Classes
struct	IndexTypes
	This structure determines Morton index type and underlying unsigned integer type for the floating point coordinate type and number of dimensions. More...

struct	Interleaver

struct	Interleaver< ND, IntT, Morton96 >

struct	MortonIndex
	This structure binds the size of accesible memory to store the Morton index to the Morton index type. More...

struct	MortonIndex< 1 >

struct	MortonIndex< 12 >

struct	MortonIndex< 16 >

struct	MortonIndex< 2 >

struct	MortonIndex< 4 >

struct	MortonIndex< 8 >

struct	UnderlyingInt
	This structure binds floating point types to the unsigned integer types of the same width. More...

struct	UnderlyingInt< double >

struct	UnderlyingInt< float >

Typedefs
template<typename CoordT , size_t ND>
using	AffineND = Eigen::Transform< CoordT, static_cast< int >(ND), Eigen::Affine >

template<size_t ND>
using	BinIndices = Eigen::Matrix< size_t, 1, static_cast< int >(ND)>

template<size_t ND, typename IntT >
using	IntArray = Eigen::Array< IntT, static_cast< int >(ND), 1 >

template<size_t ND>
using	MDCoordinate = Eigen::Array< float, static_cast< int >(ND), 1 >

template<size_t ND>
using	MDSpaceBounds = Eigen::Array< float, static_cast< int >(ND), 2 >

template<size_t ND>
using	MDSpaceDimensions = Eigen::Array< float, static_cast< int >(ND), 1 >

template<size_t ND>
using	MDSpaceSteps = Eigen::Array< float, static_cast< int >(ND), 1 >

using	Morton96 = uint96_t
	This class implements the structure of size 96bit, that can be used as Morton index. More...

using	uint128_t = std::uint128_t

using	uint256_t = std::uint256_t

using	uint96_t = std::wide_uint< 96 >

Functions
template<size_t ND, typename IntT , typename MortonT >
MortonT	calculateDefaultBound (IntT intBound)

template<int ND>
size_t	CalculateRequiredCoordinateIntegerWidth (const MDSpaceBounds< ND > &bounds, const MDSpaceSteps< ND > &steps)
	Calculates the required width of the interleaved integer to accurately represent coordinates in a given space at a given resolution. More...

template<int ND>
bool	CheckCoordinatesInMDSpace (const MDSpaceBounds< ND > &bounds, const MDCoordinate< ND > &coord)
	Checks that a coordinate is within the extents of an MD space. More...

template<size_t N, typename IntT , typename MortonT >
IntT	compact (MortonT)
	Compacts (removes padding from) an integer with a given number of padding bits. More...

template<>
uint16_t	compact< 1, uint16_t, uint32_t > (uint32_t x)

template<>
uint16_t	compact< 1, uint16_t, uint64_t > (uint64_t x)

template<>
uint32_t	compact< 1, uint32_t, uint128_t > (uint128_t x)

template<>
uint16_t	compact< 2, uint16_t, uint64_t > (uint64_t x)

template<>
uint32_t	compact< 2, uint32_t, uint128_t > (uint128_t x)

template<>
uint64_t	compact< 2, uint64_t, uint256_t > (uint256_t x)

template<>
uint8_t	compact< 2, uint8_t, uint32_t > (uint32_t x)

template<>
uint16_t	compact< 3, uint16_t, uint64_t > (uint64_t x)

template<>
uint32_t	compact< 3, uint32_t, uint128_t > (uint128_t x)

template<>
uint64_t	compact< 3, uint64_t, uint256_t > (uint256_t x)

template<typename IntT >
float	ConvertCoordinateFromIntegerRange (IntT value, float lower, float upper)
	Converts a single integer coordinate to a floating point. More...

template<int ND, typename IntT >
MDCoordinate< ND >	ConvertCoordinatesFromIntegerRange (const MDSpaceBounds< ND > &bounds, const Eigen::Array< IntT, ND, 1 > &intCoord)
	Converts a point expressed as integer coordinates back to floating point, given bounds of the original coordinate space. More...

template<int ND, typename IntT >
Eigen::Array< IntT, ND, 1 >	ConvertCoordinatesToIntegerRange (const MDSpaceBounds< ND > &bounds, const float *crd)
	Converts a point to integer range given a range of floating point coordinates. More...

template<typename IntT >
IntT	ConvertCoordinateToIntegerRange (float value, float lower, float upper)
	Converts a single floating point coordinate to an integer range. More...

