Utilities to compute intersections between different geometries. More...

#include <intersection_utilities.h>

Collaboration diagram for Kratos::IntersectionUtilities:

Public Member Functions
Type Definitions
	KRATOS_CLASS_POINTER_DEFINITION (IntersectionUtilities)
	Pointer definition of IntersectionUtilities. More...

Operators
	IntersectionUtilities ()
	Default constructor. More...

virtual	~IntersectionUtilities ()
	Destructor. More...

Static Public Member Functions
Operations
template<class TGeometryType >
static int	ComputeTriangleLineIntersection (const TGeometryType &rTriangleGeometry, const array_1d< double, 3 > &rLinePoint1, const array_1d< double, 3 > &rLinePoint2, array_1d< double, 3 > &rIntersectionPoint, const double epsilon=1e-12)

template<class TGeometryType >
static bool	TriangleLineIntersection2D (const TGeometryType &rTriangle, const array_1d< double, 3 > &rPoint0, const array_1d< double, 3 > &rPoint1)

static bool	TriangleLineIntersection2D (const array_1d< double, 3 > &rVert0, const array_1d< double, 3 > &rVert1, const array_1d< double, 3 > &rVert2, const array_1d< double, 3 > &rPoint0, const array_1d< double, 3 > &rPoint1)

static bool	PointInTriangle (const array_1d< double, 3 > &rVert0, const array_1d< double, 3 > &rVert1, const array_1d< double, 3 > &rVert2, const array_1d< double, 3 > &rPoint, const double Tolerance=std::numeric_limits< double >::epsilon())
	This uses the Cramer's rule for solving a linear system and obtain the barycentric coordinates. More...

template<class TGeometryType , class TCoordinatesType >
static int	ComputeTriangleLineIntersectionInTheSamePlane (const TGeometryType &rTriangleGeometry, const TCoordinatesType &rLinePoint1, const TCoordinatesType &rLinePoint2, TCoordinatesType &rIntersectionPoint1, TCoordinatesType &rIntersectionPoint2, int &rSolution, const double Epsilon=1e-12)
	Find the 3D intersection of a line (bounded) with a triangle (bounded) in the same plane. More...

template<class TGeometryType , class TCoordinatesType , bool TConsiderInsidePoints = true>
static int	ComputeTetrahedraLineIntersection (const TGeometryType &rTetrahedraGeometry, const TCoordinatesType &rLinePoint1, const TCoordinatesType &rLinePoint2, TCoordinatesType &rIntersectionPoint1, TCoordinatesType &rIntersectionPoint2, const double Epsilon=1e-12)
	Find the 3D intersection of a line (bounded) with a tetrahedra (bounded) More...

template<class TGeometryType >
static PointerVector< Point >	ComputeShortestLineBetweenTwoLines (const TGeometryType &rSegment1, const TGeometryType &rSegment2)
	Calculates the line to line intersection (shortest line). If line is length 0, it is considered a point and therefore there is intersection (3D version) More...

template<class TGeometryType >
static int	ComputeLineLineIntersection (const TGeometryType &rLineGeometry, const array_1d< double, 3 > &rLinePoint0, const array_1d< double, 3 > &rLinePoint1, array_1d< double, 3 > &rIntersectionPoint, const double epsilon=1e-12)

static int	ComputeLineLineIntersection (const array_1d< double, 3 > &rLine1Point0, const array_1d< double, 3 > &rLine1Point1, const array_1d< double, 3 > &rLine2Point0, const array_1d< double, 3 > &rLine2Point1, array_1d< double, 3 > &rIntersectionPoint, const double epsilon=1e-12)

static int	ComputePlaneLineIntersection (const array_1d< double, 3 > &rPlaneBasePoint, const array_1d< double, 3 > &rPlaneNormal, const array_1d< double, 3 > &rLinePoint1, const array_1d< double, 3 > &rLinePoint2, array_1d< double, 3 > &rIntersectionPoint, const double epsilon=1e-12)
	Find the 3D intersection of a plane (infinite) with a segment (bounded) More...

static int	ComputeLineBoxIntersection (const array_1d< double, 3 > &rBoxPoint0, const array_1d< double, 3 > &rBoxPoint1, const array_1d< double, 3 > &rLinePoint0, const array_1d< double, 3 > &rLinePoint1)
	Compute a segment box intersection Provided the minimum and maximum points of a box cell, this method checks if the segment intersects it. If it does intersect, it returns the rIntersectionPointpoint as well. Note that the cell box is assumed to be aligned to the cartesian axes. Adapted from: https://www.3dkingdoms.com/weekly/weekly.php?a=3. More...

