2D Perlin and Value noise generator. More...

#include <perlin.h>

Public Member Functions
	CPerlinNoise2D ()
	Constructor. More...

	~CPerlinNoise2D ()
	Destructor. More...

const float	generate (float, float, eNoise, size_t, float=0.5f, float=2.0f) const
	Generate noise at a point. More...

void	SetSeed ()
	Set seed for PRNG. More...

void	RandomizeTable (eDistribution)
	Randomize table from distribution. More...

bool	DoubleTableSize ()
	Double table size. More...

bool	HalveTableSize ()
	Halve table size. More...

bool	DefaultTableSize ()
	Set table size to default. More...

void	SetSpline (eSpline)
	Set spline function. More...

void	SetHash (eHash)
	Set hash function. More...

const size_t	GetTableSize () const
	Get table size. More...

const size_t	GetMinTableSize () const
	Get minimum table size. More...

const size_t	GetMaxTableSize () const
	Get maximum table size. More...

const size_t	GetDefTableSize () const
	Get default table size. More...

const eHash	GetHash () const
	Get hash function type. More...

const eSpline	GetSpline () const
	Get spline function type. More...

const eDistribution	GetDistribution () const
	Get distribution type. More...

Private Member Functions
const size_t	pair (size_t, size_t) const
	Perlin pairing function. More...

const size_t	pairstd (size_t, size_t) const
	Std pairing function. More...

const size_t	hash (size_t) const
	Perlin hash function. More...

const size_t	hashstd (size_t) const
	std::hash function. More...

const size_t	hash2 (size_t, size_t) const
	Hash function. More...

void	HashCorners (size_t, size_t, size_t[4]) const
	Hash grid corners. More...

void	RandomizeTableUniform ()
	Randomize table using uniform distribution. More...

void	RandomizeTableCos ()
	Randomize table using cosine. More...

void	RandomizeTableNormal ()
	Randomize table using normal distribution. More...

void	RandomizeTableExp ()
	Randomize table using exponential distribution. More...

void	RandomizeTableMaximal ()
	Randomize table using large magnitude values. More...

void	RandomizeTableMidpoint (size_t, size_t, float)
	Midpoint displacement. More...

void	RandomizeTableMidpoint ()
	Randomize table using midpoint displacement. More...

const float	spline (float) const
	Spline curve. More...

const float	z (size_t, float, float, eNoise) const
	Apply gradients. More...

const float	Lerp (float, float, float, size_t *, eNoise) const
	Linear interpolation. More...

const float	noise (float, float, eNoise) const
	Perlin noise. More...

void	RandomizePermutation ()
	Randomize permutation. More...

void	Initialize ()
	Initialize. More...

Private Attributes
eHash	m_eHash = eHash::Permutation
	Hash function type. More...

eSpline	m_eSpline = eSpline::Cubic
	Spline function type. More...

eDistribution	m_eDistribution = eDistribution::Uniform
	Uniform distribution.. More...

size_t *	m_nPerm = nullptr
	Random permutation, used for hash function. More...

float *	m_fTable = nullptr
	Table of gradients or values. More...

std::default_random_engine	m_stdRandom
	PRNG. More...

UINT	m_nSeed = 0
	PRNG seed. More...

const size_t	m_nDefTableSize = 256
	Default table size. More...

const size_t	m_nMinTableSize = 16
	Min table size. More...

const size_t	m_nMaxTableSize = 1024
	Max table size. More...

size_t	m_nSize = m_nDefTableSize
	Table size, must be a power of 2. More...

size_t	m_nMask = m_nDefTableSize - 1
	Mask for values less than `m_nSize`. More...

Detailed Description

This implementation of a Perlin noise generator can generate either Perlin or Value noise using gradients or values (respectively) from a table that can be filled with pseudo-random numbers from various probability distributions. There is a choice of hash functions including Perlin's original pseudo-random permutation method and various non-repeating hash functions. There is a choice of spline functions including cubic and quintic splines. The table size can be doubled or halved within hard-coded limits. The source of pseudo-randomness is std::default_random_engine

Definition at line 48 of file perlin.h.

Constructor & Destructor Documentation

◆ CPerlinNoise2D()

CPerlinNoise2D::CPerlinNoise2D ( )

Set the PRNG seed and initialize.

