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 vtkTypeBool	IsA (const char *type)
	Return 1 if this class is the same type of (or a subclass of) the named class. More...

vtkMath *	NewInstance () const

void	PrintSelf (ostream &os, vtkIndent indent) override
	Methods invoked by print to print information about the object including superclasses. More...

template<class T1 , class T2 >
void	TensorFromSymmetricTensor (const T1 symmTensor[9], T2 tensor[9])

Public Member Functions inherited from vtkObject
	vtkBaseTypeMacro (vtkObject, vtkObjectBase)

virtual void	DebugOn ()
	Turn debugging output on. More...

virtual void	DebugOff ()
	Turn debugging output off. More...

bool	GetDebug ()
	Get the value of the debug flag. More...

void	SetDebug (bool debugFlag)
	Set the value of the debug flag. More...

virtual void	Modified ()
	Update the modification time for this object. More...

virtual vtkMTimeType	GetMTime ()
	Return this object's modified time. More...

void	PrintSelf (ostream &os, vtkIndent indent) override
	Methods invoked by print to print information about the object including superclasses. More...

void	RemoveObserver (unsigned long tag)

void	RemoveObservers (unsigned long event)

void	RemoveObservers (const char *event)

void	RemoveAllObservers ()

vtkTypeBool	HasObserver (unsigned long event)

vtkTypeBool	HasObserver (const char *event)

int	InvokeEvent (unsigned long event)

int	InvokeEvent (const char *event)

unsigned long	AddObserver (unsigned long event, vtkCommand *, float priority=0.0f)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...

unsigned long	AddObserver (const char event, vtkCommand , float priority=0.0f)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...

vtkCommand *	GetCommand (unsigned long tag)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...

void	RemoveObserver (vtkCommand *)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...

void	RemoveObservers (unsigned long event, vtkCommand *)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...

void	RemoveObservers (const char event, vtkCommand )
	Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...

vtkTypeBool	HasObserver (unsigned long event, vtkCommand *)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...

vtkTypeBool	HasObserver (const char event, vtkCommand )
	Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, void(T::*callback)(), float priority=0.0f)
	Overloads to AddObserver that allow developers to add class member functions as callbacks for events. More...

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, void(T::callback)(vtkObject , unsigned long, void *), float priority=0.0f)
	Overloads to AddObserver that allow developers to add class member functions as callbacks for events. More...

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, bool(T::callback)(vtkObject , unsigned long, void *), float priority=0.0f)
	Allow user to set the AbortFlagOn() with the return value of the callback method. More...

int	InvokeEvent (unsigned long event, void *callData)
	This method invokes an event and return whether the event was aborted or not. More...

int	InvokeEvent (const char event, void callData)
	This method invokes an event and return whether the event was aborted or not. More...

Public Member Functions inherited from vtkObjectBase
const char *	GetClassName () const
	Return the class name as a string. More...

virtual void	Delete ()
	Delete a VTK object. More...

virtual void	FastDelete ()
	Delete a reference to this object. More...

void	InitializeObjectBase ()

void	Print (ostream &os)
	Print an object to an ostream. More...

virtual void	Register (vtkObjectBase *o)
	Increase the reference count (mark as used by another object). More...

virtual void	UnRegister (vtkObjectBase *o)
	Decrease the reference count (release by another object). More...

int	GetReferenceCount ()
	Return the current reference count of this object. More...

void	SetReferenceCount (int)
	Sets the reference count. More...

void	PrintRevisions (ostream &)
	Legacy. More...

virtual void	PrintHeader (ostream &os, vtkIndent indent)
	Methods invoked by print to print information about the object including superclasses. More...

virtual void	PrintTrailer (ostream &os, vtkIndent indent)
	Methods invoked by print to print information about the object including superclasses. More...

Static Public Member Functions
static vtkMath *	New ()

static vtkTypeBool	IsTypeOf (const char *type)

static vtkMath *	SafeDownCast (vtkObjectBase *o)

static double	Pi ()
	A mathematical constant. More...

static int	Round (float f)
	Rounds a float to the nearest integer. More...

static int	Round (double f)

template<typename OutT >
static void	RoundDoubleToIntegralIfNecessary (double val, OutT *ret)
	Round a double to type OutT if OutT is integral, otherwise simply clamp the value to the output range. More...

static int	Floor (double x)
	Rounds a double to the nearest integer not greater than itself. More...

static int	Ceil (double x)
	Rounds a double to the nearest integer not less than itself. More...

static int	CeilLog2 (vtkTypeUInt64 x)
	Gives the exponent of the lowest power of two not less than x. More...

template<class T >
static T	Min (const T &a, const T &b)
	Returns the minimum of the two arguments provided. More...

template<class T >
static T	Max (const T &a, const T &b)
	Returns the maximum of the two arguments provided. More...

static bool	IsPowerOfTwo (vtkTypeUInt64 x)
	Returns true if integer is a power of two. More...

static int	NearestPowerOfTwo (int x)
	Compute the nearest power of two that is not less than x. More...

