cml::detail Namespace Reference


Classes
struct	CrossPromote
struct	determinant_f
struct	determinant_f< MatT, 2 >
struct	determinant_f< MatT, 3 >
struct	determinant_f< MatT, 4 >
struct	DotPromote
struct	inverse_f
struct	inverse_f< MatT, 2 >
struct	inverse_f< MatT, 3 >
struct	inverse_f< MatT, 4 >
struct	nlerp_f< MatT_1, MatT_2, 2 >
struct	nlerp_f< MatT_1, MatT_2, 3 >
struct	OuterPromote
struct	slerp_f< MatT_1, MatT_2, 2 >
struct	slerp_f< MatT_1, MatT_2, 3 >
struct	SumOp< negative_cross, Real >
struct	SumOp< positive_cross, Real >
struct	TypePromote3< T1, T2, T3, et::matrix_result_tag >
struct	TypePromote3< T1, T2, T3, et::quaternion_result_tag >
struct	TypePromote4< T1, T2, T3, T4, et::matrix_result_tag >
struct	TypePromote4< T1, T2, T3, T4, et::quaternion_result_tag >
struct	TypePromote< T, T, et::scalar_result_tag >
struct	TypePromote< T1, T2, et::matrix_result_tag >
struct	TypePromote< T1, T2, et::quaternion_result_tag >
struct	TypePromote< T1, T2, et::scalar_result_tag >
struct	TypePromote< T1, T2, et::vector_result_tag >
Typedefs
typedef true_type	mul_Ax
typedef false_type	mul_xA
Functions
void	CheckIndex2 (size_t index)
	Check for a valid integer index with value < 2.
void	CheckIndex3 (size_t index)
	Check for a valid integer index with value < 3.
template<size_t N>
void	CheckIndexN (size_t index)
	Check for a valid integer index with value < N.
template<class MatT >
void	CheckMat (const MatT &)
	Compile-time check for a matrix argument.
template<class MatT >
void	CheckMat2x2 (const MatT &m)
	Check for a square matrix of size 2x2.
template<class MatT >
void	CheckMat3x3 (const MatT &m)
	Check for a square matrix of size 3x3.
template<class MatT >
void	CheckMat4x4 (const MatT &m)
	Check for a square matrix of size 4x4.
template<class MatT >
void	CheckMatAffine2D (const MatT &m)
	Check for a matrix that can represent a 2D affine transform.
template<class MatT >
void	CheckMatAffine2D (const MatT &m, col_basis)
	Check for a matrix that can represent a 2D col-basis affine transform.
template<class MatT >
void	CheckMatAffine2D (const MatT &m, row_basis)
	Check for a matrix that can represent a 2D row-basis affine transform.
template<class MatT >
void	CheckMatAffine3D (const MatT &m)
	Check for a matrix that can represent a 3D affine transform.
template<class MatT >
void	CheckMatAffine3D (const MatT &m, col_basis)
	Check for a matrix that can represent a 3D col-basis affine transform.
template<class MatT >
void	CheckMatAffine3D (const MatT &m, row_basis)
	Check for a matrix that can represent a 3D row-basis affine transform.
template<class MatT >
void	CheckMatHomogeneous3D (const MatT &m)
	Check for a matrix that can represent a 3D homogenous transform.
template<class MatT >
void	CheckMatLinear2D (const MatT &m)
	Check for a matrix that can represent a 2D linear transform.
template<class MatT >
void	CheckMatLinear3D (const MatT &m)
	Check for a matrix that can represent a 3D linear transform.
template<class MatT >
void	CheckMatMin2x2 (const MatT &m)
	Check for a matrix with minimum dimensions 2x2.
template<class MatT >
void	CheckMatMin3x3 (const MatT &m)
	Check for a matrix with minimum dimensions 3x3.
template<class MatT >
void	CheckMatMin4x4 (const MatT &m)
	Check for a matrix with minimum dimensions 4x4.
template<class MatT , size_t N, class ErrorT >
void	CheckMatMinN (const MatT &m)
	Check for a matrix with minimum dimensions NxN.
template<class MatT , size_t N, size_t M, class ErrorT >
void	CheckMatMinNxM (const MatT &m)
	Check for a matrix with minimum dimensions NxM.
template<class MatT , size_t N, size_t M, class >
void	CheckMatMinNxM (const MatT &m, dynamic_size_tag)
	Run-time check for a matrix with minimum dimensions NxM.
template<class MatT , size_t N, size_t M, class ErrorT >
void	CheckMatMinNxM (const MatT &m, fixed_size_tag)
	Compile-time check for a matrix with minimum dimensions NxM.
template<class MatT , size_t N, class ErrorT >
void	CheckMatN (const MatT &m)
	Check for a square matrix of size NxN.
template<class MatT , size_t N, size_t M, class ErrorT >
void	CheckMatNxM (const MatT &m)
	Check for a matrix of size NxM.
template<class MatT , size_t N, size_t M, class >
void	CheckMatNxM (const MatT &m, dynamic_size_tag)
	Run-time check for a matrix of size NxM.
template<class MatT , size_t N, size_t M, class ErrorT >
void	CheckMatNxM (const MatT &m, fixed_size_tag)
	Compile-time check for a matrix of size NxM.
template<class MatT >
void	CheckMatSquare (const MatT &m)
	Check for a square matrix.
template<class MatT , class >
void	CheckMatSquare (const MatT &m, dynamic_size_tag)
	Run-time check for a square matrix.
template<class MatT , class ErrorT >
void	CheckMatSquare (const MatT &m, fixed_size_tag)
	Compile-time check for a square matrix.
template<class QuatT >
void	CheckQuat (const QuatT &)
	Compile-time check for a quaternion argument.
void	CheckValidArg (bool valid)
	Run-time check for a valid argument.
template<class VecT >
void	CheckVec (const VecT &)
	Compile-time check for a vector argument.
template<class VecT >
void	CheckVec2 (const VecT &v)
	Check for a vector of size 2.
