Common geometry operations. More...

Collaboration diagram for Geometry toolbox:

Functions
template<class T , class U , typename Int >
T	GeometryToolbox::SquaredDistance (Int nDim, const T a, const U b)

template<class T , class U , typename Int >
T	GeometryToolbox::Distance (Int nDim, const T a, const U b)

template<class T , typename Int >
void	GeometryToolbox::Distance (Int nDim, const T a, const T b, T *d)
	d = a-b

template<class T , typename Int >
void	GeometryToolbox::PointPointReflect (Int nDim, const T a, const T b, T *d)
	Reflect a at b: c = 2*b - a.

template<class T , typename Int >
T	GeometryToolbox::DotProduct (Int nDim, const T a, const T b)

template<class T , typename Int >
T	GeometryToolbox::SquaredNorm (Int nDim, const T *a)

template<class T , typename Int >
T	GeometryToolbox::Norm (Int nDim, const T *a)

template<class T , typename Int >
T	GeometryToolbox::NormalDistance (Int nDim, const T n, const T a, const T *b)
	dn = max(abs(n.(a-b)), 0.05 * \|\|a-b\|\|

template<class T >
void	GeometryToolbox::CrossProduct (const T a, const T b, T *c)
	c = a x b

template<class T , int nDim>
T	GeometryToolbox::LinePlaneIntersection (const T l0, const T d, const T p0, const T n, T *c)
	Compute the coordinate (c) where the line defined by coordinate l0 and direction d intersects the plane defined by point p0 and normal n.

template<class T , int nDim>
T	GeometryToolbox::PointPlaneProjection (const T p1, const T p0, const T n, T c)
	Compute the coordinate (c) where point p1 intersects the plane defined by point p0 and normal n if projected perpendicular to it.

template<class T , class U >
void	GeometryToolbox::LineNormal (const T &coords, U *normal)
	Set U as the normal to a 2D line defined by coords[iPoint][iDim].

template<class T , class U >
void	GeometryToolbox::TriangleNormal (const T &coords, U *normal)
	Normal vector of a triangle, cross product of two sides.

template<class T , class U >
void	GeometryToolbox::QuadrilateralNormal (const T &coords, U *normal)
	Normal vector of a quadrilateral, cross product of the two diagonals.

template<class T , class U >
U	GeometryToolbox::PointToPlaneDistance (const T &coords, const U *point)
	Signed distance from a point to a plane defined by 3 coordinates.

template<class Scalar , class Matrix >
void	GeometryToolbox::RotationMatrix (Scalar theta, Scalar phi, Scalar psi, Matrix &mat)
	Compute a 3D rotation matrix.

template<class Scalar , class Matrix >
void	GeometryToolbox::RotationMatrix (Scalar psi, Matrix &mat)
	Compute a 2D rotation matrix.

template<class Scalar , int nDim>
void	GeometryToolbox::Rotate (const Scalar R[][nDim], const Scalar O, const Scalar d, Scalar *c)
	Apply a rotation matrix (R) about origin (O) to a point at distance (d) from it to obtain new coordinate (c).

template<class Scalar >
bool	GeometryToolbox::HasRotation (const Scalar *angles)

template<class Scalar , int nDim>
void	GeometryToolbox::RotateBox (const Scalar R[][nDim], Scalar vMin, Scalar vMax)
	Rotate component bounds in place, enclosing the rotated box.

template<class Mat , class Scalar , class Int >
void	GeometryToolbox::TangentProjection (Int nDim, const Mat &tensor, const Scalar vector, Scalar proj)
	Tangent projection

Detailed Description

Common geometry operations.

Function Documentation

◆ CrossProduct()

template<class T >

void GeometryToolbox::CrossProduct	(	const T *	a,
		const T *	b,
		T *	c
	)

inline

c = a x b

◆ Distance() [1/2]

template<class T , typename Int >

void GeometryToolbox::Distance	(	Int	nDim,
		const T *	a,
		const T *	b,
		T *	d
	)

inline

d = a-b

◆ Distance() [2/2]

template<class T , class U , typename Int >

T GeometryToolbox::Distance	(	Int	nDim,
		const T *	a,
		const U *	b
	)

inline

Returns: ||a-b||

◆ DotProduct()

template<class T , typename Int >

T GeometryToolbox::DotProduct	(	Int	nDim,
		const T *	a,
		const T *	b
	)

inline

Returns: a.b

◆ HasRotation()

template<class Scalar >

bool GeometryToolbox::HasRotation ( const Scalar * angles )

inline

Returns: Whether any of the three supplied rotation angles is nonzero.

◆ LineNormal()

template<class T , class U >

void GeometryToolbox::LineNormal	(	const T &	coords,
		U *	normal
	)

inline

Set U as the normal to a 2D line defined by coords[iPoint][iDim].

