Aim: the common part of all geometric kernels for computing the convex hull or Delaunay triangulation of a range of points. More...

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

Inheritance diagram for DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >:

Data Structures
class	HalfSpace

Public Types
typedef TCoordinateInteger	CoordinateInteger

typedef TInternalInteger	InternalInteger

typedef CoordinateInteger	CoordinateScalar

typedef InternalInteger	InternalScalar

typedef DGtal::PointVector< dim, CoordinateInteger >	CoordinatePoint

typedef DGtal::PointVector< dim, CoordinateInteger >	CoordinateVector

typedef DGtal::PointVector< dim, InternalInteger >	InternalPoint

typedef DGtal::PointVector< dim, InternalInteger >	InternalVector

typedef std::size_t	Size

typedef Size	Index

typedef std::vector< Index >	IndexRange

typedef std::array< Index, dim >	CombinatorialPlaneSimplex

typedef IntegerConverter< dim, CoordinateInteger >	Outer
	Converter to outer coordinate integers or lattice points / vector. More...

typedef IntegerConverter< dim, InternalInteger >	Inner
	Converter to inner internal integers or lattice points / vector. More...

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CInteger< TCoordinateInteger >))

	BOOST_CONCEPT_ASSERT ((concepts::CInteger< TInternalInteger >))

	ConvexHullCommonKernel ()=default
	Default constructor. More...

HalfSpace	compute (const std::vector< CoordinatePoint > &vpoints, const CombinatorialPlaneSimplex &simplex, Index idx_below)

HalfSpace	compute (const std::vector< CoordinatePoint > &vpoints, const CombinatorialPlaneSimplex &simplex)

CoordinateVector	normal (const HalfSpace &H) const

CoordinateScalar	intercept (const HalfSpace &H) const

InternalScalar	dot (const HalfSpace &H1, const HalfSpace &H2) const

bool	equal (const HalfSpace &H1, const HalfSpace &H2) const

InternalScalar	height (const HalfSpace &H, const CoordinatePoint &p) const

InternalScalar	volume (const HalfSpace &H, const CoordinatePoint &p) const

bool	above (const HalfSpace &H, const CoordinatePoint &p) const

bool	aboveOrOn (const HalfSpace &H, const CoordinatePoint &p) const

bool	on (const HalfSpace &H, const CoordinatePoint &p) const

Static Public Attributes
static const Dimension	dimension = dim

Detailed Description

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>
struct DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >

Aim: the common part of all geometric kernels for computing the convex hull or Delaunay triangulation of a range of points.

Description of template class 'ConvexHullCommonKernel'

Template Parameters

dim	the dimension of the space that is used for computing the convex hull (either the same as input points for convex hull, or one more than input points for Delaunay triangulation)
TCoordinateInteger	the integer type that represents coordinates of lattice points, a model of concepts::CInteger.
TInternalInteger	the integer type that is used for internal computations of above/below plane tests, a model of concepts::CInteger. Must be at least as precise as TCoordinateInteger.

Definition at line 178 of file QuickHullKernels.h.

Member Typedef Documentation

◆ CombinatorialPlaneSimplex

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef std::array< Index, dim > DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::CombinatorialPlaneSimplex

Definition at line 195 of file QuickHullKernels.h.

◆ CoordinateInteger

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef TCoordinateInteger DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::CoordinateInteger

Definition at line 181 of file QuickHullKernels.h.

◆ CoordinatePoint

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef DGtal::PointVector< dim, CoordinateInteger > DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::CoordinatePoint

Definition at line 188 of file QuickHullKernels.h.

◆ CoordinateScalar

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef CoordinateInteger DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::CoordinateScalar

Definition at line 184 of file QuickHullKernels.h.

◆ CoordinateVector

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef DGtal::PointVector< dim, CoordinateInteger > DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::CoordinateVector

Definition at line 189 of file QuickHullKernels.h.

◆ Index

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef Size DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::Index

Definition at line 193 of file QuickHullKernels.h.

◆ IndexRange

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef std::vector< Index > DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::IndexRange

Definition at line 194 of file QuickHullKernels.h.

◆ Inner

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef IntegerConverter< dim, InternalInteger > DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::Inner

Converter to inner internal integers or lattice points / vector.

Definition at line 201 of file QuickHullKernels.h.

◆ InternalInteger

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef TInternalInteger DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::InternalInteger

Definition at line 182 of file QuickHullKernels.h.

◆ InternalPoint

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef DGtal::PointVector< dim, InternalInteger > DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::InternalPoint

Definition at line 190 of file QuickHullKernels.h.

