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.

vtkMath *	NewInstance () const

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

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.

virtual void	DebugOff ()
	Turn debugging output off.

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

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

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

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

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

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.

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

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

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

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

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

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

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

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.

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.

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.

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

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

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

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

virtual vtkIdType	GetNumberOfGenerationsFromBase (const char *name)
	Given the name of a base class of this class type, return the distance of inheritance between this class type and the named class (how many generations of inheritance are there between this class and the named class).

virtual void	Delete ()
	Delete a VTK object.

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

void	InitializeObjectBase ()

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

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

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

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

void	SetReferenceCount (int)
	Sets the reference count.

bool	GetIsInMemkind () const
	A local state flag that remembers whether this object lives in the normal or extended memory space.

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

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

Static Public Member Functions
static vtkMath *	New ()

static vtkTypeBool	IsTypeOf (const char *type)

static vtkMath *	SafeDownCast (vtkObjectBase *o)

static constexpr double	Pi ()
	A mathematical constant.

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

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.

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

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

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

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

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

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

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

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

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

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

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.

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

static void	RandomSeed (int s)
	Initialize seed value.

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

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

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

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

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

template<class VectorT1 , class VectorT2 >
static void	Assign (const VectorT1 &a, VectorT2 &&b)
	Assign values to a 3-vector (templated version).

static void	Assign (const double a[3], double b[3])
	Assign values to a 3-vector (double version).

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

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

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

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

template<class VectorT1 , class VectorT2 , class VectorT3 >
static void	Subtract (const VectorT1 &a, const VectorT2 &b, VectorT3 &&c)
	Subtraction of two 3-vectors (templated version).

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

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

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

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

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

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

template<typename ReturnTypeT = double, typename TupleRangeT1 , typename TupleRangeT2 , typename EnableT = typename std::conditional<!std::is_pointer<TupleRangeT1>::value && !std::is_array<TupleRangeT1>::value, TupleRangeT1, TupleRangeT2>::type::value_type>
static ReturnTypeT	Dot (const TupleRangeT1 &a, const TupleRangeT2 &b)
	Compute dot product between two points p1 and p2.

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

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

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

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

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

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

template<typename ReturnTypeT = double, typename TupleRangeT >
static ReturnTypeT	SquaredNorm (const TupleRangeT &v)
	Compute the squared norm of a 3-vector.

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

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

template<typename ReturnTypeT = double, typename TupleRangeT1 , typename TupleRangeT2 , typename EnableT = typename std::conditional<!std::is_pointer<TupleRangeT1>::value && !std::is_array<TupleRangeT1>::value, TupleRangeT1, TupleRangeT2>::type::value_type>
static ReturnTypeT	Distance2BetweenPoints (const TupleRangeT1 &p1, const TupleRangeT2 &p2)
	Compute distance squared between two points p1 and p2.

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

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

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

static double	SignedAngleBetweenVectors (const double v1[3], const double v2[3], const double vn[3])
	Compute signed angle in radians between two vectors with regard to a third orthogonal vector.

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

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

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

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.

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

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

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

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

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

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

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

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

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

template<int RowsT, int MidDimT, int ColsT, class LayoutT1 = vtkMatrixUtilities::Layout::Identity, class LayoutT2 = vtkMatrixUtilities::Layout::Identity, class MatrixT1 , class MatrixT2 , class MatrixT3 >
static void	MultiplyMatrix (const MatrixT1 &M1, const MatrixT2 &M2, MatrixT3 &&M3)
	Multiply matrices such that M3 = M1 x M2.

template<int RowsT, int ColsT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class MatrixT , class VectorT1 , class VectorT2 >
static void	MultiplyMatrixWithVector (const MatrixT &M, const VectorT1 &X, VectorT2 &&Y)
	Multiply matrix M with vector Y such that Y = M x X.

template<class ScalarT , int SizeT, class VectorT1 , class VectorT2 >
static ScalarT	Dot (const VectorT1 &x, const VectorT2 &y)
	Computes the dot product between 2 vectors x and y.

template<int SizeT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class MatrixT >
static vtkMatrixUtilities::ScalarTypeExtractor< MatrixT >::value_type	Determinant (const MatrixT &M)
	Computes the determinant of input square SizeT x SizeT matrix M.

