morton::Morton< Dim, Bits > Class Template Reference

A Morton (Z-order) code interleaving Dim unsigned coordinates of Bits bits each. More...

#include <morton.hpp>

Public Types
using	code_type = detail::uint_for_t< Dim *Bits >
using	coord_type = detail::uint_for_t< Bits >

Public Member Functions
MORTON_HD constexpr	Morton () noexcept
MORTON_HD constexpr code_type	code () const noexcept
MORTON_HD constexpr coord_type	get (unsigned d) const
	Decode coordinate of a single axis.
MORTON_HD constexpr std::array< coord_type, Dim >	decode () const
	Decode all coordinates.
MORTON_HD constexpr void	set (unsigned d, coord_type value)
	Replace one axis' coordinate (other axes untouched). Wraps mod 2^Bits.
MORTON_HD constexpr void	add (unsigned d, coord_type k)
	Add k to axis d (wraps). O(1), branchless.
MORTON_HD constexpr void	sub (unsigned d, coord_type k)
	Subtract k from axis d (wraps). O(1), branchless.
MORTON_HD constexpr void	inc (unsigned d)
	Increment axis d by one. O(1).
MORTON_HD constexpr void	dec (unsigned d)
	Decrement axis d by one. O(1).
MORTON_HD constexpr Morton	neighbor (unsigned d, int dir) const
	Morton code of the neighbour one step along ± axis d (wraps).
MORTON_HD constexpr void	add_sat (unsigned d, coord_type k)
	Add k to axis d, clamping at coord_max instead of wrapping.
MORTON_HD constexpr void	sub_sat (unsigned d, coord_type k)
	Subtract k from axis d, clamping at 0 instead of wrapping.
MORTON_HD constexpr bool	try_add (unsigned d, coord_type k)
	Add k to axis d only if it does not overflow past coord_max.
MORTON_HD constexpr bool	try_sub (unsigned d, coord_type k)
	Subtract k from axis d only if it does not underflow past 0.
MORTON_HD constexpr std::array< Morton, 2 *Dim >	face_neighbors () const
	The 2*Dim von Neumann (face) neighbours, ordered {axis0-, axis0+, axis1-, axis1+, ...}.
MORTON_HD constexpr std::array< Morton, detail::pow3(Dim) - 1 >	all_neighbors () const
	The 3^Dim - 1 Moore neighbours (all cells differing by -1/0/+1 on each axis, excluding self), in odometer order.
MORTON_HD constexpr Morton	ancestor (unsigned level) const
	Ancestor cell origin at the given level (clears the low level*Dim bits).
MORTON_HD constexpr unsigned	child_index (unsigned level) const
	Index (0 .
MORTON_HD constexpr Morton	child (unsigned level, unsigned octant) const
	The octant-th child origin of a cell that is an ancestor at level (i.e.
MORTON_HD constexpr Morton &	operator++ () noexcept
MORTON_HD constexpr Morton	operator++ (int) noexcept
MORTON_HD constexpr Morton &	operator-- () noexcept
MORTON_HD constexpr Morton	operator-- (int) noexcept

Static Public Member Functions
static MORTON_HD constexpr Morton	from_code (code_type raw) noexcept
	Wrap a raw, already-interleaved code value.
template<typename... Cs, typename = std::enable_if_t<sizeof...(Cs) == Dim>>
static MORTON_HD constexpr Morton	encode (Cs... coords)
	Encode Dim coordinates into a Morton code.
static MORTON_HD constexpr Morton	encode (const std::array< coord_type, Dim > &c)
	Encode from an array of coordinates.
static MORTON_HD constexpr code_type	deposit (coord_type x, unsigned d)
static MORTON_HD constexpr coord_type	extract (code_type c, unsigned d)
static MORTON_HD constexpr code_type	axis_mask (unsigned d)
	Mask of bits belonging to axis d.

Static Public Attributes
static constexpr unsigned	dimensions = Dim
static constexpr unsigned	bits_per_axis = Bits
static constexpr unsigned	code_bits = Dim * Bits
static constexpr code_type	field_mask
	Mask of all valid code bits (handles code_bits == width without UB).
static constexpr coord_type	coord_max
	Largest representable coordinate value per axis.
static constexpr unsigned	octants = unsigned(1) << Dim

Friends
MORTON_HD constexpr bool	operator== (Morton a, Morton b) noexcept
MORTON_HD constexpr bool	operator!= (Morton a, Morton b) noexcept
MORTON_HD constexpr bool	operator< (Morton a, Morton b) noexcept
MORTON_HD constexpr bool	operator<= (Morton a, Morton b) noexcept
MORTON_HD constexpr bool	operator> (Morton a, Morton b) noexcept
MORTON_HD constexpr bool	operator>= (Morton a, Morton b) noexcept

Detailed Description

template<unsigned Dim, unsigned Bits>
class morton::Morton< Dim, Bits >

A Morton (Z-order) code interleaving Dim unsigned coordinates of Bits bits each.