Detailed Description

Utilities to compute intersections between different geometries.

This class provides static methods to check if there is intersections between different entities, and if there is, give back the intersection points.

Author: Ruben Zorrilla; Vicente Mataix Ferrandiz

Constructor & Destructor Documentation

◆ IntersectionUtilities()

Kratos::IntersectionUtilities::IntersectionUtilities ( )

inline

Default constructor.

◆ ~IntersectionUtilities()

virtual Kratos::IntersectionUtilities::~IntersectionUtilities ( )

inlinevirtual

Destructor.

Member Function Documentation

◆ ComputeLineBoxIntersection()

static int Kratos::IntersectionUtilities::ComputeLineBoxIntersection	(	const array_1d< double, 3 > &	rBoxPoint0,
		const array_1d< double, 3 > &	rBoxPoint1,
		const array_1d< double, 3 > &	rLinePoint0,
		const array_1d< double, 3 > &	rLinePoint1
	)

inlinestatic

Compute a segment box intersection Provided the minimum and maximum points of a box cell, this method checks if the segment intersects it. If it does intersect, it returns the rIntersectionPointpoint as well. Note that the cell box is assumed to be aligned to the cartesian axes. Adapted from: https://www.3dkingdoms.com/weekly/weekly.php?a=3.

Parameters

rBoxPoint0	Minimum point of the box cell
rBoxPoint1	Maximum point of the box cell
rLinePoint0	Segment origin point
rLinePoint1	Segment end point

Returns: int Returns 0 if there is no intersection and 1 otherwise

◆ ComputeLineLineIntersection() [1/2]

static int Kratos::IntersectionUtilities::ComputeLineLineIntersection	(	const array_1d< double, 3 > &	rLine1Point0,
		const array_1d< double, 3 > &	rLine1Point1,
		const array_1d< double, 3 > &	rLine2Point0,
		const array_1d< double, 3 > &	rLine2Point1,
		array_1d< double, 3 > &	rIntersectionPoint,
		const double	epsilon = `1e-12`
	)

inlinestatic

Find the 2D intersection of two lines (both bounded)

Parameters

rLine1Point0	Coordinates of the first point of the first line
rLine1Point1	Coordinates of the second point of the first line
rLine2Point0	Coordinates of the first point of the second line
rLine2Point1	Coordinates of the second point of the second line

Returns: rIntersectionPoint The intersection point coordinates; The intersection type index: 0 (disjoint - no intersection) 1 (intersect in a unique point) 2 (overlap) 3 (intersect in one endpoint)

◆ ComputeLineLineIntersection() [2/2]

template<class TGeometryType >

static int Kratos::IntersectionUtilities::ComputeLineLineIntersection	(	const TGeometryType &	rLineGeometry,
		const array_1d< double, 3 > &	rLinePoint0,
		const array_1d< double, 3 > &	rLinePoint1,
		array_1d< double, 3 > &	rIntersectionPoint,
		const double	epsilon = `1e-12`
	)

inlinestatic

Find the 2D intersection of two lines (both bounded)

Parameters

rLineGeometry	Is the line to intersect
rLinePoint1	Coordinates of the first point of the intersecting line
rLinePoint2	Coordinates of the second point of the intersecting line

Returns: rIntersectionPoint The intersection point coordinates; The intersection type index: 0 (disjoint - no intersection) 1 (intersect in a unique point) 2 (overlap) 3 (intersect in one endpoint)

◆ ComputePlaneLineIntersection()

static int Kratos::IntersectionUtilities::ComputePlaneLineIntersection	(	const array_1d< double, 3 > &	rPlaneBasePoint,
		const array_1d< double, 3 > &	rPlaneNormal,
		const array_1d< double, 3 > &	rLinePoint1,
		const array_1d< double, 3 > &	rLinePoint2,
		array_1d< double, 3 > &	rIntersectionPoint,
		const double	epsilon = `1e-12`
	)

inlinestatic

Find the 3D intersection of a plane (infinite) with a segment (bounded)

Parameters

rPlaneBasePoint	Base point of the plane to intersect with
rPlaneNormal	Normal vector of the plane to intersect with
rLinePoint1	Coordinates of the first point of the segment
rLinePoint2	Coordinates of the second point of the segment
rIntersectionPoint	The intersection point coordinates

Returns: The intersection type index: 0 (parallel or out of bounds - no intersection) 1 (unique intersection point) 2 (edge and plane coincide - no intersection)