template<class VecT >
void	CheckVec2Or3 (const VecT &v)
	Check for a vector of size 2 or 3.
template<class VecT >
void	CheckVec2Or3 (const VecT &v, dynamic_size_tag)
	Run-time check for a vector of size 2 or 3.
template<class VecT >
void	CheckVec2Or3 (const VecT &v, fixed_size_tag)
	Compile-time check for a vector of size 2 or 3.
template<class VecT >
void	CheckVec3 (const VecT &v)
	Check for a vector of size 3.
template<class VecT >
void	CheckVec4 (const VecT &v)
	Check for a vector of size 4.
template<class VecT , size_t N, class ErrorT >
void	CheckVecN (const VecT &v)
	Check for a vector of size N.
template<class VecT , size_t N, class >
void	CheckVecN (const VecT &v, dynamic_size_tag)
	Run-time check for a vector of size N.
template<class VecT , size_t N, class ErrorT >
void	CheckVecN (const VecT &v, fixed_size_tag)
	Compile-time check for a vector of size N.
template<class MatT , typename Real >
void	depth_range_from_viewport_matrix (const MatT &viewport, Real &n, Real &f)
template<typename MatT >
MatT::value_type	determinant (const MatT &M, dynamic_size_tag)
template<typename MatT >
MatT::value_type	determinant (const MatT &M, fixed_size_tag)
template<typename E >
void	divide_by_w (vector< E, fixed< 4 > > &v)
template<typename E , class A , class B , class L , class MatT >
void	InterpResize (matrix< E, A, B, L > &m, const MatT &target, dynamic_size_tag)
template<typename E , class A , class VecT >
void	InterpResize (vector< E, A > &v, const VecT &target, dynamic_size_tag)
template<class T1 , class T2 , class SizeTag >
void	InterpResize (T1 &t1, const T2 &t2, SizeTag)
template<typename Real >
vector< Real, fixed< 3 > >	intersect_planes (Real p1[4], Real p2[4], Real p3[4])
template<typename MatT >
MatT::temporary_type	inverse (const MatT &M, dynamic_size_tag)
template<typename MatT >
MatT::temporary_type	inverse (const MatT &M, fixed_size_tag)
template<class MatT >
MatT::temporary_type	lu_copy (const MatT &M)
template<class MatT >
void	lu_inplace (MatT &A)
template<typename LeftT , typename RightT >
matrix_size	MatMulCheckedSize (const LeftT &left, const RightT &right, dynamic_size_tag)
	Verify the sizes of the argument matrices for matrix multiplication.
template<typename LeftT , typename RightT >
matrix_size	MatMulCheckedSize (const LeftT &, const RightT &, fixed_size_tag)
	Verify the sizes of the argument matrices for matrix multiplication.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_3X3	matrix_concat_rotations (const MatT_1 &m1, const MatT_2 &m2)
	Concatenate two 3D rotation matrices in the order m1->m2.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_3X3	matrix_concat_rotations (const MatT_1 &m1, const MatT_2 &m2, col_basis)
	Concatenate two 3D col-basis rotation matrices in the order m1->m2.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_3X3	matrix_concat_rotations (const MatT_1 &m1, const MatT_2 &m2, row_basis)
	Concatenate two 3D row-basis rotation matrices in the order m1->m2.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_2X2	matrix_concat_rotations_2D (const MatT_1 &m1, const MatT_2 &m2)
	Concatenate two 2D rotation matrices in the order m1->m2.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_2X2	matrix_concat_rotations_2D (const MatT_1 &m1, const MatT_2 &m2, col_basis)
	Concatenate two 2D col-basis rotation matrices in the order m1->m2.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_2X2	matrix_concat_rotations_2D (const MatT_1 &m1, const MatT_2 &m2, row_basis)
	Concatenate two 2D row-basis rotation matrices in the order m1->m2.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_4X4	matrix_concat_transforms_4x4 (const MatT_1 &m1, const MatT_2 &m2)
	Concatenate two 3D rotation matrices in the order m1->m2.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_4X4	matrix_concat_transforms_4x4 (const MatT_1 &m1, const MatT_2 &m2, col_basis)
	Concatenate two 3D col-basis rotation matrices in the order m1->m2.
template<class MatT_1 , class MatT_2 >
MAT_TEMP_4X4	matrix_concat_transforms_4x4 (const MatT_1 &m1, const MatT_2 &m2, row_basis)
template<typename LeftT , typename RightT , typename OpT >
bool	matrix_total_order (const LeftT &left, const RightT &right, OpT)
	Matrix total order relationship.
template<typename LeftT , typename RightT , typename OpT >
bool	matrix_weak_order (const LeftT &left, const RightT &right, OpT)
	Matrix strict weak ordering relationship.
template<typename LeftT , typename RightT >
et::MatVecPromote< typename et::ExprTraits< LeftT > ::result_type, typename et::ExprTraits< RightT > ::result_type > ::temporary_type	mul (const LeftT &x, const RightT &A, mul_xA)
	Compute y = x*A.
template<typename LeftT , typename RightT >
et::MatVecPromote< typename et::ExprTraits< LeftT > ::result_type, typename et::ExprTraits< RightT > ::result_type > ::temporary_type	mul (const LeftT &A, const RightT &x, mul_Ax)
	Compute y = A*x.
template<class LeftT , class RightT >
et::MatrixPromote< typename et::ExprTraits< LeftT > ::result_type, typename et::ExprTraits< RightT > ::result_type > ::temporary_type	mul (const LeftT &left, const RightT &right)