template<size_t nd, typename IntT , typename MortonT , typename coord_t = float>
MortonT	coordinatesToIndex (coord_t *coord, const MDSpaceBounds< nd > &space)

template<size_t ND, typename IntT >
IntArray< ND, IntT >	deinterleave (const Morton96 &z)

template<size_t ND, typename IntT , typename MortonT >
IntArray< ND, IntT >	deinterleave (const MortonT z)
	Deinterleaves a Morton number into an integer coordinate. More...

template<int ND>
void	ExpandBounds (MDSpaceBounds< ND > &bounds)
	Expands a coordinate space enough that floating point error cannot cause an overflow when mapping a value at the upper limit of the range to an integer range. More...

template<size_t nd, typename IntT , typename MortonT >
MDCoordinate< nd >	indexToCoordinates (const MortonT &idx, const MDSpaceBounds< nd > &space)

template<size_t ND, typename IntT >
Morton96	interleave (const IntArray< 3, uint32_t > &coord)

template<size_t ND, typename IntT , typename MortonT >
MortonT	interleave (const IntArray< ND, IntT > &coord)
	Interleaves an integer coordinate. More...

template<typename MortonT >
bool	morton_contains (const MortonT lower, const MortonT upper, const MortonT value)
	Checks if a point defined by a Morton number is within the box bounds (as defined by an upper and lower Morton number). More...

template<size_t N, typename IntT , typename MortonT >
MortonT	pad (IntT)
	Pad an integer with a given number of padding bits. More...

template<>
uint32_t	pad< 1, uint16_t, uint32_t > (uint16_t v)

template<>
uint64_t	pad< 1, uint16_t, uint64_t > (uint16_t v)

template<>
uint128_t	pad< 1, uint32_t, uint128_t > (uint32_t v)

template<>
uint64_t	pad< 2, uint16_t, uint64_t > (uint16_t v)

template<>
uint128_t	pad< 2, uint32_t, uint128_t > (uint32_t v)

template<>
uint256_t	pad< 2, uint64_t, uint256_t > (uint64_t v)

template<>
uint32_t	pad< 2, uint8_t, uint32_t > (uint8_t v)

template<>
uint64_t	pad< 3, uint16_t, uint64_t > (uint16_t v)

template<>
uint128_t	pad< 3, uint32_t, uint128_t > (uint32_t v)

template<>
uint256_t	pad< 3, uint64_t, uint256_t > (uint64_t v)

Typedef Documentation

◆ AffineND

template<typename CoordT , size_t ND>

using morton_index::AffineND = typedef Eigen::Transform<CoordT, static_cast<int>(ND), Eigen::Affine>

Definition at line 35 of file Types.h.

◆ BinIndices

template<size_t ND>

using morton_index::BinIndices = typedef Eigen::Matrix<size_t, 1, static_cast<int>(ND)>

Definition at line 37 of file Types.h.

◆ IntArray

template<size_t ND, typename IntT >

using morton_index::IntArray = typedef Eigen::Array<IntT, static_cast<int>(ND), 1>

Definition at line 27 of file Types.h.

◆ MDCoordinate

template<size_t ND>

using morton_index::MDCoordinate = typedef Eigen::Array<float, static_cast<int>(ND), 1>

Definition at line 29 of file Types.h.

◆ MDSpaceBounds

template<size_t ND>

using morton_index::MDSpaceBounds = typedef Eigen::Array<float, static_cast<int>(ND), 2>

Definition at line 31 of file Types.h.

◆ MDSpaceDimensions

template<size_t ND>

using morton_index::MDSpaceDimensions = typedef Eigen::Array<float, static_cast<int>(ND), 1>

Definition at line 32 of file Types.h.

◆ MDSpaceSteps

template<size_t ND>

using morton_index::MDSpaceSteps = typedef Eigen::Array<float, static_cast<int>(ND), 1>

Definition at line 33 of file Types.h.

◆ Morton96

using morton_index::Morton96 = typedef uint96_t

This class implements the structure of size 96bit, that can be used as Morton index.

Definition at line 43 of file Types.h.

◆ uint128_t

using morton_index::uint128_t = typedef std::uint128_t

Definition at line 21 of file Types.h.

◆ uint256_t

using morton_index::uint256_t = typedef std::uint256_t

Definition at line 22 of file Types.h.

