performs common math operations More...

#include <vtkMath.h>

Inheritance diagram for vtkMath:

Collaboration diagram for vtkMath:

Public Types
typedef vtkObject	Superclass
Public Member Functions
virtual int	IsA (const char *type)
vtkMath *	NewInstance () const
void	PrintSelf (ostream &os, vtkIndent indent)
Static Public Member Functions
static vtkMath *	New ()
static int	IsTypeOf (const char *type)
static vtkMath *	SafeDownCast (vtkObjectBase *o)
static double	Pi ()
static double	DoublePi ()
static double	DoubleTwoPi ()
static int	Floor (double x)
static int	Ceil (double x)
static int	CeilLog2 (vtkTypeUInt64 x)
static bool	IsPowerOfTwo (vtkTypeUInt64 x)
static int	NearestPowerOfTwo (int x)
static vtkTypeInt64	Factorial (int N)
static vtkTypeInt64	Binomial (int m, int n)
static int *	BeginCombination (int m, int n)
static int	NextCombination (int m, int n, int *combination)
static void	FreeCombination (int *combination)
static void	RandomSeed (int s)
static int	GetSeed ()
static double	Random ()
static double	Random (double min, double max)
static double	Gaussian ()
static double	Gaussian (double mean, double std)
static void	Cross (const float x[3], const float y[3], float z[3])
static void	Cross (const double x[3], const double y[3], double z[3])
static float	Normalize (float x[3])
static double	Normalize (double x[3])
static float	Distance2BetweenPoints (const float x[3], const float y[3])
static double	Distance2BetweenPoints (const double x[3], const double y[3])
static double	GaussianAmplitude (const double variance, const double distanceFromMean)
static double	GaussianAmplitude (const double mean, const double variance, const double position)
static double	GaussianWeight (const double variance, const double distanceFromMean)
static double	GaussianWeight (const double mean, const double variance, const double position)
static float	Normalize2D (float x[2])
static double	Normalize2D (double x[2])
static int	SolveLinearSystem (double *A, double x, int size)
static int	InvertMatrix (double A, double AI, int size)
static int	LUFactorLinearSystem (double *A, int index, int size)
static double	EstimateMatrixCondition (double **A, int size)
static int	ExtentIsWithinOtherExtent (int extent1[6], int extent2[6])
static int	BoundsIsWithinOtherBounds (double bounds1[6], double bounds2[6], double delta[3])
static int	PointIsWithinBounds (double point[3], double bounds[6], double delta[3])
static double	Solve3PointCircle (const double p1[3], const double p2[3], const double p3[3], double center[3])
static double	Inf ()
static double	NegInf ()
static double	Nan ()
static int	IsInf (double x)
static int	IsNan (double x)
static bool	IsFinite (double x)

static float	RadiansFromDegrees (float degrees)
static double	RadiansFromDegrees (double degrees)

static float	DegreesFromRadians (float radians)
static double	DegreesFromRadians (double radians)

static int	Round (float f)
static int	Round (double f)

static void	Add (const float a[3], const float b[3], float c[3])

static void	Add (const double a[3], const double b[3], double c[3])

static void	Subtract (const float a[3], const float b[3], float c[3])

static void	Subtract (const double a[3], const double b[3], double c[3])

static void	MultiplyScalar (float a[3], float s)

static void	MultiplyScalar2D (float a[2], float s)

static void	MultiplyScalar (double a[3], double s)

static void	MultiplyScalar2D (double a[2], double s)

static float	Dot (const float x[3], const float y[3])

static double	Dot (const double x[3], const double y[3])

static void	Outer (const float x[3], const float y[3], float A[3][3])

static void	Outer (const double x[3], const double y[3], double A[3][3])

static float	Norm (const float *x, int n)
static double	Norm (const double *x, int n)

static float	Norm (const float x[3])

static double	Norm (const double x[3])

static void	Perpendiculars (const double x[3], double y[3], double z[3], double theta)
static void	Perpendiculars (const float x[3], float y[3], float z[3], double theta)

static bool	ProjectVector (const float a[3], const float b[3], float projection[3])
static bool	ProjectVector (const double a[3], const double b[3], double projection[3])

static bool	ProjectVector2D (const float a[2], const float b[2], float projection[2])
static bool	ProjectVector2D (const double a[2], const double b[2], double projection[2])

static float	Dot2D (const float x[2], const float y[2])

static double	Dot2D (const double x[2], const double y[2])

static void	Outer2D (const float x[2], const float y[2], float A[2][2])

static void	Outer2D (const double x[2], const double y[2], double A[2][2])

static float	Norm2D (const float x[2])

static double	Norm2D (const double x[2])

static float	Determinant2x2 (const float c1[2], const float c2[2])

static double	Determinant2x2 (double a, double b, double c, double d)
static double	Determinant2x2 (const double c1[2], const double c2[2])

static void	LUFactor3x3 (float A[3][3], int index[3])
static void	LUFactor3x3 (double A[3][3], int index[3])

static void	LUSolve3x3 (const float A[3][3], const int index[3], float x[3])
static void	LUSolve3x3 (const double A[3][3], const int index[3], double x[3])

static void	LinearSolve3x3 (const float A[3][3], const float x[3], float y[3])
static void	LinearSolve3x3 (const double A[3][3], const double x[3], double y[3])

static void	Multiply3x3 (const float A[3][3], const float in[3], float out[3])
static void	Multiply3x3 (const double A[3][3], const double in[3], double out[3])

static void	Multiply3x3 (const float A[3][3], const float B[3][3], float C[3][3])
static void	Multiply3x3 (const double A[3][3], const double B[3][3], double C[3][3])

static void	MultiplyMatrix (const double A, const double B, unsigned int rowA, unsigned int colA, unsigned int rowB, unsigned int colB, double **C)