template<int SizeT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class MatrixT1 , class MatrixT2 >
static void	InvertMatrix (const MatrixT1 &M1, MatrixT2 &&M2)
	Computes the inverse of input matrix M1 into M2.

template<int RowsT, int ColsT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class MatrixT , class VectorT1 , class VectorT2 >
static void	LinearSolve (const MatrixT &M, const VectorT1 &x, VectorT2 &y)
	This method solves linear systems M * x = y.

template<class ScalarT , int SizeT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class VectorT1 , class MatrixT , class VectorT2 >
static ScalarT	Dot (const VectorT1 &x, const MatrixT &M, const VectorT2 &y)
	Computes the dot product x^T M y, where x and y are vectors and M is a metric matrix.

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.

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

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

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 \|.

static vtkTypeBool	SolveLinearSystemGEPP2x2 (double a00, double a01, double a10, double a11, double b0, double b1, double &x0, double &x1)
	Solve linear equation Ax = b using Gaussian Elimination with Partial Pivoting for a 2x2 system.

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

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

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

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.

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

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.

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

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'.

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'.

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

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

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.

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

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.

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

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.

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)

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)

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.

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.

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

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

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

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

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

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

static int	QuadraticRoot (double a, double b, double c, double min, double max, double *u)
	find roots of ax^2+bx+c=0 in the interval min,max.


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

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


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

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


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

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


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.

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.


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].

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].


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].

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].


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

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


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

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


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

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


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.

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.


static void	Multiply3x3 (const float A[3][3], const float v[3], float u[3])
	Multiply a vector by a 3x3 matrix.

static void	Multiply3x3 (const double A[3][3], const double v[3], double u[3])
	Multiply a vector by a 3x3 matrix.


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.

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.


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

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


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

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


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

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


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

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


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

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

template<class QuaternionT , class MatrixT , class EnableT = typename std::enable_if<!vtkMatrixUtilities::MatrixIs2DArray<MatrixT>()>::type>
static void	QuaternionToMatrix3x3 (const QuaternionT &q, MatrixT &&A)
	Convert a quaternion to a 3x3 rotation matrix.


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

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

template<class MatrixT , class QuaternionT , class EnableT = typename std::enable_if<!vtkMatrixUtilities::MatrixIs2DArray<MatrixT>()>::type>
static void	Matrix3x3ToQuaternion (const MatrixT &A, QuaternionT &&q)
	Convert a 3x3 matrix into a quaternion.


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

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


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

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


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

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


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

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


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.

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.


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.

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.


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

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


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.

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.


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

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).

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

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).


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

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).

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

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).


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

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.


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

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.


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

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


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

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


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

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.


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

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.


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


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


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.

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.

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.

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.

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.

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

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

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

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

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

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.

static vtkIdType	GetNumberOfGenerationsFromBaseType (const char *name)
	Given a the name of a base class of this class type, return the distance of inheritance between this class type and the named class (how many generations of inheritance are there between this class and the named class).

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

static void	SetMemkindDirectory (const char *directoryname)
	The name of a directory, ideally mounted -o dax, to memory map an extended memory space within.

static bool	GetUsingMemkind ()
	A global state flag that controls whether vtkObjects are constructed in the usual way (the default) or within the extended memory space.

Protected Member Functions
virtual vtkObjectBase *	NewInstanceInternal () const

	vtkMath ()=default

	~vtkMath () override=default

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.

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

Protected Member Functions inherited from vtkObjectBase
	vtkObjectBase ()

virtual	~vtkObjectBase ()

virtual void	RegisterInternal (vtkObjectBase *, vtkTypeBool check)

virtual void	UnRegisterInternal (vtkObjectBase *, vtkTypeBool check)

virtual void	ReportReferences (vtkGarbageCollector *)

	vtkObjectBase (const vtkObjectBase &)

void	operator= (const vtkObjectBase &)

Static Protected Attributes
static vtkSmartPointer< vtkMathInternal >	Internal

Additional Inherited Members
Static Protected Member Functions inherited from vtkObjectBase
static vtkMallocingFunction	GetCurrentMallocFunction ()

static vtkReallocingFunction	GetCurrentReallocFunction ()

static vtkFreeingFunction	GetCurrentFreeFunction ()

static vtkFreeingFunction	GetAlternateFreeFunction ()

Protected Attributes inherited from vtkObject
bool	Debug

vtkTimeStamp	MTime

vtkSubjectHelper *	SubjectHelper

Protected Attributes inherited from vtkObjectBase
std::atomic< int32_t >	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

Online Examples:

VisualizeModifiedBSPTree

ConstrainedDelaunay2D

TriangulateTerrainMap

ImageClip

Delaunay3D

CurvaturesAdjustEdges

Definition at line 196 of file vtkMath.h.