◆ ComputeShortestLineBetweenTwoLines()

template<class TGeometryType >

static PointerVector<Point> Kratos::IntersectionUtilities::ComputeShortestLineBetweenTwoLines	(	const TGeometryType &	rSegment1,
		const TGeometryType &	rSegment2
	)

inlinestatic

Calculates the line to line intersection (shortest line). If line is length 0, it is considered a point and therefore there is intersection (3D version)

Calculate the line segment PaPb that is the shortest route between two lines P1P2 and P3P4. Calculate also the values of mua and mub where Pa = P1 + mua (P2 - P1) Pb = P3 + mub (P4 - P3) http://paulbourke.net/geometry/pointlineplane/

Parameters

rSegment1	The first segment
rSegment2	The second segment

Template Parameters

TGeometryType The geometry type

Returns: Return empty points array if no solution exists. Otherwise returns the line intersection points array

◆ ComputeTetrahedraLineIntersection()

template<class TGeometryType , class TCoordinatesType , bool TConsiderInsidePoints = true>

static int Kratos::IntersectionUtilities::ComputeTetrahedraLineIntersection	(	const TGeometryType &	rTetrahedraGeometry,
		const TCoordinatesType &	rLinePoint1,
		const TCoordinatesType &	rLinePoint2,
		TCoordinatesType &	rIntersectionPoint1,
		TCoordinatesType &	rIntersectionPoint2,
		const double	Epsilon = `1e-12`
	)

inlinestatic

Find the 3D intersection of a line (bounded) with a tetrahedra (bounded)

Template Parameters

TGeometryType	The geometry type
TCoordinatesType	The type of coordinates
TConsiderInsidePoints	If considering inside points or just the intersections in the faces

Parameters

[in]	rTetrahedraGeometry	Is the tetrahedra to intersect
[in]	rLinePoint1	Coordinates of the first point of the intersecting line
[in]	rLinePoint2	Coordinates of the second point of the intersecting line
[out]	rIntersectionPoint1	The first intersection point coordinates
[out]	rIntersectionPoint2	The second intersection point coordinates

Returns: The intersection type index: NO_INTERSECTION (disjoint - no intersection) TWO_POINTS_INTERSECTION (intersect in two points) ONE_POINT_INTERSECTION (intersect in one point) TWO_POINTS_INTERSECTION_BOTH_INSIDE (intersect in two points inside the tetrahedra) TWO_POINTS_INTERSECTION_ONE_INSIDE (intersect in two points, one inside the tetrahedra) FIRST_CORNER (intersect in the first corner of the tetrahedra) SECOND_CORNER (intersect in the second corner of the tetrahedra) THIRD_CORNER (intersect in the thid corner of the tetrahedra) FOURTH_CORNER (intersect in the fourth corner of the tetrahedra) Equivalent enum: enum class IntersectionUtilitiesTetrahedraLineIntersectionStatus { NO_INTERSECTION = 0, // (disjoint - no intersection) TWO_POINTS_INTERSECTION = 1, // (intersect in two points) ONE_POINT_INTERSECTION = 2, // (intersect in one point) TWO_POINTS_INTERSECTION_BOTH_INSIDE = 3, // (intersect in two points inside the tetrahedra) TWO_POINTS_INTERSECTION_ONE_INSIDE = 4, // (intersect in two points, one inside the tetrahedra) FIRST_CORNER = 5, // (intersect in the first corner of the tetrahedra) SECOND_CORNER = 6, // (intersect in the second corner of the tetrahedra) THIRD_CORNER = 7, // (intersect in the thid corner of the tetrahedra) FOURTH_CORNER = 8 // (intersect in the fourth corner of the tetrahedra) };

Parameters

Epsilon The tolerance

◆ ComputeTriangleLineIntersection()

template<class TGeometryType >

static int Kratos::IntersectionUtilities::ComputeTriangleLineIntersection	(	const TGeometryType &	rTriangleGeometry,
		const array_1d< double, 3 > &	rLinePoint1,
		const array_1d< double, 3 > &	rLinePoint2,
		array_1d< double, 3 > &	rIntersectionPoint,
		const double	epsilon = `1e-12`
	)

inlinestatic

Find the 3D intersection of a line (bounded) with a triangle (bounded)

Parameters

rTriangleGeometry	Is the triangle to intersect
rLinePoint1	Coordinates of the first point of the intersecting line
rLinePoint2	Coordinates of the second point of the intersecting line

Returns: rIntersectionPoint The intersection point coordinates; The intersection type index: -1 (the triangle is degenerate) 0 (disjoint - no intersection) 1 (intersect in a unique point) 2 (are in the same plane)

◆ ComputeTriangleLineIntersectionInTheSamePlane()

template<class TGeometryType , class TCoordinatesType >

static int Kratos::IntersectionUtilities::ComputeTriangleLineIntersectionInTheSamePlane	(	const TGeometryType &	rTriangleGeometry,
		const TCoordinatesType &	rLinePoint1,
		const TCoordinatesType &	rLinePoint2,
		TCoordinatesType &	rIntersectionPoint1,
		TCoordinatesType &	rIntersectionPoint2,
		int &	rSolution,
		const double	Epsilon = `1e-12`
	)

inlinestatic

Find the 3D intersection of a line (bounded) with a triangle (bounded) in the same plane.