◆ InternalScalar

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef InternalInteger DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::InternalScalar

Definition at line 185 of file QuickHullKernels.h.

◆ InternalVector

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef DGtal::PointVector< dim, InternalInteger > DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::InternalVector

Definition at line 191 of file QuickHullKernels.h.

◆ Outer

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef IntegerConverter< dim, CoordinateInteger > DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::Outer

Converter to outer coordinate integers or lattice points / vector.

Definition at line 199 of file QuickHullKernels.h.

◆ Size

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

typedef std::size_t DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::Size

Definition at line 192 of file QuickHullKernels.h.

Constructor & Destructor Documentation

◆ ConvexHullCommonKernel()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::ConvexHullCommonKernel ( )

default

Default constructor.

Member Function Documentation

◆ above()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

bool DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::above	(	const HalfSpace &	H,
		const CoordinatePoint &	p
	)		const

inline

Parameters

H	the half-space
p	any point

Returns: 'true' iff p is strictly above this plane (so in direction N ).

Definition at line 334 of file QuickHullKernels.h.

335 { return height( H, p ) > 0; }

DGtal::ProbingMode::H

@ H

References DGtal::H.

◆ aboveOrOn()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

bool DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::aboveOrOn	(	const HalfSpace &	H,
		const CoordinatePoint &	p
	)		const

inline

Parameters

H	the half-space
p	any point

Returns: 'true' iff p is above or lies on this plane (so in direction N ).

Definition at line 340 of file QuickHullKernels.h.

341 { return height( H, p ) >= 0; }

References DGtal::H.

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< TCoordinateInteger >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< TInternalInteger >) )

◆ compute() [1/2]

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

HalfSpace DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::compute	(	const std::vector< CoordinatePoint > &	vpoints,
		const CombinatorialPlaneSimplex &	simplex
	)

inline

Computes an halfspace from dimension points specified by simplex with vertices in a range vpoints of Point. Orientation is induced by the order of the points. If the simplex is degenrated, the half-space is invalid and has null normal.

Parameters

[in]	vpoints	a range of points over which the simplex is defined.
[in]	simplex	a range of dimension indices of points defining an hyperplane.

Returns: the corresponding halfspace (has null normal vector if simplex was not full dimensional)

Definition at line 257 of file QuickHullKernels.h.

    {
      typedef DGtal::SimpleMatrix< InternalScalar, dimension, dimension > Matrix;
      Matrix A;
      InternalVector N;
      InternalScalar c;
      for ( Dimension i = 1; i < dimension; i++ )
        for ( Dimension j = 0; j < dimension; j++ )
          A.setComponent( i-1, j,
                          Inner::cast( vpoints[ simplex[ i ] ][ j ]
                                       - vpoints[ simplex[ 0 ] ][ j ] ) );
      for ( Dimension j = 0; j < dimension; j++ )
        N[ j ] = A.cofactor( dimension-1, j );
      const InternalPoint ip = Inner::cast( vpoints[ simplex[ 0 ] ] );
      // c = N.dot( vpoints[ simplex[ 0 ] ] );
      return HalfSpace { N, N.dot( ip ) };
    }

References DGtal::IntegerConverter< dim, TInteger >::cast(), DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::dimension, and DGtal::PointVector< dim, TEuclideanRing, TContainer >::dot().

◆ compute() [2/2]

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

HalfSpace DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::compute	(	const std::vector< CoordinatePoint > &	vpoints,
		const CombinatorialPlaneSimplex &	simplex,
		Index	idx_below
	)

inline

Computes an halfspace from dimension points specified by simplex with vertices in a range vpoints of Point. It is oriented such that the point of index idx_below is included in the half-space (i.e. below).

Parameters

[in]	vpoints	a range of points over which the simplex is defined.
[in]	simplex	a range of dimension indices of points defining an hyperplane.
[in]	idx_below	the index of a p-oint that is below the hyperplane.

Returns: the corresponding halfspace (has null normal vector if simplex was not full dimensional)

Definition at line 230 of file QuickHullKernels.h.

    {
      HalfSpace hs = compute( vpoints, simplex );
      if ( hs.N != InternalVector::zero ) 
        {
          const InternalPoint  ip = Inner::cast( vpoints[ idx_below ] );
          const InternalScalar nu = hs.N.dot( ip );
          //const Scalar nu = hs.N.dot( vpoints[ idx_below ] );
          if ( nu > hs.c ) { hs.N = -hs.N; hs.c = -hs.c; }
        }
      return hs;
    }

References DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::HalfSpace::c, DGtal::IntegerConverter< dim, TInteger >::cast(), DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::compute(), DGtal::PointVector< dim, TEuclideanRing, TContainer >::dot(), DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::HalfSpace::N, and DGtal::PointVector< dim, InternalInteger >::zero.