Member Typedef Documentation

◆ Superclass

typedef vtkObject vtkMath::Superclass

Definition at line 200 of file vtkMath.h.

Constructor & Destructor Documentation

◆ vtkMath()

vtkMath::vtkMath ( )

protecteddefault

◆ ~vtkMath()

vtkMath::~vtkMath ( )

overrideprotecteddefault

Member Function Documentation

◆ New()

static vtkMath * vtkMath::New ( )

static

◆ IsTypeOf()

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

static

◆ IsA()

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.

◆ SafeDownCast()

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

static

◆ NewInstanceInternal()

virtual vtkObjectBase * vtkMath::NewInstanceInternal ( ) const

protectedvirtual

◆ NewInstance()

vtkMath * vtkMath::NewInstance ( ) const

◆ PrintSelf()

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.

◆ Pi()

static constexpr double vtkMath::Pi ( )

inlinestaticconstexpr

A mathematical constant.

This version is atan(1.0) * 4.0

Definition at line 206 of file vtkMath.h.

◆ RadiansFromDegrees() [1/2]

float vtkMath::RadiansFromDegrees ( float degrees )

inlinestatic

Convert degrees into radians.

Definition at line 1658 of file vtkMath.h.

◆ RadiansFromDegrees() [2/2]

double vtkMath::RadiansFromDegrees ( double degrees )

inlinestatic

Convert degrees into radians.

Definition at line 1664 of file vtkMath.h.

◆ DegreesFromRadians() [1/2]

float vtkMath::DegreesFromRadians ( float radians )

inlinestatic

Convert radians into degrees.

Definition at line 1670 of file vtkMath.h.

◆ DegreesFromRadians() [2/2]

double vtkMath::DegreesFromRadians ( double radians )

inlinestatic

Convert radians into degrees.

Definition at line 1676 of file vtkMath.h.

◆ Round() [1/2]

static int vtkMath::Round ( float f )

inlinestatic

Rounds a float to the nearest integer.

Definition at line 228 of file vtkMath.h.

◆ Round() [2/2]

static int vtkMath::Round ( double f )

inlinestatic

Definition at line 229 of file vtkMath.h.

◆ RoundDoubleToIntegralIfNecessary()

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 237 of file vtkMath.h.

◆ Floor()

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 1703 of file vtkMath.h.

◆ Ceil()

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 1712 of file vtkMath.h.

◆ CeilLog2()

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.

◆ Min()

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 1720 of file vtkMath.h.

◆ Max()

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 1727 of file vtkMath.h.

◆ IsPowerOfTwo()

bool vtkMath::IsPowerOfTwo ( vtkTypeUInt64 x )

inlinestatic

Returns true if integer is a power of two.

Definition at line 1682 of file vtkMath.h.

◆ NearestPowerOfTwo()

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 1689 of file vtkMath.h.

◆ Factorial()

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.

◆ Binomial()

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 or $\left(\begin{array}{c}m \\ n\end{array}\right)$ .

◆ BeginCombination()

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.)

◆ NextCombination()

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.

◆ FreeCombination()

static void vtkMath::FreeCombination ( int * combination )

static

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

◆ RandomSeed()

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.

◆ GetSeed()

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.

◆ Random() [1/2]

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.

◆ Random() [2/2]

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.

◆ Gaussian() [1/2]

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.

◆ Gaussian() [2/2]

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.

◆ Assign() [1/2]

template<class VectorT1 , class VectorT2 >

static void vtkMath::Assign	(	const VectorT1 &	a,
		VectorT2 &&	b
	)

inlinestatic

Assign values to a 3-vector (templated version).

Result is stored in b according to b = a. Each parameter must implement operator[].

Definition at line 426 of file vtkMath.h.