static vtkTypeInt64	Factorial (int N)
	Compute N factorial, N! = N(N-1) (N-2)...32*1. More...

static vtkTypeInt64	Binomial (int m, int n)
	The number of combinations of n objects from a pool of m objects (m>n). More...

static int *	BeginCombination (int m, int n)
	Start iterating over "m choose n" objects. More...

static int	NextCombination (int m, int n, int *combination)
	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. More...

static void	FreeCombination (int *combination)
	Free the "iterator" array created by vtkMath::BeginCombination. More...

static void	RandomSeed (int s)
	Initialize seed value. More...

static int	GetSeed ()
	Return the current seed used by the random number generator. More...

static double	Random ()
	Generate pseudo-random numbers distributed according to the uniform distribution between 0.0 and 1.0. More...

static double	Random (double min, double max)
	Generate pseudo-random numbers distributed according to the uniform distribution between min and max. More...

static double	Gaussian ()
	Generate pseudo-random numbers distributed according to the standard normal distribution. More...

static double	Gaussian (double mean, double std)
	Generate pseudo-random numbers distributed according to the Gaussian distribution with mean mean and standard deviation std. More...

static void	Add (const float a[3], const float b[3], float c[3])
	Addition of two 3-vectors (float version). More...

static void	Add (const double a[3], const double b[3], double c[3])
	Addition of two 3-vectors (double version). More...

static void	Subtract (const float a[3], const float b[3], float c[3])
	Subtraction of two 3-vectors (float version). More...

static void	Subtract (const double a[3], const double b[3], double c[3])
	Subtraction of two 3-vectors (double version). More...

static void	MultiplyScalar (float a[3], float s)
	Multiplies a 3-vector by a scalar (float version). More...

static void	MultiplyScalar2D (float a[2], float s)
	Multiplies a 2-vector by a scalar (float version). More...

static void	MultiplyScalar (double a[3], double s)
	Multiplies a 3-vector by a scalar (double version). More...

static void	MultiplyScalar2D (double a[2], double s)
	Multiplies a 2-vector by a scalar (double version). More...

static float	Dot (const float a[3], const float b[3])
	Dot product of two 3-vectors (float version). More...

static double	Dot (const double a[3], const double b[3])
	Dot product of two 3-vectors (double version). More...

static void	Outer (const float a[3], const float b[3], float c[3][3])
	Outer product of two 3-vectors (float version). More...

static void	Outer (const double a[3], const double b[3], double c[3][3])
	Outer product of two 3-vectors (double version). More...

static void	Cross (const float a[3], const float b[3], float c[3])
	Cross product of two 3-vectors. More...

static void	Cross (const double a[3], const double b[3], double c[3])
	Cross product of two 3-vectors. More...

static float	Norm (const float v[3])
	Compute the norm of 3-vector (float version). More...

static double	Norm (const double v[3])
	Compute the norm of 3-vector (double version). More...

static float	Normalize (float v[3])
	Normalize (in place) a 3-vector. More...

static double	Normalize (double v[3])
	Normalize (in place) a 3-vector. More...

static float	Distance2BetweenPoints (const float p1[3], const float p2[3])
	Compute distance squared between two points p1 and p2. More...

static double	Distance2BetweenPoints (const double p1[3], const double p2[3])
	Compute distance squared between two points p1 and p2. More...

static double	AngleBetweenVectors (const double v1[3], const double v2[3])
	Compute angle in radians between two vectors. More...

static double	GaussianAmplitude (const double variance, const double distanceFromMean)
	Compute the amplitude of a Gaussian function with mean=0 and specified variance. More...

static double	GaussianAmplitude (const double mean, const double variance, const double position)
	Compute the amplitude of a Gaussian function with specified mean and variance. More...

static double	GaussianWeight (const double variance, const double distanceFromMean)
	Compute the amplitude of an unnormalized Gaussian function with mean=0 and specified variance. More...

static double	GaussianWeight (const double mean, const double variance, const double position)
	Compute the amplitude of an unnormalized Gaussian function with specified mean and variance. More...

static float	Dot2D (const float x[2], const float y[2])
	Dot product of two 2-vectors. More...

static double	Dot2D (const double x[2], const double y[2])
	Dot product of two 2-vectors. More...

static void	Outer2D (const float x[2], const float y[2], float A[2][2])
	Outer product of two 2-vectors (float version). More...

static void	Outer2D (const double x[2], const double y[2], double A[2][2])
	Outer product of two 2-vectors (double version). More...

static float	Norm2D (const float x[2])
	Compute the norm of a 2-vector. More...

static double	Norm2D (const double x[2])
	Compute the norm of a 2-vector. More...

static float	Normalize2D (float v[2])
	Normalize (in place) a 2-vector. More...

static double	Normalize2D (double v[2])
	Normalize (in place) a 2-vector. More...

static float	Determinant2x2 (const float c1[2], const float c2[2])
	Compute determinant of 2x2 matrix. More...