The whole code occupies Dim * Bits bits and is stored in the smallest unsigned integer that fits.

Member Typedef Documentation

code_type

template<unsigned Dim, unsigned Bits>

using morton::Morton< Dim, Bits >::code_type = detail::uint_for_t<Dim * Bits>

coord_type

template<unsigned Dim, unsigned Bits>

using morton::Morton< Dim, Bits >::coord_type = detail::uint_for_t<Bits>

Constructor & Destructor Documentation

Morton()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr morton::Morton< Dim, Bits >::Morton ( )

inlineconstexprnoexcept

Member Function Documentation

from_code()

template<unsigned Dim, unsigned Bits>

static MORTON_HD constexpr Morton morton::Morton< Dim, Bits >::from_code ( code_type  raw )

inlinestaticconstexprnoexcept

Wrap a raw, already-interleaved code value.

encode() [1/2]

template<unsigned Dim, unsigned Bits>

template<typename... Cs, typename = std::enable_if_t<sizeof...(Cs) == Dim>>

static MORTON_HD constexpr Morton morton::Morton< Dim, Bits >::encode ( Cs...  coords )

inlinestaticconstexpr

Encode Dim coordinates into a Morton code.

encode() [2/2]

template<unsigned Dim, unsigned Bits>

static MORTON_HD constexpr Morton morton::Morton< Dim, Bits >::encode ( const std::array< coord_type, Dim > &  c )

inlinestaticconstexpr

Encode from an array of coordinates.

code()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr code_type morton::Morton< Dim, Bits >::code ( ) const

inlineconstexprnoexcept

get()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr coord_type morton::Morton< Dim, Bits >::get ( unsigned  d ) const

inlineconstexpr

Decode coordinate of a single axis.

decode()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr std::array< coord_type, Dim > morton::Morton< Dim, Bits >::decode ( ) const

inlineconstexpr

Decode all coordinates.

set()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr void morton::Morton< Dim, Bits >::set ( unsigned  d, coord_type  value  )

inlineconstexpr

Replace one axis' coordinate (other axes untouched). Wraps mod 2^Bits.

add()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr void morton::Morton< Dim, Bits >::add ( unsigned  d, coord_type  k  )

inlineconstexpr

Add k to axis d (wraps). O(1), branchless.

sub()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr void morton::Morton< Dim, Bits >::sub ( unsigned  d, coord_type  k  )

inlineconstexpr

Subtract k from axis d (wraps). O(1), branchless.

inc()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr void morton::Morton< Dim, Bits >::inc ( unsigned  d )

inlineconstexpr

Increment axis d by one. O(1).

dec()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr void morton::Morton< Dim, Bits >::dec ( unsigned  d )

inlineconstexpr

Decrement axis d by one. O(1).

neighbor()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr Morton morton::Morton< Dim, Bits >::neighbor ( unsigned  d, int  dir  ) const

inlineconstexpr

Morton code of the neighbour one step along ± axis d (wraps).

add_sat()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr void morton::Morton< Dim, Bits >::add_sat ( unsigned  d, coord_type  k  )

inlineconstexpr

Add k to axis d, clamping at coord_max instead of wrapping.

sub_sat()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr void morton::Morton< Dim, Bits >::sub_sat ( unsigned  d, coord_type  k  )

inlineconstexpr

Subtract k from axis d, clamping at 0 instead of wrapping.

try_add()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr bool morton::Morton< Dim, Bits >::try_add ( unsigned  d, coord_type  k  )

inlineconstexpr

Add k to axis d only if it does not overflow past coord_max.

Returns false (and leaves the code unchanged) if it would.

try_sub()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr bool morton::Morton< Dim, Bits >::try_sub ( unsigned  d, coord_type  k  )

inlineconstexpr

Subtract k from axis d only if it does not underflow past 0.

face_neighbors()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr std::array< Morton, 2 *Dim > morton::Morton< Dim, Bits >::face_neighbors ( ) const

inlineconstexpr

The 2*Dim von Neumann (face) neighbours, ordered {axis0-, axis0+, axis1-, axis1+, ...}.

