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template<typename ElementType , int DIM>
static ElementType	dot_product (const ElementType v1[DIM], const ElementType v2[DIM])
	Compute v1 * v2 scalar product. More...

template<typename ElementType >
static ElementType	dot_product (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)
	Compute v1 * v2 scalar product. More...

template<typename GeometryTraits >
static GeometryTraits::Scalar	dot_product (const typename GeometryTraits::Vector &v1, const typename GeometryTraits::Vector &v2, const GeometryTraits &gt)

template<typename ElementType , int DIM>
static std::vector< ElementType >	cross_product (const ElementType v1[DIM], const ElementType v2[DIM])

template<typename ElementType >
static std::vector< ElementType >	cross_product (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)
	Compute v1 x v2 cross product. More...

template<typename GeometryTraits >
static GeometryTraits::Vector	cross_product (const typename GeometryTraits::Vector &v1, const typename GeometryTraits::Vector &v2, const GeometryTraits &gt)

template<typename ElementType , int DIM>
static std::vector< ElementType >	sub (const ElementType v1[DIM], const ElementType v2[DIM])
	Compute v1 - v2 (subtraction) More...

template<typename ElementType >
static std::vector< ElementType >	sub (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)
	Compute v1 - v2 (subtraction) More...

template<typename GeometryTraits >
static GeometryTraits::Vector	sub (const typename GeometryTraits::Point &p1, const typename GeometryTraits::Point &p2, const GeometryTraits &gt)
	Compute p1 - p2 (subtraction) More...

template<typename ElementType , int DIM>
static std::vector< ElementType >	add (const ElementType v1[DIM], const ElementType v2[DIM])
	Compute v1 + v2 (addition) More...

template<typename ElementType >
static std::vector< ElementType >	add (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)
	Compute v1 + v2 (addition) More...

template<typename GeometryTraits >
static GeometryTraits::Point	add (const typename GeometryTraits::Point &p, const typename GeometryTraits::Vector &v, const GeometryTraits &gt)
	Compute p + v (addition) More...

template<typename ElementType , int DIM>
static double	l2_distance (const ElementType v1[DIM], const ElementType v2[DIM])
	Compute \|\|v1 - v2\|\|_L2 norm (distance between v1 and v2) More...

template<typename ElementType , int DIM>
static double	l2_distance (const ElementType v[DIM])
	Compute \|\|V\|\|_L2 norm (distance between v1 and v2) More...

template<typename GeometryTraits >
static double	l2_distance (const typename GeometryTraits::Point &p1, const typename GeometryTraits::Point &p2, const GeometryTraits &gt)
	Compute \|\|p1 - p2\|\|_L2 norm (distance between p1 and p2) More...

template<typename ElementType >
static double	l2_distance (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)
	Compute \|\|v1 - v2\|\|_L2 norm (distance between v1 and v2) More...

template<typename GeometryTraits >
static double	l2_distance (const typename GeometryTraits::Vector &v, const GeometryTraits &gt)
	Compute \|\|V\|\|_L2 norm (distance between v1 and v2) More...

template<typename ElementType >
static double	l2_distance (const std::vector< ElementType > &v)
	Compute \|\|V\|\|_L2 norm (distance between v1 and v2) More...

template<typename GeometryTraits >
static GeometryTraits::Vector	normalize (const typename GeometryTraits::Vector &v, const GeometryTraits &gt)

template<typename ElementType >
static bool	are_collinear (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)
	Tells if 2 nD vectors are collinear or not. More...

template<typename GeometryTraits >
static bool	are_collinear (const typename GeometryTraits::Vector &v1, const typename GeometryTraits::Vector &v2)

template<typename ElementType >
static bool	are_aligned (const std::vector< ElementType > &p1, const std::vector< ElementType > &p2, const std::vector< ElementType > &p3)
	Tells if 3 nD points are aligned or not. More...