static void	MultiplyMatrix (const double const A, const double const B, unsigned int rowA, unsigned int colA, unsigned int rowB, unsigned int colB, double **C)
	General matrix multiplication. More...

static float	Determinant3x3 (const float c1[3], const float c2[3], const float c3[3])
	Compute determinant of 3x3 matrix. More...

static double	Determinant3x3 (const double c1[3], const double c2[3], const double c3[3])
	Compute determinant of 3x3 matrix. More...

static double	Determinant3x3 (double a1, double a2, double a3, double b1, double b2, double b3, double c1, double c2, double c3)
	Calculate the determinant of a 3x3 matrix in the form: \| a1, b1, c1 \| \| a2, b2, c2 \| \| a3, b3, c3 \|. More...

static vtkTypeBool	SolveLinearSystem (double *A, double x, int size)
	Solve linear equations Ax = b using Crout's method. More...

static vtkTypeBool	InvertMatrix (double A, double AI, int size)
	Invert input square matrix A into matrix AI. More...

static vtkTypeBool	InvertMatrix (double A, double AI, int size, int tmp1Size, double tmp2Size)
	Thread safe version of InvertMatrix method. More...

static vtkTypeBool	LUFactorLinearSystem (double *A, int index, int size)
	Factor linear equations Ax = b using LU decomposition into the form A = LU where L is a unit lower triangular matrix and U is upper triangular matrix. More...

static vtkTypeBool	LUFactorLinearSystem (double *A, int index, int size, double *tmpSize)
	Thread safe version of LUFactorLinearSystem method. More...

static void	LUSolveLinearSystem (double *A, int index, double *x, int size)
	Solve linear equations Ax = b using LU decomposition A = LU where L is lower triangular matrix and U is upper triangular matrix. More...

static double	EstimateMatrixCondition (const double const A, int size)
	Estimate the condition number of a LU factored matrix. More...

static vtkTypeBool	SolveHomogeneousLeastSquares (int numberOfSamples, double xt, int xOrder, double mt)
	Solves for the least squares best fit matrix for the homogeneous equation X'M' = 0'. More...

static vtkTypeBool	SolveLeastSquares (int numberOfSamples, double xt, int xOrder, double yt, int yOrder, double **mt, int checkHomogeneous=1)
	Solves for the least squares best fit matrix for the equation X'M' = Y'. More...

template<class T >
static T	ClampValue (const T &value, const T &min, const T &max)
	Clamp some value against a range, return the result. More...

static double	ClampAndNormalizeValue (double value, const double range[2])
	Clamp a value against a range and then normalize it between 0 and 1. More...

template<class T1 , class T2 >
static void	TensorFromSymmetricTensor (const T1 symmTensor[6], T2 tensor[9])
	Convert a 6-Component symmetric tensor into a 9-Component tensor, no allocation performed. More...

template<class T >
static void	TensorFromSymmetricTensor (T tensor[9])
	Convert a 6-Component symmetric tensor into a 9-Component tensor, overwriting the tensor input. More...

static int	GetScalarTypeFittingRange (double range_min, double range_max, double scale=1.0, double shift=0.0)
	Return the scalar type that is most likely to have enough precision to store a given range of data once it has been scaled and shifted (i.e. More...

static vtkTypeBool	GetAdjustedScalarRange (vtkDataArray *array, int comp, double range[2])
	Get a vtkDataArray's scalar range for a given component. More...

static vtkTypeBool	ExtentIsWithinOtherExtent (const int extent1[6], const int extent2[6])
	Return true if first 3D extent is within second 3D extent Extent is x-min, x-max, y-min, y-max, z-min, z-max. More...

static vtkTypeBool	BoundsIsWithinOtherBounds (const double bounds1[6], const double bounds2[6], const double delta[3])
	Return true if first 3D bounds is within the second 3D bounds Bounds is x-min, x-max, y-min, y-max, z-min, z-max Delta is the error margin along each axis (usually a small number) More...

static vtkTypeBool	PointIsWithinBounds (const double point[3], const double bounds[6], const double delta[3])
	Return true if point is within the given 3D bounds Bounds is x-min, x-max, y-min, y-max, z-min, z-max Delta is the error margin along each axis (usually a small number) More...

static int	PlaneIntersectsAABB (const double bounds[6], const double normal[3], const double point[3])
	Implements Plane / Axis-Aligned Bounding-Box intersection as described in Graphics Gems IV, Ned Greene; pp. More...

static double	Solve3PointCircle (const double p1[3], const double p2[3], const double p3[3], double center[3])
	In Euclidean space, there is a unique circle passing through any given three non-collinear points P1, P2, and P3. More...

static double	Inf ()
	Special IEEE-754 number used to represent positive infinity. More...

static double	NegInf ()
	Special IEEE-754 number used to represent negative infinity. More...

static double	Nan ()
	Special IEEE-754 number used to represent Not-A-Number (Nan). More...

static vtkTypeBool	IsInf (double x)
	Test if a number is equal to the special floating point value infinity. More...

static vtkTypeBool	IsNan (double x)
	Test if a number is equal to the special floating point value Not-A-Number (Nan). More...