◆ Assign() [2/2]

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

inlinestatic

Assign values to a 3-vector (double version).

Result is stored in b according to b = a.

Definition at line 436 of file vtkMath.h.

◆ Add() [1/2]

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 441 of file vtkMath.h.

◆ Add() [2/2]

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 452 of file vtkMath.h.

◆ Subtract() [1/3]

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 463 of file vtkMath.h.

◆ Subtract() [2/3]

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 474 of file vtkMath.h.

◆ Subtract() [3/3]

template<class VectorT1 , class VectorT2 , class VectorT3 >

static void vtkMath::Subtract	(	const VectorT1 &	a,
		const VectorT2 &	b,
		VectorT3 &&	c
	)

inlinestatic

Subtraction of two 3-vectors (templated version).

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

Each paramameter needs to implement operator[].

Definition at line 488 of file vtkMath.h.

◆ MultiplyScalar() [1/2]

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 499 of file vtkMath.h.

◆ MultiplyScalar2D() [1/2]

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 511 of file vtkMath.h.

◆ MultiplyScalar() [2/2]

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 523 of file vtkMath.h.

◆ MultiplyScalar2D() [2/2]

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 535 of file vtkMath.h.

◆ Dot() [1/5]

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

inlinestatic

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

Definition at line 546 of file vtkMath.h.

◆ Dot() [2/5]

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

inlinestatic

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

Definition at line 554 of file vtkMath.h.

◆ Dot() [3/5]

template<typename ReturnTypeT = double, typename TupleRangeT1 , typename TupleRangeT2 , typename EnableT = typename std::conditional<!std::is_pointer<TupleRangeT1>::value && !std::is_array<TupleRangeT1>::value, TupleRangeT1, TupleRangeT2>::type::value_type>

static ReturnTypeT vtkMath::Dot	(	const TupleRangeT1 &	a,
		const TupleRangeT2 &	b
	)

inlinestatic

Compute dot product between two points p1 and p2.

This version allows for custom range and iterator types to be used. These types must implement operator[], and at least one of them must have a value_type typedef.

The first template parameter ReturnTypeT sets the return type of this method. By default, it is set to double, but it can be overridden.

The EnableT template parameter is used to make sure that this version doesn't capture the float*, float[], double*, double[] as those should go to the other Distance2BetweenPoints functions.

Warning: This method assumes that both parameters have 3 components.

Definition at line 578 of file vtkMath.h.

◆ Outer() [1/2]

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 586 of file vtkMath.h.

◆ Outer() [2/2]

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 600 of file vtkMath.h.

◆ Cross() [1/2]

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 1834 of file vtkMath.h.

◆ Cross() [2/2]

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 1846 of file vtkMath.h.

◆ Norm() [1/4]

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

static

Compute the norm of n-vector.

x is the vector, n is its length.

◆ Norm() [2/4]

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

static

Compute the norm of n-vector.

x is the vector, n is its length.

◆ Norm() [3/4]

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

inlinestatic

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

Definition at line 634 of file vtkMath.h.

◆ Norm() [4/4]

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

inlinestatic

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

Definition at line 639 of file vtkMath.h.

◆ SquaredNorm()

template<typename ReturnTypeT = double, typename TupleRangeT >

static ReturnTypeT vtkMath::SquaredNorm ( const TupleRangeT & v )

inlinestatic

Compute the squared norm of a 3-vector.

The first template parameter ReturnTypeT sets the return type of this method. By default, it is set to double, but it can be overridden.

The parameter of this function must be a container, and array, or a range of 3 components implementing operator[].

Definition at line 654 of file vtkMath.h.

◆ Normalize() [1/2]

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

inlinestatic

Normalize (in place) a 3-vector.

Returns norm of vector. (float version)

Definition at line 1733 of file vtkMath.h.

◆ Normalize() [2/2]

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

inlinestatic

Normalize (in place) a 3-vector.

Returns norm of vector (double version).

Definition at line 1747 of file vtkMath.h.

◆ Perpendiculars() [1/2]

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.

◆ Perpendiculars() [2/2]

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.

◆ ProjectVector() [1/2]

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.

◆ ProjectVector() [2/2]

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.

◆ ProjectVector2D() [1/2]

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.

◆ ProjectVector2D() [2/2]

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.