Definition at line 42 of file perlin.cpp.

◆ ~CPerlinNoise2D()

CPerlinNoise2D::~CPerlinNoise2D ( )

Deletes the permutation and gradient/value table.

Definition at line 49 of file perlin.cpp.

Member Function Documentation

◆ DefaultTableSize()

bool CPerlinNoise2D::DefaultTableSize ( )

Set table size to the default and call Initialize() to re-initialize.

Returns: true if the table size changed.

Definition at line 278 of file perlin.cpp.

◆ DoubleTableSize()

bool CPerlinNoise2D::DoubleTableSize ( )

Double the size of the permutation and gradient/value tables up to a maximum of m_nMaxTableSize and call Initialize() to re-initialize.

Returns: true if the table size changed.

Definition at line 245 of file perlin.cpp.

◆ generate()

const float CPerlinNoise2D::generate	(	float	x,
		float	y,
		eNoise	t,
		size_t	n,
		float	alpha = `0.5f`,
		float	beta = `2.0f`
	)		const

Add multiple octaves of Perlin or Value noise to compute an effect similar to turbulence at a single point. Each successive octave has its amplitude multiplied by a value called the lacunarity and its frequency multiplied by a value called the persistence. These are usually set to 0.5 and 2.0, respectively.

Parameters

x	X-coordinate of a 2D point.
y	Y-coordinate of a 2D point.
t	Noise type.
n	Number of octaves.
alpha	Lacunarity. Defaults to 0.5f.
beta	Persistence. Defaults to 2.0f.

Returns: Smooth noise in \([-1, 1]\) at point \((\mathsf{x}, \mathsf{y})\).

Definition at line 548 of file perlin.cpp.

◆ GetDefTableSize()

const size_t CPerlinNoise2D::GetDefTableSize ( ) const

Reader function for the default table size.

Returns: The default table size.

Definition at line 602 of file perlin.cpp.

◆ GetDistribution()

const eDistribution CPerlinNoise2D::GetDistribution ( ) const

Reader function for the distribution type.

Returns: The distribution type.

Definition at line 623 of file perlin.cpp.

◆ GetHash()

const eHash CPerlinNoise2D::GetHash ( ) const

Reader function for the hash function type.

Returns: The hash function type.

Definition at line 609 of file perlin.cpp.

◆ GetMaxTableSize()

const size_t CPerlinNoise2D::GetMaxTableSize ( ) const

Reader function for the maximum table size.

Returns: The maximum table size.

Definition at line 595 of file perlin.cpp.

◆ GetMinTableSize()

const size_t CPerlinNoise2D::GetMinTableSize ( ) const

Reader function for the minimum table size.

Returns: The minimum table size.

Definition at line 588 of file perlin.cpp.

◆ GetSpline()

const eSpline CPerlinNoise2D::GetSpline ( ) const

Reader function for the spline function type.

Returns: The spline function type.

Definition at line 616 of file perlin.cpp.

◆ GetTableSize()

const size_t CPerlinNoise2D::GetTableSize ( ) const

Reader function for the table size.

Returns: The table size.

Definition at line 581 of file perlin.cpp.

◆ HalveTableSize()

bool CPerlinNoise2D::HalveTableSize ( )

Halve the size of the permutation and gradient/value tables down to a minimum of m_nMinTableSize and call Initialize() to re-initialize.

Returns: true if the table size changed.

Definition at line 262 of file perlin.cpp.

◆ hash()

const size_t CPerlinNoise2D::hash ( size_t x ) const

inlineprivate

Perlin's hash function, which uses a random permutation. Note that this means that it repeats with a period of m_nSize.

Parameters

x A number.

Returns: Hashed number in the range [0, m_nSize - 1].

Definition at line 367 of file perlin.cpp.

◆ hash2()

const size_t CPerlinNoise2D::hash2	(	size_t	x,
		size_t	y
	)		const

inlineprivate

A 2D linear congruential hash function. For fixed primes \(p_0, p_1, p_2\) and parameters \(x, y\), this function returns \((p_0x + p_1y) \bmod p_2 \) right-shifted by 8 bits and masked with m_nMask.