◆ LinePlaneIntersection()

template<class T , int nDim>

T GeometryToolbox::LinePlaneIntersection	(	const T *	l0,
		const T *	d,
		const T *	p0,
		const T *	n,
		T *	c
	)

inline

Compute the coordinate (c) where the line defined by coordinate l0 and direction d intersects the plane defined by point p0 and normal n.

Returns: The intersection distance.

◆ Norm()

template<class T , typename Int >

T GeometryToolbox::Norm	(	Int	nDim,
		const T *	a
	)

inline

Returns: ||a||

◆ NormalDistance()

template<class T , typename Int >

T GeometryToolbox::NormalDistance	(	Int	nDim,
		const T *	n,
		const T *	a,
		const T *	b
	)

inline

dn = max(abs(n.(a-b)), 0.05 * ||a-b||

◆ PointPlaneProjection()

template<class T , int nDim>

T GeometryToolbox::PointPlaneProjection	(	const T *	p1,
		const T *	p0,
		const T *	n,
		T *	c
	)

inline

Compute the coordinate (c) where point p1 intersects the plane defined by point p0 and normal n if projected perpendicular to it.

Returns: The normal distance.

◆ PointPointReflect()

template<class T , typename Int >

void GeometryToolbox::PointPointReflect	(	Int	nDim,
		const T *	a,
		const T *	b,
		T *	d
	)

inline

Reflect a at b: c = 2*b - a.

◆ PointToPlaneDistance()

template<class T , class U >

U GeometryToolbox::PointToPlaneDistance	(	const T &	coords,
		const U *	point
	)

inline

Signed distance from a point to a plane defined by 3 coordinates.

◆ QuadrilateralNormal()

template<class T , class U >

void GeometryToolbox::QuadrilateralNormal	(	const T &	coords,
		U *	normal
	)

inline

Normal vector of a quadrilateral, cross product of the two diagonals.

◆ Rotate()

template<class Scalar , int nDim>

void GeometryToolbox::Rotate	(	const Scalar	R[][nDim],
		const Scalar *	O,
		const Scalar *	d,
		Scalar *	c
	)

inline

Apply a rotation matrix (R) about origin (O) to a point at distance (d) from it to obtain new coordinate (c).

◆ RotateBox()

template<class Scalar , int nDim>

void GeometryToolbox::RotateBox	(	const Scalar	R[][nDim],
		Scalar *	vMin,
		Scalar *	vMax
	)

inline

Rotate component bounds in place, enclosing the rotated box.

◆ RotationMatrix() [1/2]

template<class Scalar , class Matrix >

void GeometryToolbox::RotationMatrix	(	Scalar	psi,
		Matrix &	mat
	)

inline

Compute a 2D rotation matrix.

◆ RotationMatrix() [2/2]

template<class Scalar , class Matrix >

void GeometryToolbox::RotationMatrix	(	Scalar	theta,
		Scalar	phi,
		Scalar	psi,
		Matrix &	mat
	)

inline

Compute a 3D rotation matrix.

Note: The implicit ordering is rotation about the x, y, and then z axis.

◆ SquaredDistance()

template<class T , class U , typename Int >

T GeometryToolbox::SquaredDistance	(	Int	nDim,
		const T *	a,
		const U *	b
	)

inline

Returns: ||a-b||^2

◆ SquaredNorm()

template<class T , typename Int >

T GeometryToolbox::SquaredNorm	(	Int	nDim,
		const T *	a
	)

inline

Returns: ||a||^2

◆ TangentProjection()

template<class Mat , class Scalar , class Int >

void GeometryToolbox::TangentProjection	(	Int	nDim,
		const Mat &	tensor,
		const Scalar *	vector,
		Scalar *	proj
	)

inline

Tangent projection

◆ TriangleNormal()

template<class T , class U >

void GeometryToolbox::TriangleNormal	(	const T &	coords,
		U *	normal
	)

inline

Normal vector of a triangle, cross product of two sides.

Functions

Detailed Description

Function Documentation

◆ CrossProduct()

◆ Distance() [1/2]

◆ Distance() [2/2]

◆ DotProduct()

◆ HasRotation()

◆ LineNormal()

◆ LinePlaneIntersection()

◆ Norm()

◆ NormalDistance()

◆ PointPlaneProjection()

◆ PointPointReflect()

◆ PointToPlaneDistance()

◆ QuadrilateralNormal()

◆ Rotate()

◆ RotateBox()

◆ RotationMatrix() [1/2]

◆ RotationMatrix() [2/2]

◆ SquaredDistance()

◆ SquaredNorm()

◆ TangentProjection()

◆ TriangleNormal()