Aim: Represent a triangle drawn onto a sphere of radius 1. More...

#include <DGtal/geometry/tools/SphericalTriangle.h>

Public Member Functions
	~SphericalTriangle ()

	SphericalTriangle (const RealVector &va, const RealVector &vb, const RealVector &vc, bool normalize=true)
	Default constructor. The object is invalid. More...

	SphericalTriangle (const SphericalTriangle &other)=default

SphericalTriangle &	operator= (const SphericalTriangle &other)=default

const RealVector &	A () const

const RealVector &	B () const

const RealVector &	C () const

void	setA (const RealVector &va, bool normalize=true)

void	setB (const RealVector &vb, bool normalize=true)

void	setC (const RealVector &vc, bool normalize=true)

bool	isDegenerate () const

Self	polarTriangle () const

void	interiorAngles (Scalar &alpha, Scalar &beta, Scalar &gamma) const

Scalar	area () const

Scalar	algebraicArea () const

Protected Attributes
RealVector	myA
	The point A of the triangle ABC, of unit length. More...

RealVector	myB
	The point B of the triangle ABC, of unit length. More...

RealVector	myC
	The point C of the triangle ABC, of unit length. More...

Private Types
typedef TSpace	Space

typedef SphericalTriangle< Space >	Self

typedef Space::RealPoint	RealPoint

typedef Space::RealVector	RealVector

typedef RealVector::Component	Scalar

Private Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CSpace< TSpace >))

	BOOST_STATIC_ASSERT ((Space::dimension==3))

Detailed Description

template<typename TSpace>
class DGtal::SphericalTriangle< TSpace >

Aim: Represent a triangle drawn onto a sphere of radius 1.

Description of class 'SphericalTriangle'

Template Parameters

TSpace any type of 3-dimensional digital space.

Definition at line 61 of file SphericalTriangle.h.

Member Typedef Documentation

◆ RealPoint

template<typename TSpace >

typedef Space::RealPoint DGtal::SphericalTriangle< TSpace >::RealPoint

private

Definition at line 66 of file SphericalTriangle.h.

◆ RealVector

template<typename TSpace >

typedef Space::RealVector DGtal::SphericalTriangle< TSpace >::RealVector

private

Definition at line 67 of file SphericalTriangle.h.

◆ Scalar

template<typename TSpace >

typedef RealVector::Component DGtal::SphericalTriangle< TSpace >::Scalar

private

Definition at line 68 of file SphericalTriangle.h.

◆ Self

template<typename TSpace >

typedef SphericalTriangle<Space> DGtal::SphericalTriangle< TSpace >::Self

private

Definition at line 65 of file SphericalTriangle.h.

◆ Space

template<typename TSpace >

typedef TSpace DGtal::SphericalTriangle< TSpace >::Space

private

Definition at line 64 of file SphericalTriangle.h.

Constructor & Destructor Documentation

◆ ~SphericalTriangle()

template<typename TSpace >

DGtal::SphericalTriangle< TSpace >::~SphericalTriangle ( )

inline

Destructor.

Definition at line 79 of file SphericalTriangle.h.

79{}

◆ SphericalTriangle() [1/2]

template<typename TSpace >

DGtal::SphericalTriangle< TSpace >::SphericalTriangle	(	const RealVector &	va,
		const RealVector &	vb,
		const RealVector &	vc,
		bool	normalize = `true`
	)

inline

Default constructor. The object is invalid.

Definition at line 82 of file SphericalTriangle.h.

    {
      setA( va, normalize );
      setB( vb, normalize );
      setC( vc, normalize );
    }

References DGtal::SphericalTriangle< TSpace >::setA(), DGtal::SphericalTriangle< TSpace >::setB(), and DGtal::SphericalTriangle< TSpace >::setC().

◆ SphericalTriangle() [2/2]

template<typename TSpace >

DGtal::SphericalTriangle< TSpace >::SphericalTriangle ( const SphericalTriangle< TSpace > & other )

default

Copy constructor.

Parameters

other the object to clone.

Member Function Documentation

◆ A()

template<typename TSpace >

const RealVector & DGtal::SphericalTriangle< TSpace >::A ( ) const

inline

Returns: the point A of the spherical triangle.

Definition at line 104 of file SphericalTriangle.h.

104{ return myA; }

DGtal::SphericalTriangle::myA

RealVector myA

The point A of the triangle ABC, of unit length.

Definition: SphericalTriangle.h:231

References DGtal::SphericalTriangle< TSpace >::myA.

Referenced by DGtal::SphericalTriangle< TSpace >::interiorAngles().

◆ algebraicArea()

template<typename TSpace >

Scalar DGtal::SphericalTriangle< TSpace >::algebraicArea ( ) const

inline

Returns: the (signed) area of the spherical triangle (below 2pi).