Parameters

x	A number.
y	A number.

Returns: Hashed number in the range [0, m_nSize - 1].

Definition at line 389 of file perlin.cpp.

◆ HashCorners()

void CPerlinNoise2D::HashCorners	(	size_t	x,
		size_t	y,
		size_t	c[4]
	)		const

private

Get hash values at grid corners (at whole number coordinates).

Parameters

x	X-coordinate.
y	Y-coordinate.
c	[OUT] Array of four hash values for corners in row-major order.

Definition at line 404 of file perlin.cpp.

◆ hashstd()

const size_t CPerlinNoise2D::hashstd ( size_t x ) const

inlineprivate

A hash function using std::hash. Note: The C++ Standard does not require that std::hash be a good hash function, but we'll assume that it is. Most implementations are.

Parameters

x A number.

Returns: Hashed number in the range [0, m_nSize - 1].

Definition at line 377 of file perlin.cpp.

◆ Initialize()

void CPerlinNoise2D::Initialize ( )

private

Initialize the generator. Assumes that m_nSize has set initialized to the table size, which must be a power of two. Create and initialize the permutation and gradient/value tables. Initialize the bit mask.

Definition at line 58 of file perlin.cpp.

◆ Lerp()

const float CPerlinNoise2D::Lerp	(	float	sX,
		float	fX,
		float	fY,
		size_t *	c,
		eNoise	t
	)		const

private

Linear interpolation of gradients or heights (depending on whether we're generating Perlin or Value noise) along the X-axis.

Parameters

sX	Smoothed fractional part of X-coordinate.
fX	Fractional part of X-coordinate (ignored in Value noise).
fY	Fractional part of Y-coordinate (ignored in Value noise).
c	Array of two gradients at grid points along X-axis.
t	Noise type.

Returns: Linearly interpolated gradient or value.

Definition at line 466 of file perlin.cpp.

◆ noise()

const float CPerlinNoise2D::noise	(	float	x,
		float	y,
		eNoise	t
	)		const

private

Compute a single octave of Perlin or Value noise at a 2D point.

Parameters

x	X-coordinate of point.
y	Y-coordinate of point.
t	Noise type.

Returns: A smoothed noise value in [-1, 1] at the given point.

Definition at line 506 of file perlin.cpp.

◆ pair()

const size_t CPerlinNoise2D::pair	(	size_t	x,
		size_t	y
	)		const

inlineprivate

Perlin's pairing function, which combines two unsigned integers into one.

Parameters

x	First unsigned integer.
y	Second unsigned integer.

Returns: An unsigned integer that depends upon x and y.

Definition at line 346 of file perlin.cpp.

◆ pairstd()

const size_t CPerlinNoise2D::pairstd	(	size_t	x,
		size_t	y
	)		const

inlineprivate

Alternate version of Perlin's pairing function. Note: This function depends on the implementation of std::hash. The C++ Standard does not require that it be a good hash function, but we'll assume that it is. Most implementations are.

Parameters

x	First number.
y	Second number.

Returns: An unsigned integer that combines the parameters into a single number.

Definition at line 358 of file perlin.cpp.

◆ RandomizePermutation()

void CPerlinNoise2D::RandomizePermutation ( )

private

Use the standard algorithm to set the permutation in m_nPerm to a pseudo-random permutation with each permutation equally likely . The source of randomness is std::default_random_engine with std::uniform_int_distribution. This function should be called during initialization and when the table size changes. The pseudo-random number generator is re-seeded from m_nSeed before the permutation is generated. This means that the permutation used for each table size remains the same until m_nSeed is changed.

Definition at line 86 of file perlin.cpp.

◆ RandomizeTable()

void CPerlinNoise2D::RandomizeTable ( eDistribution d )

Set m_fTable to pseudo-random values in \([-1, 1]\) according to some probability distribution. The pseudo-random number generator is re-seeded from m_nSeed before the table is generated. This means that the table contents for each table size remains the same until m_nSeed is changed.

Parameters

d	Probability distribution enumerated type.

Definition at line 227 of file perlin.cpp.

