Ken Perlin's gradient-noise implicit function. More...

#include <EBGeometry_AnalyticDistanceFunctions.hpp>

Inheritance diagram for EBGeometry::PerlinSDF< T >:

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Collaboration diagram for EBGeometry::PerlinSDF< T >:

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Public Member Functions
	PerlinSDF ()=default
	Default constructor. Constructs a single-octave Perlin noise field with unit amplitude, unit frequency along all axes, and persistence 0.5.

	PerlinSDF (const T a_noiseAmplitude, const Vec3T< T > a_noiseFrequency, const T a_noisePersistence, const unsigned int a_noiseOctaves) noexcept
	Full constructor.

	PerlinSDF (const PerlinSDF &)=default
	Copy constructor.

	PerlinSDF (PerlinSDF &&)=default
	Move constructor.

PerlinSDF &	operator= (const PerlinSDF &)=default
	Copy assignment.

PerlinSDF &	operator= (PerlinSDF &&)=default
	Move assignment.

	~PerlinSDF () override=default
	Destructor.

T	signedDistance (const Vec3T< T > &a_point) const noexcept override
	Signed distance function. Generates a noise value on [0, m_noiseAmplitude].

template<class URNG >
void	shuffle (URNG &g) noexcept
	Shuffle the permutation table with the provided uniform random number generator.

std::array< int, 512 > &	getPermutationTable () noexcept
	Get the internal permutation table.

Public Member Functions inherited from EBGeometry::SignedDistanceFunction< T >
	SignedDistanceFunction ()=default
	Default constructor.

	~SignedDistanceFunction () override=default
	Destructor.

T	value (const Vec3T< T > &a_point) const noexcept final
	Implementation of ImplicitFunction::value; delegates to signedDistance().

virtual Vec3T< T >	normal (const Vec3T< T > &a_point, const T &a_delta) const noexcept
	Compute the outward normal using central finite differences.

Public Member Functions inherited from EBGeometry::ImplicitFunction< T >
	ImplicitFunction ()=default
	Default constructor.

virtual	~ImplicitFunction ()=default
	Default destructor.

T	operator() (const Vec3T< T > &a_point) const noexcept
	Call operator — alternative signature for the value function.

template<class BV >
BV	approximateBoundingVolumeOctree (const Vec3T< T > &a_initialLowCorner, const Vec3T< T > &a_initialHighCorner, const unsigned int a_maxTreeDepth, const T &a_safety=0.0) const
	Compute an approximation to the bounding volume for the implicit surface using octree subdivision.

Protected Member Functions
virtual T	lerp (const T t, const T a, const T b) const noexcept
	Ken Perlin's linear interpolation helper.

virtual T	fade (const T t) const noexcept
	Ken Perlin's fade (smoothstep) function: 6t^5 - 15t^4 + 10t^3.

T	grad (const int hash, const T x, const T y, const T z) const noexcept
	Ken Perlin's gradient hash function.

T	noise (const Vec3T< T > &a_point) const noexcept
	Single-octave Perlin noise evaluation.

Protected Attributes
Vec3T< T >	m_noiseFrequency = Vec3T<T>(T(1), T(1), T(1))
	Spatial noise frequency along each Cartesian axis.

T	m_noiseAmplitude = T(1)
	Noise amplitude (output scale).

T	m_noisePersistence = T(0.5)
	Per-octave amplitude decay factor.

std::array< int, 512 >	m_permutationTable = {}
	Integer hash permutation table (512 entries: [0..255] mirrored).

unsigned int	m_noiseOctaves = 1U
	Number of noise octaves.

Static Protected Attributes
static constexpr std::array< int, 256 >	s_perlinPermutationTable
	Ken Perlin's original 256-entry permutation table.

Detailed Description

template<class T>
class EBGeometry::PerlinSDF< T >

Ken Perlin's gradient-noise implicit function.