◆ uint96_t

using morton_index::uint96_t = typedef std::wide_uint<96>

Definition at line 20 of file Types.h.

Function Documentation

◆ calculateDefaultBound()

template<size_t ND, typename IntT , typename MortonT >

MortonT morton_index::calculateDefaultBound ( IntT intBound )

Definition at line 30 of file CoordinateConversion.h.

References morton_index::Interleaver< ND, IntT, MortonT >::interleave().

◆ CalculateRequiredCoordinateIntegerWidth()

template<int ND>

size_t morton_index::CalculateRequiredCoordinateIntegerWidth	(	const MDSpaceBounds< ND > &	bounds,
		const MDSpaceSteps< ND > &	steps
	)

Calculates the required width of the interleaved integer to accurately represent coordinates in a given space at a given resolution.

Definition at line 41 of file CoordinateConversion.h.

◆ CheckCoordinatesInMDSpace()

template<int ND>

bool morton_index::CheckCoordinatesInMDSpace	(	const MDSpaceBounds< ND > &	bounds,
		const MDCoordinate< ND > &	coord
	)

Checks that a coordinate is within the extents of an MD space.

Definition at line 72 of file CoordinateConversion.h.

◆ compact()

template<size_t N, typename IntT , typename MortonT >

IntT morton_index::compact ( MortonT )

Compacts (removes padding from) an integer with a given number of padding bits.

Template Parameters

N	Number of padding bits to remove
IntT	Integer type
MortonT	Padded integer type

Returns: Original integer

Definition at line 37 of file BitInterleaving.h.

Referenced by deinterleave().

◆ compact< 1, uint16_t, uint32_t >()

template<>

uint16_t morton_index::compact< 1, uint16_t, uint32_t > ( uint32_t x )

inline

Definition at line 55 of file BitInterleaving.h.

◆ compact< 1, uint16_t, uint64_t >()

template<>

uint16_t morton_index::compact< 1, uint16_t, uint64_t > ( uint64_t x )

inline

Definition at line 74 of file BitInterleaving.h.

◆ compact< 1, uint32_t, uint128_t >()

template<>

uint32_t morton_index::compact< 1, uint32_t, uint128_t > ( uint128_t x )

inline

Definition at line 153 of file BitInterleaving.h.

◆ compact< 2, uint16_t, uint64_t >()

template<>

uint16_t morton_index::compact< 2, uint16_t, uint64_t > ( uint64_t x )

inline

Definition at line 110 of file BitInterleaving.h.

◆ compact< 2, uint32_t, uint128_t >()

template<>

uint32_t morton_index::compact< 2, uint32_t, uint128_t > ( uint128_t x )

inline

Definition at line 176 of file BitInterleaving.h.

◆ compact< 2, uint64_t, uint256_t >()

template<>

uint64_t morton_index::compact< 2, uint64_t, uint256_t > ( uint256_t x )

inline

Definition at line 227 of file BitInterleaving.h.

◆ compact< 2, uint8_t, uint32_t >()

template<>

uint8_t morton_index::compact< 2, uint8_t, uint32_t > ( uint32_t x )

inline

Definition at line 92 of file BitInterleaving.h.

◆ compact< 3, uint16_t, uint64_t >()

template<>

uint16_t morton_index::compact< 3, uint16_t, uint64_t > ( uint64_t x )

inline

Definition at line 131 of file BitInterleaving.h.

◆ compact< 3, uint32_t, uint128_t >()

template<>

uint32_t morton_index::compact< 3, uint32_t, uint128_t > ( uint128_t x )

inline

Definition at line 201 of file BitInterleaving.h.

◆ compact< 3, uint64_t, uint256_t >()

template<>

uint64_t morton_index::compact< 3, uint64_t, uint256_t > ( uint256_t x )

inline

Definition at line 254 of file BitInterleaving.h.

◆ ConvertCoordinateFromIntegerRange()

template<typename IntT >

float morton_index::ConvertCoordinateFromIntegerRange	(	IntT	value,
		float	lower,
		float	upper
	)

Converts a single integer coordinate to a floating point.

Definition at line 128 of file CoordinateConversion.h.

References lower, upper, and value.

