til::geo Namespace Reference

Classes
struct	AreIntersecting
	A namespace structure collecting geometrical object intersection algorithms. More...
struct	IsIncludedIn
	A namespace structure collecting geometrical object inclusion algorithms. More...
struct	Project
	A namespace structure collecting geometrical projection algorithms. More...
class	Triangle2Segment
	Approximate an ill-conditionned triangle by a segment. More...
class	TriangleNormal
	Compute the normal of a triangle. More...

Functions
template<typename T >
T	herons_formula (T a, T b, T c)
	Heron's formula. More...
template<typename T >
T	herons_formula (numeric_array< T, 3 > const &lengths)
	Heron's formula. More...
template<typename T >
T	law_of_cosines (T a, T b, T c)
	Returns the cosine of angle A given the lengths of the triangle edges. More...
template<typename T >
T	law_of_tangents (T a, T b, T c, T area)
	Returns the tangent of angle A given the area and the lengths of the edges of the triangle. More...
template<typename T >
T	law_of_tangents (T a, T b, T c)
	Returns the tangent of angle A given the lengths of the edges of the triangle. More...
template<typename T >
T	angle (T x, T y, T norm)
	Returns the angle between (x,y) and the x-axis, with the norm of (x,y) provided. More...
template<typename T >
T	angle (T x, T y)
	Returns the angle between (x,y) and the x-axis. More...
template<typename T >
void	cartesian2spherical (T x, T y, T z, T &theta, T &phi, T &rho)
	Converts cartesian coordinates into spherical coordinates. More...
template<typename T >
void	spherical2cartesian (T theta, T phi, T rho, T &x, T &y, T &z)
	Converts spherical coordinates into cartesian coordinates. More...
template<typename TArray >
bool	triangle2segment (const TArray &A, const TArray &B, const TArray &C, TArray &X, TArray &Y)
template<typename TArray , typename TResArray >
bool	triangle_normal (const TArray &A, const TArray &B, const TArray &C, TResArray &result)
	Compute the normal of a triangle. More...
template<typename TPrec , typename TPoint >
bool	is_in_circumcircle (const TPoint &p, const TPoint &a, const TPoint &b, const TPoint &c)
	Check whether a point lies within the circumcircle of a given triangle. More...

Function Documentation

angle() [1/2]

template<typename T >

T til::geo::angle ( T  x, T  y, T  norm  )

inline

Returns the angle between (x,y) and the x-axis, with the norm of (x,y) provided.

NB: this version is clearly intended for fast computation and thus no checking on norm is done: in particular, you have to check yourself that the norm is not too small.

Referenced by til::myComplexPow(), til::MeshWaveletEnergy< TVertexCollection, TNeighborhoods, TPrec >::operator()(), and til::simple_delaunay_triangulation().

angle() [2/2]

template<typename T >

T til::geo::angle ( T  x, T  y  )

inline

Returns the angle between (x,y) and the x-axis.

cartesian2spherical()

template<typename T >

void til::geo::cartesian2spherical	(	T	x,
		T	y,
		T	z,
		T &	theta,
		T &	phi,
		T &	rho
	)

Converts cartesian coordinates into spherical coordinates.

herons_formula() [1/2]

template<typename T >

T til::geo::herons_formula ( T  a, T  b, T  c  )

inline

Heron's formula.

The Heron's formula yields the surface of a triangle given the length of its edges.

herons_formula() [2/2]

template<typename T >

T til::geo::herons_formula ( numeric_array< T, 3 > const &  lengths )

inline

Heron's formula.

The Heron's formula yields the surface of a triangle given the length of its edges.

is_in_circumcircle()

template<typename TPrec , typename TPoint >

bool til::geo::is_in_circumcircle ( const TPoint &  p, const TPoint &  a, const TPoint &  b, const TPoint &  c  )

inline

Check whether a point lies within the circumcircle of a given triangle.

Parameters

p	a point
a	first triangle vertex
b	second triangle vertex
c	third triangle vertex

Definition at line 750 of file geometrics.h.

Referenced by til::geo::AreIntersecting::Triangles3D< TArray >::operator()().

law_of_cosines()

template<typename T >

T til::geo::law_of_cosines ( T  a, T  b, T  c  )

inline

Returns the cosine of angle A given the lengths of the triangle edges.

law_of_tangents() [1/2]

template<typename T >

T til::geo::law_of_tangents ( T  a, T  b, T  c, T  area  )

inline

Returns the tangent of angle A given the area and the lengths of the edges of the triangle.

law_of_tangents() [2/2]

template<typename T >

T til::geo::law_of_tangents ( T  a, T  b, T  c  )

inline

Returns the tangent of angle A given the lengths of the edges of the triangle.

spherical2cartesian()

template<typename T >

void til::geo::spherical2cartesian ( T  theta, T  phi, T  rho, T &  x, T &  y, T &  z  )

inline

Converts spherical coordinates into cartesian coordinates.

triangle2segment()

template<typename TArray >

bool til::geo::triangle2segment	(	const TArray &	A,
		const TArray &	B,
		const TArray &	C,
		TArray &	X,
		TArray &	Y
	)

Definition at line 130 of file geometrics.h.

Referenced by til::geo::Project::PointOnTriangle3D< TArray, TOutputArray >::operator()().

triangle_normal()

template<typename TArray , typename TResArray >

bool til::geo::triangle_normal	(	const TArray &	A,
		const TArray &	B,
		const TArray &	C,
		TResArray &	result
	)

Compute the normal of a triangle.

Referenced by til::closest_normal(), til::geo::Project::PointOnTriangle3D< TArray, TOutputArray >::operator()(), and til::geo::AreIntersecting::Triangles3D< TArray >::operator()().