The namespace fwMath contains classes which provide the implementation of several mathematic functions and objects (plane, line, point). More...

Functions
template<typename TYPE >
bool	isEqual (TYPE a, TYPE b, const float epsilon=0.00001F)
	Returns true iff a and b are equal with 'epsilon' error margin. More...

template<typename CONTAINER >
bool	isContainerEqual (CONTAINER &containerA, CONTAINER &containerB, const float epsilon=0.00001F)
	Returns true iff container a and b are equal with 'epsilon' error margin. More...

FWMATH_API bool	getClosestPoints (const fwLine &_ray1, const fwLine &_ray2, fwVec3d &_pointOnThis, fwVec3d &_pointOnfwLine)
	Compute the closest points between two rays. More...

FWMATH_API fwVec3d	getClosestPoint (const fwLine &_ray, const fwVec3d &_point)
	Compute the projection of a point in a given direction. More...

FWMATH_API bool	intersect (const fwLine &_ray, double _radius, const fwVec3d &_point)
	Compute the projection of a point in a given direction and test if this intersection is inside a given radius. More...

FWMATH_API bool	intersect (const fwLine &_line, double _radius, const fwVec3d &_origin, const fwVec3d &_direction, fwVec3d &_point)
	Compute the closest points between two rays and test these points lie inside a sphere of a given radius. More...

FWMATH_API bool	intersect (const fwLine &_line, const fwVec3d &_v1, const fwVec3d &_v2, const fwVec3d &_v3, fwVec3d &_point, fwVec3d &_barycentric, bool &_front)
	Give the intersection between a plane and a line. The result is returned in a point (_point). More...

FWMATH_API void	multVecMatrix (const fwMatrix4x4 &_matrix, const fwVec3d &_source, fwVec3d &_dest)
	Multiply a matrix by a vector. More...

FWMATH_API fwMatrix4x4	getRotationMatrix (const fwVec3d &_vecNorm)
	Compute a matrix rotation. More...

FWMATH_API fwMatrix4x4	getInverse (const fwMatrix4x4 &matrix)
	Computes the inverse of a matrix. More...

FWMATH_API bool	IsInclosedVolume (const fwVertexPosition &_vertex, const fwVertexIndex &_vertexIndex, const fwVec3d &_p)

FWMATH_API bool	intersect_triangle (fwVec3d _orig, fwVec3d _dir, fwVec3d _vert0, fwVec3d _vert1, fwVec3d _vert2, double &_t, double &_u, double &_v)
	Compute the intersection between triangle(define by threes vertex vert1, vert2, vert3) and the Oz parallel line and cross by the point P. The function return true if intersection is found (false otherwise). t is the oriented distance of P to the intersection point. u and v is the coordinate of the intersection point in the (O, u, v) triangle coordinate system with : O = vert1. u = vert2 - O. v = vert3 - O. "Fast, Minimum Storage Ray/Triangle Intersection", Tomas Muller, Ben Trumbore.

FWMATH_API bool	isBorderlessSurface (const fwVertexIndex &_vertexIndex)
	test whatever a vertex is duplicated or not

FWMATH_API void	findBorderEdges (const fwVertexIndex &_vertexIndex, std::vector< std::vector< std::pair< int, int > > > &contours)

FWMATH_API bool	closeSurface (fwVertexPosition &_vertex, fwVertexIndex &_vertexIndex)
	Closes the surface if necessary. More...

FWMATH_API bool	removeOrphanVertices (fwVertexPosition &_vertex, fwVertexIndex &_vertexIndex)

template<typename T , typename U >
std::pair< T, U >	makeOrderedPair (const T first, const U second)

template<typename T , typename U , typename V >
bool	isBorderlessSurface (T cellDataBegin, T cellDataEnd, U cellDataOffsetsBegin, U cellDataOffsetsEnd, V *cellTypesBegin)

FWMATH_API fwPlane	getPlane (const fwVec3d &_point1, const fwVec3d &_point2, const fwVec3d &_point3)

FWMATH_API fwPlane	getPlane (const fwVec3d &_normal, const fwVec3d &_point)
	compute a plane from a normal and a point which must be in the plane. More...

FWMATH_API void	setValues (fwPlane &_plane, const fwVec3d &_point1, const fwVec3d &_point2, const fwVec3d &_point3)
	Initialize a plane _plane with three points (_point1, _point2, _point3). It computes the plane's normal and the distance from the origin. More...