◆ ConvertCoordinatesFromIntegerRange()

template<int ND, typename IntT >

MDCoordinate< ND > morton_index::ConvertCoordinatesFromIntegerRange	(	const MDSpaceBounds< ND > &	bounds,
		const Eigen::Array< IntT, ND, 1 > &	intCoord
	)

Converts a point expressed as integer coordinates back to floating point, given bounds of the original coordinate space.

Definition at line 109 of file CoordinateConversion.h.

◆ ConvertCoordinatesToIntegerRange()

template<int ND, typename IntT >

Eigen::Array< IntT, ND, 1 > morton_index::ConvertCoordinatesToIntegerRange	(	const MDSpaceBounds< ND > &	bounds,
		const float *	crd
	)

Converts a point to integer range given a range of floating point coordinates.

Definition at line 90 of file CoordinateConversion.h.

References n.

◆ ConvertCoordinateToIntegerRange()

template<typename IntT >

IntT morton_index::ConvertCoordinateToIntegerRange	(	float	value,
		float	lower,
		float	upper
	)

Converts a single floating point coordinate to an integer range.

Definition at line 119 of file CoordinateConversion.h.

References lower, upper, and value.

◆ coordinatesToIndex()

template<size_t nd, typename IntT , typename MortonT , typename coord_t = float>

MortonT morton_index::coordinatesToIndex	(	coord_t *	coord,
		const MDSpaceBounds< nd > &	space
	)

Definition at line 140 of file CoordinateConversion.h.

References morton_index::Interleaver< ND, IntT, MortonT >::interleave().

◆ deinterleave() [1/2]

template<size_t ND, typename IntT >

IntArray< ND, IntT > morton_index::deinterleave ( const Morton96 & z )

Definition at line 306 of file BitInterleaving.h.

◆ deinterleave() [2/2]

template<size_t ND, typename IntT , typename MortonT >

IntArray< ND, IntT > morton_index::deinterleave ( const MortonT z )

Deinterleaves a Morton number into an integer coordinate.

Template Parameters

ND	Number of dimensions
IntT	Intermediate integer type
MortonT	Morton number type

Parameters

z	Morton number

Returns: Integer coordinate

Definition at line 298 of file BitInterleaving.h.

References compact().

◆ ExpandBounds()

template<int ND>

void morton_index::ExpandBounds ( MDSpaceBounds< ND > & bounds )

Expands a coordinate space enough that floating point error cannot cause an overflow when mapping a value at the upper limit of the range to an integer range.

Sets bounds to the next lowest (for lower axis bound) or highest (for upper axis bound) representable floating point value.

Definition at line 62 of file CoordinateConversion.h.

◆ indexToCoordinates()

template<size_t nd, typename IntT , typename MortonT >

MDCoordinate< nd > morton_index::indexToCoordinates	(	const MortonT &	idx,
		const MDSpaceBounds< nd > &	space
	)

Definition at line 134 of file CoordinateConversion.h.

◆ interleave() [1/2]

template<size_t ND, typename IntT >

Morton96 morton_index::interleave ( const IntArray< 3, uint32_t > & coord )

Definition at line 285 of file BitInterleaving.h.

◆ interleave() [2/2]

template<size_t ND, typename IntT , typename MortonT >

MortonT morton_index::interleave ( const IntArray< ND, IntT > & coord )

Interleaves an integer coordinate.

Template Parameters

ND	Number of dimensions
IntT	Intermediate integer type
MortonT	Morton number type

Parameters

coord Coordinate in intermediate integer space

Returns: Interleaved integer (Morton number)

Definition at line 277 of file BitInterleaving.h.

References pad().

◆ morton_contains()

template<typename MortonT >

bool morton_index::morton_contains	(	const MortonT	lower,
		const MortonT	upper,
		const MortonT	value
	)

Checks if a point defined by a Morton number is within the box bounds (as defined by an upper and lower Morton number).

A box contains a Morton number if it is within the upper and lower bounds, inclusive of the box bounds themselves.

Parameters

lower	Lower bound
upper	Upper bound
value	Morton value to test

Definition at line 26 of file CoordinateConversion.h.

References lower, upper, and value.

◆ pad()

template<size_t N, typename IntT , typename MortonT >

MortonT morton_index::pad ( IntT )

Pad an integer with a given number of padding bits.

Template Parameters

N	Number of padding bits to add
IntT	Integer type
MortonT	Padded integer type

Returns: Padded integer

Definition at line 24 of file BitInterleaving.h.

Referenced by interleave().