static void	Transpose3x3 (const float A[3][3], float AT[3][3])
static void	Transpose3x3 (const double A[3][3], double AT[3][3])

static void	Invert3x3 (const float A[3][3], float AI[3][3])
static void	Invert3x3 (const double A[3][3], double AI[3][3])

static void	Identity3x3 (float A[3][3])
static void	Identity3x3 (double A[3][3])

static double	Determinant3x3 (float A[3][3])
static double	Determinant3x3 (double A[3][3])

static float	Determinant3x3 (const float c1[3], const float c2[3], const float c3[3])

static double	Determinant3x3 (const double c1[3], const double c2[3], const double c3[3])

static double	Determinant3x3 (double a1, double a2, double a3, double b1, double b2, double b3, double c1, double c2, double c3)

static void	QuaternionToMatrix3x3 (const float quat[4], float A[3][3])
static void	QuaternionToMatrix3x3 (const double quat[4], double A[3][3])

static void	Matrix3x3ToQuaternion (const float A[3][3], float quat[4])
static void	Matrix3x3ToQuaternion (const double A[3][3], double quat[4])

static void	MultiplyQuaternion (const float q1[4], const float q2[4], float q[4])
static void	MultiplyQuaternion (const double q1[4], const double q2[4], double q[4])

static void	Orthogonalize3x3 (const float A[3][3], float B[3][3])
static void	Orthogonalize3x3 (const double A[3][3], double B[3][3])

static void	Diagonalize3x3 (const float A[3][3], float w[3], float V[3][3])
static void	Diagonalize3x3 (const double A[3][3], double w[3], double V[3][3])

static void	SingularValueDecomposition3x3 (const float A[3][3], float U[3][3], float w[3], float VT[3][3])
static void	SingularValueDecomposition3x3 (const double A[3][3], double U[3][3], double w[3], double VT[3][3])

static int	InvertMatrix (double A, double AI, int size, int tmp1Size, double tmp2Size)

static int	LUFactorLinearSystem (double *A, int index, int size, double *tmpSize)

static void	LUSolveLinearSystem (double *A, int index, double *x, int size)

static int	Jacobi (float *a, float w, float **v)
static int	Jacobi (double *a, double w, double **v)

static int	JacobiN (float *a, int n, float w, float **v)
static int	JacobiN (double *a, int n, double w, double **v)

static int	SolveHomogeneousLeastSquares (int numberOfSamples, double xt, int xOrder, double mt)

static int	SolveLeastSquares (int numberOfSamples, double xt, int xOrder, double yt, int yOrder, double **mt, int checkHomogeneous=1)

static void	RGBToHSV (const float rgb[3], float hsv[3])
static void	RGBToHSV (float r, float g, float b, float h, float s, float *v)
static double *	RGBToHSV (const double rgb[3])
static double *	RGBToHSV (double r, double g, double b)
static void	RGBToHSV (const double rgb[3], double hsv[3])
static void	RGBToHSV (double r, double g, double b, double h, double s, double *v)

static void	HSVToRGB (const float hsv[3], float rgb[3])
static void	HSVToRGB (float h, float s, float v, float r, float g, float *b)
static double *	HSVToRGB (const double hsv[3])
static double *	HSVToRGB (double h, double s, double v)
static void	HSVToRGB (const double hsv[3], double rgb[3])
static void	HSVToRGB (double h, double s, double v, double r, double g, double *b)

static void	LabToXYZ (const double lab[3], double xyz[3])
static void	LabToXYZ (double L, double a, double b, double x, double y, double *z)
static double *	LabToXYZ (const double lab[3])

static void	XYZToLab (const double xyz[3], double lab[3])
static void	XYZToLab (double x, double y, double z, double L, double a, double *b)
static double *	XYZToLab (const double xyz[3])

static void	XYZToRGB (const double xyz[3], double rgb[3])
static void	XYZToRGB (double x, double y, double z, double r, double g, double *b)
static double *	XYZToRGB (const double xyz[3])

static void	RGBToXYZ (const double rgb[3], double xyz[3])
static void	RGBToXYZ (double r, double g, double b, double x, double y, double *z)
static double *	RGBToXYZ (const double rgb[3])

static void	RGBToLab (const double rgb[3], double lab[3])
static void	RGBToLab (double red, double green, double blue, double L, double a, double *b)
static double *	RGBToLab (const double rgb[3])

static void	LabToRGB (const double lab[3], double rgb[3])
static void	LabToRGB (double L, double a, double b, double red, double green, double *blue)
static double *	LabToRGB (const double lab[3])

static void	UninitializeBounds (double bounds[6])

static int	AreBoundsInitialized (double bounds[6])

static void	ClampValue (double *value, const double range[2])
static void	ClampValue (double value, const double range[2], double *clamped_value)
static void	ClampValues (double *values, int nb_values, const double range[2])
static void	ClampValues (const double values, int nb_values, const double range[2], double clamped_values)

static double	ClampAndNormalizeValue (double value, const double range[2])

static int	GetScalarTypeFittingRange (double range_min, double range_max, double scale=1.0, double shift=0.0)

static int	GetAdjustedScalarRange (vtkDataArray *array, int comp, double range[2])
Protected Member Functions
virtual vtkObjectBase *	NewInstanceInternal () const
	vtkMath ()
	~vtkMath ()
Static Protected Attributes
static vtkMathInternal	Internal

Detailed Description

performs common math operations

vtkMath provides methods to perform common math operations. These include providing constants such as Pi; conversion from degrees to radians; vector operations such as dot and cross products and vector norm; matrix determinant for 2x2 and 3x3 matrices; univariate polynomial solvers; and for random number generation (for backward compatibility only).