Template Parameters

TGeometryType	The geometry type
TCoordinatesType	The type of coordinates
TConsiderInsidePoints	If considering inside points or just the intersections in the faces

Parameters

[in]	rTriangleGeometry	Is the tetrahedra to intersect
[in]	rLinePoint1	Coordinates of the first point of the intersecting line
[in]	rLinePoint2	Coordinates of the second point of the intersecting line
[out]	rIntersectionPoint1	The first intersection point coordinates
[out]	rIntersectionPoint2	The second intersection point coordinates
[out]	rSolution	The intersection type index: NO_INTERSECTION (disjoint - no intersection) TWO_POINTS_INTERSECTION (intersect in two points) ONE_POINT_INTERSECTION (intersect in one point)
	Epsilon	The tolerance

◆ KRATOS_CLASS_POINTER_DEFINITION()

Kratos::IntersectionUtilities::KRATOS_CLASS_POINTER_DEFINITION ( IntersectionUtilities )

Pointer definition of IntersectionUtilities.

◆ PointInTriangle()

static bool Kratos::IntersectionUtilities::PointInTriangle	(	const array_1d< double, 3 > &	rVert0,
		const array_1d< double, 3 > &	rVert1,
		const array_1d< double, 3 > &	rVert2,
		const array_1d< double, 3 > &	rPoint,
		const double	Tolerance = `std::numeric_limits<double>::epsilon()`
	)

inlinestatic

This uses the Cramer's rule for solving a linear system and obtain the barycentric coordinates.

Check if a point is inside a 2D triangle

Parameters

rVert0	The first vertex of the triangle to intersect
rVert1	The second vertex of the triangle to intersect
rVert2	The third vertex of the triangle to intersect
rPoint	Coordinates of the point

Returns: The intersection type index: -1 (the triangle is degenerate) 0 (disjoint - no intersection) 1 (intersect)

◆ TriangleLineIntersection2D() [1/2]

static bool Kratos::IntersectionUtilities::TriangleLineIntersection2D	(	const array_1d< double, 3 > &	rVert0,
		const array_1d< double, 3 > &	rVert1,
		const array_1d< double, 3 > &	rVert2,
		const array_1d< double, 3 > &	rPoint0,
		const array_1d< double, 3 > &	rPoint1
	)

inlinestatic

Find the 2D intersection of a line (bounded) with a triangle (bounded)

Parameters

rVert1	The first vertex of the triangle to intersect
rVert2	The second vertex of the triangle to intersect
rVert3	The third vertex of the triangle to intersect
rPoint1	Coordinates of the first point of the intersecting line
rPoint2	Coordinates of the second point of the intersecting line

Returns: If there is intersection

◆ TriangleLineIntersection2D() [2/2]

template<class TGeometryType >

static bool Kratos::IntersectionUtilities::TriangleLineIntersection2D	(	const TGeometryType &	rTriangle,
		const array_1d< double, 3 > &	rPoint0,
		const array_1d< double, 3 > &	rPoint1
	)

inlinestatic

Find the 2D intersection of a line (bounded) with a triangle (bounded)

Parameters

rTriangle	Is the triangle to intersect
rPoint0	Coordinates of the first point of the intersecting line
rPoint1	Coordinates of the second point of the intersecting line

Returns: If there is intersection

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

/home/runner/work/Documentation/Documentation/master/kratos/utilities/intersection_utilities.h

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ IntersectionUtilities()

◆ ~IntersectionUtilities()

Member Function Documentation

◆ ComputeLineBoxIntersection()

◆ ComputeLineLineIntersection() [1/2]

◆ ComputeLineLineIntersection() [2/2]

◆ ComputePlaneLineIntersection()

◆ ComputeShortestLineBetweenTwoLines()

◆ ComputeTetrahedraLineIntersection()

◆ ComputeTriangleLineIntersection()

◆ ComputeTriangleLineIntersectionInTheSamePlane()

◆ KRATOS_CLASS_POINTER_DEFINITION()

◆ PointInTriangle()

◆ TriangleLineIntersection2D() [1/2]

◆ TriangleLineIntersection2D() [2/2]