template<typename GeometryTraits >
static bool	are_aligned (const typename GeometryTraits::Point &p1, const typename GeometryTraits::Point &p2, const typename GeometryTraits::Point &p3)

template<typename ElementType >
static std::vector< ElementType >	scalar_mult (const std::vector< ElementType > &v1, ElementType coef)
	Compute v1 * coef. More...

template<typename GeometryTraits >
static GeometryTraits::Vector	scalar_mult (const typename GeometryTraits::Vector &v, double coef, const GeometryTraits &gt)

template<typename ElementType , int DIM>
static double	get_angle_from_unit_vectors (const ElementType v1[DIM], const ElementType v2[DIM])
	V1 and V2 must be unit vectors! More...

template<typename ElementType , int DIM>
static double	get_angle_in_degree_from_unit_vectors (const ElementType v1[DIM], const ElementType v2[DIM])

template<typename ElementType >
static double	get_angle_from_unit_vectors (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)
	V1 and V2 must be unit vectors! More...

template<typename ElementType >
static double	get_angle_in_degree_from_unit_vectors (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)

template<class ElementType >
static double	get_angle_from_non_unit_vectors (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)
	V1 and V2 does not need to be unit vectors! More...

template<typename ElementType >
static double	get_angle_in_degree_from_non_unit_vectors (const std::vector< ElementType > &v1, const std::vector< ElementType > &v2)

template<class ElementType >
static double	get_angle_from3positions (const std::vector< ElementType > &p1, const std::vector< ElementType > &p2, const std::vector< ElementType > &p3)

template<typename ElementType >
static double	get_angle_in_degree_from3positions (const std::vector< ElementType > &p1, const std::vector< ElementType > &p2, const std::vector< ElementType > &p3)

template<typename ElementType >
static void	rot_coord_sys (const std::vector< ElementType > &old_u, const std::vector< ElementType > &old_v, const std::vector< ElementType > &new_norm, std::vector< ElementType > &new_u, std::vector< ElementType > &new_v)

template<typename ElementType >
void	proj_curv (const std::vector< ElementType > &old_u, const std::vector< ElementType > &old_v, ElementType old_ku, ElementType old_kuv, ElementType old_kv, const std::vector< ElementType > &new_u, const std::vector< ElementType > &new_v, ElementType &new_ku, ElementType &new_kuv, ElementType &new_kv)

Function Documentation

◆ add() [1/3]

template<typename ElementType , int DIM>

static std::vector< ElementType > FEVV::Math::Vector::add	(	const ElementType	v1[DIM],
		const ElementType	v2[DIM]
	)

static

Compute v1 + v2 (addition)

Definition at line 548 of file MatrixOperations.hpp.

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◆ add() [2/3]

template<typename ElementType >

static std::vector< ElementType > FEVV::Math::Vector::add	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

Compute v1 + v2 (addition)

Definition at line 561 of file MatrixOperations.hpp.

◆ add() [3/3]

template<typename GeometryTraits >

static GeometryTraits::Point FEVV::Math::Vector::add	(	const typename GeometryTraits::Point &	p,
		const typename GeometryTraits::Vector &	v,
		const GeometryTraits &	gt
	)

static

Compute p + v (addition)

Definition at line 578 of file MatrixOperations.hpp.

◆ are_aligned() [1/2]

template<typename ElementType >

static bool FEVV::Math::Vector::are_aligned	(	const std::vector< ElementType > &	p1,
		const std::vector< ElementType > &	p2,
		const std::vector< ElementType > &	p3
	)

static

Tells if 3 nD points are aligned or not.

Parameters

p2	the central point

Definition at line 691 of file MatrixOperations.hpp.

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◆ are_aligned() [2/2]

template<typename GeometryTraits >

static bool FEVV::Math::Vector::are_aligned	(	const typename GeometryTraits::Point &	p1,
		const typename GeometryTraits::Point &	p2,
		const typename GeometryTraits::Point &	p3
	)

static

Parameters

p2	the central point

Definition at line 701 of file MatrixOperations.hpp.

