DGtal: DGtal::SurfaceMeshHelper< TRealPoint, TRealVector

Aim: An helper class for building classical meshes. More...

#include <DGtal/shapes/SurfaceMeshHelper.h>

Public Types
enum class	NormalsType { NO_NORMALS , VERTEX_NORMALS , FACE_NORMALS }

typedef TRealPoint	RealPoint

typedef TRealVector	RealVector

typedef SurfaceMeshHelper< RealPoint, RealVector >	Self

typedef DGtal::SurfaceMesh< RealPoint, RealVector >	SurfaceMesh

typedef RealVector::Component	Scalar

typedef std::vector< Scalar >	Scalars

typedef std::vector< RealVector >	RealVectors

typedef SurfaceMesh::Size	Size

typedef SurfaceMesh::Index	Index

typedef SurfaceMesh::Vertices	Vertices

typedef SurfaceMesh::Faces	Faces

Public Member Functions
	BOOST_STATIC_ASSERT ((dimension==3))

Static Public Member Functions
Sphere services
static SurfaceMesh	makeSphere (const Scalar radius, const RealPoint &center, Size m, Size n, NormalsType normals)

static Scalars	sphereMeanCurvatures (const Scalar radius, Size m, Size n)

static Scalars	sphereGaussianCurvatures (const Scalar radius, Size m, Size n)

static Scalars	sphereFirstPrincipalCurvatures (const Scalar radius, Size m, Size n)

static Scalars	sphereSecondPrincipalCurvatures (const Scalar radius, Size m, Size n)

static RealVectors	sphereFirstPrincipalDirections (const Scalar radius, Size m, Size n)

static RealVectors	sphereSecondPrincipalDirections (const Scalar radius, Size m, Size n)

Schwarz lantern services
static SurfaceMesh	makeLantern (const Scalar radius, const Scalar height, const RealPoint &center, Size m, Size n, const NormalsType normals)

static Scalars	lanternMeanCurvatures (const Scalar radius, Size m, Size n)

static Scalars	lanternGaussianCurvatures (const Scalar radius, Size m, Size n)

static Scalars	lanternFirstPrincipalCurvatures (const Scalar radius, Size m, Size n)

static Scalars	lanternSecondPrincipalCurvatures (const Scalar radius, Size m, Size n)

static RealVectors	lanternFirstPrincipalDirections (const Scalar radius, Size m, Size n)

static RealVectors	lanternSecondPrincipalDirections (const Scalar radius, Size m, Size n)

Torus services
static SurfaceMesh	makeTorus (const Scalar big_radius, const Scalar small_radius, const RealPoint &center, Size m, Size n, const int twist, const NormalsType normals)

static Scalars	torusMeanCurvatures (const Scalar big_radius, const Scalar small_radius, Size m, Size n, const int twist)

static Scalars	torusGaussianCurvatures (const Scalar big_radius, const Scalar small_radius, Size m, Size n, const int twist)

static Scalars	torusFirstPrincipalCurvatures (const Scalar big_radius, const Scalar small_radius, Size m, Size n, const int twist)

static Scalars	torusSecondPrincipalCurvatures (const Scalar big_radius, const Scalar small_radius, Size m, Size n, const int twist)

static RealVectors	torusFirstPrincipalDirections (const Scalar big_radius, const Scalar small_radius, Size m, Size n, const int twist)

static RealVectors	torusSecondPrincipalDirections (const Scalar big_radius, const Scalar small_radius, Size m, Size n, const int twist)

Static Public Attributes
static const Dimension	dimension = RealPoint::dimension

Detailed Description

template<typename TRealPoint, typename TRealVector>
struct DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >

Aim: An helper class for building classical meshes.

Description of template class 'SurfaceMeshHelper'

Template Parameters

TRealPoint	an arbitrary model of RealPoint.
TRealVector	an arbitrary model of RealVector.

Definition at line 63 of file SurfaceMeshHelper.h.

Member Typedef Documentation

◆ Faces

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMesh::Faces DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::Faces

Definition at line 78 of file SurfaceMeshHelper.h.

◆ Index

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMesh::Index DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::Index

Definition at line 76 of file SurfaceMeshHelper.h.