See also:: vtkMinimalStandardRandomSequence, vtkBoxMuellerRandomSequence, vtkQuaternion

Examples:: vtkMath (Examples)

Tests:: vtkMath (Tests)

Definition at line 80 of file vtkMath.h.

Member Typedef Documentation

typedef vtkObject vtkMath::Superclass

Reimplemented from vtkObject.

Definition at line 84 of file vtkMath.h.

Constructor & Destructor Documentation

vtkMath::vtkMath ( ) [inline, protected]

Definition at line 952 of file vtkMath.h.

vtkMath::~vtkMath ( ) [inline, protected]

Definition at line 953 of file vtkMath.h.

Member Function Documentation

static vtkMath* vtkMath::New ( ) [static]

Create an object with Debug turned off, modified time initialized to zero, and reference counting on.

Reimplemented from vtkObject.

static int vtkMath::IsTypeOf ( const char * name ) [static]

Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkObject.

virtual int vtkMath::IsA ( const char * name ) [virtual]

Return 1 if this class is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkObject.

static vtkMath* vtkMath::SafeDownCast ( vtkObjectBase * o ) [static]

Reimplemented from vtkObject.

virtual vtkObjectBase* vtkMath::NewInstanceInternal ( ) const [protected, virtual]

Reimplemented from vtkObject.

vtkMath* vtkMath::NewInstance ( ) const

Reimplemented from vtkObject.

void vtkMath::PrintSelf	(	ostream &	os,
		vtkIndent	indent
	)		`[virtual]`

Methods invoked by print to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from vtkObject.

static double vtkMath::Pi ( ) [inline, static]

A mathematical constant. This version is atan(1.0) * 4.0

Definition at line 88 of file vtkMath.h.

static double vtkMath::DoublePi ( ) [static]

Deprecated. Use vtkMath::Pi() instead.

static double vtkMath::DoubleTwoPi ( ) [static]

Deprecated. Use 2.0 * vtkMath::Pi() instead.

float vtkMath::RadiansFromDegrees ( float degrees ) [inline, static]

Convert degrees into radians

Definition at line 962 of file vtkMath.h.

double vtkMath::RadiansFromDegrees ( double degrees ) [inline, static]

Convert degrees into radians

Definition at line 968 of file vtkMath.h.

float vtkMath::DegreesFromRadians ( float radians ) [inline, static]

Convert radians into degrees

Definition at line 974 of file vtkMath.h.

double vtkMath::DegreesFromRadians ( double radians ) [inline, static]

Convert radians into degrees

Definition at line 980 of file vtkMath.h.

static int vtkMath::Round ( float f ) [inline, static]

Rounds a float to the nearest integer.

Definition at line 110 of file vtkMath.h.

static int vtkMath::Round ( double f ) [inline, static]

Rounds a float to the nearest integer.

Definition at line 112 of file vtkMath.h.

int vtkMath::Floor ( double x ) [inline, static]

Rounds a double to the nearest integer not greater than itself. This is faster than floor() but provides undefined output on overflow.

Definition at line 1018 of file vtkMath.h.

int vtkMath::Ceil ( double x ) [inline, static]

Rounds a double to the nearest integer not less than itself. This is faster than ceil() but provides undefined output on overflow.

Definition at line 1027 of file vtkMath.h.

static int vtkMath::CeilLog2 ( vtkTypeUInt64 x ) [static]

Gives the exponent of the lowest power of two not less than x. Or in mathspeak, return the smallest "i" for which 2^i >= x. If x is zero, then the return value will be zero.

bool vtkMath::IsPowerOfTwo ( vtkTypeUInt64 x ) [inline, static]

Returns true if integer is a power of two.

Definition at line 997 of file vtkMath.h.

int vtkMath::NearestPowerOfTwo ( int x ) [inline, static]

Compute the nearest power of two that is not less than x. The return value is 1 if x is less than or equal to zero, and is VTK_INT_MIN if result is too large to fit in an int.

Definition at line 1004 of file vtkMath.h.

vtkTypeInt64 vtkMath::Factorial ( int N ) [inline, static]

Compute N factorial, N! = N*(N-1) * (N-2)...*3*2*1. 0! is taken to be

Definition at line 986 of file vtkMath.h.

static vtkTypeInt64 vtkMath::Binomial	(	int	m,
		int	n
	)		`[static]`

The number of combinations of n objects from a pool of m objects (m>n). This is commonly known as "m choose n" and sometimes denoted $_mC_n$ or $\left(\begin{array}{c}m \\ n\end{array}\right)$ .

static int* vtkMath::BeginCombination	(	int	m,
		int	n
	)		`[static]`

Start iterating over "m choose n" objects. This function returns an array of n integers, each from 0 to m-1. These integers represent the n items chosen from the set [0,m[. You are responsible for calling vtkMath::FreeCombination() once the iterator is no longer needed. Warning: this gets large very quickly, especially when n nears m/2! (Hint: think of Pascal's triangle.)

static int vtkMath::NextCombination	(	int	m,
		int	n,
		int *	combination
	)		`[static]`

Given m, n, and a valid combination of n integers in the range [0,m[, this function alters the integers into the next combination in a sequence of all combinations of n items from a pool of m. If the combination is the last item in the sequence on input, then combination is unaltered and 0 is returned. Otherwise, 1 is returned and combination is updated.

static void vtkMath::FreeCombination ( int * combination ) [static]

Free the "iterator" array created by vtkMath::BeginCombination.

static void vtkMath::RandomSeed ( int s ) [static]

Initialize seed value. NOTE: Random() has the bad property that the first random number returned after RandomSeed() is called is proportional to the seed value! To help solve this, call RandomSeed() a few times inside seed. This doesn't ruin the repeatability of Random(). DON'T USE Random(), RandomSeed(), GetSeed(), Gaussian() THIS IS STATIC SO THIS IS PRONE TO ERRORS (SPECIALLY FOR REGRESSION TESTS) THIS IS HERE FOR BACKWARD COMPATIBILITY ONLY. Instead, for a sequence of random numbers with a uniform distribution create a vtkMinimalStandardRandomSequence object. For a sequence of random numbers with a gaussian/normal distribution create a vtkBoxMuellerRandomSequence object.