Definition at line 217 of file SphericalTriangle.h.

    {
      Scalar     S = area();
      RealVector M = myA + myB + myC;
      RealVector X = ( myB - myA ).crossProduct( myC - myA );
      if ( M.norm1() <= 1e-8 || X.norm1() <= 1e-8 ) return 0.0;
      return M.dot( X ) < 0.0 ? -S : S;
    }

References DGtal::SphericalTriangle< TSpace >::area(), DGtal::crossProduct(), DGtal::PointVector< dim, TEuclideanRing, TContainer >::dot(), DGtal::SphericalTriangle< TSpace >::myA, DGtal::SphericalTriangle< TSpace >::myB, DGtal::SphericalTriangle< TSpace >::myC, and DGtal::PointVector< dim, TEuclideanRing, TContainer >::norm1().

Referenced by DGtal::CorrectedNormalCurrentFormula< TRealPoint, TRealVector >::mu2InterpolatedU().

◆ area()

template<typename TSpace >

Scalar DGtal::SphericalTriangle< TSpace >::area ( ) const

inline

Returns: the (unsigned) area of the spherical triangle (below 2pi).

Definition at line 207 of file SphericalTriangle.h.

    {
      Scalar alpha, beta, gamma;
      if ( isDegenerate() ) return 0.0;
      interiorAngles( alpha, beta, gamma );
      return ( (alpha == 0.0) || (beta == 0.0) || (gamma == 0.0) )
               ? 0.0 : 2.0*M_PI - alpha - beta - gamma;
    }

References DGtal::SphericalTriangle< TSpace >::interiorAngles(), and DGtal::SphericalTriangle< TSpace >::isDegenerate().

Referenced by DGtal::SphericalTriangle< TSpace >::algebraicArea().

◆ B()

template<typename TSpace >

const RealVector & DGtal::SphericalTriangle< TSpace >::B ( ) const

inline

Returns: the point B of the spherical triangle.

Definition at line 106 of file SphericalTriangle.h.

106{ return myB; }

References DGtal::SphericalTriangle< TSpace >::myB.

Referenced by DGtal::SphericalTriangle< TSpace >::interiorAngles().

◆ BOOST_CONCEPT_ASSERT()

template<typename TSpace >

DGtal::SphericalTriangle< TSpace >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >) )

private

◆ BOOST_STATIC_ASSERT()

template<typename TSpace >

DGtal::SphericalTriangle< TSpace >::BOOST_STATIC_ASSERT ( (Space::dimension==3) )

private

◆ C()

template<typename TSpace >

const RealVector & DGtal::SphericalTriangle< TSpace >::C ( ) const

inline

Returns: the point C of the spherical triangle.

Definition at line 108 of file SphericalTriangle.h.

108{ return myC; }

References DGtal::SphericalTriangle< TSpace >::myC.

Referenced by DGtal::SphericalTriangle< TSpace >::interiorAngles().

◆ interiorAngles()

template<typename TSpace >

void DGtal::SphericalTriangle< TSpace >::interiorAngles	(	Scalar &	alpha,
		Scalar &	beta,
		Scalar &	gamma
	)		const

inline

Returns the interior angles of the spherical triangle ABC.

Parameters

[out]	alpha	the interior angle at vertex A.
[out]	beta	the interior angle at vertex B.
[out]	gamma	the interior angle at vertex C.

Definition at line 190 of file SphericalTriangle.h.

    {
      Self    T = polarTriangle();
      if ( T.A() == RealVector::zero || T.B() == RealVector::zero || T.C() == RealVector::zero )
        alpha = beta = gamma = 0.0;
      else
        {
          Scalar ca = std::max( -1.0, std::min( 1.0, T.B().dot( T.C() ) ) );
          Scalar cb = std::max( -1.0, std::min( 1.0, T.C().dot( T.A() ) ) );
          Scalar cc = std::max( -1.0, std::min( 1.0, T.A().dot( T.B() ) ) );
          alpha     = acos( ca );
          beta      = acos( cb );
          gamma     = acos( cc );
        }
    }

References DGtal::SphericalTriangle< TSpace >::A(), DGtal::SphericalTriangle< TSpace >::B(), DGtal::SphericalTriangle< TSpace >::C(), DGtal::PointVector< dim, TEuclideanRing, TContainer >::dot(), DGtal::SphericalTriangle< TSpace >::polarTriangle(), and DGtal::PointVector< dim, TEuclideanRing, TContainer >::zero.

Referenced by DGtal::SphericalTriangle< TSpace >::area().

◆ isDegenerate()

template<typename TSpace >

bool DGtal::SphericalTriangle< TSpace >::isDegenerate ( ) const

inline

Returns: 'true' if the spherical triangle is too small or too thin.