This class evaluates multi-octave Perlin noise at a 3-D point and returns the result as a scalar. It is not a true signed distance function (the gradient magnitude is not guaranteed to equal 1), but it can serve as a procedural displacement field when added to or subtracted from a conventional SDF.

The output of signedDistance is on the range [0, m_noiseAmplitude] for a single octave. Multiple octaves sum scaled contributions: each successive octave doubles the spatial frequency (controlled by m_noisePersistence dividing the frequency) and attenuates the amplitude by m_noisePersistence.

Note: The default constructor leaves the permutation table all-zeros, producing constant-zero noise. Use the full constructor (which initialises the table from Ken Perlin's reference permutation and then shuffles it) or call shuffle() explicitly before use.

Template Parameters

T	Floating-point precision.

Constructor & Destructor Documentation

◆ PerlinSDF()

template<class T >

EBGeometry::PerlinSDF< T >::PerlinSDF	(	const T	a_noiseAmplitude,
		const Vec3T< T >	a_noiseFrequency,
		const T	a_noisePersistence,
		const unsigned int	a_noiseOctaves
	)

inlinenoexcept

Full constructor.

Parameters

[in]	a_noiseAmplitude	Noise amplitude (output scale).
[in]	a_noiseFrequency	Spatial frequency along each Cartesian axis.
[in]	a_noisePersistence	Per-octave amplitude decay factor. Clamped to [0, 1].
[in]	a_noiseOctaves	Number of noise octaves. Clamped to >= 1.

Member Function Documentation

◆ fade()

template<class T >

virtual T EBGeometry::PerlinSDF< T >::fade ( const T t ) const

inlineprotectedvirtualnoexcept

Ken Perlin's fade (smoothstep) function: 6t^5 - 15t^4 + 10t^3.

Parameters

[in] t Input in [0,1].

Returns: Smoothed value in [0,1].

◆ getPermutationTable()

template<class T >

std::array< int, 512 > & EBGeometry::PerlinSDF< T >::getPermutationTable ( )

inlinenoexcept

Get the internal permutation table.

Returns: m_permutationTable.

◆ grad()

template<class T >

T EBGeometry::PerlinSDF< T >::grad	(	const int	hash,
		const T	x,
		const T	y,
		const T	z
	)		const

inlineprotectednoexcept

Ken Perlin's gradient hash function.

Parameters

[in]	hash	Hash value selecting one of 16 gradient directions.
[in]	x	x-component of the relative position.
[in]	y	y-component of the relative position.
[in]	z	z-component of the relative position.

Returns: Dot product of the selected pseudo-random gradient with (x, y, z).

◆ lerp()

template<class T >

virtual T EBGeometry::PerlinSDF< T >::lerp	(	const T	t,
		const T	a,
		const T	b
	)		const

inlineprotectedvirtualnoexcept

Ken Perlin's linear interpolation helper.

Parameters

[in]	t	Interpolation weight in [0,1].
[in]	a	Start value.
[in]	b	End value.

Returns: a + t*(b - a).

◆ noise()

template<class T >

T EBGeometry::PerlinSDF< T >::noise ( const Vec3T< T > & a_point ) const

inlineprotectednoexcept

Single-octave Perlin noise evaluation.

Parameters

[in] a_point Input point in noise space.

Returns: Noise value in [-1, 1].

◆ operator=() [1/2]

template<class T >

PerlinSDF & EBGeometry::PerlinSDF< T >::operator= ( const PerlinSDF< T > & )

default

Copy assignment.

Returns: Reference to (*this).

◆ operator=() [2/2]

template<class T >

PerlinSDF & EBGeometry::PerlinSDF< T >::operator= ( PerlinSDF< T > && )

default

Move assignment.

Returns: Reference to (*this).

◆ shuffle()

template<class T >

template<class URNG >

void EBGeometry::PerlinSDF< T >::shuffle ( URNG & g )

inlinenoexcept

Shuffle the permutation table with the provided uniform random number generator.

Reseeds the 256-entry permutation table using std::shuffle and then mirrors it into the upper 256 entries. The URNG type must satisfy the C++ UniformRandomBitGenerator concept (e.g., std::mt19937).