static int vtkMath::GetSeed ( ) [static]

Return the current seed used by the random number generator. DON'T USE Random(), RandomSeed(), GetSeed(), Gaussian() THIS IS STATIC SO THIS IS PRONE TO ERRORS (SPECIALLY FOR REGRESSION TESTS) THIS IS HERE FOR BACKWARD COMPATIBILITY ONLY. Instead, for a sequence of random numbers with a uniform distribution create a vtkMinimalStandardRandomSequence object. For a sequence of random numbers with a gaussian/normal distribution create a vtkBoxMuellerRandomSequence object.

static double vtkMath::Random ( ) [static]

Generate pseudo-random numbers distributed according to the uniform distribution between 0.0 and 1.0. This is used to provide portability across different systems. DON'T USE Random(), RandomSeed(), GetSeed(), Gaussian() THIS IS STATIC SO THIS IS PRONE TO ERRORS (SPECIALLY FOR REGRESSION TESTS) THIS IS HERE FOR BACKWARD COMPATIBILITY ONLY. Instead, for a sequence of random numbers with a uniform distribution create a vtkMinimalStandardRandomSequence object. For a sequence of random numbers with a gaussian/normal distribution create a vtkBoxMuellerRandomSequence object.

static double vtkMath::Random	(	double	min,
		double	max
	)		`[static]`

Generate pseudo-random numbers distributed according to the uniform distribution between min and max. DON'T USE Random(), RandomSeed(), GetSeed(), Gaussian() THIS IS STATIC SO THIS IS PRONE TO ERRORS (SPECIALLY FOR REGRESSION TESTS) THIS IS HERE FOR BACKWARD COMPATIBILITY ONLY. Instead, for a sequence of random numbers with a uniform distribution create a vtkMinimalStandardRandomSequence object. For a sequence of random numbers with a gaussian/normal distribution create a vtkBoxMuellerRandomSequence object.

static double vtkMath::Gaussian ( ) [static]

Generate pseudo-random numbers distributed according to the standard normal distribution. DON'T USE Random(), RandomSeed(), GetSeed(), Gaussian() THIS IS STATIC SO THIS IS PRONE TO ERRORS (SPECIALLY FOR REGRESSION TESTS) THIS IS HERE FOR BACKWARD COMPATIBILITY ONLY. Instead, for a sequence of random numbers with a uniform distribution create a vtkMinimalStandardRandomSequence object. For a sequence of random numbers with a gaussian/normal distribution create a vtkBoxMuellerRandomSequence object.

static double vtkMath::Gaussian	(	double	mean,
		double	std
	)		`[static]`

Generate pseudo-random numbers distributed according to the Gaussian distribution with mean mean and standard deviation std. DON'T USE Random(), RandomSeed(), GetSeed(), Gaussian() THIS IS STATIC SO THIS IS PRONE TO ERRORS (SPECIALLY FOR REGRESSION TESTS) THIS IS HERE FOR BACKWARD COMPATIBILITY ONLY. Instead, for a sequence of random numbers with a uniform distribution create a vtkMinimalStandardRandomSequence object. For a sequence of random numbers with a gaussian/normal distribution create a vtkBoxMuellerRandomSequence object.

static void vtkMath::Add	(	const float	a[3],
		const float	b[3],
		float	c[3]
	)		`[inline, static]`

Addition of two 3-vectors (float version). Result is stored in c.

Definition at line 232 of file vtkMath.h.

static void vtkMath::Add	(	const double	a[3],
		const double	b[3],
		double	c[3]
	)		`[inline, static]`

Addition of two 3-vectors (double version). Result is stored in c.

Definition at line 240 of file vtkMath.h.

static void vtkMath::Subtract	(	const float	a[3],
		const float	b[3],
		float	c[3]
	)		`[inline, static]`

Subtraction of two 3-vectors (float version). Result is stored in c according to c = a - b.

Definition at line 249 of file vtkMath.h.

static void vtkMath::Subtract	(	const double	a[3],
		const double	b[3],
		double	c[3]
	)		`[inline, static]`

Subtraction of two 3-vectors (double version). Result is stored in c according to c = a - b.

Definition at line 258 of file vtkMath.h.

static void vtkMath::MultiplyScalar	(	float	a[3],
		float	s
	)		`[inline, static]`

Multiplies a 3-vector by a scalar (float version). This modifies the input 3-vector.

Definition at line 267 of file vtkMath.h.

static void vtkMath::MultiplyScalar2D	(	float	a[2],
		float	s
	)		`[inline, static]`

Multiplies a 2-vector by a scalar (float version). This modifies the input 2-vector.

Definition at line 276 of file vtkMath.h.

static void vtkMath::MultiplyScalar	(	double	a[3],
		double	s
	)		`[inline, static]`

Multiplies a 3-vector by a scalar (double version). This modifies the input 3-vector.

Definition at line 285 of file vtkMath.h.

static void vtkMath::MultiplyScalar2D	(	double	a[2],
		double	s
	)		`[inline, static]`

Multiplies a 2-vector by a scalar (double version). This modifies the input 2-vector.

Definition at line 294 of file vtkMath.h.

static float vtkMath::Dot	(	const float	x[3],
		const float	y[3]
	)		`[inline, static]`

Dot product of two 3-vectors (float version).

Definition at line 302 of file vtkMath.h.

static double vtkMath::Dot	(	const double	x[3],
		const double	y[3]
	)		`[inline, static]`

Dot product of two 3-vectors (double-precision version).