FWMATH_API fwVec3d	getNormal (const fwPlane &_plane)
	Return the normal of the given plane _plane. More...

FWMATH_API void	setNormal (fwPlane &_plane, const fwVec3d &_normal)
	Set the normal of the given plane _plane. More...

FWMATH_API double	getDistance (const fwPlane &_plane)
	Get the distance from origin for the given plan (_plane). More...

FWMATH_API void	setDistance (fwPlane &_plane, const double _distance)
	Set the distance from origin (_distance) for the given plan (_plane). More...

FWMATH_API bool	intersect (const fwPlane &_fwPlane, const fwLine &_line, fwVec3d &_point)
	Give the intersection between a plane and a line. The result is returned in a point (_point) More...

FWMATH_API bool	isInHalfSpace (const fwPlane &_plane, const fwVec3d &_point)
	Compute if a point is in a half plane. More...

FWMATH_API void	transform (fwPlane &_plane, const fwMatrix4x4 &_matrix)
	Apply a transformation to a plane. The transformation is defined by a matrix 4x4. More...

FWMATH_API void	offset (fwPlane &_plane, double _offset)
	Add an offset at the distance of origin which define the plane (_plane). More...

FWMATH_API double	normalize (fwVec3d &vec)
	Normalize a vector.

FWMATH_API fwVec3d	normalized (const fwVec3d &vec)
	Return a normalized vector. More...

FWMATH_API double	dot (const fwVec3d &v1, const fwVec3d &v2)
	Compute the Dot product between two vectors. More...

FWMATH_API fwVec3d	cross (const fwVec3d &v1, const fwVec3d &v2)
	Compute the Cross product between two vectors. More...

FWMATH_API double	vecLength (const fwVec3d &_vec)
	Compute the length of the vector. More...

FWMATH_API void	negate (fwVec3d &_vec)
	Compute the negate of the vector. More...

Detailed Description

The namespace fwMath contains classes which provide the implementation of several mathematic functions and objects (plane, line, point).

Function Documentation

bool fwMath::closeSurface	(	fwVertexPosition &	_vertex,
		fwVertexIndex &	_vertexIndex
	)

Closes the surface if necessary.

Returns: True if container mesh is changed

Definition at line 239 of file MeshFunctions.cpp.

fwVec3d fwMath::cross	(	const fwVec3d &	v1,
		const fwVec3d &	v2
	)

Compute the Cross product between two vectors.

Parameters

[in]	v1
[in]	v2

Returns: the cross product.

Definition at line 47 of file VectorFunctions.cpp.

Referenced by intersect().

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double fwMath::dot	(	const fwVec3d &	v1,
		const fwVec3d &	v2
	)

Compute the Dot product between two vectors.

Parameters

[in]	v1
[in]	v2

Returns: the dot product.

Definition at line 39 of file VectorFunctions.cpp.

Referenced by intersect().

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fwVec3d fwMath::getClosestPoint	(	const fwLine &	_ray,
		const fwVec3d &	_point
	)

Compute the projection of a point in a given direction.

Parameters

[in]	_ray	ray (origin,direction). Direction vector is assumed be normalized.
[in]	_point	point to be projected

Returns: closest point of the line if an intersection is found.

Definition at line 56 of file LineFunctions.cpp.

Referenced by intersect().

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bool fwMath::getClosestPoints	(	const fwLine &	_ray1,
		const fwLine &	_ray2,
		fwVec3d &	_pointOnThis,
		fwVec3d &	_pointOnfwLine
	)

Compute the closest points between two rays.

Parameters

[in]	_ray1	ray (origin,direction). Direction vector is assumed be normalized.
[in]	_ray2	ray (origin,direction). Direction vector is assumed be normalized.
[out]	_pointOnThis	intersection point.
[out]	_pointOnfwLine	barycenter of the triangle defined by the three points of the place. Return FALSE if the lines are parallel, TRUE otherwise. p1 + t1 * d1 p2 + t2 * d2 (p2 - p1 + t2 * d2 - t1 * d1) * d1 = 0 (p2 - p1 + t2 * d2 - t1 * d1) * d2 = 0 t2 * (d2.d1) - t1 = (p1 - p2).d1 t2 - t1 * (d1.d2) = (p1 - p2).d2 delta = 1 - (d1.d2)*2 t2 = [ d2.(p1-p2) - d1.(p1-p2) (d1.d2)]/delta t1 = [-d1.(p1-p2) + d2.(p1-p2) * (d1.d2)]/delta

Definition at line 21 of file LineFunctions.cpp.