	Matrix multiplication.
template<class MatT_1 , class MatT_2 , typename Real >
detail::TypePromote< MatT_1, MatT_2, typename et::ExprTraits< MatT_1 > ::result_tag >::temporary_type	nlerp (const MatT_1 &m1, const MatT_2 &m2, Real t, et::matrix_result_tag, dynamic_size_tag)
template<class MatT_1 , class MatT_2 , typename Real >
detail::TypePromote< MatT_1, MatT_2, typename et::ExprTraits< MatT_1 > ::result_tag >::temporary_type	nlerp (const MatT_1 &m1, const MatT_2 &m2, Real t, et::matrix_result_tag, fixed_size_tag)
template<class QuatT_1 , class QuatT_2 , typename Real , class SizeT >
detail::TypePromote< QuatT_1, QuatT_2, typename et::ExprTraits< QuatT_1 > ::result_tag >::temporary_type	nlerp (const QuatT_1 &q1, const QuatT_2 &q2, Real t, et::quaternion_result_tag, SizeT)
template<class VecT_1 , class VecT_2 , typename Real , class SizeT >
detail::TypePromote< VecT_1, VecT_2, typename et::ExprTraits< VecT_1 > ::result_tag >::temporary_type	nlerp (const VecT_1 &v1, const VecT_2 &v2, Real t, et::vector_result_tag, SizeT)
AxisOrder	pack_axis_order (size_t i, bool odd)
template<class LeftT , class RightT >
detail::DotPromote< LeftT, RightT >::promoted_scalar	quaternion_dot (const LeftT &p, const RightT &q)
template<class QuatT_1 , class QuatT_2 >
et::QuaternionPromote2 < QuatT_1, QuatT_2 > ::temporary_type	quaternion_rotation_difference (const QuatT_1 &q1, const QuatT_2 &q2, negative_cross)
	Concatenate two quaternions in the order q1->q2.
template<class QuatT_1 , class QuatT_2 >
et::QuaternionPromote2 < QuatT_1, QuatT_2 > ::temporary_type	quaternion_rotation_difference (const QuatT_1 &q1, const QuatT_2 &q2, positive_cross)
	Concatenate two quaternions in the order q1->q2.
template<typename LeftT , typename RightT , typename OpT >
bool	quaternion_total_order (const LeftT &left, const RightT &right, OpT)
	Quaternion total order relationship.
template<typename LeftT , typename RightT , typename OpT >
bool	quaternion_weak_order (const LeftT &left, const RightT &right, OpT)
	Quaternion strict weak ordering relationship.
template<class Quat1_T , class Quat2_T >
et::QuaternionPromote < typename Quat1_T::temporary_type, typename Quat2_T::temporary_type > ::temporary_type	QuaternionMult (const Quat1_T &q1, const Quat2_T &q2)
template<typename VecT >
void	Require2D (const VecT &v, dynamic_size_tag)
	For perp_dot(): run-time check for a 2D vector.
template<typename VecT >
void	Require2D (const VecT &v, fixed_size_tag)
	For perp_dot(): compile-time check for a 2D vector.
template<typename VecT >
void	Require3D (const VecT &v, dynamic_size_tag)
	For cross(): run-time check for a 3D vector.
template<typename VecT >
void	Require3D (const VecT &, fixed_size_tag)
	For cross(): compile-time check for a 3D vector.
template<class MatT_1 , class MatT_2 , typename Real >
detail::TypePromote< MatT_1, MatT_2, typename et::ExprTraits< MatT_1 > ::result_tag >::temporary_type	slerp (const MatT_1 &m1, const MatT_2 &m2, Real t, Real tolerance, et::matrix_result_tag, dynamic_size_tag)
template<class MatT_1 , class MatT_2 , typename Real >
detail::TypePromote< MatT_1, MatT_2, typename et::ExprTraits< MatT_1 > ::result_tag >::temporary_type	slerp (const MatT_1 &m1, const MatT_2 &m2, Real t, Real tolerance, et::matrix_result_tag, fixed_size_tag)
template<class QuatT_1 , class QuatT_2 , typename Real , class SizeT >
detail::TypePromote< QuatT_1, QuatT_2, typename et::ExprTraits< QuatT_1 > ::result_tag >::temporary_type	slerp (const QuatT_1 &q1, const QuatT_2 &q2, Real t, Real tolerance, et::quaternion_result_tag, SizeT)
template<class VecT_1 , class VecT_2 , typename Real , class SizeT >
detail::TypePromote< VecT_1, VecT_2, typename et::ExprTraits< VecT_1 > ::result_tag >::temporary_type	slerp (const VecT_1 &v1, const VecT_2 &v2, Real t, Real tolerance, et::vector_result_tag, SizeT)
AxisOrder	swap_axis_order (AxisOrder order)
template<class MatT , class VecT >
TEMP_VEC4	transform_vector_4D (const MatT &m, const VecT &v, col_basis)
template<class MatT , class VecT >
TEMP_VEC4	transform_vector_4D (const MatT &m, const VecT &v, row_basis)
void	unpack_axis_order (AxisOrder order, size_t &i, size_t &j, size_t &k, bool &odd)
void	unpack_axis_order_2D (AxisOrder2D order, size_t &i, size_t &j, bool &odd)
void	unpack_euler_order (EulerOrder order, size_t &i, size_t &j, size_t &k, bool &odd, bool &repeat)
template<typename LeftT , typename RightT >
DotPromote< LeftT, RightT > ::promoted_scalar	UnrollDot (const LeftT &left, const RightT &right, dynamic_size_tag)
	Use a loop to compute the dot product for dynamic arrays.
template<typename LeftT , typename RightT >
DotPromote< LeftT, RightT > ::promoted_scalar	UnrollDot (const LeftT &left, const RightT &right, fixed_size_tag)
	Construct a dot unroller for fixed-size arrays.
template<typename LeftT , typename RightT , typename OpT >
bool	vector_total_order (const LeftT &left, const RightT &right, OpT)
	Vector total order relationship.
template<typename LeftT , typename RightT , typename OpT >
bool	vector_weak_order (const LeftT &left, const RightT &right, OpT)
	Vector strict weak ordering relationship.