Definition at line 308 of file vtkMath.h.

static void vtkMath::Outer	(	const float	x[3],
		const float	y[3],
		float	A[3][3]
	)		`[inline, static]`

Outer product of two 3-vectors (float version).

Definition at line 314 of file vtkMath.h.

static void vtkMath::Outer	(	const double	x[3],
		const double	y[3],
		double	A[3][3]
	)		`[inline, static]`

Outer product of two 3-vectors (double-precision version).

Definition at line 322 of file vtkMath.h.

void vtkMath::Cross	(	const float	x[3],
		const float	y[3],
		float	z[3]
	)		`[inline, static]`

Cross product of two 3-vectors. Result (a x b) is stored in z.

Definition at line 1137 of file vtkMath.h.

void vtkMath::Cross	(	const double	x[3],
		const double	y[3],
		double	z[3]
	)		`[inline, static]`

Cross product of two 3-vectors. Result (a x b) is stored in z. (double-precision version)

Definition at line 1147 of file vtkMath.h.

static float vtkMath::Norm	(	const float *	x,
		int	n
	)		`[static]`

Compute the norm of n-vector. x is the vector, n is its length.

static double vtkMath::Norm	(	const double *	x,
		int	n
	)		`[static]`

Compute the norm of n-vector. x is the vector, n is its length.

static float vtkMath::Norm ( const float x[3] ) [inline, static]

Compute the norm of 3-vector.

Definition at line 344 of file vtkMath.h.

static double vtkMath::Norm ( const double x[3] ) [inline, static]

Compute the norm of 3-vector (double-precision version).

Definition at line 350 of file vtkMath.h.

float vtkMath::Normalize ( float x[3] ) [inline, static]

Normalize (in place) a 3-vector. Returns norm of vector.

Definition at line 1034 of file vtkMath.h.

double vtkMath::Normalize ( double x[3] ) [inline, static]

Normalize (in place) a 3-vector. Returns norm of vector (double-precision version).

Definition at line 1048 of file vtkMath.h.

static void vtkMath::Perpendiculars	(	const double	x[3],
		double	y[3],
		double	z[3],
		double	theta
	)		`[static]`

Given a unit vector x, find two unit vectors y and z such that x cross y = z (i.e. the vectors are perpendicular to each other). There is an infinite number of such vectors, specify an angle theta to choose one set. If you want only one perpendicular vector, specify NULL for z.

static void vtkMath::Perpendiculars	(	const float	x[3],
		float	y[3],
		float	z[3],
		double	theta
	)		`[static]`

Given a unit vector x, find two unit vectors y and z such that x cross y = z (i.e. the vectors are perpendicular to each other). There is an infinite number of such vectors, specify an angle theta to choose one set. If you want only one perpendicular vector, specify NULL for z.

static bool vtkMath::ProjectVector	(	const float	a[3],
		const float	b[3],
		float	projection[3]
	)		`[static]`

Compute the projection of vector a on vector b and return it in projection[3]. If b is a zero vector, the function returns false and 'projection' is invalid. Otherwise, it returns true.

static bool vtkMath::ProjectVector	(	const double	a[3],
		const double	b[3],
		double	projection[3]
	)		`[static]`

Compute the projection of vector a on vector b and return it in projection[3]. If b is a zero vector, the function returns false and 'projection' is invalid. Otherwise, it returns true.

static bool vtkMath::ProjectVector2D	(	const float	a[2],
		const float	b[2],
		float	projection[2]
	)		`[static]`

Compute the projection of 2D vector 'a' on 2D vector 'b' and returns the result in projection[2]. If b is a zero vector, the function returns false and 'projection' is invalid. Otherwise, it returns true.

static bool vtkMath::ProjectVector2D	(	const double	a[2],
		const double	b[2],
		double	projection[2]
	)		`[static]`

Compute the projection of 2D vector 'a' on 2D vector 'b' and returns the result in projection[2]. If b is a zero vector, the function returns false and 'projection' is invalid. Otherwise, it returns true.

float vtkMath::Distance2BetweenPoints	(	const float	x[3],
		const float	y[3]
	)		`[inline, static]`

Compute distance squared between two points x and y.

Definition at line 1118 of file vtkMath.h.

double vtkMath::Distance2BetweenPoints	(	const double	x[3],
		const double	y[3]
	)		`[inline, static]`

Compute distance squared between two points x and y(double precision version).

Definition at line 1127 of file vtkMath.h.

static double vtkMath::GaussianAmplitude	(	const double	variance,
		const double	distanceFromMean
	)		`[static]`

Compute the amplitude of a Gaussian function with mean=0 and specified variance. That is, 1./(sqrt(2 Pi * variance)) * exp(-distanceFromMean^2/(2.*variance)).

static double vtkMath::GaussianAmplitude	(	const double	mean,
		const double	variance,
		const double	position
	)		`[static]`

Compute the amplitude of a Gaussian function with specified mean and variance. That is, 1./(sqrt(2 Pi * variance)) * exp(-(position - mean)^2/(2.*variance)).

static double vtkMath::GaussianWeight	(	const double	variance,
		const double	distanceFromMean
	)		`[static]`

Compute the amplitude of an unnormalized Gaussian function with mean=0 and specified variance. That is, exp(-distanceFromMean^2/(2.*variance)). When distanceFromMean = 0, this function returns 1.

static double vtkMath::GaussianWeight	(	const double	mean,
		const double	variance,
		const double	position
	)		`[static]`

Compute the amplitude of an unnormalized Gaussian function with specified mean and variance. That is, exp(-(position - mean)^2/(2.*variance)). When the distance from 'position' to 'mean' is 0, this function returns 1.

static float vtkMath::Dot2D	(	const float	x[2],
		const float	y[2]
	)		`[inline, static]`

Dot product of two 2-vectors.