◆ Distance2BetweenPoints() [1/3]

template<typename ReturnTypeT , typename TupleRangeT1 , typename TupleRangeT2 , typename EnableT >

ReturnTypeT vtkMath::Distance2BetweenPoints	(	const TupleRangeT1 &	p1,
		const TupleRangeT2 &	p2
	)

inlinestatic

Compute distance squared between two points p1 and p2.

This version allows for custom range and iterator types to be used. These types must implement operator[], and at least one of them must have a value_type typedef.

The first template parameter ReturnTypeT sets the return type of this method. By default, it is set to double, but it can be overridden.

The EnableT template parameter is used to make sure that this version doesn't capture the float*, float[], double*, double[] as those should go to the other Distance2BetweenPoints functions.

Warning: This method assumes that both parameters have 3 components.

Definition at line 1826 of file vtkMath.h.

◆ Distance2BetweenPoints() [2/3]

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 1811 of file vtkMath.h.

◆ Distance2BetweenPoints() [3/3]

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 1818 of file vtkMath.h.

◆ AngleBetweenVectors()

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

static

Compute angle in radians between two vectors.

◆ SignedAngleBetweenVectors()

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

static

Compute signed angle in radians between two vectors with regard to a third orthogonal vector.

◆ GaussianAmplitude() [1/2]

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./(std::sqrt(2 Pi * variance)) * exp(-distanceFromMean^2/(2.*variance)).

◆ GaussianAmplitude() [2/2]

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./(std::sqrt(2 Pi * variance)) * exp(-(position - mean)^2/(2.*variance)).

◆ GaussianWeight() [1/2]

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.

◆ GaussianWeight() [2/2]

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.

◆ Dot2D() [1/2]

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

inlinestatic

Dot product of two 2-vectors.

(float version).

Definition at line 777 of file vtkMath.h.

◆ Dot2D() [2/2]

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

inlinestatic

Dot product of two 2-vectors.

(double version).

Definition at line 782 of file vtkMath.h.

◆ Outer2D() [1/2]

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 787 of file vtkMath.h.

◆ Outer2D() [2/2]

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 801 of file vtkMath.h.

◆ Norm2D() [1/2]

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

inlinestatic

Compute the norm of a 2-vector.

(float version).

Definition at line 816 of file vtkMath.h.

◆ Norm2D() [2/2]

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

inlinestatic

Compute the norm of a 2-vector.

(double version).

Definition at line 822 of file vtkMath.h.

◆ Normalize2D() [1/2]

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

inlinestatic

Normalize (in place) a 2-vector.

Returns norm of vector. (float version).

Definition at line 1761 of file vtkMath.h.

◆ Normalize2D() [2/2]

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

inlinestatic

Normalize (in place) a 2-vector.

Returns norm of vector. (double version).

Definition at line 1775 of file vtkMath.h.

◆ Determinant2x2() [1/3]

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 839 of file vtkMath.h.

◆ Determinant2x2() [2/3]

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 848 of file vtkMath.h.

◆ Determinant2x2() [3/3]

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 849 of file vtkMath.h.

◆ LUFactor3x3() [1/2]

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

static

LU Factorization of a 3x3 matrix.

◆ LUFactor3x3() [2/2]

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

static

LU Factorization of a 3x3 matrix.

◆ LUSolve3x3() [1/2]

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

static

LU back substitution for a 3x3 matrix.

◆ LUSolve3x3() [2/2]

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

static

LU back substitution for a 3x3 matrix.

◆ LinearSolve3x3() [1/2]

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.

◆ LinearSolve3x3() [2/2]

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.

◆ Multiply3x3() [1/4]

static void vtkMath::Multiply3x3	(	const float	A[3][3],
		const float	v[3],
		float	u[3]
	)

static

Multiply a vector by a 3x3 matrix.

The result is placed in out.

◆ Multiply3x3() [2/4]

static void vtkMath::Multiply3x3	(	const double	A[3][3],
		const double	v[3],
		double	u[3]
	)

static

Multiply a vector by a 3x3 matrix.

The result is placed in out.

◆ Multiply3x3() [3/4]

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.

◆ Multiply3x3() [4/4]

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.