Typedef Documentation

typedef true_type cml::detail::mul_Ax

Definition at line 41 of file matvec_mul.h.

typedef false_type cml::detail::mul_xA

Definition at line 42 of file matvec_mul.h.

Function Documentation

void cml::detail::CheckIndex2 ( size_t index ) [inline]

Check for a valid integer index with value < 2.

Definition at line 370 of file checking.h.

Referenced by cml::matrix_get_basis_vector_2D(), cml::matrix_get_transposed_basis_vector_2D(), cml::matrix_ortho_project_2D(), cml::matrix_reflect_2D(), cml::matrix_set_basis_vector_2D(), cml::matrix_set_transposed_basis_vector_2D(), cml::matrix_shear_2D(), and cml::orthonormalize().

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void cml::detail::CheckIndex3 ( size_t index ) [inline]

Check for a valid integer index with value < 3.

Definition at line 375 of file checking.h.

Referenced by cml::cartesian_to_cylindrical(), cml::cartesian_to_spherical(), cml::cross_cardinal(), cml::cylindrical_to_cartesian(), cml::matrix_get_basis_vector(), cml::matrix_get_transposed_basis_vector(), cml::matrix_ortho_project(), cml::matrix_reflect(), cml::matrix_rotate_about_local_axis(), cml::matrix_rotate_about_world_axis(), cml::matrix_rotation_world_axis(), cml::matrix_set_basis_vector(), cml::matrix_set_transposed_basis_vector(), cml::matrix_shear(), cml::orthonormalize(), cml::quaternion_get_basis_vector(), cml::quaternion_rotate_about_local_axis(), cml::quaternion_rotate_about_world_axis(), cml::quaternion_rotation_world_axis(), and cml::spherical_to_cartesian().

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template<size_t N>

void cml::detail::CheckIndexN ( size_t index ) [inline]

Check for a valid integer index with value < N.

Definition at line 365 of file checking.h.

References CheckValidArg().

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template<class MatT >

void cml::detail::CheckMat ( const MatT & ) [inline]

Compile-time check for a matrix argument.

Definition at line 135 of file checking.h.

References CML_STATIC_REQUIRE_M.

Referenced by CheckMatMinNxM(), CheckMatNxM(), and CheckMatSquare().

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template<class MatT >

void cml::detail::CheckMat2x2 ( const MatT & m ) [inline]

Check for a square matrix of size 2x2.

Definition at line 182 of file checking.h.

template<class MatT >

void cml::detail::CheckMat3x3 ( const MatT & m ) [inline]

Check for a square matrix of size 3x3.

Definition at line 188 of file checking.h.

template<class MatT >

void cml::detail::CheckMat4x4 ( const MatT & m ) [inline]

Check for a square matrix of size 4x4.

Definition at line 194 of file checking.h.

template<class MatT >

void cml::detail::CheckMatAffine2D ( const MatT & m ) [inline]

Check for a matrix that can represent a 2D affine transform.

Definition at line 295 of file checking.h.

References CheckMatAffine2D().

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template<class MatT >

void cml::detail::CheckMatAffine2D	(	const MatT &	m,
		col_basis
	)			`[inline]`

Check for a matrix that can represent a 2D col-basis affine transform.

Definition at line 283 of file checking.h.

template<class MatT >

void cml::detail::CheckMatAffine2D	(	const MatT &	m,
		row_basis
	)			`[inline]`

Check for a matrix that can represent a 2D row-basis affine transform.

Definition at line 277 of file checking.h.

Referenced by CheckMatAffine2D(), cml::matrix_decompose_SRT_2D(), cml::matrix_get_translation_2D(), cml::matrix_set_translation_2D(), and cml::transform_point_2D().

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template<class MatT >

void cml::detail::CheckMatAffine3D ( const MatT & m ) [inline]

Check for a matrix that can represent a 3D affine transform.

Definition at line 289 of file checking.h.

References CheckMatAffine3D().

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template<class MatT >

void cml::detail::CheckMatAffine3D	(	const MatT &	m,
		col_basis
	)			`[inline]`

Check for a matrix that can represent a 3D col-basis affine transform.

Definition at line 271 of file checking.h.

template<class MatT >

void cml::detail::CheckMatAffine3D	(	const MatT &	m,
		row_basis
	)			`[inline]`

Check for a matrix that can represent a 3D row-basis affine transform.

Definition at line 265 of file checking.h.

Referenced by CheckMatAffine3D(), cml::matrix_decompose_SRT(), cml::matrix_get_translation(), cml::matrix_look_at(), cml::matrix_set_translation(), and cml::transform_point().

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template<class MatT >

void cml::detail::CheckMatHomogeneous3D ( const MatT & m ) [inline]

Check for a matrix that can represent a 3D homogenous transform.

Definition at line 301 of file checking.h.

References CheckMatMin4x4().

Referenced by depth_range_from_viewport_matrix(), cml::extract_frustum_planes(), cml::matrix_orthographic(), cml::matrix_perspective(), and cml::matrix_pick().

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template<class MatT >

void cml::detail::CheckMatLinear2D ( const MatT & m ) [inline]

Check for a matrix that can represent a 2D linear transform.

Definition at line 259 of file checking.h.

References CheckMatMin2x2().

Referenced by cml::matrix_decompose_SRT_2D(), cml::matrix_get_basis_vector_2D(), cml::matrix_get_transposed_basis_vector_2D(), cml::matrix_linear_transform_2D(), cml::matrix_ortho_project_2D(), cml::matrix_reflect_2D(), cml::matrix_rotate_2D(), cml::matrix_rotation_2D(), cml::matrix_scale_2D(), cml::matrix_set_basis_vector_2D(), cml::matrix_set_transposed_basis_vector_2D(), cml::matrix_shear_2D(), cml::matrix_to_rotation_2D(), and cml::transform_vector_2D().

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template<class MatT >

void cml::detail::CheckMatLinear3D ( const MatT & m ) [inline]

Check for a matrix that can represent a 3D linear transform.

Definition at line 253 of file checking.h.

References CheckMatMin3x3().

Referenced by cml::matrix_decompose_SRT(), cml::matrix_get_basis_vector(), cml::matrix_get_transposed_basis_vector(), cml::matrix_linear_transform(), cml::matrix_ortho_project(), cml::matrix_reflect(), cml::matrix_rotate_about_local_axis(), cml::matrix_rotate_about_world_axis(), cml::matrix_rotation_axis_angle(), cml::matrix_rotation_euler(), cml::matrix_rotation_euler_derivatives(), cml::matrix_rotation_quaternion(), cml::matrix_rotation_world_axis(), cml::matrix_scale(), cml::matrix_set_basis_vector(), cml::matrix_set_transposed_basis_vector(), cml::matrix_shear(), cml::matrix_to_axis_angle(), cml::matrix_to_euler(), cml::quaternion_rotation_matrix(), and cml::transform_vector().

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template<class MatT >

void cml::detail::CheckMatMin2x2 ( const MatT & m ) [inline]

Check for a matrix with minimum dimensions 2x2.

Definition at line 235 of file checking.h.

Referenced by CheckMatLinear2D(), cml::matrix_skew_symmetric_2D(), and cml::trace_2x2().