Definition at line 421 of file vtkMath.h.

static double vtkMath::Dot2D	(	const double	x[2],
		const double	y[2]
	)		`[inline, static]`

Dot product of two 2-vectors. (double-precision version).

Definition at line 427 of file vtkMath.h.

static void vtkMath::Outer2D	(	const float	x[2],
		const float	y[2],
		float	A[2][2]
	)		`[inline, static]`

Outer product of two 2-vectors (float version).

Definition at line 433 of file vtkMath.h.

static void vtkMath::Outer2D	(	const double	x[2],
		const double	y[2],
		double	A[2][2]
	)		`[inline, static]`

Outer product of two 2-vectors (float version).

Definition at line 446 of file vtkMath.h.

static float vtkMath::Norm2D ( const float x[2] ) [inline, static]

Compute the norm of a 2-vector.

Definition at line 460 of file vtkMath.h.

static double vtkMath::Norm2D ( const double x[2] ) [inline, static]

Compute the norm of a 2-vector. (double-precision version).

Definition at line 466 of file vtkMath.h.

static float vtkMath::Normalize2D ( float x[2] ) [static]

Normalize (in place) a 2-vector. Returns norm of vector.

static double vtkMath::Normalize2D ( double x[2] ) [static]

Normalize (in place) a 2-vector. Returns norm of vector. (double-precision version).

static float vtkMath::Determinant2x2	(	const float	c1[2],
		const float	c2[2]
	)		`[inline, static]`

Compute determinant of 2x2 matrix. Two columns of matrix are input.

Definition at line 479 of file vtkMath.h.

static double vtkMath::Determinant2x2	(	double	a,
		double	b,
		double	c,
		double	d
	)		`[inline, static]`

Calculate the determinant of a 2x2 matrix: | a b | | c d |

Definition at line 485 of file vtkMath.h.

static double vtkMath::Determinant2x2	(	const double	c1[2],
		const double	c2[2]
	)		`[inline, static]`

Calculate the determinant of a 2x2 matrix: | a b | | c d |

Definition at line 487 of file vtkMath.h.

static void vtkMath::LUFactor3x3	(	float	A[3][3],
		int	index[3]
	)		`[static]`

LU Factorization of a 3x3 matrix.

static void vtkMath::LUFactor3x3	(	double	A[3][3],
		int	index[3]
	)		`[static]`

LU Factorization of a 3x3 matrix.

static void vtkMath::LUSolve3x3	(	const float	A[3][3],
		const int	index[3],
		float	x[3]
	)		`[static]`

LU back substitution for a 3x3 matrix.

static void vtkMath::LUSolve3x3	(	const double	A[3][3],
		const int	index[3],
		double	x[3]
	)		`[static]`

LU back substitution for a 3x3 matrix.

static void vtkMath::LinearSolve3x3	(	const float	A[3][3],
		const float	x[3],
		float	y[3]
	)		`[static]`

Solve Ay = x for y and place the result in y. The matrix A is destroyed in the process.

static void vtkMath::LinearSolve3x3	(	const double	A[3][3],
		const double	x[3],
		double	y[3]
	)		`[static]`

Solve Ay = x for y and place the result in y. The matrix A is destroyed in the process.

static void vtkMath::Multiply3x3	(	const float	A[3][3],
		const float	in[3],
		float	out[3]
	)		`[static]`

Multiply a vector by a 3x3 matrix. The result is placed in out.

static void vtkMath::Multiply3x3	(	const double	A[3][3],
		const double	in[3],
		double	out[3]
	)		`[static]`

Multiply a vector by a 3x3 matrix. The result is placed in out.

static void vtkMath::Multiply3x3	(	const float	A[3][3],
		const float	B[3][3],
		float	C[3][3]
	)		`[static]`

Multiply one 3x3 matrix by another according to C = AB.

static void vtkMath::Multiply3x3	(	const double	A[3][3],
		const double	B[3][3],
		double	C[3][3]
	)		`[static]`

Multiply one 3x3 matrix by another according to C = AB.

static void vtkMath::MultiplyMatrix	(	const double **	A,
		const double **	B,
		unsigned int	rowA,
		unsigned int	colA,
		unsigned int	rowB,
		unsigned int	colB,
		double **	C
	)		`[static]`

General matrix multiplication. You must allocate output storage. colA == rowB and matrix C is rowA x colB

static void vtkMath::Transpose3x3	(	const float	A[3][3],
		float	AT[3][3]
	)		`[static]`

Transpose a 3x3 matrix. The input matrix is A. The output is stored in AT.

static void vtkMath::Transpose3x3	(	const double	A[3][3],
		double	AT[3][3]
	)		`[static]`

Transpose a 3x3 matrix. The input matrix is A. The output is stored in AT.

static void vtkMath::Invert3x3	(	const float	A[3][3],
		float	AI[3][3]
	)		`[static]`

Invert a 3x3 matrix. The input matrix is A. The output is stored in AI.

static void vtkMath::Invert3x3	(	const double	A[3][3],
		double	AI[3][3]
	)		`[static]`

Invert a 3x3 matrix. The input matrix is A. The output is stored in AI.

static void vtkMath::Identity3x3 ( float A[3][3] ) [static]

Set A to the identity matrix.

static void vtkMath::Identity3x3 ( double A[3][3] ) [static]

Set A to the identity matrix.

double vtkMath::Determinant3x3 ( float A[3][3] ) [inline, static]

Return the determinant of a 3x3 matrix.

Definition at line 1167 of file vtkMath.h.

double vtkMath::Determinant3x3 ( double A[3][3] ) [inline, static]

Return the determinant of a 3x3 matrix.

