Provides computational geometry operations. More...

Classes
struct	ConvexityResult

Enumerations
enum	ResultConstants { NO_INTERSECTION , INTERSECTION , TOUCHING , NOT_CONTAINED , CONTAINED }

Functions
bool	lineIntersection (const Eigen::Ref< const Eigen::Vector2d > &a, const Eigen::Ref< const Eigen::Vector2d > &b, const Eigen::Ref< const Eigen::Vector2d > &c, const Eigen::Ref< const Eigen::Vector2d > &d, Eigen::Ref< Eigen::Vector2d > &intersectionPoint)
	Determines the intersection point of two lines, if one exists.

ResultConstants	segmentPlaneIntersection (const Eigen::Vector3d &pointOnPlane, const Eigen::Vector3d &planeNormal, const Eigen::Vector3d &firstPointSegment, const Eigen::Vector3d &secondPointSegment, Eigen::Vector3d &intersectionPoint)
	Determines the intersection point of a segment with a plane in 3D.

double	triangleArea (const Eigen::VectorXd &a, const Eigen::VectorXd &b, const Eigen::VectorXd &c)
	Computes the signed area of a triangle in 2D.

double	tetraVolume (const Eigen::Vector3d &a, const Eigen::Vector3d &b, const Eigen::Vector3d &c, const Eigen::Vector3d &d)
	Computes the (unsigned) area of a triangle in 3D.

Eigen::Vector2d	projectVector (const Eigen::Vector3d &vector, const int indexDimensionToRemove)
	Projects a 3D vector to a 2D one by removing one dimension.

ConvexityResult	isConvexQuad (std::array< Eigen::VectorXd, 4 > coords)

template<typename VECTORA_T , typename VECTORB_T , typename VECTORC_T >
bool	between (const VECTORA_T &a, const VECTORB_T &b, const VECTORC_T &toCheck)
	Determines, if a point lies on the line segment defined by a, b.

template<typename Derived >
bool	collinear (const Eigen::MatrixBase< Derived > &a, const Eigen::MatrixBase< Derived > &b, const Eigen::MatrixBase< Derived > &c)
	Determines, if three points are collinear (on one line)

template<typename Derived >
static bool	parallel (const Eigen::MatrixBase< Derived > &a, const Eigen::MatrixBase< Derived > &b, const Eigen::MatrixBase< Derived > &c, const Eigen::MatrixBase< Derived > &d)
	Determines, if two lines are parallel to each other.

template<class Derived >
int	containedInHyperrectangle (const Eigen::MatrixBase< Derived > &sidelengths, const Eigen::MatrixBase< Derived > &center, const Eigen::MatrixBase< Derived > &testPoint)
	Tests, if a vertex is contained in a hyperrectangle.

template<class Derived >
bool	parallel (const Eigen::MatrixBase< Derived > &a, const Eigen::MatrixBase< Derived > &b, const Eigen::MatrixBase< Derived > &c, const Eigen::MatrixBase< Derived > &d)
	Determines, if two lines are parallel to each other.

Variables
logging::Logger	_log ("math::geometry")

Detailed Description

Provides computational geometry operations.

Enumeration Type Documentation

◆ ResultConstants

enum precice::math::geometry::ResultConstants

Enumerator
NO_INTERSECTION
INTERSECTION
TOUCHING
NOT_CONTAINED
CONTAINED

Definition at line 14 of file geometry.hpp.

Function Documentation

◆ between()

template<typename VECTORA_T , typename VECTORB_T , typename VECTORC_T >

bool precice::math::geometry::between	(	const VECTORA_T &	a,
		const VECTORB_T &	b,
		const VECTORC_T &	toCheck )

Determines, if a point lies on the line segment defined by a, b.

Works for 2D and 3D.

Parameters

[in]	a	First point of line segment
[in]	b	Second point of line segment
[in]	toCheck	Point to be checked for "betweenness"

Returns: True, if toCheck lies between a and b. False, otherwise

Definition at line 151 of file geometry.hpp.

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◆ collinear()

template<typename Derived >

bool precice::math::geometry::collinear	(	const Eigen::MatrixBase< Derived > &	a,
		const Eigen::MatrixBase< Derived > &	b,
		const Eigen::MatrixBase< Derived > &	c )

Determines, if three points are collinear (on one line)

Works for Dim2 and Dim3.

Parameters

[in]	a	First point to check
[in]	b	Second point to check
[in]	c	Third point to check

Returns: True, if collinear. False, otherwise

Definition at line 170 of file geometry.hpp.

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◆ containedInHyperrectangle()

template<class Derived >

int precice::math::geometry::containedInHyperrectangle	(	const Eigen::MatrixBase< Derived > &	sidelengths,
		const Eigen::MatrixBase< Derived > &	center,
		const Eigen::MatrixBase< Derived > &	testPoint )

Tests, if a vertex is contained in a hyperrectangle.

