
z::math::Vector< Scalar, 3 >	quat_rotate_inverse (const z::math::Vector< Scalar, 4 > &q, const z::math::Vector< Scalar, 3 > &v)
	Rotate a 3D vector by the inverse of a quaternion.

template<typename Scalar>
z::math::Vector< Scalar, 4 >	quat_from_euler_xyz (const z::math::Vector< Scalar, 3 > &euler)
	Convert Euler angles (in radians) to quaternion representation.

template<typename Scalar>
z::math::Vector< Scalar, 3 >	get_euler_xyz (const z::math::Vector< Scalar, 4 > &quat)
	Convert quaternion representation to Euler angles (in radians).

template<typename Scalar>
z::math::Vector< Scalar, 3 >	so3_from_quat (const z::math::Vector< Scalar, 4 > &quat)
	Convert a quaternion to an so(3) vector representation.

template<typename Scalar>
z::math::Vector< Scalar, 4 >	so3_to_quat (const z::math::Vector< Scalar, 3 > &so3)
	Convert an so(3) vector representation to a quaternion.

template<typename Scalar>
z::math::Vector< Scalar, 4 >	quat_slerp (const z::math::Vector< Scalar, 4 > &a, const z::math::Vector< Scalar, 4 > &b, Scalar t)
	Perform spherical linear interpolation (SLERP) between two quaternions.

template<typename Scalar>
z::math::Vector< Scalar, 4 >	quat_diff (const z::math::Vector< Scalar, 4 > &a, const z::math::Vector< Scalar, 4 > &b)
	Compute the difference between two quaternions, ensuring the shortest path.

template<typename Scalar>
z::math::Vector< Scalar, 3 >	so3_diff (const z::math::Vector< Scalar, 3 > &a, const z::math::Vector< Scalar, 3 > &b)
	Compute the difference between two so(3) vectors, ensuring the shortest path.

template<typename T, size_t... Ns>
constexpr auto	cat (const std::array< T, Ns > &... arrays)
	concatenate multiple std::array

template<typename T, size_t ... Ns>
constexpr auto	cat (Vector< T, Ns > &... vectors)
	concatenate multiple z Vector

详细描述

math namespace, contains some math functions

函数说明

◆ cat() [1/2]

template<typename T, size_t... Ns>

auto z::math::cat ( const std::array< T, Ns > &... arrays )

constexpr

concatenate multiple std::array

模板参数

T	type
Ns	length of arrays

参数

arrays arrays

返回: auto

◆ cat() [2/2]

template<typename T, size_t ... Ns>

auto z::math::cat ( Vector< T, Ns > &... vectors )

constexpr

concatenate multiple z Vector

模板参数

T	type
Ns	length of vectors

参数

vectors vectors

返回: auto

◆ cross()

template<typename Scalar>

z::math::Vector< Scalar, 3 > z::math::cross	(	const z::math::Vector< Scalar, 3 > &	a,
		const z::math::Vector< Scalar, 3 > &	b )

cross product of two 3D vectors.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

a	3D vector a
b	3D vector b

返回: z::math::Vector<Scalar, 3> Resulting vector from the cross product of a and b.

◆ get_euler_xyz()

template<typename Scalar>

z::math::Vector< Scalar, 3 > z::math::get_euler_xyz ( const z::math::Vector< Scalar, 4 > & quat )

Convert quaternion representation to Euler angles (in radians).

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

quat	A vector containing the quaternion representation in XYZW format.

返回: z::math::Vector<Scalar, 3> Euler angles in radians, in the order of (roll, pitch, yaw).

◆ quat_conjugate()

template<typename Scalar>

z::math::Vector< Scalar, 4 > z::math::quat_conjugate ( const z::math::Vector< Scalar, 4 > & quat )

Compute the conjugate of a quaternion.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

quat	A quaternion represented as a vector in XYZW format.

返回: z::math::Vector<Scalar, 4> Quaternion conjugate in XYZW format.

◆ quat_diff()

template<typename Scalar>

z::math::Vector< Scalar, 4 > z::math::quat_diff	(	const z::math::Vector< Scalar, 4 > &	a,
		const z::math::Vector< Scalar, 4 > &	b )

Compute the difference between two quaternions, ensuring the shortest path.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

a	quaternion a represented as the first quaternion in XYZW format.
b	quaternion b represented as the second quaternion in XYZW format.

返回: z::math::Vector<Scalar, 4> Quaternion representing the difference between a and b, ensuring the shortest path.

◆ quat_from_euler_xyz()

template<typename Scalar>

z::math::Vector< Scalar, 4 > z::math::quat_from_euler_xyz ( const z::math::Vector< Scalar, 3 > & euler )

Convert Euler angles (in radians) to quaternion representation.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

euler A vector containing the Euler angles in radians, in the order of (roll, pitch, yaw).

