Fractal Brownian motion from a simplex noise function. More...

#include <turbulence.h>

Inheritance diagram for SimplexTurbulence:

Public Member Functions
	SimplexTurbulence (const double &, const double &, const double &, const double &=0.5, const double &=0.5, int=8, const Vector &=Vector::Null)
	Create a scaled turbulence.

	SimplexTurbulence ()
	Unit turbulence.

	~SimplexTurbulence ()
	Empty.

double	Value (const Vector &) const
	Computes the turbulence value at a given point.

double	GetAlpha () const
	Return the amplitude dampening coefficient.

double	GetLambda () const
	Return the wavelength dampening coefficient.

double	GetOctaves () const
	Number of octaves.

double	K () const
	Return the global Lipschitz constant.

double	Maximum () const
	Return the maximum of the turbulence.

Protected Member Functions
double	UnitAt (const Vector &) const
	Computes the turbulence value at a given point.

Protected Member Functions inherited from SimplexNoise
	SimplexNoise ()
	Empty.

	~SimplexNoise ()
	Empty.

Protected Member Functions inherited from AnalyticScalarField
bool	Find (Vector &, bool, const Box &, int=10000, Random &=Random::R239) const
	Find a random sample point inside or outside the surface.

	AnalyticScalarField (bool=true)
	Constructor.

virtual Vector	Gradient (const Vector &) const
	Compute the gradient of the field.

Matrix	Hessian (const Vector &) const
	Compute the Hessian symmetric matrix of the field function.

virtual Vector	Normal (const Vector &) const
	Compute the normal to the surface.

bool	Inside (const double &) const
	Check if the value is considered as inside or outside.

virtual Color	GetMaterial (const Vector &, const Vector &=Vector::Null) const
	Compute the color.

virtual Box	GetBox () const
	Compute the bounding box of the scalar field.

void	Curvature (const Vector &, double &, double &) const
	Compute the gaussian and mean curvatures.

Vector	Cast (const Vector &, const double &, const double &=1e-6, int n=100) const
	Given a starting vertex x, project it onto the implicit surface following the gradient.

Vector	Dichotomy (Vector, Vector, double, double, double, const double &=1.0e-4) const
	Compute the intersection between a segment and an implicit surface.

virtual bool	GetSample (Vector &, const Box &, Random &=Random::R239) const
	Find a point sample on the implicit surface.

virtual int	GetSamples (QVector< Vector > &, const Box &, int, Random &=Random::R239) const
	Find a set of random sample points on the implicit surface.

virtual QVector< Vector >	Poisson (double, int, Random &=Random::R239) const
	Compute a Poisson sphere distribution on an implicit surface.

virtual ScalarField2	Sample (const Rectangles &, int, int) const
	Compute the field function at the vertices a lattice.

virtual ScalarField2	Sample (const Quadrangle &, int) const
	Sample the scalar field on a quadrangle.

virtual ScalarField	Sample (const Box &, int) const
	Sample the implicit surface to get a scalar field.

int	Roots (const Ray &, const double &, const double &, const double &, double *, int=1, const double &=1.0e-4) const
	Find the intersections between a ray and an implicit surface on a given interval.

int	Roots (const Ray &, const double &, const double &, const double &, const double &, const double &, double *, int=1, const double &=1.0e-4) const
	This functions searches the intersections between a ray and an implicit surface on a given interval.

virtual double	K (const Box &) const
	Compute the local Lipschitz constant inside a box.

virtual double	K (const Sphere &) const
	Compute the local Lipschitz constant inside a box.

virtual double	K (const Segment &) const
	Compute the local Lipschitz constant along a segment.

virtual void	Polygonize (int, Mesh &, const Box &, const double &=1e-4) const
	Compute the polygonal mesh approximating the implicit surface.

virtual void	PolygonizeLucie (const Box &, Mesh &, bool, bool) const
	Implementation of the original continuation polygonization method.

virtual void	PolygonizeLucie (const double &, Mesh &, bool, bool) const
	Wyvill's original marching cubes algorithm.

virtual void	Dual (int, Mesh &, const Box &) const
	Dual polygonization.

virtual bool	SphereTrace (const Ray &, const double &, const double &, const double &, double &, int &, const double &=1e-4) const
	Find the first intersection between a ray and an implicit surface on a given interval, using sphere tracing.

virtual void	Polygonize (const Box &, QVector< Triangle > &, const double &=1e-4, bool=false) const
	Polygonize a cube.