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template<class MatT >

void cml::detail::CheckMatMin3x3 ( const MatT & m ) [inline]

Check for a matrix with minimum dimensions 3x3.

Definition at line 241 of file checking.h.

Referenced by CheckMatLinear3D(), cml::matrix_skew_symmetric(), and cml::trace_3x3().

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template<class MatT >

void cml::detail::CheckMatMin4x4 ( const MatT & m ) [inline]

Check for a matrix with minimum dimensions 4x4.

Definition at line 247 of file checking.h.

Referenced by CheckMatHomogeneous3D().

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template<class MatT , size_t N, class ErrorT >

void cml::detail::CheckMatMinN ( const MatT & m ) [inline]

Check for a matrix with minimum dimensions NxN.

Definition at line 229 of file checking.h.

template<class MatT , size_t N, size_t M, class ErrorT >

void cml::detail::CheckMatMinNxM ( const MatT & m ) [inline]

Check for a matrix with minimum dimensions NxM.

Definition at line 220 of file checking.h.

template<class MatT , size_t N, size_t M, class >

void cml::detail::CheckMatMinNxM	(	const MatT &	m,
		dynamic_size_tag
	)			`[inline]`

Run-time check for a matrix with minimum dimensions NxM.

Definition at line 209 of file checking.h.

References CheckMat().

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template<class MatT , size_t N, size_t M, class ErrorT >

void cml::detail::CheckMatMinNxM	(	const MatT &	m,
		fixed_size_tag
	)			`[inline]`

Compile-time check for a matrix with minimum dimensions NxM.

Definition at line 200 of file checking.h.

References CheckMat(), and CML_STATIC_REQUIRE_M.

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template<class MatT , size_t N, class ErrorT >

void cml::detail::CheckMatN ( const MatT & m ) [inline]

Check for a square matrix of size NxN.

Definition at line 176 of file checking.h.

template<class MatT , size_t N, size_t M, class ErrorT >

void cml::detail::CheckMatNxM ( const MatT & m ) [inline]

Check for a matrix of size NxM.

Definition at line 167 of file checking.h.

template<class MatT , size_t N, size_t M, class >

void cml::detail::CheckMatNxM	(	const MatT &	m,
		dynamic_size_tag
	)			`[inline]`

Run-time check for a matrix of size NxM.

Definition at line 156 of file checking.h.

References CheckMat().

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template<class MatT , size_t N, size_t M, class ErrorT >

void cml::detail::CheckMatNxM	(	const MatT &	m,
		fixed_size_tag
	)			`[inline]`

Compile-time check for a matrix of size NxM.

Definition at line 147 of file checking.h.

References CheckMat(), and CML_STATIC_REQUIRE_M.

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template<class MatT >

void cml::detail::CheckMatSquare ( const MatT & m ) [inline]

Check for a square matrix.

Definition at line 327 of file checking.h.

References CheckMatSquare().

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template<class MatT , class >

void cml::detail::CheckMatSquare	(	const MatT &	m,
		dynamic_size_tag
	)			`[inline]`

Run-time check for a square matrix.

Definition at line 316 of file checking.h.

References CheckMat().

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template<class MatT , class ErrorT >

void cml::detail::CheckMatSquare	(	const MatT &	m,
		fixed_size_tag
	)			`[inline]`

Compile-time check for a square matrix.

Definition at line 307 of file checking.h.

References CheckMat(), and CML_STATIC_REQUIRE_M.

Referenced by CheckMatSquare(), and cml::trace().

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template<class QuatT >

void cml::detail::CheckQuat ( const QuatT & ) [inline]

Compile-time check for a quaternion argument.

Definition at line 341 of file checking.h.

References CML_STATIC_REQUIRE_M.

Referenced by cml::exp(), cml::log(), cml::matrix_rotation_quaternion(), cml::quaternion_get_basis_vector(), cml::quaternion_to_axis_angle(), and QuaternionMult().

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void cml::detail::CheckValidArg ( bool valid ) [inline]

Run-time check for a valid argument.

Definition at line 356 of file checking.h.

Referenced by cml::axis(), and CheckIndexN().

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template<class VecT >

void cml::detail::CheckVec ( const VecT & ) [inline]

Compile-time check for a vector argument.

Definition at line 46 of file checking.h.

References CML_STATIC_REQUIRE_M.

Referenced by CheckVec2Or3(), and CheckVecN().

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template<class VecT >

void cml::detail::CheckVec2 ( const VecT & v ) [inline]

Check for a vector of size 2.

Definition at line 84 of file checking.h.

Referenced by cml::cartesian_to_polar(), cml::matrix_scale_2D(), cml::matrix_scale_along_axis_2D(), cml::matrix_set_basis_vector_2D(), cml::matrix_set_translation_2D(), cml::matrix_set_transposed_basis_vector_2D(), cml::orthonormalize(), cml::perp(), cml::rotate_vector_2D(), cml::transform_point_2D(), and cml::transform_vector_2D().

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template<class VecT >

void cml::detail::CheckVec2Or3 ( const VecT & v ) [inline]

Check for a vector of size 2 or 3.

Definition at line 122 of file checking.h.

References CheckVec2Or3().

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template<class VecT >

void cml::detail::CheckVec2Or3	(	const VecT &	v,
		dynamic_size_tag
	)			`[inline]`

Run-time check for a vector of size 2 or 3.

Definition at line 112 of file checking.h.

References CheckVec().

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template<class VecT >

void cml::detail::CheckVec2Or3	(	const VecT &	v,
		fixed_size_tag
	)			`[inline]`

Compile-time check for a vector of size 2 or 3.

Definition at line 102 of file checking.h.

References CheckVec(), and CML_STATIC_REQUIRE_M.

Referenced by CheckVec2Or3(), and cml::matrix_set_translation().

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template<class VecT >

void cml::detail::CheckVec3 ( const VecT & v ) [inline]

Check for a vector of size 3.

Definition at line 90 of file checking.h.