◆ RealPoint

template<typename TRealPoint , typename TRealVector >

typedef TRealPoint DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::RealPoint

Definition at line 65 of file SurfaceMeshHelper.h.

◆ RealVector

template<typename TRealPoint , typename TRealVector >

typedef TRealVector DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::RealVector

Definition at line 66 of file SurfaceMeshHelper.h.

◆ RealVectors

template<typename TRealPoint , typename TRealVector >

typedef std::vector<RealVector> DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::RealVectors

Definition at line 74 of file SurfaceMeshHelper.h.

◆ Scalar

template<typename TRealPoint , typename TRealVector >

typedef RealVector::Component DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::Scalar

Definition at line 72 of file SurfaceMeshHelper.h.

◆ Scalars

template<typename TRealPoint , typename TRealVector >

typedef std::vector<Scalar> DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::Scalars

Definition at line 73 of file SurfaceMeshHelper.h.

◆ Self

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMeshHelper< RealPoint, RealVector > DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::Self

Definition at line 67 of file SurfaceMeshHelper.h.

◆ Size

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMesh::Size DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::Size

Definition at line 75 of file SurfaceMeshHelper.h.

◆ SurfaceMesh

template<typename TRealPoint , typename TRealVector >

typedef DGtal::SurfaceMesh< RealPoint, RealVector > DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::SurfaceMesh

Definition at line 71 of file SurfaceMeshHelper.h.

◆ Vertices

template<typename TRealPoint , typename TRealVector >

typedef SurfaceMesh::Vertices DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::Vertices

Definition at line 77 of file SurfaceMeshHelper.h.

Member Enumeration Documentation

◆ NormalsType

template<typename TRealPoint , typename TRealVector >

enum DGtal::SurfaceMeshHelper::NormalsType

strong

Enum type for specifying if the mesh should have after construction: NO_NORMALS no normals, VERTEX_NORMALS the normals at each vertex, FACE_NORMALS the normals at each face.

Enumerator
NO_NORMALS
VERTEX_NORMALS
FACE_NORMALS

Definition at line 83 of file SurfaceMeshHelper.h.

83 { NO_NORMALS, VERTEX_NORMALS, FACE_NORMALS };

Member Function Documentation

◆ BOOST_STATIC_ASSERT()

template<typename TRealPoint , typename TRealVector >

DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::BOOST_STATIC_ASSERT ( (dimension==3) )

◆ lanternFirstPrincipalCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::lanternFirstPrincipalCurvatures	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the first principal curvature at each vertex of a Schwarz lantern of given parameters with m latitudes and n longitudes.

Parameters

[in]	radius	the radius of the lantern.
[in]	m	the number of latitudes, minimum is 2.
[in]	n	the number of longitudes, minimum is 3.

Returns: the first principal curvature at each vertex (zero).

◆ lanternFirstPrincipalDirections()

template<typename TRealPoint , typename TRealVector >

static RealVectors DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::lanternFirstPrincipalDirections	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the first principal direction at each vertex of a Schwarz lantern of given parameters with m latitudes and n longitudes.

Parameters

[in]	radius	the radius of the lantern.
[in]	m	the number of latitudes, minimum is 2.
[in]	n	the number of longitudes, minimum is 3.

Returns: the first principal direction at each vertex (z-axis).

◆ lanternGaussianCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::lanternGaussianCurvatures	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the Gaussian curvature at each vertex of a Schwarz lantern of given parameters with m latitudes and n longitudes.

Parameters

[in]	radius	the radius of the lantern.
[in]	m	the number of latitudes, minimum is 2.
[in]	n	the number of longitudes, minimum is 3.

Returns: the Gaussian curvature at each vertex.

◆ lanternMeanCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::lanternMeanCurvatures	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the mean curvature at each vertex of a Schwarz lantern of given parameters with m latitudes and n longitudes.

Parameters

[in]	radius	the radius of the lantern.
[in]	m	the number of latitudes, minimum is 2.
[in]	n	the number of longitudes, minimum is 3.

Returns: the mean curvature at each vertex.

◆ lanternSecondPrincipalCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::lanternSecondPrincipalCurvatures	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the second principal curvature at each vertex of a Schwarz lantern of given parameters with m latitudes and n longitudes.