Definition at line 158 of file SphericalTriangle.h.

    {
      Scalar d[ 3 ] = { ( myA - myB ).norm(),
                        ( myA - myC ).norm(),
                        ( myB - myC ).norm() };
      // Checks that the spherical triangle is small or thin.
      if ( ( d[ 0 ] < 1e-8 ) || ( d[ 1 ] < 1e-8 ) || ( d[ 2 ] < 1e-8 ) )
        return true;
      // Checks that the spherical triangle is flat.
      Dimension m = 0;
      if ( d[ 1 ] > d[ m ] ) m = 1;
      if ( d[ 2 ] > d[ m ] ) m = 2;
      return ( fabs( d[ m ] - d[ (m+1)%3 ] - d[ (m+2)%3 ] ) < 1e-8 );
    }

References DGtal::SphericalTriangle< TSpace >::myA, DGtal::SphericalTriangle< TSpace >::myB, and DGtal::SphericalTriangle< TSpace >::myC.

Referenced by DGtal::SphericalTriangle< TSpace >::area().

◆ operator=()

template<typename TSpace >

SphericalTriangle & DGtal::SphericalTriangle< TSpace >::operator= ( const SphericalTriangle< TSpace > & other )

default

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'.

◆ polarTriangle()

template<typename TSpace >

Self DGtal::SphericalTriangle< TSpace >::polarTriangle ( ) const

inline

Returns: the polar triangle associated with this triangle.

Definition at line 174 of file SphericalTriangle.h.

    {
      auto Ap = myB.crossProduct(myC);
      auto Bp = myC.crossProduct(myA);
      auto Cp = myA.crossProduct(myB);
      // Reorient points.
      if ( Ap.dot( myA ) < 0.0 ) Ap = -Ap;
      if ( Bp.dot( myB ) < 0.0 ) Bp = -Bp;
      if ( Cp.dot( myC ) < 0.0 ) Cp = -Cp;
      return Self( Ap, Bp, Cp, true );
    }

References DGtal::PointVector< dim, TEuclideanRing, TContainer >::crossProduct(), DGtal::SphericalTriangle< TSpace >::myA, DGtal::SphericalTriangle< TSpace >::myB, and DGtal::SphericalTriangle< TSpace >::myC.

Referenced by DGtal::SphericalTriangle< TSpace >::interiorAngles().

◆ setA()

template<typename TSpace >

void DGtal::SphericalTriangle< TSpace >::setA	(	const RealVector &	va,
		bool	normalize = `true`
	)

inline

Sets the point A of the triangle.

Parameters

va	the new point A
normalize	if true, force normalization, otherwise va should be of unit length.

Definition at line 115 of file SphericalTriangle.h.

    {
      myA = va;
      if ( normalize )
        {
          Scalar n = myA.norm();
          if ( fabs( n ) > 1e-8 ) myA /= n;
          else myA = RealVector::zero;
        }
    }

References DGtal::SphericalTriangle< TSpace >::myA, DGtal::PointVector< dim, TEuclideanRing, TContainer >::norm(), and DGtal::PointVector< dim, TEuclideanRing, TContainer >::zero.

Referenced by DGtal::SphericalTriangle< TSpace >::SphericalTriangle().

◆ setB()

template<typename TSpace >

void DGtal::SphericalTriangle< TSpace >::setB	(	const RealVector &	vb,
		bool	normalize = `true`
	)

inline

Sets the point B of the triangle.

Parameters

vb	the new point B
normalize	if true, force normalization, otherwise vb should be of unit length.

Definition at line 131 of file SphericalTriangle.h.

    {
      myB = vb;
      if ( normalize )
        {
          Scalar n = myB.norm();
          if ( fabs( n ) > 1e-8 ) myB /= n;
          else myB = RealVector::zero;
        }
    }

References DGtal::SphericalTriangle< TSpace >::myB, DGtal::PointVector< dim, TEuclideanRing, TContainer >::norm(), and DGtal::PointVector< dim, TEuclideanRing, TContainer >::zero.

Referenced by DGtal::SphericalTriangle< TSpace >::SphericalTriangle().

◆ setC()

template<typename TSpace >

void DGtal::SphericalTriangle< TSpace >::setC	(	const RealVector &	vc,
		bool	normalize = `true`
	)

inline

Sets the point C of the triangle.

Parameters

vc	the new point C
normalize	if true, force normalization, otherwise vc should be of unit length.

Definition at line 146 of file SphericalTriangle.h.

    {
      myC = vc;
      if ( normalize )
        {
          Scalar n = myC.norm();
          if ( fabs( n ) > 1e-8 ) myC /= n;
          else myC = RealVector::zero;
        }
    }