◆ pad< 1, uint16_t, uint32_t >()

template<>

uint32_t morton_index::pad< 1, uint16_t, uint32_t > ( uint16_t v )

inline

Definition at line 45 of file BitInterleaving.h.

◆ pad< 1, uint16_t, uint64_t >()

template<>

uint64_t morton_index::pad< 1, uint16_t, uint64_t > ( uint16_t v )

inline

Definition at line 64 of file BitInterleaving.h.

◆ pad< 1, uint32_t, uint128_t >()

template<>

uint128_t morton_index::pad< 1, uint32_t, uint128_t > ( uint32_t v )

inline

Definition at line 142 of file BitInterleaving.h.

◆ pad< 2, uint16_t, uint64_t >()

template<>

uint64_t morton_index::pad< 2, uint16_t, uint64_t > ( uint16_t v )

inline

Definition at line 100 of file BitInterleaving.h.

◆ pad< 2, uint32_t, uint128_t >()

template<>

uint128_t morton_index::pad< 2, uint32_t, uint128_t > ( uint32_t v )

inline

Definition at line 164 of file BitInterleaving.h.

◆ pad< 2, uint64_t, uint256_t >()

template<>

uint256_t morton_index::pad< 2, uint64_t, uint256_t > ( uint64_t v )

inline

Definition at line 214 of file BitInterleaving.h.

◆ pad< 2, uint8_t, uint32_t >()

template<>

uint32_t morton_index::pad< 2, uint8_t, uint32_t > ( uint8_t v )

inline

Definition at line 83 of file BitInterleaving.h.

◆ pad< 3, uint16_t, uint64_t >()

template<>

uint64_t morton_index::pad< 3, uint16_t, uint64_t > ( uint16_t v )

inline

Definition at line 119 of file BitInterleaving.h.

◆ pad< 3, uint32_t, uint128_t >()

template<>

uint128_t morton_index::pad< 3, uint32_t, uint128_t > ( uint32_t v )

inline

Definition at line 187 of file BitInterleaving.h.

◆ pad< 3, uint64_t, uint256_t >()

template<>

uint256_t morton_index::pad< 3, uint64_t, uint256_t > ( uint64_t v )

inline

Definition at line 239 of file BitInterleaving.h.

Classes

Typedefs

Functions

Typedef Documentation

◆ AffineND

◆ BinIndices

◆ IntArray

◆ MDCoordinate

◆ MDSpaceBounds

◆ MDSpaceDimensions

◆ MDSpaceSteps

◆ Morton96

◆ uint128_t

◆ uint256_t

◆ uint96_t

Function Documentation

◆ calculateDefaultBound()

◆ CalculateRequiredCoordinateIntegerWidth()

◆ CheckCoordinatesInMDSpace()

◆ compact()

◆ compact< 1, uint16_t, uint32_t >()

◆ compact< 1, uint16_t, uint64_t >()

◆ compact< 1, uint32_t, uint128_t >()

◆ compact< 2, uint16_t, uint64_t >()

◆ compact< 2, uint32_t, uint128_t >()

◆ compact< 2, uint64_t, uint256_t >()

◆ compact< 2, uint8_t, uint32_t >()

◆ compact< 3, uint16_t, uint64_t >()

◆ compact< 3, uint32_t, uint128_t >()

◆ compact< 3, uint64_t, uint256_t >()

◆ ConvertCoordinateFromIntegerRange()

◆ ConvertCoordinatesFromIntegerRange()

◆ ConvertCoordinatesToIntegerRange()

◆ ConvertCoordinateToIntegerRange()

◆ coordinatesToIndex()

◆ deinterleave() [1/2]

◆ deinterleave() [2/2]

◆ ExpandBounds()

◆ indexToCoordinates()

◆ interleave() [1/2]

◆ interleave() [2/2]

◆ morton_contains()

◆ pad()

◆ pad< 1, uint16_t, uint32_t >()

◆ pad< 1, uint16_t, uint64_t >()

◆ pad< 1, uint32_t, uint128_t >()

◆ pad< 2, uint16_t, uint64_t >()

◆ pad< 2, uint32_t, uint128_t >()

◆ pad< 2, uint64_t, uint256_t >()

◆ pad< 2, uint8_t, uint32_t >()

◆ pad< 3, uint16_t, uint64_t >()

◆ pad< 3, uint32_t, uint128_t >()

◆ pad< 3, uint64_t, uint256_t >()