static bool	IsFinite (double x)
	Test if a number has finite value i.e. More...


static float	RadiansFromDegrees (float degrees)
	Convert degrees into radians. More...

static double	RadiansFromDegrees (double degrees)
	Convert degrees into radians. More...


static float	DegreesFromRadians (float radians)
	Convert radians into degrees. More...

static double	DegreesFromRadians (double radians)
	Convert radians into degrees. More...


static float	Norm (const float *x, int n)
	Compute the norm of n-vector. More...

static double	Norm (const double *x, int n)
	Compute the norm of n-vector. More...


static void	Perpendiculars (const double v1[3], double v2[3], double v3[3], double theta)
	Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3 (i.e. More...

static void	Perpendiculars (const float v1[3], float v2[3], float v3[3], double theta)
	Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3 (i.e. More...


static bool	ProjectVector (const float a[3], const float b[3], float projection[3])
	Compute the projection of vector a on vector b and return it in projection[3]. More...

static bool	ProjectVector (const double a[3], const double b[3], double projection[3])
	Compute the projection of vector a on vector b and return it in projection[3]. More...


static bool	ProjectVector2D (const float a[2], const float b[2], float projection[2])
	Compute the projection of 2D vector a on 2D vector b and returns the result in projection[2]. More...

static bool	ProjectVector2D (const double a[2], const double b[2], double projection[2])
	Compute the projection of 2D vector a on 2D vector b and returns the result in projection[2]. More...


static double	Determinant2x2 (double a, double b, double c, double d)
	Calculate the determinant of a 2x2 matrix: \| a b \| \| c d \|. More...

static double	Determinant2x2 (const double c1[2], const double c2[2])
	Calculate the determinant of a 2x2 matrix: \| a b \| \| c d \|. More...


static void	LUFactor3x3 (float A[3][3], int index[3])
	LU Factorization of a 3x3 matrix. More...

static void	LUFactor3x3 (double A[3][3], int index[3])
	LU Factorization of a 3x3 matrix. More...


static void	LUSolve3x3 (const float A[3][3], const int index[3], float x[3])
	LU back substitution for a 3x3 matrix. More...

static void	LUSolve3x3 (const double A[3][3], const int index[3], double x[3])
	LU back substitution for a 3x3 matrix. More...


static void	LinearSolve3x3 (const float A[3][3], const float x[3], float y[3])
	Solve Ay = x for y and place the result in y. More...

static void	LinearSolve3x3 (const double A[3][3], const double x[3], double y[3])
	Solve Ay = x for y and place the result in y. More...


static void	Multiply3x3 (const float A[3][3], const float in[3], float out[3])
	Multiply a vector by a 3x3 matrix. More...

static void	Multiply3x3 (const double A[3][3], const double in[3], double out[3])
	Multiply a vector by a 3x3 matrix. More...


static void	Multiply3x3 (const float A[3][3], const float B[3][3], float C[3][3])
	Multiply one 3x3 matrix by another according to C = AB. More...

static void	Multiply3x3 (const double A[3][3], const double B[3][3], double C[3][3])
	Multiply one 3x3 matrix by another according to C = AB. More...


static void	Transpose3x3 (const float A[3][3], float AT[3][3])
	Transpose a 3x3 matrix. More...

static void	Transpose3x3 (const double A[3][3], double AT[3][3])
	Transpose a 3x3 matrix. More...


static void	Invert3x3 (const float A[3][3], float AI[3][3])
	Invert a 3x3 matrix. More...

static void	Invert3x3 (const double A[3][3], double AI[3][3])
	Invert a 3x3 matrix. More...


static void	Identity3x3 (float A[3][3])
	Set A to the identity matrix. More...

static void	Identity3x3 (double A[3][3])
	Set A to the identity matrix. More...


static double	Determinant3x3 (const float A[3][3])
	Return the determinant of a 3x3 matrix. More...

static double	Determinant3x3 (const double A[3][3])
	Return the determinant of a 3x3 matrix. More...


static void	QuaternionToMatrix3x3 (const float quat[4], float A[3][3])
	Convert a quaternion to a 3x3 rotation matrix. More...

static void	QuaternionToMatrix3x3 (const double quat[4], double A[3][3])
	Convert a quaternion to a 3x3 rotation matrix. More...


static void	Matrix3x3ToQuaternion (const float A[3][3], float quat[4])
	Convert a 3x3 matrix into a quaternion. More...

static void	Matrix3x3ToQuaternion (const double A[3][3], double quat[4])
	Convert a 3x3 matrix into a quaternion. More...


static void	MultiplyQuaternion (const float q1[4], const float q2[4], float q[4])
	Multiply two quaternions. More...

static void	MultiplyQuaternion (const double q1[4], const double q2[4], double q[4])
	Multiply two quaternions. More...


static void	RotateVectorByNormalizedQuaternion (const float v[3], const float q[4], float r[3])
	rotate a vector by a normalized quaternion using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula More...