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◆ are_collinear() [1/2]

template<typename ElementType >

static bool FEVV::Math::Vector::are_collinear	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

Tells if 2 nD vectors are collinear or not.

Parameters

v2	equals to P2 - P1 equals to P1 - P3

Definition at line 653 of file MatrixOperations.hpp.

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◆ are_collinear() [2/2]

template<typename GeometryTraits >

static bool FEVV::Math::Vector::are_collinear	(	const typename GeometryTraits::Vector &	v1,
		const typename GeometryTraits::Vector &	v2
	)

static

Parameters

v2	equals to P2 - P1 equals to P1 - P3

Definition at line 679 of file MatrixOperations.hpp.

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◆ cross_product() [1/3]

template<typename ElementType , int DIM>

static std::vector< ElementType > FEVV::Math::Vector::cross_product	(	const ElementType	v1[DIM],
		const ElementType	v2[DIM]
	)

static

Compute v1 x v2 cross product. Usually for such a function one can expect to get a return value as a "ElementType*" (dynamic allocation via new), however, with the purpose to avoid as many as possible unfreed chunk of memory, we rather use std::vector.

Definition at line 460 of file MatrixOperations.hpp.

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◆ cross_product() [2/3]

template<typename ElementType >

static std::vector< ElementType > FEVV::Math::Vector::cross_product	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

Compute v1 x v2 cross product.

Definition at line 479 of file MatrixOperations.hpp.

◆ cross_product() [3/3]

template<typename GeometryTraits >

static GeometryTraits::Vector FEVV::Math::Vector::cross_product	(	const typename GeometryTraits::Vector &	v1,
		const typename GeometryTraits::Vector &	v2,
		const GeometryTraits &	gt
	)

static

Definition at line 498 of file MatrixOperations.hpp.

◆ dot_product() [1/3]

template<typename ElementType , int DIM>

static ElementType FEVV::Math::Vector::dot_product	(	const ElementType	v1[DIM],
		const ElementType	v2[DIM]
	)

static

Compute v1 * v2 scalar product.

Definition at line 421 of file MatrixOperations.hpp.

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◆ dot_product() [2/3]

template<typename ElementType >

static ElementType FEVV::Math::Vector::dot_product	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

Compute v1 * v2 scalar product.

Definition at line 431 of file MatrixOperations.hpp.

◆ dot_product() [3/3]

template<typename GeometryTraits >

static GeometryTraits::Scalar FEVV::Math::Vector::dot_product	(	const typename GeometryTraits::Vector &	v1,
		const typename GeometryTraits::Vector &	v2,
		const GeometryTraits &	gt
	)

static

Definition at line 446 of file MatrixOperations.hpp.

◆ get_angle_from3positions()

template<class ElementType >

static double FEVV::Math::Vector::get_angle_from3positions	(	const std::vector< ElementType > &	p1,
		const std::vector< ElementType > &	p2,
		const std::vector< ElementType > &	p3
	)

static

Definition at line 809 of file MatrixOperations.hpp.

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◆ get_angle_from_non_unit_vectors()

template<class ElementType >

static double FEVV::Math::Vector::get_angle_from_non_unit_vectors	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

V1 and V2 does not need to be unit vectors!

Definition at line 779 of file MatrixOperations.hpp.

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◆ get_angle_from_unit_vectors() [1/2]

template<typename ElementType , int DIM>

static double FEVV::Math::Vector::get_angle_from_unit_vectors	(	const ElementType	v1[DIM],
		const ElementType	v2[DIM]
	)

static

V1 and V2 must be unit vectors!

Definition at line 738 of file MatrixOperations.hpp.

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◆ get_angle_from_unit_vectors() [2/2]

template<typename ElementType >

static double FEVV::Math::Vector::get_angle_from_unit_vectors	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

V1 and V2 must be unit vectors!

Definition at line 759 of file MatrixOperations.hpp.