Parameters

[in]	radius	the radius of the lantern.
[in]	m	the number of latitudes, minimum is 2.
[in]	n	the number of longitudes, minimum is 3.

Returns: the second principal curvature at each vertex (1/radius).

◆ lanternSecondPrincipalDirections()

template<typename TRealPoint , typename TRealVector >

static RealVectors DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::lanternSecondPrincipalDirections	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the second principal direction at each vertex of a Schwarz lantern of given parameters with m latitudes and n longitudes.

Parameters

[in]	radius	the radius of the lantern.
[in]	m	the number of latitudes, minimum is 2.
[in]	n	the number of longitudes, minimum is 3.

Returns: the second principal direction at each vertex (xy-plane).

◆ makeLantern()

template<typename TRealPoint , typename TRealVector >

static SurfaceMesh DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::makeLantern	(	const Scalar	radius,
		const Scalar	height,
		const RealPoint &	center,
		Size	m,
		Size	n,
		const NormalsType	normals
	)

static

Builds a surface mesh representing a Schwarz lantern with m latitudes and n longitudes.

Parameters

[in]	radius	the radius of the lantern.
[in]	height	the height of the lantern.
[in]	center	the center of the lantern.
[in]	m	the number of latitudes, minimum is 2.
[in]	n	the number of longitudes, minimum is 3.
[in]	normals	specifies built-time normals of the output mesh: NO_NORMALS no normals, VERTEX_NORMALS the normals at each vertex, FACE_NORMALS the normals at each face.

Returns: the corresponding surface mesh.

◆ makeSphere()

template<typename TRealPoint , typename TRealVector >

static SurfaceMesh DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::makeSphere	(	const Scalar	radius,
		const RealPoint &	center,
		Size	m,
		Size	n,
		NormalsType	normals
	)

static

Builds a surface mesh representing a sphere of given parameters with m latitudes (poles excluded) and n longitudes.

Parameters

[in]	radius	the radius of the sphere.
[in]	center	the center of the sphere.
[in]	m	the number of latitudes (poles excepted), minimum is 1.
[in]	n	the number of longitudes, minimum is 3.
[in]	normals	specifies built-time normals of the output mesh: NO_NORMALS no normals, VERTEX_NORMALS the normals at each vertex, FACE_NORMALS the normals at each face.

Returns: the corresponding surface mesh.

◆ makeTorus()

template<typename TRealPoint , typename TRealVector >

static SurfaceMesh DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::makeTorus	(	const Scalar	big_radius,
		const Scalar	small_radius,
		const RealPoint &	center,
		Size	m,
		Size	n,
		const int	twist,
		const NormalsType	normals
	)

static

Builds a surface mesh representing a torus with m latitudes and n longitudes.

Parameters

[in]	big_radius	the big radius of the torus.
[in]	small_radius	the small radius of the torus.
[in]	center	the center of the torus.
[in]	m	the number of latitudes, minimum is 3.
[in]	n	the number of longitudes, minimum is 3.
[in]	twist	the integer shift when visiting a whole parallel: 0 is a natural torus parameterization, +n or -n makes the visitor arriving on another parallel after one turn.
[in]	normals	specifies built-time normals of the output mesh: NO_NORMALS no normals, VERTEX_NORMALS the normals at each vertex, FACE_NORMALS the normals at each face.

Returns: the corresponding surface mesh.

◆ sphereFirstPrincipalCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::sphereFirstPrincipalCurvatures	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the first principal curvature at each vertex of a sphere of given parameters with m latitudes (poles excluded) and n longitudes.

Parameters

[in]	radius	the radius of the sphere.
[in]	m	the number of latitudes (poles excepted), minimum is 1.
[in]	n	the number of longitudes, minimum is 3.

Returns: the first principal curvature at each vertex.

◆ sphereFirstPrincipalDirections()

template<typename TRealPoint , typename TRealVector >

static RealVectors DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::sphereFirstPrincipalDirections	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the first principal direction at each vertex of a sphere of given parameters with m latitudes (poles excluded) and n longitudes.

Parameters

[in]	radius	the radius of the sphere.
[in]	m	the number of latitudes (poles excepted), minimum is 1.
[in]	n	the number of longitudes, minimum is 3.