◆ RandomizeTableCos()

void CPerlinNoise2D::RandomizeTableCos ( )

private

Fill the gradient/value table m_fTable using a cosine distribution. The source of randomness is std::default_random_engine with std::uniform_real_distribution<float>(0.0f, 1.0f). It simply multiplies the each pseudo-random number by \(pi\) and enters the cosine of the result into the table.

Definition at line 194 of file perlin.cpp.

◆ RandomizeTableExp()

void CPerlinNoise2D::RandomizeTableExp ( )

private

Fill the gradient/value table m_fTable using an exponential distribution. The source of randomness is std::default_random_engine with std::exponential_distribution<float>(8.0f). It fills half of the table with negative gradients and half with positive gradients.

Definition at line 208 of file perlin.cpp.

◆ RandomizeTableMaximal()

void CPerlinNoise2D::RandomizeTableMaximal ( )

private

Fill the gradient/value table m_fTable with large magnitude entries, that is, either -1 ot +1, using a uniform distribution. The source of randomness is std::default_random_engine with std::uniform_real_distribution<float>(-1.0f, 1.0f).

Definition at line 166 of file perlin.cpp.

◆ RandomizeTableMidpoint() [1/2]

void CPerlinNoise2D::RandomizeTableMidpoint ( )

private

Fill the gradient/value table m_fTable using midpoint displacement. This function fills in the first and last entries then calls the recursive RandomizeTableMidpoint(size_t, size_t, float) to fill in the rest.

Definition at line 141 of file perlin.cpp.

◆ RandomizeTableMidpoint() [2/2]

void CPerlinNoise2D::RandomizeTableMidpoint	(	size_t	i,
		size_t	j,
		float	alpha
	)

private

Initialize a chunk of the gradient/value table m_fTable using midpoint displacement. Given \(\mathsf{i}\) and \(\mathsf{j}\) such that \(\mathsf{j} > \mathsf{i}+1\) and \(0 \leq \mathsf{i}, \mathsf{j} \leq\) m_nSize, where \(\mathsf{j} - \mathsf{i}\) is a power of 2, this function assumes that m_fTable \([\mathsf{i}]\) and m_fTable \([\mathsf{j}]\) have been set, and fills in the entries m_fTable \([\mathsf{i} + 1]\) through m_fTable \([\mathsf{j}-1]\) recursively using midpoint displacement. That is, it sets the middle entry to the average of the first and last entry offset by a pseudo-random value in \([-1,1]\) times a value called the lacunarity. The function then halves the lacunarity and calls itself recursively on the top and bottom halves of the table chunk. The source of randomness is std::default_random_engine with std::uniform_real_distribution<float>(-1.0f, 1.0f).

Parameters

i	Lower index.
j	Upper index.
alpha	Lacunarity.

Definition at line 116 of file perlin.cpp.

◆ RandomizeTableNormal()

void CPerlinNoise2D::RandomizeTableNormal ( )

private

Fill the gradient/value table m_fTable using a normal distribution. The source of randomness is std::default_random_engine with std::normal_distribution<float>(500.0f, 200.0f).

Definition at line 179 of file perlin.cpp.

◆ RandomizeTableUniform()

void CPerlinNoise2D::RandomizeTableUniform ( )

private

Fill the gradient/value table m_fTable using a uniform distribution. The source of randomness is std::default_random_engine with std::uniform_real_distribution<float>(-1.0f, 1.0f).

Definition at line 152 of file perlin.cpp.

◆ SetHash()

void CPerlinNoise2D::SetHash ( eHash d )

Set the hash function type.

Parameters

d	Hash function enumerated type.

Definition at line 309 of file perlin.cpp.

◆ SetSeed()

void CPerlinNoise2D::SetSeed ( )

Set the pseudo-random number generator seed to timeGetTime(), the number of milliseconds since Windows last rebooted. This should be sufficiently unpredictable to make a good seed.

Definition at line 295 of file perlin.cpp.

◆ SetSpline()

void CPerlinNoise2D::SetSpline ( eSpline d )

Set the spline function type.

Parameters

d	Spline function enumerated type.

Definition at line 302 of file perlin.cpp.

◆ spline()

const float CPerlinNoise2D::spline ( float x ) const

inlineprivate

Compute a spline function. Depending on the value of m_eSpline this will be either identity function, a cubic spline, or a quintic spline.