Referenced by intersect().

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double fwMath::getDistance ( const fwPlane & _plane )

Get the distance from origin for the given plan (_plane).

Parameters

[in] _plane

Returns: the distance of origin of the plane.

Definition at line 73 of file PlaneFunctions.cpp.

Referenced by offset().

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fwMatrix4x4 fwMath::getInverse ( const fwMatrix4x4 & matrix )

Computes the inverse of a matrix.

Parameters

[in] matrix

Returns: inverted matrix

Definition at line 39 of file MatrixFunctions.cpp.

fwVec3d fwMath::getNormal ( const fwPlane & _plane )

Return the normal of the given plane _plane.

Parameters

[in] _plane

Returns: the normalize normal of the plane.

Definition at line 54 of file PlaneFunctions.cpp.

Referenced by intersect().

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fwPlane fwMath::getPlane	(	const fwVec3d &	_normal,
		const fwVec3d &	_point
	)

compute a plane from a normal and a point which must be in the plane.

Parameters

[in]	_point	a point of the plan/
[in]	_normal	the normal of the new plane.

Returns: the new plane.

Definition at line 171 of file PlaneFunctions.cpp.

fwMatrix4x4 fwMath::getRotationMatrix ( const fwVec3d & _vecNorm )

Compute a matrix rotation.

Deprecated:: The function implementation seems very dodgy, prefer ::glm::yawPitchRoll() or ::glm::orientate4()

Parameters

[in] _vecNorm

Returns: rotation matrix

Definition at line 60 of file MatrixFunctions.cpp.

bool fwMath::intersect	(	const fwLine &	_ray,
		double	_radius,
		const fwVec3d &	_point
	)

Compute the projection of a point in a given direction and test if this intersection is inside a given radius.

Parameters

[in]	_ray	ray (origin,direction). Direction vector is assumed be normalized.
[in]	_radius	maximum distance of the point
[in]	_point	point to be projected

Returns: closest point of the line if an intersection is found.

Definition at line 75 of file LineFunctions.cpp.

References getClosestPoint().

Referenced by intersect().

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bool fwMath::intersect	(	const fwLine &	_line,
		double	_radius,
		const fwVec3d &	_origin,
		const fwVec3d &	_direction,
		fwVec3d &	_point
	)

Compute the closest points between two rays and test these points lie inside a sphere of a given radius.

Parameters

[in]	_line	ray (origin,direction). Direction vector is assumed be normalized.
[in]	_radius	maximum distance of the point
[in]	_origin	origin of the second ray
[in]	_direction	direction of the second ray
[in]	_point	point to be projected

Returns: closest point of the line if an intersection is found.

Definition at line 87 of file LineFunctions.cpp.

References getClosestPoints().

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bool fwMath::intersect	(	const fwPlane &	_fwPlane,
		const fwLine &	_line,
		fwVec3d &	_point
	)

Give the intersection between a plane and a line. The result is returned in a point (_point)

Parameters

[in]	_fwPlane
[in]	_line
[out]	_point	intersection point.

Returns: true if an intersection is found.

Definition at line 87 of file PlaneFunctions.cpp.

bool fwMath::intersect	(	const fwLine &	_line,
		const fwVec3d &	_v1,
		const fwVec3d &	_v2,
		const fwVec3d &	_v3,
		fwVec3d &	_point,
		fwVec3d &	_barycentric,
		bool &	_front
	)

Give the intersection between a plane and a line. The result is returned in a point (_point).

Deprecated:: This function was added for a specific purpose and will be removed in a future release.

Parameters

[in]	_line	input line (2 positions)
[in]	_v1	first point of the plane
[in]	_v2	second point of the plane
[in]	_v3	third point of the plane
[out]	_point	intersection point.
[out]	_barycentric	barycenter of the triangle defined by the three points of the plane.
[out]	_front	true if the dot product of the plane normal and ths positive Z axis (0,0,1) is positive.

Returns: true if an intersection is found.

Definition at line 106 of file LineFunctions.cpp.

References cross(), dot(), getNormal(), and intersect().