Returns: the first principal direction at each vertex (umbilic, any tangent direction is ok).

◆ sphereGaussianCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::sphereGaussianCurvatures	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the Gaussian curvature at each vertex of a sphere of given parameters with m latitudes (poles excluded) and n longitudes.

Parameters

[in]	radius	the radius of the sphere.
[in]	m	the number of latitudes (poles excepted), minimum is 1.
[in]	n	the number of longitudes, minimum is 3.

Returns: the Gaussian curvature at each vertex.

◆ sphereMeanCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::sphereMeanCurvatures	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the mean curvature at each vertex of a sphere of given parameters with m latitudes (poles excluded) and n longitudes.

Parameters

[in]	radius	the radius of the sphere.
[in]	m	the number of latitudes (poles excepted), minimum is 1.
[in]	n	the number of longitudes, minimum is 3.

Returns: the mean curvature at each vertex.

◆ sphereSecondPrincipalCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::sphereSecondPrincipalCurvatures	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the second principal curvature at each vertex of a sphere of given parameters with m latitudes (poles excluded) and n longitudes.

Parameters

[in]	radius	the radius of the sphere.
[in]	m	the number of latitudes (poles excepted), minimum is 1.
[in]	n	the number of longitudes, minimum is 3.

Returns: the second principal curvature at each vertex.

◆ sphereSecondPrincipalDirections()

template<typename TRealPoint , typename TRealVector >

static RealVectors DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::sphereSecondPrincipalDirections	(	const Scalar	radius,
		Size	m,
		Size	n
	)

static

Returns the second principal direction at each vertex of a sphere of given parameters with m latitudes (poles excluded) and n longitudes.

Parameters

[in]	radius	the radius of the sphere.
[in]	m	the number of latitudes (poles excepted), minimum is 1.
[in]	n	the number of longitudes, minimum is 3.

Returns: the second principal direction at each vertex (umbilic, any tangent direction is ok).

◆ torusFirstPrincipalCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::torusFirstPrincipalCurvatures	(	const Scalar	big_radius,
		const Scalar	small_radius,
		Size	m,
		Size	n,
		const int	twist
	)

static

Returns the first principal curvature at each vertex of a torus of given parameters with m latitudes and n longitudes.

Parameters

[in]	big_radius	the big radius of the torus.
[in]	small_radius	the small radius of the torus.
[in]	m	the number of latitudes, minimum is 3.
[in]	n	the number of longitudes, minimum is 3.
[in]	twist	the integer shift when visiting a whole parallel: 0 is a natural torus parameterization, +n or -n makes the visitor arriving on another parallel after one turn.

Returns: the first principal curvature at each vertex.

◆ torusFirstPrincipalDirections()

template<typename TRealPoint , typename TRealVector >

static RealVectors DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::torusFirstPrincipalDirections	(	const Scalar	big_radius,
		const Scalar	small_radius,
		Size	m,
		Size	n,
		const int	twist
	)

static

Returns the first principal direction at each vertex of a torus of given parameters with m latitudes and n longitudes.

Parameters

[in]	big_radius	the big radius of the torus.
[in]	small_radius	the small radius of the torus.
[in]	m	the number of latitudes, minimum is 3.
[in]	n	the number of longitudes, minimum is 3.
[in]	twist	the integer shift when visiting a whole parallel: 0 is a natural torus parameterization, +n or -n makes the visitor arriving on another parallel after one turn.

Returns: the first principal direction at each vertex (in xy-plane).

◆ torusGaussianCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::torusGaussianCurvatures	(	const Scalar	big_radius,
		const Scalar	small_radius,
		Size	m,
		Size	n,
		const int	twist
	)

static

Returns the Gaussian curvature at each vertex of a torus of given parameters with m latitudes and n longitudes.

Parameters

[in]	big_radius	the big radius of the torus.
[in]	small_radius	the small radius of the torus.
[in]	m	the number of latitudes, minimum is 3.
[in]	n	the number of longitudes, minimum is 3.
[in]	twist	the integer shift when visiting a whole parallel: 0 is a natural torus parameterization, +n or -n makes the visitor arriving on another parallel after one turn.