Definition at line 1173 of file vtkMath.h.

float vtkMath::Determinant3x3	(	const float	c1[3],
		const float	c2[3],
		const float	c3[3]
	)		`[inline, static]`

Compute determinant of 3x3 matrix. Three columns of matrix are input.

Definition at line 1090 of file vtkMath.h.

double vtkMath::Determinant3x3	(	const double	c1[3],
		const double	c2[3],
		const double	c3[3]
	)		`[inline, static]`

Compute determinant of 3x3 matrix. Three columns of matrix are input.

Definition at line 1099 of file vtkMath.h.

double vtkMath::Determinant3x3	(	double	a1,
		double	a2,
		double	a3,
		double	b1,
		double	b2,
		double	b3,
		double	c1,
		double	c2,
		double	c3
	)		`[inline, static]`

Calculate the determinant of a 3x3 matrix in the form: | a1, b1, c1 | | a2, b2, c2 | | a3, b3, c3 |

Definition at line 1108 of file vtkMath.h.

static void vtkMath::QuaternionToMatrix3x3	(	const float	quat[4],
		float	A[3][3]
	)		`[static]`

Convert a quaternion to a 3x3 rotation matrix. The quaternion does not have to be normalized beforehand. The quaternion must be in the form [w, x, y, z].

See also:: Matrix3x3ToQuaternion() MultiplyQuaternion(); vtkQuaternion

static void vtkMath::QuaternionToMatrix3x3	(	const double	quat[4],
		double	A[3][3]
	)		`[static]`

Convert a quaternion to a 3x3 rotation matrix. The quaternion does not have to be normalized beforehand. The quaternion must be in the form [w, x, y, z].

See also:: Matrix3x3ToQuaternion() MultiplyQuaternion(); vtkQuaternion

static void vtkMath::Matrix3x3ToQuaternion	(	const float	A[3][3],
		float	quat[4]
	)		`[static]`

Convert a 3x3 matrix into a quaternion. This will provide the best possible answer even if the matrix is not a pure rotation matrix. The quaternion is in the form [w, x, y, z]. The method used is that of B.K.P. Horn.

See also:: QuaternionToMatrix3x3() MultiplyQuaternion(); vtkQuaternion

static void vtkMath::Matrix3x3ToQuaternion	(	const double	A[3][3],
		double	quat[4]
	)		`[static]`

Convert a 3x3 matrix into a quaternion. This will provide the best possible answer even if the matrix is not a pure rotation matrix. The quaternion is in the form [w, x, y, z]. The method used is that of B.K.P. Horn.

See also:: QuaternionToMatrix3x3() MultiplyQuaternion(); vtkQuaternion

static void vtkMath::MultiplyQuaternion	(	const float	q1[4],
		const float	q2[4],
		float	q[4]
	)		`[static]`

Multiply two quaternions. This is used to concatenate rotations. Quaternions are in the form [w, x, y, z].

See also:: Matrix3x3ToQuaternion() QuaternionToMatrix3x3(); vtkQuaternion

static void vtkMath::MultiplyQuaternion	(	const double	q1[4],
		const double	q2[4],
		double	q[4]
	)		`[static]`

Multiply two quaternions. This is used to concatenate rotations. Quaternions are in the form [w, x, y, z].

See also:: Matrix3x3ToQuaternion() QuaternionToMatrix3x3(); vtkQuaternion

static void vtkMath::Orthogonalize3x3	(	const float	A[3][3],
		float	B[3][3]
	)		`[static]`

Orthogonalize a 3x3 matrix and put the result in B. If matrix A has a negative determinant, then B will be a rotation plus a flip i.e. it will have a determinant of -1.

static void vtkMath::Orthogonalize3x3	(	const double	A[3][3],
		double	B[3][3]
	)		`[static]`

Orthogonalize a 3x3 matrix and put the result in B. If matrix A has a negative determinant, then B will be a rotation plus a flip i.e. it will have a determinant of -1.

static void vtkMath::Diagonalize3x3	(	const float	A[3][3],
		float	w[3],
		float	V[3][3]
	)		`[static]`

Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V. The matrix V will have a positive determinant, and the three eigenvectors will be aligned as closely as possible with the x, y, and z axes.

static void vtkMath::Diagonalize3x3	(	const double	A[3][3],
		double	w[3],
		double	V[3][3]
	)		`[static]`

Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V. The matrix V will have a positive determinant, and the three eigenvectors will be aligned as closely as possible with the x, y, and z axes.

static void vtkMath::SingularValueDecomposition3x3	(	const float	A[3][3],
		float	U[3][3],
		float	w[3],
		float	VT[3][3]
	)		`[static]`

Perform singular value decomposition on a 3x3 matrix. This is not done using a conventional SVD algorithm, instead it is done using Orthogonalize3x3 and Diagonalize3x3. Both output matrices U and VT will have positive determinants, and the w values will be arranged such that the three rows of VT are aligned as closely as possible with the x, y, and z axes respectively. If the determinant of A is negative, then the three w values will be negative.

static void vtkMath::SingularValueDecomposition3x3	(	const double	A[3][3],
		double	U[3][3],
		double	w[3],
		double	VT[3][3]
	)		`[static]`

Perform singular value decomposition on a 3x3 matrix. This is not done using a conventional SVD algorithm, instead it is done using Orthogonalize3x3 and Diagonalize3x3. Both output matrices U and VT will have positive determinants, and the w values will be arranged such that the three rows of VT are aligned as closely as possible with the x, y, and z axes respectively. If the determinant of A is negative, then the three w values will be negative.

static int vtkMath::SolveLinearSystem	(	double **	A,
		double *	x,
		int	size
	)		`[static]`

Solve linear equations Ax = b using Crout's method. Input is square matrix A and load vector x. Solution x is written over load vector. The dimension of the matrix is specified in size. If error is found, method returns a 0.

static int vtkMath::InvertMatrix	(	double **	A,
		double **	AI,
		int	size
	)		`[static]`