Template Parameters

URNG	Uniform random number generator type (e.g., std::mt19937).

Parameters

[in] g Uniform random number generator instance to drive the shuffle.

Note: When using parallel calculations it is exceptionally important that the input RNG produces the same sequence across all threads/ranks. Otherwise, each thread/rank will generate a different permutation table and therefore a different noise field, resulting in no single coherent geometry.

◆ signedDistance()

template<class T >

T EBGeometry::PerlinSDF< T >::signedDistance ( const Vec3T< T > & a_point ) const

inlineoverridevirtualnoexcept

Signed distance function. Generates a noise value on [0, m_noiseAmplitude].

Parameters

[in] a_point Input point.

Returns: Octave-summed Perlin noise value scaled by m_noiseAmplitude.

Implements EBGeometry::SignedDistanceFunction< T >.

Member Data Documentation

◆ m_permutationTable

template<class T >

std::array<int, 512> EBGeometry::PerlinSDF< T >::m_permutationTable = {}

protected

Integer hash permutation table (512 entries: [0..255] mirrored).

Default-constructed with all zeros (degenerate, constant-zero noise). Use the full constructor or shuffle() to populate with a real permutation.

◆ s_perlinPermutationTable

template<class T >

constexpr std::array<int, 256> EBGeometry::PerlinSDF< T >::s_perlinPermutationTable

staticconstexprprotected

Initial value:

= {
    151, 160, 137, 91,  90,  15,  131, 13,  201, 95,  96,  53,  194, 233, 7,   225, 140, 36,  103, 30,  69,  142,
    8,   99,  37,  240, 21,  10,  23,  190, 6,   148, 247, 120, 234, 75,  0,   26,  197, 62,  94,  252, 219, 203,
    117, 35,  11,  32,  57,  177, 33,  88,  237, 149, 56,  87,  174, 20,  125, 136, 171, 168, 68,  175, 74,  165,
    71,  134, 139, 48,  27,  166, 77,  146, 158, 231, 83,  111, 229, 122, 60,  211, 133, 230, 220, 105, 92,  41,
    55,  46,  245, 40,  244, 102, 143, 54,  65,  25,  63,  161, 1,   216, 80,  73,  209, 76,  132, 187, 208, 89,
    18,  169, 200, 196, 135, 130, 116, 188, 159, 86,  164, 100, 109, 198, 173, 186, 3,   64,  52,  217, 226, 250,
    124, 123, 5,   202, 38,  147, 118, 126, 255, 82,  85,  212, 207, 206, 59,  227, 47,  16,  58,  17,  182, 189,
    28,  42,  223, 183, 170, 213, 119, 248, 152, 2,   44,  154, 163, 70,  221, 153, 101, 155, 167, 43,  172, 9,
    129, 22,  39,  253, 19,  98,  108, 110, 79,  113, 224, 232, 178, 185, 112, 104, 218, 246, 97,  228, 251, 34,
    242, 193, 238, 210, 144, 12,  191, 179, 162, 241, 81,  51,  145, 235, 249, 14,  239, 107, 49,  192, 214, 31,
    181, 199, 106, 157, 184, 84,  204, 176, 115, 121, 50,  45,  127, 4,   150, 254, 138, 236, 205, 93,  222, 114,
    67,  29,  24,  72,  243, 141, 128, 195, 78,  66,  215, 61,  156, 180}

Ken Perlin's original 256-entry permutation table.

Used by the full constructor and shuffle() to seed m_permutationTable. Stored as a static constexpr member so it is available to subclasses without polluting the enclosing namespace.

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

Source/EBGeometry_AnalyticDistanceFunctions.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PerlinSDF()

Member Function Documentation

◆ fade()

◆ getPermutationTable()

◆ grad()

◆ lerp()

◆ noise()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ shuffle()

◆ signedDistance()

Member Data Documentation

◆ m_permutationTable

◆ s_perlinPermutationTable