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

#include <EBGeometry_AnalyticDistanceFunctions.hpp>

Collaboration diagram for EBGeometry::PerlinSDF< T >:

[legend]

Public Member Functions
	PerlinSDF () noexcept
	Default constructor. Constructs a single-octave Perlin noise field with unit amplitude, unit frequency along all axes, and persistence 0.5: the full constructor with those values.

	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.

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

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

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

BoundingVolumes::AABBT< T >	computeBoundingVolume () const noexcept
	The shape's axis-aligned bounding box.

Static Public Attributes
static constexpr DistanceQuality	distanceQuality = DistanceQuality::NotADistance
	How far signedDistance() can be trusted as a distance: not at all. The value is noise, so only its sign means anything.

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

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.

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

unsigned int	m_noiseOctaves = 1U
	Number of noise octaves.

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 divides the spatial frequency by m_noisePersistence (doubling it at the default 0.5) and multiplies the amplitude by m_noisePersistence.

The full constructor shuffles the permutation table with a std::mt19937 seeded with 0, so every PerlinSDF built with the same parameters is the same noise field; call shuffle() for another.

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, at most 1. A value of zero or less keeps only the first octave, since every later one would have zero amplitude.
[in]	a_noiseOctaves	Number of noise octaves. Clamped to >= 1.

Member Function Documentation

◆ computeBoundingVolume()

template<class T >

BoundingVolumes::AABBT< T > EBGeometry::PerlinSDF< T >::computeBoundingVolume ( ) const

inlinenoexcept

The shape's axis-aligned bounding box.

Noise fills all of space, so the box is the whole space.

Returns: The bounding box.

◆ fade()

template<class T >

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

inlineprotectednoexcept

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 >

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 >

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

inlineprotectednoexcept

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.

Resets the first 256 entries of the permutation table to 0, ..., 255, permutes them with std::shuffle and then mirrors them 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

inlinenoexcept

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

Parameters

[in] a_point Input point.

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

Member Data Documentation

◆ m_permutationTable

template<class T >

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

protected

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

Filled by every constructor (the default constructor delegates to the full one) and refilled by shuffle().

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

Source/EBGeometry_AnalyticDistanceFunctions.hpp

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PerlinSDF()

Member Function Documentation

◆ computeBoundingVolume()

◆ fade()

◆ getPermutationTable()

◆ grad()

◆ lerp()

◆ noise()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ shuffle()

◆ signedDistance()

Member Data Documentation

◆ m_permutationTable