Returns: the Gaussian curvature at each vertex.

◆ torusMeanCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::torusMeanCurvatures	(	const Scalar	big_radius,
		const Scalar	small_radius,
		Size	m,
		Size	n,
		const int	twist
	)

static

Returns the mean curvature at each vertex of a torus of given parameters with m latitudes and n longitudes.

Parameters

[in]	big_radius	the big radius of the torus.
[in]	small_radius	the small radius of the torus.
[in]	m	the number of latitudes, minimum is 3.
[in]	n	the number of longitudes, minimum is 3.
[in]	twist	the integer shift when visiting a whole parallel: 0 is a natural torus parameterization, +n or -n makes the visitor arriving on another parallel after one turn.

Returns: the mean curvature at each vertex.

◆ torusSecondPrincipalCurvatures()

template<typename TRealPoint , typename TRealVector >

static Scalars DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::torusSecondPrincipalCurvatures	(	const Scalar	big_radius,
		const Scalar	small_radius,
		Size	m,
		Size	n,
		const int	twist
	)

static

Returns the second principal curvature at each vertex of a torus of given parameters with m latitudes and n longitudes.

Parameters

[in]	big_radius	the big radius of the torus.
[in]	small_radius	the small radius of the torus.
[in]	m	the number of latitudes, minimum is 3.
[in]	n	the number of longitudes, minimum is 3.
[in]	twist	the integer shift when visiting a whole parallel: 0 is a natural torus parameterization, +n or -n makes the visitor arriving on another parallel after one turn.

Returns: the second principal curvature at each vertex.

◆ torusSecondPrincipalDirections()

template<typename TRealPoint , typename TRealVector >

static RealVectors DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::torusSecondPrincipalDirections	(	const Scalar	big_radius,
		const Scalar	small_radius,
		Size	m,
		Size	n,
		const int	twist
	)

static

Returns the second principal direction at each vertex of a torus of given parameters with m latitudes and n longitudes.

Parameters

[in]	big_radius	the big radius of the torus.
[in]	small_radius	the small radius of the torus.
[in]	m	the number of latitudes, minimum is 3.
[in]	n	the number of longitudes, minimum is 3.
[in]	twist	the integer shift when visiting a whole parallel: 0 is a natural torus parameterization, +n or -n makes the visitor arriving on another parallel after one turn.

Returns: the second principal direction at each vertex (in meridian-sliced plane).

Field Documentation

◆ dimension

template<typename TRealPoint , typename TRealVector >

const Dimension DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >::dimension = RealPoint::dimension

static

Definition at line 68 of file SurfaceMeshHelper.h.

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

SurfaceMeshHelper.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

template<typename TRealPoint, typename TRealVector> struct DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >

Member Typedef Documentation

◆ Faces

◆ Index

◆ RealPoint

◆ RealVector

◆ RealVectors

◆ Scalar

◆ Scalars

◆ Self

◆ Size

◆ SurfaceMesh

◆ Vertices

Member Enumeration Documentation

◆ NormalsType

Member Function Documentation

◆ BOOST_STATIC_ASSERT()

◆ lanternFirstPrincipalCurvatures()

◆ lanternFirstPrincipalDirections()

◆ lanternGaussianCurvatures()

◆ lanternMeanCurvatures()

◆ lanternSecondPrincipalCurvatures()

◆ lanternSecondPrincipalDirections()

◆ makeLantern()

◆ makeSphere()

◆ makeTorus()

◆ sphereFirstPrincipalCurvatures()

◆ sphereFirstPrincipalDirections()

◆ sphereGaussianCurvatures()

◆ sphereMeanCurvatures()

◆ sphereSecondPrincipalCurvatures()

◆ sphereSecondPrincipalDirections()

◆ torusFirstPrincipalCurvatures()

◆ torusFirstPrincipalDirections()

◆ torusGaussianCurvatures()

◆ torusMeanCurvatures()

◆ torusSecondPrincipalCurvatures()

◆ torusSecondPrincipalDirections()

Field Documentation

◆ dimension

template<typename TRealPoint, typename TRealVector>
struct DGtal::SurfaceMeshHelper< TRealPoint, TRealVector >