static void	RotateVectorByNormalizedQuaternion (const double v[3], const double q[4], double r[3])
	rotate a vector by a normalized quaternion using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula More...


static void	RotateVectorByWXYZ (const float v[3], const float q[4], float r[3])
	rotate a vector by WXYZ using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula More...

static void	RotateVectorByWXYZ (const double v[3], const double q[4], double r[3])
	rotate a vector by WXYZ using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula More...


static void	Orthogonalize3x3 (const float A[3][3], float B[3][3])
	Orthogonalize a 3x3 matrix and put the result in B. More...

static void	Orthogonalize3x3 (const double A[3][3], double B[3][3])
	Orthogonalize a 3x3 matrix and put the result in B. More...


static void	Diagonalize3x3 (const float A[3][3], float w[3], float V[3][3])
	Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V. More...

static void	Diagonalize3x3 (const double A[3][3], double w[3], double V[3][3])
	Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V. More...


static void	SingularValueDecomposition3x3 (const float A[3][3], float U[3][3], float w[3], float VT[3][3])
	Perform singular value decomposition on a 3x3 matrix. More...

static void	SingularValueDecomposition3x3 (const double A[3][3], double U[3][3], double w[3], double VT[3][3])
	Perform singular value decomposition on a 3x3 matrix. More...


static vtkTypeBool	Jacobi (float *a, float w, float **v)
	Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix. More...

static vtkTypeBool	Jacobi (double *a, double w, double **v)
	Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix. More...


static vtkTypeBool	JacobiN (float *a, int n, float w, float **v)
	JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. More...

static vtkTypeBool	JacobiN (double *a, int n, double w, double **v)
	JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. More...


static void	RGBToHSV (const float rgb[3], float hsv[3])
	Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...

static void	RGBToHSV (float r, float g, float b, float h, float s, float *v)
	Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...

static double *	RGBToHSV (const double rgb[3])
	Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...

static double *	RGBToHSV (double r, double g, double b)
	Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...

static void	RGBToHSV (const double rgb[3], double hsv[3])
	Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...

static void	RGBToHSV (double r, double g, double b, double h, double s, double *v)
	Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...


static void	HSVToRGB (const float hsv[3], float rgb[3])
	Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...

static void	HSVToRGB (float h, float s, float v, float r, float g, float *b)
	Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...

static double *	HSVToRGB (const double hsv[3])
	Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...

static double *	HSVToRGB (double h, double s, double v)
	Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...

static void	HSVToRGB (const double hsv[3], double rgb[3])
	Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...

static void	HSVToRGB (double h, double s, double v, double r, double g, double *b)
	Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...


static void	LabToXYZ (const double lab[3], double xyz[3])
	Convert color from the CIE-L*ab system to CIE XYZ. More...

static void	LabToXYZ (double L, double a, double b, double x, double y, double *z)
	Convert color from the CIE-L*ab system to CIE XYZ. More...

static double *	LabToXYZ (const double lab[3])
	Convert color from the CIE-L*ab system to CIE XYZ. More...


static void	XYZToLab (const double xyz[3], double lab[3])
	Convert Color from the CIE XYZ system to CIE-L*ab. More...

static void	XYZToLab (double x, double y, double z, double L, double a, double *b)
	Convert Color from the CIE XYZ system to CIE-L*ab. More...

static double *	XYZToLab (const double xyz[3])
	Convert Color from the CIE XYZ system to CIE-L*ab. More...


static void	XYZToRGB (const double xyz[3], double rgb[3])
	Convert color from the CIE XYZ system to RGB. More...

static void	XYZToRGB (double x, double y, double z, double r, double g, double *b)
	Convert color from the CIE XYZ system to RGB. More...

static double *	XYZToRGB (const double xyz[3])
	Convert color from the CIE XYZ system to RGB. More...


static void	RGBToXYZ (const double rgb[3], double xyz[3])
	Convert color from the RGB system to CIE XYZ. More...

static void	RGBToXYZ (double r, double g, double b, double x, double y, double *z)
	Convert color from the RGB system to CIE XYZ. More...

static double *	RGBToXYZ (const double rgb[3])
	Convert color from the RGB system to CIE XYZ. More...


static void	RGBToLab (const double rgb[3], double lab[3])
	Convert color from the RGB system to CIE-L*ab. More...

static void	RGBToLab (double red, double green, double blue, double L, double a, double *b)
	Convert color from the RGB system to CIE-L*ab. More...

static double *	RGBToLab (const double rgb[3])
	Convert color from the RGB system to CIE-L*ab. More...


static void	LabToRGB (const double lab[3], double rgb[3])
	Convert color from the CIE-L*ab system to RGB. More...

static void	LabToRGB (double L, double a, double b, double red, double green, double *blue)
	Convert color from the CIE-L*ab system to RGB. More...

static double *	LabToRGB (const double lab[3])
	Convert color from the CIE-L*ab system to RGB. More...


static void	UninitializeBounds (double bounds[6])
	Set the bounds to an uninitialized state. More...


static vtkTypeBool	AreBoundsInitialized (const double bounds[6])
	Are the bounds initialized? More...


static void	ClampValue (double *value, const double range[2])
	Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. More...

static void	ClampValue (double value, const double range[2], double *clamped_value)
	Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. More...

static void	ClampValues (double *values, int nb_values, const double range[2])
	Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. More...

static void	ClampValues (const double values, int nb_values, const double range[2], double clamped_values)
	Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. More...