◆ MultiplyMatrix() [1/2]

template<int RowsT, int MidDimT, int ColsT, class LayoutT1 = vtkMatrixUtilities::Layout::Identity, class LayoutT2 = vtkMatrixUtilities::Layout::Identity, class MatrixT1 , class MatrixT2 , class MatrixT3 >

static void vtkMath::MultiplyMatrix	(	const MatrixT1 &	M1,
		const MatrixT2 &	M2,
		MatrixT3 &&	M3
	)

inlinestatic

Multiply matrices such that M3 = M1 x M2.

M3 must already be allocated.

LayoutT1 (resp. LayoutT2) allow to perform basic matrix reindexing for M1 (resp. M2). It should be set to a component of MatrixLayout.

Matrices are assumed to be a 1D array implementing operator[]. The matrices are indexed row by row. Let us develop the effect of LayoutT1 on M1 (the same is true for LayoutT2 on M2). If LayoutT1 == vtkMatrixUtilities::Layout::Identity (default), then M1 indexing is untouched. If LayoutT1 == vtkMatrixUtilities::Layout::Transpose, then M1 is read column-wise. If LayoutT1 == vtkMatrixUtilities::Layout::Diag, then M1 is considered to be composed of non zero elements of a diagonal matrix.

Note: M3 components indexing can be entirely controlled by swapping M1, M2, and turning on or off the appropriate transposition flag. Remember that M3^T = (M1 x M2)^T = M2^T x M1^T

Warning: If both M1 and M2 are used with both layout being diagonal, then M3 will be diagonal as well (i.e. there won't be allocated memory for elements outsize of the diagonal).

Definition at line 923 of file vtkMath.h.

◆ MultiplyMatrixWithVector()

template<int RowsT, int ColsT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class MatrixT , class VectorT1 , class VectorT2 >

static void vtkMath::MultiplyMatrixWithVector	(	const MatrixT &	M,
		const VectorT1 &	X,
		VectorT2 &&	Y
	)

inlinestatic

Multiply matrix M with vector Y such that Y = M x X.

Y must be allocated.

LayoutT allow to perform basic matrix reindexing. It should be set to a component of MatrixLayout.

Matrix M is assumed to be a 1D array implementing operator[]. The matrix is indexed row by row. If the input array is indexed columns by colums. If LayoutT == vtkMatrixUtilities::Layout::Identity (default), then M indexing is untouched. If LayoutT == vtkMatrixUtilities::Layout::Transpose, then M is read column-wise. If LayoutT == vtkMatrixUtilities::Layout::Diag, then M is considered to be composed of non zero elements of a diagonal matrix.

VectorT1 and VectorT2 are arrays of size RowsT, and must implement operator[].

Warning: In the particular case where M1 and M2 BOTH have layout vtkMatrixUtilities::Layout::Diag, RowsT, MidDimT and ColsT MUST match.

Definition at line 950 of file vtkMath.h.

◆ Dot() [4/5]

template<class ScalarT , int SizeT, class VectorT1 , class VectorT2 >

static ScalarT vtkMath::Dot	(	const VectorT1 &	x,
		const VectorT2 &	y
	)

inlinestatic

Computes the dot product between 2 vectors x and y.

VectorT1 and VectorT2 are arrays of size SizeT, and must implement operator[].

Definition at line 961 of file vtkMath.h.

◆ Determinant()

template<int SizeT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class MatrixT >

static vtkMatrixUtilities::ScalarTypeExtractor< MatrixT >::value_type vtkMath::Determinant ( const MatrixT & M )

inlinestatic

Computes the determinant of input square SizeT x SizeT matrix M.

The return type is the same as the underlying scalar type of MatrixT.

LayoutT allow to perform basic matrix reindexing. It should be set to a component of MatrixLayout.

Matrix M is assumed to be a 1D array implementing operator[]. The matrix is indexed row by row. If the input array is indexed columns by colums. If LayoutT == vtkMatrixUtilities::Layout::Identity (default), then M indexing is untouched. If LayoutT == vtkMatrixUtilities::Layout::Transpose, then M is read column-wise. If LayoutT == vtkMatrixUtilities::Layout::Diag, then M is considered to be composed of non zero elements of a diagonal matrix.

This method is currently implemented for SizeT lower or equal to 3.

Definition at line 984 of file vtkMath.h.