Invert input square matrix A into matrix AI. Note that A is modified during the inversion. The size variable is the dimension of the matrix. Returns 0 if inverse not computed.

static int vtkMath::InvertMatrix	(	double **	A,
		double **	AI,
		int	size,
		int *	tmp1Size,
		double *	tmp2Size
	)		`[static]`

Thread safe version of InvertMatrix method. Working memory arrays tmp1SIze and tmp2Size of length size must be passed in.

static int vtkMath::LUFactorLinearSystem	(	double **	A,
		int *	index,
		int	size
	)		`[static]`

Factor linear equations Ax = b using LU decomposition A = LU where L is lower triangular matrix and U is upper triangular matrix. Input is square matrix A, integer array of pivot indices index[0->n-1], and size of square matrix n. Output factorization LU is in matrix A. If error is found, method returns 0.

static int vtkMath::LUFactorLinearSystem	(	double **	A,
		int *	index,
		int	size,
		double *	tmpSize
	)		`[static]`

Thread safe version of LUFactorLinearSystem method. Working memory array tmpSize of length size must be passed in.

static void vtkMath::LUSolveLinearSystem	(	double **	A,
		int *	index,
		double *	x,
		int	size
	)		`[static]`

Solve linear equations Ax = b using LU decomposition A = LU where L is lower triangular matrix and U is upper triangular matrix. Input is factored matrix A=LU, integer array of pivot indices index[0->n-1], load vector x[0->n-1], and size of square matrix n. Note that A=LU and index[] are generated from method LUFactorLinearSystem). Also, solution vector is written directly over input load vector.

static double vtkMath::EstimateMatrixCondition	(	double **	A,
		int	size
	)		`[static]`

Estimate the condition number of a LU factored matrix. Used to judge the accuracy of the solution. The matrix A must have been previously factored using the method LUFactorLinearSystem. The condition number is the ratio of the infinity matrix norm (i.e., maximum value of matrix component) divided by the minimum diagonal value. (This works for triangular matrices only: see Conte and de Boor, Elementary Numerical Analysis.)

static int vtkMath::Jacobi	(	float **	a,
		float *	w,
		float **	v
	)		`[static]`

Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix. Square 3x3 matrix a; output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized.

static int vtkMath::Jacobi	(	double **	a,
		double *	w,
		double **	v
	)		`[static]`

Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix. Square 3x3 matrix a; output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized.

static int vtkMath::JacobiN	(	float **	a,
		int	n,
		float *	w,
		float **	v
	)		`[static]`

JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. Square nxn matrix a; size of matrix in n; output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized. w and v need to be allocated previously

static int vtkMath::JacobiN	(	double **	a,
		int	n,
		double *	w,
		double **	v
	)		`[static]`

JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. Square nxn matrix a; size of matrix in n; output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized. w and v need to be allocated previously

static int vtkMath::SolveHomogeneousLeastSquares	(	int	numberOfSamples,
		double **	xt,
		int	xOrder,
		double **	mt
	)		`[static]`

Solves for the least squares best fit matrix for the homogeneous equation X'M' = 0'. Uses the method described on pages 40-41 of Computer Vision by Forsyth and Ponce, which is that the solution is the eigenvector associated with the minimum eigenvalue of T(X)X, where T(X) is the transpose of X. The inputs and output are transposed matrices. Dimensions: X' is numberOfSamples by xOrder, M' dimension is xOrder by yOrder. M' should be pre-allocated. All matrices are row major. The resultant matrix M' should be pre-multiplied to X' to get 0', or transposed and then post multiplied to X to get 0

static int vtkMath::SolveLeastSquares	(	int	numberOfSamples,
		double **	xt,
		int	xOrder,
		double **	yt,
		int	yOrder,
		double **	mt,
		int	checkHomogeneous = `1`
	)		`[static]`

Solves for the least squares best fit matrix for the equation X'M' = Y'. Uses pseudoinverse to get the ordinary least squares. The inputs and output are transposed matrices. Dimensions: X' is numberOfSamples by xOrder, Y' is numberOfSamples by yOrder, M' dimension is xOrder by yOrder. M' should be pre-allocated. All matrices are row major. The resultant matrix M' should be pre-multiplied to X' to get Y', or transposed and then post multiplied to X to get Y By default, this method checks for the homogeneous condition where Y==0, and if so, invokes SolveHomogeneousLeastSquares. For better performance when the system is known not to be homogeneous, invoke with checkHomogeneous=0.

static void vtkMath::RGBToHSV	(	const float	rgb[3],
		float	hsv[3]
	)		`[inline, static]`

Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. The input RGB must be float values in the range [0,1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

Definition at line 755 of file vtkMath.h.

static void vtkMath::RGBToHSV	(	float	r,
		float	g,
		float	b,
		float *	h,
		float *	s,
		float *	v
	)		`[static]`

Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. The input RGB must be float values in the range [0,1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

static double* vtkMath::RGBToHSV ( const double rgb[3] ) [static]

Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. The input RGB must be float values in the range [0,1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

static double* vtkMath::RGBToHSV	(	double	r,
		double	g,
		double	b
	)		`[static]`

Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. The input RGB must be float values in the range [0,1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

static void vtkMath::RGBToHSV	(	const double	rgb[3],
		double	hsv[3]
	)		`[inline, static]`

Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. The input RGB must be float values in the range [0,1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

Definition at line 760 of file vtkMath.h.

static void vtkMath::RGBToHSV	(	double	r,
		double	g,
		double	b,
		double *	h,
		double *	s,
		double *	v
	)		`[static]`

Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. The input RGB must be float values in the range [0,1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

static void vtkMath::HSVToRGB	(	const float	hsv[3],
		float	rgb[3]
	)		`[inline, static]`