Static Public Member Functions inherited from vtkObject
static vtkObject *	New ()
	Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More...

static void	BreakOnError ()
	This method is called when vtkErrorMacro executes. More...

static void	SetGlobalWarningDisplay (int val)
	This is a global flag that controls whether any debug, warning or error messages are displayed. More...

static void	GlobalWarningDisplayOn ()
	This is a global flag that controls whether any debug, warning or error messages are displayed. More...

static void	GlobalWarningDisplayOff ()
	This is a global flag that controls whether any debug, warning or error messages are displayed. More...

static int	GetGlobalWarningDisplay ()
	This is a global flag that controls whether any debug, warning or error messages are displayed. More...

Static Public Member Functions inherited from vtkObjectBase
static vtkTypeBool	IsTypeOf (const char *name)
	Return 1 if this class type is the same type of (or a subclass of) the named class. More...

static vtkObjectBase *	New ()
	Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More...

Protected Member Functions
virtual vtkObjectBase *	NewInstanceInternal () const

	vtkMath ()

	~vtkMath () override

Protected Member Functions inherited from vtkObject
	vtkObject ()

	~vtkObject () override

void	RegisterInternal (vtkObjectBase *, vtkTypeBool check) override

void	UnRegisterInternal (vtkObjectBase *, vtkTypeBool check) override

void	InternalGrabFocus (vtkCommand mouseEvents, vtkCommand keypressEvents=nullptr)
	These methods allow a command to exclusively grab all events. More...

void	InternalReleaseFocus ()
	These methods allow a command to exclusively grab all events. More...

Protected Member Functions inherited from vtkObjectBase
	vtkObjectBase ()

virtual	~vtkObjectBase ()

virtual void	CollectRevisions (ostream &)

virtual void	ReportReferences (vtkGarbageCollector *)

	vtkObjectBase (const vtkObjectBase &)

void	operator= (const vtkObjectBase &)

Static Protected Attributes
static vtkSmartPointer< vtkMathInternal >	Internal

Additional Inherited Members
Protected Attributes inherited from vtkObject
bool	Debug

vtkTimeStamp	MTime

vtkSubjectHelper *	SubjectHelper

Protected Attributes inherited from vtkObjectBase
vtkAtomicInt32	ReferenceCount

vtkWeakPointerBase **	WeakPointers

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 91 of file vtkMath.h.

Member Typedef Documentation

typedef vtkObject vtkMath::Superclass

Definition at line 95 of file vtkMath.h.

Constructor & Destructor Documentation

vtkMath::vtkMath ( )

inlineprotected

Definition at line 1289 of file vtkMath.h.

vtkMath::~vtkMath ( )

inlineoverrideprotected

Definition at line 1290 of file vtkMath.h.

Member Function Documentation

static vtkMath* vtkMath::New ( )

static

static vtkTypeBool vtkMath::IsTypeOf ( const char * type )

static

virtual vtkTypeBool 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 vtkObjectBase.

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

static

virtual vtkObjectBase* vtkMath::NewInstanceInternal ( ) const

protectedvirtual

vtkMath* vtkMath::NewInstance ( ) const

void vtkMath::PrintSelf	(	ostream &	os,
		vtkIndent	indent
	)

overridevirtual

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 vtkObjectBase.

static double vtkMath::Pi ( )

inlinestatic

A mathematical constant.

This version is atan(1.0) * 4.0

Definition at line 101 of file vtkMath.h.

float vtkMath::RadiansFromDegrees ( float degrees )

inlinestatic

Convert degrees into radians.

Definition at line 1299 of file vtkMath.h.

double vtkMath::RadiansFromDegrees ( double degrees )

inlinestatic

Convert degrees into radians.

Definition at line 1305 of file vtkMath.h.

float vtkMath::DegreesFromRadians ( float radians )

inlinestatic

Convert radians into degrees.

Definition at line 1311 of file vtkMath.h.

double vtkMath::DegreesFromRadians ( double radians )

inlinestatic

Convert radians into degrees.

Definition at line 1317 of file vtkMath.h.

static int vtkMath::Round ( float f )

inlinestatic

Rounds a float to the nearest integer.

Definition at line 123 of file vtkMath.h.

static int vtkMath::Round ( double f )

inlinestatic

Definition at line 125 of file vtkMath.h.

template<typename OutT >

static void vtkMath::RoundDoubleToIntegralIfNecessary	(	double	val,
		OutT *	ret
	)

inlinestatic

Round a double to type OutT if OutT is integral, otherwise simply clamp the value to the output range.