Referenced by cml::cartesian_to_cylindrical(), cml::cartesian_to_spherical(), cml::cross_cardinal(), cml::cylindrical_to_cartesian(), cml::matrix_rotation_axis_angle(), cml::matrix_scale(), cml::matrix_scale_along_axis(), cml::matrix_set_basis_vector(), cml::matrix_set_transposed_basis_vector(), cml::matrix_skew_symmetric(), cml::orthonormal_basis(), cml::orthonormalize(), cml::project_point(), cml::quaternion_rotation_axis_angle(), cml::rotate_vector(), cml::spherical_to_cartesian(), cml::transform_point(), cml::transform_vector(), and cml::unproject_point().

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template<class VecT >

void cml::detail::CheckVec4 ( const VecT & v ) [inline]

Check for a vector of size 4.

Definition at line 96 of file checking.h.

template<class VecT , size_t N, class ErrorT >

void cml::detail::CheckVecN ( const VecT & v ) [inline]

Check for a vector of size N.

Definition at line 75 of file checking.h.

template<class VecT , size_t N, class >

void cml::detail::CheckVecN	(	const VecT &	v,
		dynamic_size_tag
	)			`[inline]`

Run-time check for a vector of size N.

Definition at line 66 of file checking.h.

References CheckVec().

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template<class VecT , size_t N, class ErrorT >

void cml::detail::CheckVecN	(	const VecT &	v,
		fixed_size_tag
	)			`[inline]`

Compile-time check for a vector of size N.

Definition at line 58 of file checking.h.

References CheckVec(), and CML_STATIC_REQUIRE_M.

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template<class MatT , typename Real >

void cml::detail::depth_range_from_viewport_matrix	(	const MatT &	viewport,
		Real &	n,
		Real &	f
	)			`[inline]`

Definition at line 32 of file picking.h.

References CheckMatHomogeneous3D().

Referenced by cml::make_pick_ray().

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template<typename MatT >

MatT::value_type cml::detail::determinant	(	const MatT &	M,
		dynamic_size_tag
	)			`[inline]`

Definition at line 155 of file determinant.h.

References cml::et::CheckedSquare().

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template<typename MatT >

MatT::value_type cml::detail::determinant	(	const MatT &	M,
		fixed_size_tag
	)			`[inline]`

Definition at line 146 of file determinant.h.

References cml::et::CheckedSquare().

Referenced by cml::determinant().

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template<typename E >

void cml::detail::divide_by_w ( vector< E, fixed< 4 > > & v ) [inline]

Definition at line 26 of file projection.h.

Referenced by cml::project_point(), and cml::unproject_point().

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template<typename E , class A , class B , class L , class MatT >

void cml::detail::InterpResize	(	matrix< E, A, B, L > &	m,
		const MatT &	target,
		dynamic_size_tag
	)			`[inline]`

Definition at line 225 of file interpolation.h.

template<typename E , class A , class VecT >

void cml::detail::InterpResize	(	vector< E, A > &	v,
		const VecT &	target,
		dynamic_size_tag
	)			`[inline]`

Definition at line 220 of file interpolation.h.

template<class T1 , class T2 , class SizeTag >

void cml::detail::InterpResize	(	T1 &	t1,
		const T2 &	t2,
		SizeTag
	)			`[inline]`

Definition at line 215 of file interpolation.h.

Referenced by cml::bilerp(), cml::lerp(), cml::nlerp(), nlerp(), cml::slerp(), slerp(), and cml::trilerp().

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template<typename Real >

vector< Real, fixed<3> > cml::detail::intersect_planes	(	Real	p1[4],
		Real	p2[4],
		Real	p3[4]
	)			`[inline]`

Definition at line 166 of file frustum.h.

References cml::cross(), and cml::triple_product().

Referenced by cml::get_frustum_corners().

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template<typename MatT >

MatT::temporary_type cml::detail::inverse	(	const MatT &	M,
		dynamic_size_tag
	)			`[inline]`

Definition at line 396 of file inverse.h.

References cml::et::CheckedSquare().

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template<typename MatT >

MatT::temporary_type cml::detail::inverse	(	const MatT &	M,
		fixed_size_tag
	)			`[inline]`

Definition at line 378 of file inverse.h.

References cml::et::CheckedSquare().

Referenced by cml::inverse().

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template<class MatT >

MatT::temporary_type cml::detail::lu_copy ( const MatT & M ) [inline]

Definition at line 82 of file lu.h.

References CML_STATIC_REQUIRE_M, lu_inplace(), and cml::et::detail::Resize().

Referenced by cml::lu().

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template<class MatT >

void cml::detail::lu_inplace ( MatT & A ) [inline]

Definition at line 46 of file lu.h.

References cml::et::CheckedSquare(), and CML_STATIC_REQUIRE_M.

Referenced by lu_copy().

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template<typename LeftT , typename RightT >

matrix_size cml::detail::MatMulCheckedSize	(	const LeftT &	left,
		const RightT &	right,
		dynamic_size_tag
	)			`[inline]`

Verify the sizes of the argument matrices for matrix multiplication.

Returns:: a matrix_size containing the size of the resulting matrix.

Definition at line 58 of file matrix_mul.h.

template<typename LeftT , typename RightT >

matrix_size cml::detail::MatMulCheckedSize	(	const LeftT &	,
		const RightT &	,
		fixed_size_tag
	)			`[inline]`

Verify the sizes of the argument matrices for matrix multiplication.

Returns:: a matrix_size containing the size of the resulting matrix.

Definition at line 45 of file matrix_mul.h.

References CML_STATIC_REQUIRE_M.

Referenced by mul().

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template<class MatT_1 , class MatT_2 >

MAT_TEMP_3X3 cml::detail::matrix_concat_rotations	(	const MatT_1 &	m1,
		const MatT_2 &	m2
	)			`[inline]`

Concatenate two 3D rotation matrices in the order m1->m2.

Definition at line 761 of file matrix_rotation.h.

References matrix_concat_rotations().

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template<class MatT_1 , class MatT_2 >

MAT_TEMP_3X3 cml::detail::matrix_concat_rotations	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		col_basis
	)			`[inline]`

Concatenate two 3D col-basis rotation matrices in the order m1->m2.

Definition at line 755 of file matrix_rotation.h.

template<class MatT_1 , class MatT_2 >

MAT_TEMP_3X3 cml::detail::matrix_concat_rotations	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		row_basis
	)			`[inline]`

Concatenate two 3D row-basis rotation matrices in the order m1->m2.