virtual void	Polygonize (const Tetrahedra &, QVector< Triangle > &, const double &=1e-4) const
	Polygonize a tetrahedral cell.

virtual Mesh	PolygonizeOctree (const Box &, int, const double &=1e-4) const
	Compute the polygonal mesh approximating the implicit surface using an octree decomposition of space.

virtual void	Voxelize (const Box &, int, Box &, QVector< Vector > &) const
	Voxelize the scalar field.

virtual void	Voxelize (int, Voxel &, const Box &) const
	Voxelization.

virtual double	Volume (int=5) const
	Computes the volume of the BlobTree.

virtual double	Volume (const Box &, int) const
	Compute the volume of a BlobTree object.

virtual double	Volume (const Box &, int, double &) const
	Compute the volume of an implicit surface.

virtual double	StochasticVolume (const Box &, int) const
	Compute the volume of an implicit surface.

virtual Sphere	Center (int) const
	Computes the gravity center of the BlobTree.

virtual Sphere	Center (const Box &, int) const
	Compute the center of gravity of the BlobTree.

virtual void	Colorize (const Mesh &, MeshColor &) const
	Colorize the vertexes of a mesh according to the analytic scalar field.

Protected Attributes
double	alpha = 0.5
	Amplitude attenuation coefficient.

double	lambda = 0.5
	Wavelength amplification coefficient.

int	octaves = 8
	Number of octaves.

Vector	t = Vector::Null
	Translation.

double	v0 = 0.0
	Base value.

double	a0 = 1.0
	Base amplitude.

double	l0 = 1.0
	Wavelength.

Protected Attributes inherited from AnalyticScalarField
bool	sign = true
	Sign convention, used for normal computation.

Static Protected Attributes
static const Matrix	R3 = Matrix::Rotation(Vector(4.0 * Math::Pi / 19.0, 3.0 * Math::Pi / 19.0, 2.0 * Math::Pi / 19.0))
	Random incremental rotation.

Static Protected Attributes inherited from SimplexNoise
static const Vector	gradient [12]
	Array of gradients for 3D noise.

static const int	perm [512]
	Permutation table, 256 entries duplicated once to avoid modulo computations.

static const double	G3 = 1.0 / 6.0
	Unskew factors for 3D case.

Static Protected Attributes inherited from AnalyticScalarField
static int	ncubes = 0
	Number of cubes processed by polygonization algorithms.

static const double	Epsilon = 1e-6
	Epsilon value for partial derivatives.

Friends
std::ostream &	operator<< (std::ostream &s, const SimplexTurbulence &noise)
	Overloaded.

Detailed Description

Fractal Brownian motion from a simplex noise function.

A turbulence field is characterized by the number of octaves, the attenuation of the amplitude of the noise summed at every step, and by the amplification of the wavelength.

Constructor & Destructor Documentation

◆ SimplexTurbulence()

SimplexTurbulence::SimplexTurbulence	(	const double &	v,
		const double &	a,
		const double &	l,
		const double &	alpha = 0.5,
		const double &	lambda = 0.5,
		int	octaves = 8,
		const Vector &	t = Vector::Null )

explicit

Create a scaled turbulence.

Parameters

v,a,l	Base value, amplitude and wavelength.
alpha	Amplitude attenuation factor (~0.5, should be less than 1.0).
lambda	Wavelength attenuation factor (~0.5, should be less than 1.0).
octaves	Number of octaves.
t	Translation offset.

Member Function Documentation

◆ K()

double SimplexTurbulence::K ( ) const

virtual

Return the global Lipschitz constant.

See also: Noise::K()

Reimplemented from SimplexNoise.

◆ UnitAt()

double SimplexTurbulence::UnitAt ( const Vector & p ) const

protected

Computes the turbulence value at a given point.

Sums a series of scaled noise functions.

Parameters

p Point.

◆ Value()

double SimplexTurbulence::Value ( const Vector & p ) const

virtual

Computes the turbulence value at a given point.

Sums a series of scaled simplex noise functions.

Parameters

p Point.

Reimplemented from SimplexNoise.

Friends And Related Symbol Documentation

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const SimplexTurbulence &	noise )

friend

Overloaded.

Parameters

s	Stream.
noise	The noise.

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ SimplexTurbulence()

Member Function Documentation

◆ K()

◆ UnitAt()

◆ Value()

Friends And Related Symbol Documentation

◆ operator<<