Definition at line 134 of file vtkMath.h.

int vtkMath::Floor ( double x )

inlinestatic

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 1344 of file vtkMath.h.

int vtkMath::Ceil ( double x )

inlinestatic

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 1353 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.

template<class T >

T vtkMath::Min	(	const T &	a,
		const T &	b
	)

inlinestatic

Returns the minimum of the two arguments provided.

If either argument is NaN, the first argument will always be returned.

Definition at line 1361 of file vtkMath.h.

template<class T >

T vtkMath::Max	(	const T &	a,
		const T &	b
	)

inlinestatic

Returns the maximum of the two arguments provided.

If either argument is NaN, the first argument will always be returned.

Definition at line 1368 of file vtkMath.h.

bool vtkMath::IsPowerOfTwo ( vtkTypeUInt64 x )

inlinestatic

Returns true if integer is a power of two.

Definition at line 1323 of file vtkMath.h.

int vtkMath::NearestPowerOfTwo ( int x )

inlinestatic

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 1330 of file vtkMath.h.

static vtkTypeInt64 vtkMath::Factorial ( int N )

static

Compute N factorial, N! = N*(N-1) * (N-2)...*3*2*1.

0! is taken to be 1.

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]
	)

inlinestatic

Addition of two 3-vectors (float version).

Result is stored in c according to c = a + b.

Definition at line 320 of file vtkMath.h.

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

inlinestatic

Addition of two 3-vectors (double version).

Result is stored in c according to c = a + b.

Definition at line 330 of file vtkMath.h.

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

inlinestatic

Subtraction of two 3-vectors (float version).

Result is stored in c according to c = a - b.

Definition at line 340 of file vtkMath.h.

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

inlinestatic

Subtraction of two 3-vectors (double version).

Result is stored in c according to c = a - b.

Definition at line 350 of file vtkMath.h.

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

inlinestatic

Multiplies a 3-vector by a scalar (float version).

This modifies the input 3-vector.

Definition at line 361 of file vtkMath.h.

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

inlinestatic

Multiplies a 2-vector by a scalar (float version).

This modifies the input 2-vector.

Definition at line 372 of file vtkMath.h.

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

inlinestatic

Multiplies a 3-vector by a scalar (double version).

This modifies the input 3-vector.

Definition at line 383 of file vtkMath.h.

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

inlinestatic

Multiplies a 2-vector by a scalar (double version).

This modifies the input 2-vector.

Definition at line 394 of file vtkMath.h.

static float vtkMath::Dot	(	const float	a[3],
		const float	b[3]
	)

inlinestatic

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

Definition at line 404 of file vtkMath.h.

static double vtkMath::Dot	(	const double	a[3],
		const double	b[3]
	)

inlinestatic

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

Definition at line 411 of file vtkMath.h.

static void vtkMath::Outer	(	const float	a[3],
		const float	b[3],
		float	c[3][3]
	)

inlinestatic

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

Definition at line 418 of file vtkMath.h.

static void vtkMath::Outer	(	const double	a[3],
		const double	b[3],
		double	c[3][3]
	)

inlinestatic

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

Definition at line 431 of file vtkMath.h.

void vtkMath::Cross	(	const float	a[3],
		const float	b[3],
		float	c[3]
	)

inlinestatic

Cross product of two 3-vectors.

Result (a x b) is stored in c. (float version)

Definition at line 1477 of file vtkMath.h.

void vtkMath::Cross	(	const double	a[3],
		const double	b[3],
		double	c[3]
	)

inlinestatic

Cross product of two 3-vectors.

Result (a x b) is stored in c. (double version)

Definition at line 1487 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 v[3] )

inlinestatic

Compute the norm of 3-vector (float version).

Definition at line 464 of file vtkMath.h.

static double vtkMath::Norm ( const double v[3] )

inlinestatic

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

Definition at line 471 of file vtkMath.h.

float vtkMath::Normalize ( float v[3] )

inlinestatic

Normalize (in place) a 3-vector.

Returns norm of vector. (float version)

Definition at line 1374 of file vtkMath.h.

double vtkMath::Normalize ( double v[3] )

inlinestatic

Normalize (in place) a 3-vector.

Returns norm of vector (double version).

Definition at line 1388 of file vtkMath.h.

static void vtkMath::Perpendiculars	(	const double	v1[3],
		double	v2[3],
		double	v3[3],
		double	theta
	)

static

Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3 (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 nullptr for v3.

static void vtkMath::Perpendiculars	(	const float	v1[3],
		float	v2[3],
		float	v3[3],
		double	theta
	)

static

Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3 (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 nullptr for v3.

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	p1[3],
		const float	p2[3]
	)

inlinestatic

Compute distance squared between two points p1 and p2.

(float version).

Definition at line 1458 of file vtkMath.h.

double vtkMath::Distance2BetweenPoints	(	const double	p1[3],
		const double	p2[3]
	)

inlinestatic

Compute distance squared between two points p1 and p2.

(double version).

Definition at line 1467 of file vtkMath.h.

static double vtkMath::AngleBetweenVectors	(	const double	v1[3],
		const double	v2[3]
	)

static

Compute angle in radians between two vectors.