Definition at line 749 of file matrix_rotation.h.

Referenced by matrix_concat_rotations(), cml::matrix_rotation_difference(), cml::matrix_slerp(), and cml::detail::slerp_f< MatT_1, MatT_2, 3 >::operator()().

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template<class MatT_1 , class MatT_2 >

MAT_TEMP_2X2 cml::detail::matrix_concat_rotations_2D	(	const MatT_1 &	m1,
		const MatT_2 &	m2
	)			`[inline]`

Concatenate two 2D rotation matrices in the order m1->m2.

Definition at line 779 of file matrix_rotation.h.

References matrix_concat_rotations_2D().

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template<class MatT_1 , class MatT_2 >

MAT_TEMP_2X2 cml::detail::matrix_concat_rotations_2D	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		col_basis
	)			`[inline]`

Concatenate two 2D col-basis rotation matrices in the order m1->m2.

Definition at line 773 of file matrix_rotation.h.

template<class MatT_1 , class MatT_2 >

MAT_TEMP_2X2 cml::detail::matrix_concat_rotations_2D	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		row_basis
	)			`[inline]`

Concatenate two 2D row-basis rotation matrices in the order m1->m2.

Definition at line 767 of file matrix_rotation.h.

Referenced by matrix_concat_rotations_2D(), cml::matrix_rotation_difference_2D(), cml::matrix_slerp_2D(), and cml::detail::slerp_f< MatT_1, MatT_2, 2 >::operator()().

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template<class MatT_1 , class MatT_2 >

MAT_TEMP_4X4 cml::detail::matrix_concat_transforms_4x4	(	const MatT_1 &	m1,
		const MatT_2 &	m2
	)			`[inline]`

Concatenate two 3D rotation matrices in the order m1->m2.

Definition at line 53 of file matrix_concat.h.

References matrix_concat_transforms_4x4().

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template<class MatT_1 , class MatT_2 >

MAT_TEMP_4X4 cml::detail::matrix_concat_transforms_4x4	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		col_basis
	)			`[inline]`

Concatenate two 3D col-basis rotation matrices in the order m1->m2.

Definition at line 47 of file matrix_concat.h.

template<class MatT_1 , class MatT_2 >

MAT_TEMP_4X4 cml::detail::matrix_concat_transforms_4x4	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		row_basis
	)			`[inline]`

Definition at line 41 of file matrix_concat.h.

Referenced by cml::extract_frustum_planes(), cml::make_pick_volume(), matrix_concat_transforms_4x4(), cml::project_point(), and cml::unproject_point().

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template<typename LeftT , typename RightT , typename OpT >

bool cml::detail::matrix_total_order	(	const LeftT &	left,
		const RightT &	right,
		OpT
	)			`[inline]`

Matrix total order relationship.

OpT must implement a total order on the matrix element type. operator<= and operator>= on integer and floating-point types are examples.

Definition at line 147 of file matrix_comparison.h.

References cml::et::CheckedSize(), and CML_STATIC_REQUIRE_M.

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template<typename LeftT , typename RightT , typename OpT >

bool cml::detail::matrix_weak_order	(	const LeftT &	left,
		const RightT &	right,
		OpT
	)			`[inline]`

Matrix strict weak ordering relationship.

OpT must implement a strict weak order on the matrix element type. operator< and operator> on integer and floating-point types are examples.

Definition at line 87 of file matrix_comparison.h.

References cml::et::CheckedSize(), and CML_STATIC_REQUIRE_M.

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template<typename LeftT , typename RightT >

et::MatVecPromote< typename et::ExprTraits<LeftT>::result_type, typename et::ExprTraits<RightT>::result_type>::temporary_type cml::detail::mul	(	const LeftT &	x,
		const RightT &	A,
		mul_xA
	)			`[inline]`

Compute y = x*A.

Definition at line 102 of file matvec_mul.h.

References cml::et::CheckedSize(), CML_STATIC_REQUIRE_M, and cml::et::detail::Resize().

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template<typename LeftT , typename RightT >

et::MatVecPromote< typename et::ExprTraits<LeftT>::result_type, typename et::ExprTraits<RightT>::result_type>::temporary_type cml::detail::mul	(	const LeftT &	A,
		const RightT &	x,
		mul_Ax
	)			`[inline]`

Compute y = A*x.

Definition at line 50 of file matvec_mul.h.

References cml::et::CheckedSize(), CML_STATIC_REQUIRE_M, and cml::et::detail::Resize().

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template<class LeftT , class RightT >

et::MatrixPromote< typename et::ExprTraits<LeftT>::result_type, typename et::ExprTraits<RightT>::result_type>::temporary_type cml::detail::mul	(	const LeftT &	left,
		const RightT &	right
	)			`[inline]`

Matrix multiplication.

Computes C = A x B (O(N^3), non-blocked algorithm).

Definition at line 76 of file matrix_mul.h.

References CML_STATIC_REQUIRE_M, MatMulCheckedSize(), and cml::et::detail::Resize().

Referenced by cml::operator*().

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template<class MatT_1 , class MatT_2 , typename Real >

detail::TypePromote< MatT_1,MatT_2,typename et::ExprTraits<MatT_1>::result_tag>::temporary_type cml::detail::nlerp	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		Real	t,
		et::matrix_result_tag	,
		dynamic_size_tag
	)			`[inline]`

Definition at line 758 of file interpolation.h.

References cml::et::detail::Resize().

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template<class MatT_1 , class MatT_2 , typename Real >

detail::TypePromote< MatT_1,MatT_2,typename et::ExprTraits<MatT_1>::result_tag>::temporary_type cml::detail::nlerp	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		Real	t,
		et::matrix_result_tag	,
		fixed_size_tag
	)			`[inline]`

Definition at line 744 of file interpolation.h.

template<class QuatT_1 , class QuatT_2 , typename Real , class SizeT >

detail::TypePromote< QuatT_1,QuatT_2,typename et::ExprTraits<QuatT_1>::result_tag>::temporary_type cml::detail::nlerp	(	const QuatT_1 &	q1,
		const QuatT_2 &	q2,
		Real	t,
		et::quaternion_result_tag	,
		SizeT
	)			`[inline]`

Definition at line 665 of file interpolation.h.