Wraps at the grid edge.

all_neighbors()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr std::array< Morton, detail::pow3(Dim) - 1 > morton::Morton< Dim, Bits >::all_neighbors ( ) const

inlineconstexpr

The 3^Dim - 1 Moore neighbours (all cells differing by -1/0/+1 on each axis, excluding self), in odometer order.

Wraps at the grid edge.

ancestor()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr Morton morton::Morton< Dim, Bits >::ancestor ( unsigned  level ) const

inlineconstexpr

Ancestor cell origin at the given level (clears the low level*Dim bits).

level 0 is *this.

child_index()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr unsigned morton::Morton< Dim, Bits >::child_index ( unsigned  level ) const

inlineconstexpr

Index (0 .

. 2^Dim-1) of this cell within its parent at level+1, i.e. the Dim interleaved bits just above the level boundary.

child()

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr Morton morton::Morton< Dim, Bits >::child ( unsigned  level, unsigned  octant  ) const

inlineconstexpr

The octant-th child origin of a cell that is an ancestor at level (i.e.

set the Dim bits at position (level-1)*Dim). Requires level >= 1.

operator++() [1/2]

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr Morton & morton::Morton< Dim, Bits >::operator++ ( )

inlineconstexprnoexcept

operator++() [2/2]

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr Morton morton::Morton< Dim, Bits >::operator++ ( int  )

inlineconstexprnoexcept

operator--() [1/2]

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr Morton & morton::Morton< Dim, Bits >::operator-- ( )

inlineconstexprnoexcept

operator--() [2/2]

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr Morton morton::Morton< Dim, Bits >::operator-- ( int  )

inlineconstexprnoexcept

deposit()

template<unsigned Dim, unsigned Bits>

static MORTON_HD constexpr code_type morton::Morton< Dim, Bits >::deposit ( coord_type  x, unsigned  d  )

inlinestaticconstexpr

extract()

template<unsigned Dim, unsigned Bits>

static MORTON_HD constexpr coord_type morton::Morton< Dim, Bits >::extract ( code_type  c, unsigned  d  )

inlinestaticconstexpr

axis_mask()

template<unsigned Dim, unsigned Bits>

static MORTON_HD constexpr code_type morton::Morton< Dim, Bits >::axis_mask ( unsigned  d )

inlinestaticconstexpr

Mask of bits belonging to axis d.

Friends And Related Symbol Documentation

operator==

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr bool operator== ( Morton< Dim, Bits >  a, Morton< Dim, Bits >  b  )

friend

operator!=

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr bool operator!= ( Morton< Dim, Bits >  a, Morton< Dim, Bits >  b  )

friend

operator<

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr bool operator< ( Morton< Dim, Bits >  a, Morton< Dim, Bits >  b  )

friend

operator<=

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr bool operator<= ( Morton< Dim, Bits >  a, Morton< Dim, Bits >  b  )

friend

operator>

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr bool operator> ( Morton< Dim, Bits >  a, Morton< Dim, Bits >  b  )

friend

operator>=

template<unsigned Dim, unsigned Bits>

MORTON_HD constexpr bool operator>= ( Morton< Dim, Bits >  a, Morton< Dim, Bits >  b  )

friend

Member Data Documentation

dimensions

template<unsigned Dim, unsigned Bits>

constexpr unsigned morton::Morton< Dim, Bits >::dimensions = Dim

staticconstexpr

bits_per_axis

template<unsigned Dim, unsigned Bits>

constexpr unsigned morton::Morton< Dim, Bits >::bits_per_axis = Bits

staticconstexpr

code_bits

template<unsigned Dim, unsigned Bits>

constexpr unsigned morton::Morton< Dim, Bits >::code_bits = Dim * Bits

staticconstexpr

field_mask

template<unsigned Dim, unsigned Bits>

constexpr code_type morton::Morton< Dim, Bits >::field_mask

staticconstexpr

Initial value:

= (code_bits >= code_type_bits)
                                              ? code_type(~code_type(0))
                                              : code_type((code_type(1) << code_bits) - 1)

Mask of all valid code bits (handles code_bits == width without UB).

coord_max

template<unsigned Dim, unsigned Bits>

constexpr coord_type morton::Morton< Dim, Bits >::coord_max

staticconstexpr

Initial value:

= (Bits >= coord_type_bits)
                                              ? coord_type(~coord_type(0))
                                              : coord_type((coord_type(1) << Bits) - 1)

Largest representable coordinate value per axis.

octants

template<unsigned Dim, unsigned Bits>

constexpr unsigned morton::Morton< Dim, Bits >::octants = unsigned(1) << Dim

staticconstexpr

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

• morton.hpp