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]
	)

inlinestatic

Dot product of two 2-vectors.

(float version).

Definition at line 568 of file vtkMath.h.

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

inlinestatic

Dot product of two 2-vectors.

(double version).

Definition at line 575 of file vtkMath.h.

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

inlinestatic

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

Definition at line 582 of file vtkMath.h.

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

inlinestatic

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

Definition at line 596 of file vtkMath.h.

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

inlinestatic

Compute the norm of a 2-vector.

(float version).

Definition at line 611 of file vtkMath.h.

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

inlinestatic

Compute the norm of a 2-vector.

(double version).

Definition at line 619 of file vtkMath.h.

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

static

Normalize (in place) a 2-vector.

Returns norm of vector. (float version).

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

static

Normalize (in place) a 2-vector.

Returns norm of vector. (double version).

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

inlinestatic

Compute determinant of 2x2 matrix.

Two columns of matrix are input.

Definition at line 638 of file vtkMath.h.

static double vtkMath::Determinant2x2	(	double	a,
		double	b,
		double	c,
		double	d
	)

inlinestatic

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

Definition at line 646 of file vtkMath.h.

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

inlinestatic

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

Definition at line 649 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 const	A,
		const double const	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 ( const float A[3][3] )

inlinestatic

Return the determinant of a 3x3 matrix.

Definition at line 1505 of file vtkMath.h.

double vtkMath::Determinant3x3 ( const double A[3][3] )

inlinestatic

Return the determinant of a 3x3 matrix.

Definition at line 1511 of file vtkMath.h.

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

inlinestatic

Compute determinant of 3x3 matrix.

Three columns of matrix are input.

Definition at line 1430 of file vtkMath.h.

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

inlinestatic

Compute determinant of 3x3 matrix.

Three columns of matrix are input.

Definition at line 1439 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
	)

inlinestatic

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

Definition at line 1448 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: https://people.csail.mit.edu/bkph/articles/Quaternions.pdf

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: https://people.csail.mit.edu/bkph/articles/Quaternions.pdf

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::RotateVectorByNormalizedQuaternion	(	const float	v[3],
		const float	q[4],
		float	r[3]
	)

static

rotate a vector by a normalized quaternion using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

static void vtkMath::RotateVectorByNormalizedQuaternion	(	const double	v[3],
		const double	q[4],
		double	r[3]
	)

static

rotate a vector by a normalized quaternion using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

static void vtkMath::RotateVectorByWXYZ	(	const float	v[3],
		const float	q[4],
		float	r[3]
	)

static

rotate a vector by WXYZ using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

static void vtkMath::RotateVectorByWXYZ	(	const double	v[3],
		const double	q[4],
		double	r[3]
	)

static

rotate a vector by WXYZ using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

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 vtkTypeBool 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 vtkTypeBool 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 vtkTypeBool 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 vtkTypeBool vtkMath::LUFactorLinearSystem	(	double **	A,
		int *	index,
		int	size
	)

static

Factor linear equations Ax = b using LU decomposition into the form A = LU where L is a unit lower triangular matrix and U is upper triangular matrix.

The input is a square matrix A, an integer array of pivot indices index[0->n-1], and the size, n, of the square matrix. The output is provided by overwriting the input A with a matrix of the same size as A containing all of the information about L and U. If the output matrix is $A* = \left( \begin{array}{cc} a & b \\ c & d \end{array} \right)$ then L and U can be obtained as: $L = \left( \begin{array}{cc} 1 & 0 \\ c & 1 \end{array} \right)$ $U = \left( \begin{array}{cc} a & b \\ 0 & d \end{array} \right)$

That is, the diagonal of the resulting A* is the diagonal of U. The upper right triangle of A is the upper right triangle of U. The lower left triangle of A is the lower left triangle of L (and since L is unit lower triangular, the diagonal of L is all 1's). If an error is found, the function returns 0.

static vtkTypeBool 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	(	const double const	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 vtkTypeBool 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 arranged column-wise. Resulting eigenvalues/vectors are sorted in decreasing order; the most positive eigenvectors are selected for consistency; eigenvectors are normalized. NOTE: the input matrix a is modified during the solution

static vtkTypeBool 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 arranged column-wise. Resulting eigenvalues/vectors are sorted in decreasing order; the most positive eigenvectors are selected for consistency; eigenvectors are normalized. NOTE: the input matrix a is modified during the solution

static vtkTypeBool 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 arranged column-wise. Resulting eigenvalues/vectors are sorted in decreasing order; the most positive eigenvectors are selected for consistency; and eigenvectors are normalized. w and v need to be allocated previously. NOTE: the input matrix a is modified during the solution

static vtkTypeBool 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 arranged column-wise. Resulting eigenvalues/vectors are sorted in decreasing order; the most positive eigenvectors are selected for consistency; and eigenvectors are normalized. w and v need to be allocated previously. NOTE: the input matrix a is modified during the solution

static vtkTypeBool 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 vtkTypeBool 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]
	)

inlinestatic

Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value).