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◆ get_angle_in_degree_from3positions()

template<typename ElementType >

static double FEVV::Math::Vector::get_angle_in_degree_from3positions	(	const std::vector< ElementType > &	p1,
		const std::vector< ElementType > &	p2,
		const std::vector< ElementType > &	p3
	)

static

Definition at line 821 of file MatrixOperations.hpp.

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◆ get_angle_in_degree_from_non_unit_vectors()

template<typename ElementType >

static double FEVV::Math::Vector::get_angle_in_degree_from_non_unit_vectors	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

Definition at line 801 of file MatrixOperations.hpp.

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◆ get_angle_in_degree_from_unit_vectors() [1/2]

template<typename ElementType , int DIM>

static double FEVV::Math::Vector::get_angle_in_degree_from_unit_vectors	(	const ElementType	v1[DIM],
		const ElementType	v2[DIM]
	)

static

Definition at line 749 of file MatrixOperations.hpp.

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◆ get_angle_in_degree_from_unit_vectors() [2/2]

template<typename ElementType >

static double FEVV::Math::Vector::get_angle_in_degree_from_unit_vectors	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

Definition at line 770 of file MatrixOperations.hpp.

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◆ l2_distance() [1/6]

template<typename ElementType , int DIM>

static double FEVV::Math::Vector::l2_distance	(	const ElementType	v1[DIM],
		const ElementType	v2[DIM]
	)

static

Compute ||v1 - v2||_L2 norm (distance between v1 and v2)

Definition at line 588 of file MatrixOperations.hpp.

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◆ l2_distance() [2/6]

template<typename ElementType , int DIM>

static double FEVV::Math::Vector::l2_distance ( const ElementType v[DIM] )

static

Compute ||V||_L2 norm (distance between v1 and v2)

Definition at line 599 of file MatrixOperations.hpp.

◆ l2_distance() [3/6]

template<typename ElementType >

static double FEVV::Math::Vector::l2_distance ( const std::vector< ElementType > & v )

static

Compute ||V||_L2 norm (distance between v1 and v2)

Definition at line 635 of file MatrixOperations.hpp.

◆ l2_distance() [4/6]

template<typename ElementType >

static double FEVV::Math::Vector::l2_distance	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

Compute ||v1 - v2||_L2 norm (distance between v1 and v2)

Definition at line 617 of file MatrixOperations.hpp.

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◆ l2_distance() [5/6]

template<typename GeometryTraits >

static double FEVV::Math::Vector::l2_distance	(	const typename GeometryTraits::Point &	p1,
		const typename GeometryTraits::Point &	p2,
		const GeometryTraits &	gt
	)

static

Compute ||p1 - p2||_L2 norm (distance between p1 and p2)

Definition at line 607 of file MatrixOperations.hpp.

◆ l2_distance() [6/6]

template<typename GeometryTraits >

static double FEVV::Math::Vector::l2_distance	(	const typename GeometryTraits::Vector &	v,
		const GeometryTraits &	gt
	)

static

Compute ||V||_L2 norm (distance between v1 and v2)

Definition at line 627 of file MatrixOperations.hpp.

◆ normalize()

template<typename GeometryTraits >

static GeometryTraits::Vector FEVV::Math::Vector::normalize	(	const typename GeometryTraits::Vector &	v,
		const GeometryTraits &	gt
	)

static

normalize a Vector: returns a pair composed of normalized input vector and of input vector length Input Vector V is not normalized

Definition at line 645 of file MatrixOperations.hpp.

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◆ proj_curv()

template<typename ElementType >

void FEVV::Math::Vector::proj_curv	(	const std::vector< ElementType > &	old_u,
		const std::vector< ElementType > &	old_v,
		ElementType	old_ku,
		ElementType	old_kuv,
		ElementType	old_kv,
		const std::vector< ElementType > &	new_u,
		const std::vector< ElementType > &	new_v,
		ElementType &	new_ku,
		ElementType &	new_kuv,
		ElementType &	new_kv
	)

Parameters

old_v	input
old_ku	input
old_kuv	input
old_kv	input
new_u	input
new_v	input
new_ku	input
new_kuv	output
new_kv	output output

Definition at line 878 of file MatrixOperations.hpp.