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template<typename CONTAINER >

bool fwMath::isContainerEqual	(	CONTAINER &	containerA,
		CONTAINER &	containerB,
		const float	epsilon = `0.00001F`
	)

Returns true iff container a and b are equal with 'epsilon' error margin.

Parameters

containerA	container to compare
containerB	container to compare
epsilon	: error margin

Returns: true iff container a and b are equal with 'epsilon' error margin

Definition at line 36 of file Compare.hpp.

References isEqual().

Referenced by fwDataTools::Image::mergeMask().

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template<typename TYPE >

bool fwMath::isEqual	(	TYPE	a,
		TYPE	b,
		const float	epsilon = `0.00001F`
	)

Returns true iff a and b are equal with 'epsilon' error margin.

Parameters

a	value to compare
b	value to compare
epsilon	: error margin

Returns: true iff a and b are equal with 'epsilon' error margin

Definition at line 23 of file Compare.hpp.

Referenced by isContainerEqual().

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bool fwMath::isInHalfSpace	(	const fwPlane &	_plane,
		const fwVec3d &	_point
	)

Compute if a point is in a half plane.

Parameters

[in]	_plane
[in]	_point

Returns: true if point is in a half plane.

Definition at line 117 of file PlaneFunctions.cpp.

void fwMath::multVecMatrix	(	const fwMatrix4x4 &	_matrix,
		const fwVec3d &	_source,
		fwVec3d &	_dest
	)

Multiply a matrix by a vector.

Parameters

[in]	_matrix
[in]	_source
[out]	_dest

Definition at line 19 of file MatrixFunctions.cpp.

void fwMath::negate ( fwVec3d & _vec )

Compute the negate of the vector.

Parameters

[in]	_vec
[out]	_vec

Definition at line 67 of file VectorFunctions.cpp.

fwVec3d fwMath::normalized ( const fwVec3d & vec )

Return a normalized vector.

Parameters

[in] vec vector to normalize

Returns: normalized vector

Definition at line 30 of file VectorFunctions.cpp.

References normalize().

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void fwMath::offset	(	fwPlane &	_plane,
		double	_offset
	)

Add an offset at the distance of origin which define the plane (_plane).

Parameters

[in]	_plane
[in]	_offset
[out]	_plane

Definition at line 162 of file PlaneFunctions.cpp.

References getDistance(), and setDistance().

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bool fwMath::removeOrphanVertices	(	fwVertexPosition &	_vertex,
		fwVertexIndex &	_vertexIndex
	)

remove orphan vertices (i.e not used in _vertexIndex), _vertexIndex is reordered according to vertex suppressions

Definition at line 280 of file MeshFunctions.cpp.

void fwMath::setDistance	(	fwPlane &	_plane,
		const double	_distance
	)

Set the distance from origin (_distance) for the given plan (_plane).

Parameters

[in]	_distance
[in]	_plane

Returns: [out] _plane

Definition at line 80 of file PlaneFunctions.cpp.

Referenced by offset().

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void fwMath::setNormal	(	fwPlane &	_plane,
		const fwVec3d &	_normal
	)

Set the normal of the given plane _plane.

Parameters

[in]	_plane
[in]	_normal

Definition at line 61 of file PlaneFunctions.cpp.

void fwMath::setValues	(	fwPlane &	_plane,
		const fwVec3d &	_point1,
		const fwVec3d &	_point2,
		const fwVec3d &	_point3
	)

Initialize a plane _plane with three points (_point1, _point2, _point3). It computes the plane's normal and the distance from the origin.

Parameters

[out]	_plane	the new plane.
[in]	_point1	a point of the plan.
[in]	_point2	a point of the plan.
[in]	_point3	a point of the plan.

Definition at line 30 of file PlaneFunctions.cpp.

void fwMath::transform	(	fwPlane &	_plane,
		const fwMatrix4x4 &	_matrix
	)

Apply a transformation to a plane. The transformation is defined by a matrix 4x4.

Parameters

[in]	_plane
[in]	_matrix
[out]	_plane

Definition at line 128 of file PlaneFunctions.cpp.

double fwMath::vecLength ( const fwVec3d & _vec )

Compute the length of the vector.

Parameters

[in] _vec

Returns: the vector's length

Definition at line 59 of file VectorFunctions.cpp.

Referenced by normalize().

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