References cml::dot(), cml::lerp(), and cml::normalize().

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template<class VecT_1 , class VecT_2 , typename Real , class SizeT >

detail::TypePromote< VecT_1,VecT_2,typename et::ExprTraits<VecT_1>::result_tag>::temporary_type cml::detail::nlerp	(	const VecT_1 &	v1,
		const VecT_2 &	v2,
		Real	t,
		et::vector_result_tag	,
		SizeT
	)			`[inline]`

Definition at line 633 of file interpolation.h.

References InterpResize().

Referenced by cml::nlerp(), and slerp().

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AxisOrder cml::detail::pack_axis_order	(	size_t	i,
		bool	odd
	)			`[inline]`

Definition at line 97 of file helper.h.

Referenced by swap_axis_order().

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template<class LeftT , class RightT >

detail::DotPromote<LeftT,RightT>::promoted_scalar cml::detail::quaternion_dot	(	const LeftT &	p,
		const RightT &	q
	)			`[inline]`

Definition at line 24 of file quaternion_dot.h.

Referenced by cml::dot().

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template<class QuatT_1 , class QuatT_2 >

et::QuaternionPromote2<QuatT_1,QuatT_2>::temporary_type cml::detail::quaternion_rotation_difference	(	const QuatT_1 &	q1,
		const QuatT_2 &	q2,
		negative_cross
	)			`[inline]`

Concatenate two quaternions in the order q1->q2.

Definition at line 553 of file quaternion_rotation.h.

References cml::conjugate().

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template<class QuatT_1 , class QuatT_2 >

et::QuaternionPromote2<QuatT_1,QuatT_2>::temporary_type cml::detail::quaternion_rotation_difference	(	const QuatT_1 &	q1,
		const QuatT_2 &	q2,
		positive_cross
	)			`[inline]`

Concatenate two quaternions in the order q1->q2.

Definition at line 544 of file quaternion_rotation.h.

References cml::conjugate().

Referenced by cml::quaternion_rotation_difference().

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template<typename LeftT , typename RightT , typename OpT >

bool cml::detail::quaternion_total_order	(	const LeftT &	left,
		const RightT &	right,
		OpT
	)			`[inline]`

Quaternion total order relationship.

OpT must implement a total order on the quaternion element type. operator<= and operator>= on integer and floating-point types are examples.

Definition at line 138 of file quaternion_comparison.h.

References CML_STATIC_REQUIRE_M.

template<typename LeftT , typename RightT , typename OpT >

bool cml::detail::quaternion_weak_order	(	const LeftT &	left,
		const RightT &	right,
		OpT
	)			`[inline]`

Quaternion strict weak ordering relationship.

OpT must implement a strict weak order on the quaternion element type. operator< and operator> on integer and floating-point types are examples.

Definition at line 82 of file quaternion_comparison.h.

References CML_STATIC_REQUIRE_M.

template<class Quat1_T , class Quat2_T >

et::QuaternionPromote< typename Quat1_T::temporary_type, typename Quat2_T::temporary_type>::temporary_type cml::detail::QuaternionMult	(	const Quat1_T &	q1,
		const Quat2_T &	q2
	)			`[inline]`

Definition at line 43 of file quaternion_mul.h.

References CheckQuat().

Referenced by cml::operator*().

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template<typename VecT >

void cml::detail::Require2D	(	const VecT &	v,
		dynamic_size_tag
	)			`[inline]`

For perp_dot(): run-time check for a 2D vector.

Definition at line 195 of file vector_products.h.

template<typename VecT >

void cml::detail::Require2D	(	const VecT &	v,
		fixed_size_tag
	)			`[inline]`

For perp_dot(): compile-time check for a 2D vector.

Definition at line 187 of file vector_products.h.

References CML_STATIC_REQUIRE_M.

Referenced by cml::perp_dot().

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template<typename VecT >

void cml::detail::Require3D	(	const VecT &	v,
		dynamic_size_tag
	)			`[inline]`

For cross(): run-time check for a 3D vector.

Definition at line 180 of file vector_products.h.

template<typename VecT >

void cml::detail::Require3D	(	const VecT &	,
		fixed_size_tag
	)			`[inline]`

For cross(): compile-time check for a 3D vector.

Definition at line 172 of file vector_products.h.

References CML_STATIC_REQUIRE_M.

Referenced by cml::cross().

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template<class MatT_1 , class MatT_2 , typename Real >

detail::TypePromote< MatT_1,MatT_2,typename et::ExprTraits<MatT_1>::result_tag>::temporary_type cml::detail::slerp	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		Real	t,
		Real	tolerance,
		et::matrix_result_tag	,
		dynamic_size_tag
	)			`[inline]`

Definition at line 595 of file interpolation.h.

References cml::et::detail::Resize().

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template<class MatT_1 , class MatT_2 , typename Real >

detail::TypePromote< MatT_1,MatT_2,typename et::ExprTraits<MatT_1>::result_tag>::temporary_type cml::detail::slerp	(	const MatT_1 &	m1,
		const MatT_2 &	m2,
		Real	t,
		Real	tolerance,
		et::matrix_result_tag	,
		fixed_size_tag
	)			`[inline]`

Definition at line 580 of file interpolation.h.

template<class QuatT_1 , class QuatT_2 , typename Real , class SizeT >

detail::TypePromote< QuatT_1,QuatT_2,typename et::ExprTraits<QuatT_1>::result_tag>::temporary_type cml::detail::slerp	(	const QuatT_1 &	q1,
		const QuatT_2 &	q2,
		Real	t,
		Real	tolerance,
		et::quaternion_result_tag	,
		SizeT
	)			`[inline]`

Definition at line 484 of file interpolation.h.

References cml::acos_safe(), cml::dot(), cml::lerp(), and cml::normalize().

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template<class VecT_1 , class VecT_2 , typename Real , class SizeT >

detail::TypePromote< VecT_1,VecT_2,typename et::ExprTraits<VecT_1>::result_tag>::temporary_type cml::detail::slerp	(	const VecT_1 &	v1,
		const VecT_2 &	v2,
		Real	t,
		Real	tolerance,
		et::vector_result_tag	,
		SizeT
	)			`[inline]`