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◆ rot_coord_sys()

template<typename ElementType >

static void FEVV::Math::Vector::rot_coord_sys	(	const std::vector< ElementType > &	old_u,
		const std::vector< ElementType > &	old_v,
		const std::vector< ElementType > &	new_norm,
		std::vector< ElementType > &	new_u,
		std::vector< ElementType > &	new_v
	)

static

Parameters

old_v	input old_u which is assumed to be unit-length and perpendicular to old_v
new_norm	input old_v which is assumed to be unit-length and perpendicular to old_u
new_u	input new normal
new_v	output new_u which is unit-length and perpendicular to new_v output new_v which is unit-length and perpendicular to new_u

Definition at line 833 of file MatrixOperations.hpp.

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◆ scalar_mult() [1/2]

template<typename ElementType >

static std::vector< ElementType > FEVV::Math::Vector::scalar_mult	(	const std::vector< ElementType > &	v1,
		ElementType	coef
	)

static

Compute v1 * coef.

Definition at line 714 of file MatrixOperations.hpp.

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◆ scalar_mult() [2/2]

template<typename GeometryTraits >

static GeometryTraits::Vector FEVV::Math::Vector::scalar_mult	(	const typename GeometryTraits::Vector &	v,
		double	coef,
		const GeometryTraits &	gt
	)

static

Definition at line 728 of file MatrixOperations.hpp.

◆ sub() [1/3]

template<typename ElementType , int DIM>

static std::vector< ElementType > FEVV::Math::Vector::sub	(	const ElementType	v1[DIM],
		const ElementType	v2[DIM]
	)

static

Compute v1 - v2 (subtraction)

Definition at line 508 of file MatrixOperations.hpp.

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◆ sub() [2/3]

template<typename ElementType >

static std::vector< ElementType > FEVV::Math::Vector::sub	(	const std::vector< ElementType > &	v1,
		const std::vector< ElementType > &	v2
	)

static

Compute v1 - v2 (subtraction)

Definition at line 521 of file MatrixOperations.hpp.

◆ sub() [3/3]

template<typename GeometryTraits >

static GeometryTraits::Vector FEVV::Math::Vector::sub	(	const typename GeometryTraits::Point &	p1,
		const typename GeometryTraits::Point &	p2,
		const GeometryTraits &	gt
	)

static

Compute p1 - p2 (subtraction)

Definition at line 538 of file MatrixOperations.hpp.

Namespaces

Functions

Function Documentation

◆ add() [1/3]

◆ add() [2/3]

◆ add() [3/3]

◆ are_aligned() [1/2]

◆ are_aligned() [2/2]

◆ are_collinear() [1/2]

◆ are_collinear() [2/2]

◆ cross_product() [1/3]

◆ cross_product() [2/3]

◆ cross_product() [3/3]

◆ dot_product() [1/3]

◆ dot_product() [2/3]

◆ dot_product() [3/3]

◆ get_angle_from3positions()

◆ get_angle_from_non_unit_vectors()

◆ get_angle_from_unit_vectors() [1/2]

◆ get_angle_from_unit_vectors() [2/2]

◆ get_angle_in_degree_from3positions()

◆ get_angle_in_degree_from_non_unit_vectors()

◆ get_angle_in_degree_from_unit_vectors() [1/2]

◆ get_angle_in_degree_from_unit_vectors() [2/2]

◆ l2_distance() [1/6]

◆ l2_distance() [2/6]

◆ l2_distance() [3/6]

◆ l2_distance() [4/6]

◆ l2_distance() [5/6]

◆ l2_distance() [6/6]

◆ normalize()

◆ proj_curv()

◆ rot_coord_sys()

◆ scalar_mult() [1/2]

◆ scalar_mult() [2/2]

◆ sub() [1/3]

◆ sub() [2/3]

◆ sub() [3/3]