返回: z::math::Vector<Scalar, 4> Quaternion representation(XYZW format) of the Euler angles.

◆ quat_mul()

template<typename Scalar>

z::math::Vector< Scalar, 4 > z::math::quat_mul	(	const z::math::Vector< Scalar, 4 > &	a,
		const z::math::Vector< Scalar, 4 > &	b )

Multiply two quaternions.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

a	A quaternion represented as a vector in XYZW format.
b	Another quaternion represented as a vector in XYZW format.

返回: z::math::Vector<Scalar, 4> Quaternion resulting from the multiplication of a and b, in XYZW format.

◆ quat_rotate()

template<typename Scalar>

z::math::Vector< Scalar, 3 > z::math::quat_rotate	(	const z::math::Vector< Scalar, 4 > &	q,
		const z::math::Vector< Scalar, 3 > &	v )

Rotate a 3D vector by a quaternion.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

quat	A quaternion represented as a vector in XYZW format.
vec	A 3D vector to be rotated by the quaternion.

返回: z::math::Vector<Scalar, 3> Resulting vector after rotation by the quaternion.

◆ quat_rotate_inverse()

template<typename Scalar>

z::math::Vector< Scalar, 3 > z::math::quat_rotate_inverse	(	const z::math::Vector< Scalar, 4 > &	q,
		const z::math::Vector< Scalar, 3 > &	v )

Rotate a 3D vector by the inverse of a quaternion.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

quat	A quaternion represented as a vector in XYZW format.
vec	A 3D vector to be rotated by the inverse of the quaternion.

返回: z::math::Vector<Scalar, 3> Resulting vector after rotation by the inverse of the quaternion.

◆ quat_slerp()

template<typename Scalar>

z::math::Vector< Scalar, 4 > z::math::quat_slerp	(	const z::math::Vector< Scalar, 4 > &	a,
		const z::math::Vector< Scalar, 4 > &	b,
		Scalar	t )

Perform spherical linear interpolation (SLERP) between two quaternions.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

a	quaternion a represented as begin interpolation quaternion in XYZW format.
b	quaternion b represented as end interpolation quaternion in XYZW format.
t	interpolation parameter, where t = 0 corresponds to a and t = 1 corresponds to b.

返回: z::math::Vector<Scalar, 4> Interpolated quaternion in XYZW format.

◆ quat_unit()

template<typename Scalar>

z::math::Vector< Scalar, 4 > z::math::quat_unit ( const z::math::Vector< Scalar, 4 > & quat )

Normalize a quaternion to unit length.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

quat	A quaternion represented as a vector in XYZW format.

返回: z::math::Vector<Scalar, 4> Unit quaternion in XYZW format.

异常

std::runtime_error If the quaternion norm is zero, indicating it cannot be normalized.

◆ so3_diff()

template<typename Scalar>

z::math::Vector< Scalar, 3 > z::math::so3_diff	(	const z::math::Vector< Scalar, 3 > &	a,
		const z::math::Vector< Scalar, 3 > &	b )

Compute the difference between two so(3) vectors, ensuring the shortest path.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

a	so(3) vector a represented as the first vector in 3D space.
b	so(3) vector b represented as the second vector in 3D space.

返回: z::math::Vector<Scalar, 3> Vector representing the difference between a and b, ensuring the shortest path.

◆ so3_from_quat()

template<typename Scalar>

z::math::Vector< Scalar, 3 > z::math::so3_from_quat ( const z::math::Vector< Scalar, 4 > & quat )

Convert a quaternion to an so(3) vector representation.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

quat	A quaternion represented as a vector in XYZW format.

返回: z::math::Vector<Scalar, 3> so(3) vector representation of the quaternion.

◆ so3_to_quat()

template<typename Scalar>

z::math::Vector< Scalar, 4 > z::math::so3_to_quat ( const z::math::Vector< Scalar, 3 > & so3 )

Convert an so(3) vector representation to a quaternion.

模板参数

Scalar Type of the scalar (e.g., float, double).

参数

so3	A vector representing the so(3) representation of a rotation.

返回: z::math::Vector<Scalar, 4> Quaternion representation of the so(3) vector in XYZW format.

类

函数

详细描述

函数说明

◆ cat() [1/2]

◆ cat() [2/2]

◆ cross()

◆ get_euler_xyz()

◆ quat_conjugate()

◆ quat_diff()

◆ quat_from_euler_xyz()

◆ quat_mul()

◆ quat_rotate()

◆ quat_rotate_inverse()

◆ quat_slerp()

◆ quat_unit()

◆ so3_diff()

◆ so3_from_quat()

◆ so3_to_quat()