Returns

One of:

CONTAINED
NOT_CONTAINED
TOUCHING

Definition at line 198 of file geometry.hpp.

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◆ isConvexQuad()

ConvexityResult precice::math::geometry::isConvexQuad ( std::array< Eigen::VectorXd, 4 > coords )

Definition at line 143 of file geometry.cpp.

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◆ lineIntersection()

bool precice::math::geometry::lineIntersection	(	const Eigen::Ref< const Eigen::Vector2d > &	a,
		const Eigen::Ref< const Eigen::Vector2d > &	b,
		const Eigen::Ref< const Eigen::Vector2d > &	c,
		const Eigen::Ref< const Eigen::Vector2d > &	d,
		Eigen::Ref< Eigen::Vector2d > &	intersectionPoint )

Determines the intersection point of two lines, if one exists.

Works only for Dim2.

Parameters

[in]	a	First point on first line.
[in]	b	Second point on first line.
[in]	c	First point on second line.
[in]	d	Second point on second line.
[out]	intersectionPoint	Point of intersection.

Returns: True, if an intersection point exists and could be determined.

Definition at line 16 of file geometry.cpp.

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◆ parallel() [1/2]

template<typename Derived >

static bool precice::math::geometry::parallel	(	const Eigen::MatrixBase< Derived > &	a,
		const Eigen::MatrixBase< Derived > &	b,
		const Eigen::MatrixBase< Derived > &	c,
		const Eigen::MatrixBase< Derived > &	d )

static

Determines, if two lines are parallel to each other.

Works for Dim2 and Dim3.

Parameters

[in]	a	First point on first line.
[in]	b	Second point on first line.
[in]	c	First point on second line.
[in]	d	Second point on second line.

Returns: True, if the two lines are parallel to each other.

Definition at line 185 of file geometry.hpp.

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◆ parallel() [2/2]

template<class Derived >

bool precice::math::geometry::parallel	(	const Eigen::MatrixBase< Derived > &	a,
		const Eigen::MatrixBase< Derived > &	b,
		const Eigen::MatrixBase< Derived > &	c,
		const Eigen::MatrixBase< Derived > &	d )

Determines, if two lines are parallel to each other.

Works for Dim2 and Dim3.

Parameters

[in]	a	First point on first line.
[in]	b	Second point on first line.
[in]	c	First point on second line.
[in]	d	Second point on second line.

Returns: True, if the two lines are parallel to each other.

Definition at line 185 of file geometry.hpp.

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◆ projectVector()

Eigen::Vector2d precice::math::geometry::projectVector	(	const Eigen::Vector3d &	vector,
		int	indexDimensionToRemove )

Projects a 3D vector to a 2D one by removing one dimension.

Definition at line 125 of file geometry.cpp.

◆ segmentPlaneIntersection()

ResultConstants precice::math::geometry::segmentPlaneIntersection	(	const Eigen::Vector3d &	pointOnPlane,
		const Eigen::Vector3d &	planeNormal,
		const Eigen::Vector3d &	firstPointSegment,
		const Eigen::Vector3d &	secondPointSegment,
		Eigen::Vector3d &	intersectionPoint )

Determines the intersection point of a segment with a plane in 3D.

Parameters

[out] intersectionPoint Contains coordinates of intersection point, if return value equals TOUCHING or INTERSECTION.

Returns

Returns type of intersection. One of

NO_INTERSECTION
INTERSECTION
TOUCHING
CONTAINED

Definition at line 42 of file geometry.cpp.

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◆ tetraVolume()

double precice::math::geometry::tetraVolume	(	const Eigen::Vector3d &	a,
		const Eigen::Vector3d &	b,
		const Eigen::Vector3d &	c,
		const Eigen::Vector3d &	d )

Computes the (unsigned) area of a triangle in 3D.

Definition at line 116 of file geometry.cpp.

◆ triangleArea()

double precice::math::geometry::triangleArea	(	const Eigen::VectorXd &	a,
		const Eigen::VectorXd &	b,
		const Eigen::VectorXd &	c )

Computes the signed area of a triangle in 2D.

The area is negative, if the points a, b, c are given in clockwise ordering, otherwise positive.

Definition at line 93 of file geometry.cpp.

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Variable Documentation

◆ _log

logging::Logger precice::math::geometry::_log("math::geometry") ( "math::geometry" )

Classes

Enumerations

Functions

Variables

Detailed Description

Enumeration Type Documentation

◆ ResultConstants

Function Documentation

◆ between()

◆ collinear()

◆ containedInHyperrectangle()

◆ isConvexQuad()

◆ lineIntersection()

◆ parallel() [1/2]

◆ parallel() [2/2]

◆ projectVector()

◆ segmentPlaneIntersection()

◆ tetraVolume()

◆ triangleArea()

Variable Documentation

◆ _log