Referenced by DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::compute().

◆ dot()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

InternalScalar DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::dot	(	const HalfSpace &	H1,
		const HalfSpace &	H2
	)		const

inline

Equivalent of the dot product of the normals of the half-spaces.

Parameters

H1	an half-space
H2	an half-space

Returns: a positive scalar if both half-spaces points to to the same hemisphere, a negative scalar if they point to opposite hemispheres, and zero if they are orthogonal.

Definition at line 298 of file QuickHullKernels.h.

    {
      return H1.N.dot( H2.N );
    }

References DGtal::PointVector< dim, TEuclideanRing, TContainer >::dot(), and DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::HalfSpace::N.

◆ equal()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

bool DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::equal	(	const HalfSpace &	H1,
		const HalfSpace &	H2
	)		const

inline

Parameters

H1	an half-space
H2	an half-space

Returns: 'true' if the half-spaces have the smae members.

Note: two half-spaces may be not equal but may represent the same set of points. For instance H1={{1,0},3} and H1={{2,0},6}.

Definition at line 311 of file QuickHullKernels.h.

    {
      return H1.c == H2.c && H1.N == H2.N;
    }

References DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::HalfSpace::c, and DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::HalfSpace::N.

◆ height()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

InternalScalar DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::height	(	const HalfSpace &	H,
		const CoordinatePoint &	p
	)		const

inline

Parameters

H	the half-space
p	any point

Returns: the (signed) height of p wrt this plane.

Definition at line 319 of file QuickHullKernels.h.

320 { return H.N.dot( Inner::cast( p ) ) - H.c; }

References DGtal::IntegerConverter< dim, TInteger >::cast(), and DGtal::H.

◆ intercept()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

CoordinateScalar DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::intercept ( const HalfSpace & H ) const

inline

Parameters

H	the half-space

Returns: the intercept of this facet.

Definition at line 285 of file QuickHullKernels.h.

    {
      return Outer::cast( H.c );
    }

References DGtal::IntegerConverter< dim, TInteger >::cast(), and DGtal::H.

◆ normal()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

CoordinateVector DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::normal ( const HalfSpace & H ) const

inline

Parameters

H	the half-space

Returns: the normal to this facet.

Definition at line 278 of file QuickHullKernels.h.

    {
      return Outer::cast( H.N );
    }

References DGtal::IntegerConverter< dim, TInteger >::cast(), and DGtal::H.

◆ on()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

bool DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::on	(	const HalfSpace &	H,
		const CoordinatePoint &	p
	)		const

inline

Parameters

H	the half-space
p	any point

Returns: 'true' iff p lies on this plane.

Definition at line 346 of file QuickHullKernels.h.

347 { return height( H, p ) == 0; }

◆ volume()

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

InternalScalar DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::volume	(	const HalfSpace &	H,
		const CoordinatePoint &	p
	)		const

inline

Parameters

H	the half-space
p	any point

Returns: the volume of the vectors spanned by the simplex and this point.

Definition at line 325 of file QuickHullKernels.h.

    {
      InternalScalar v = height( H, p );
      return v < InternalScalar( 0 ) ? -v : v;
    }

References DGtal::H.

Field Documentation

◆ dimension

template<Dimension dim, typename TCoordinateInteger = DGtal::int64_t, typename TInternalInteger = DGtal::int64_t>

const Dimension DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::dimension = dim

static

Definition at line 196 of file QuickHullKernels.h.

Referenced by DGtal::ConvexHullCommonKernel< dim, TCoordinateInteger, TInternalInteger >::compute().

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

QuickHullKernels.h

Data Structures

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ CombinatorialPlaneSimplex

◆ CoordinateInteger

◆ CoordinatePoint

◆ CoordinateScalar

◆ CoordinateVector

◆ Index

◆ IndexRange

◆ Inner

◆ InternalInteger

◆ InternalPoint

◆ InternalScalar

◆ InternalVector

◆ Outer

◆ Size

Constructor & Destructor Documentation

◆ ConvexHullCommonKernel()

Member Function Documentation

◆ above()

◆ aboveOrOn()

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ compute() [1/2]

◆ compute() [2/2]

◆ dot()

◆ equal()

◆ height()

◆ intercept()

◆ normal()

◆ on()

◆ volume()

Field Documentation

◆ dimension