Parameters

x	A float in the range \([-1, 1]\).

Returns: The spline of \(\mathsf{x}\) in the range \([-1, 1]\).

Definition at line 325 of file perlin.cpp.

◆ z()

const float CPerlinNoise2D::z	(	size_t	h,
		float	x,
		float	y,
		eNoise	t
	)		const

inlineprivate

For Perlin noise, multiply hashed gradient from m_fTable by coordinates. Use the hash value parameter to index into the gradient table for the X gradient and rehash it for the index of the Y gradient. Add these gradients multiplied by the fractional values of the position (that is, return \(z = x \frac{dz}{dx} + y\frac{dz}{dy}\)). For Value noise, just read the \(z\) value directly from the table.

Parameters

h	Hash value for gradient table index.
x	X-coordinate of point in the range \([-1, 1]\).
y	Y-coordinate of point in the range \([-1, 1]\).
t	Noise type.

Returns: Corresponding Z-value.

Definition at line 435 of file perlin.cpp.

Member Data Documentation

◆ m_eDistribution

eDistribution CPerlinNoise2D::m_eDistribution = eDistribution::Uniform

private

Definition at line 52 of file perlin.h.

◆ m_eHash

eHash CPerlinNoise2D::m_eHash = eHash::Permutation

private

Definition at line 50 of file perlin.h.

◆ m_eSpline

eSpline CPerlinNoise2D::m_eSpline = eSpline::Cubic

private

Definition at line 51 of file perlin.h.

◆ m_fTable

float* CPerlinNoise2D::m_fTable = nullptr

private

Definition at line 55 of file perlin.h.

◆ m_nDefTableSize

const size_t CPerlinNoise2D::m_nDefTableSize = 256

private

Definition at line 60 of file perlin.h.

◆ m_nMask

size_t CPerlinNoise2D::m_nMask = m_nDefTableSize - 1

private

Definition at line 65 of file perlin.h.

◆ m_nMaxTableSize

const size_t CPerlinNoise2D::m_nMaxTableSize = 1024

private

Definition at line 62 of file perlin.h.

◆ m_nMinTableSize

const size_t CPerlinNoise2D::m_nMinTableSize = 16

private

Definition at line 61 of file perlin.h.

◆ m_nPerm

size_t* CPerlinNoise2D::m_nPerm = nullptr

private

Definition at line 54 of file perlin.h.

◆ m_nSeed

UINT CPerlinNoise2D::m_nSeed = 0

private

Definition at line 58 of file perlin.h.

◆ m_nSize

size_t CPerlinNoise2D::m_nSize = m_nDefTableSize

private

Definition at line 64 of file perlin.h.

◆ m_stdRandom

std::default_random_engine CPerlinNoise2D::m_stdRandom

private

Definition at line 57 of file perlin.h.

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ CPerlinNoise2D()

◆ ~CPerlinNoise2D()

Member Function Documentation

◆ DefaultTableSize()

◆ DoubleTableSize()

◆ generate()

◆ GetDefTableSize()

◆ GetDistribution()

◆ GetHash()

◆ GetMaxTableSize()

◆ GetMinTableSize()

◆ GetSpline()

◆ GetTableSize()

◆ HalveTableSize()

◆ hash()

◆ hash2()

◆ HashCorners()

◆ hashstd()

◆ Initialize()

◆ Lerp()

◆ noise()

◆ pair()

◆ pairstd()

◆ RandomizePermutation()

◆ RandomizeTable()

◆ RandomizeTableCos()

◆ RandomizeTableExp()

◆ RandomizeTableMaximal()

◆ RandomizeTableMidpoint() [1/2]

◆ RandomizeTableMidpoint() [2/2]

◆ RandomizeTableNormal()

◆ RandomizeTableUniform()

◆ SetHash()

◆ SetSeed()

◆ SetSpline()

◆ spline()

◆ z()

Member Data Documentation

◆ m_eDistribution

◆ m_eHash

◆ m_eSpline

◆ m_fTable

◆ m_nDefTableSize

◆ m_nMask

◆ m_nMaxTableSize

◆ m_nMinTableSize

◆ m_nPerm

◆ m_nSeed

◆ m_nSize

◆ m_stdRandom