◆ InvertMatrix() [1/3]

template<int SizeT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class MatrixT1 , class MatrixT2 >

static void vtkMath::InvertMatrix	(	const MatrixT1 &	M1,
		MatrixT2 &&	M2
	)

inlinestatic

Computes the inverse of input matrix M1 into M2.

LayoutT allow to perform basic matrix reindexing of M1. It should be set to a component of MatrixLayout.

Matrix M is assumed to be a 1D array implementing operator[]. The matrix is indexed row by row. If the input array is indexed columns by colums. If LayoutT == vtkMatrixUtilities::Layout::Identity (default), then M indexing is untouched. If LayoutT == vtkMatrixUtilities::Layout::Transpose, then M is read column-wise. If LayoutT == vtkMatrixUtilities::Layout::Diag, then M is considered to be composed of non zero elements of a diagonal matrix.

This method is currently implemented for SizeT lower or equal to 3.

Definition at line 1007 of file vtkMath.h.

◆ LinearSolve()

template<int RowsT, int ColsT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class MatrixT , class VectorT1 , class VectorT2 >

static void vtkMath::LinearSolve	(	const MatrixT &	M,
		const VectorT1 &	x,
		VectorT2 &	y
	)

inlinestatic

This method solves linear systems M * x = y.

LayoutT allow to perform basic matrix reindexing of M1. It should be set to a component of MatrixLayout.

Matrix M is assumed to be a 1D array implementing operator[]. The matrix is indexed row by row. If the input array is indexed columns by colums. If LayoutT == vtkMatrixUtilities::Layout::Identity (default), then M indexing is untouched. If LayoutT == vtkMatrixUtilities::Layout::Transpose, then M is read column-wise. If LayoutT == vtkMatrixUtilities::Layout::Diag, then M is considered to be composed of non zero elements of a diagonal matrix.

Definition at line 1027 of file vtkMath.h.

◆ Dot() [5/5]

template<class ScalarT , int SizeT, class LayoutT = vtkMatrixUtilities::Layout::Identity, class VectorT1 , class MatrixT , class VectorT2 >

static ScalarT vtkMath::Dot	(	const VectorT1 &	x,
		const MatrixT &	M,
		const VectorT2 &	y
	)

inlinestatic

Computes the dot product x^T M y, where x and y are vectors and M is a metric matrix.

VectorT1 and VectorT2 are arrays of size SizeT, and must implement operator[].

Matrix M is assumed to be a 1D array implementing operator[]. The matrix is indexed row by row. If the input array is indexed columns by colums. If LayoutT == vtkMatrixUtilities::Layout::Identity (default), then M indexing is untouched. If LayoutT == vtkMatrixUtilities::Layout::Transpose, then M is read column-wise. If LayoutT == vtkMatrixUtilities::Layout::Diag, then M is considered to be composed of non zero elements of a diagonal matrix.

Definition at line 1048 of file vtkMath.h.

◆ MultiplyMatrix() [2/2]

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

◆ Transpose3x3() [1/2]

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.

◆ Transpose3x3() [2/2]

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.

◆ Invert3x3() [1/2]

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.

◆ Invert3x3() [2/2]

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.

◆ Identity3x3() [1/2]

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

static

Set A to the identity matrix.

◆ Identity3x3() [2/2]

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

static

Set A to the identity matrix.

◆ Determinant3x3() [1/5]

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

inlinestatic

Return the determinant of a 3x3 matrix.

Definition at line 1865 of file vtkMath.h.

◆ Determinant3x3() [2/5]

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

inlinestatic

Return the determinant of a 3x3 matrix.

Definition at line 1871 of file vtkMath.h.

◆ Determinant3x3() [3/5]

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 1789 of file vtkMath.h.

◆ Determinant3x3() [4/5]

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 1796 of file vtkMath.h.

◆ Determinant3x3() [5/5]

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 1803 of file vtkMath.h.

◆ QuaternionToMatrix3x3() [1/3]

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

inlinestatic

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

Definition at line 2007 of file vtkMath.h.

◆ QuaternionToMatrix3x3() [2/3]

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

inlinestatic

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

Definition at line 2013 of file vtkMath.h.

◆ QuaternionToMatrix3x3() [3/3]

template<class QuaternionT , class MatrixT , class EnableT >

void vtkMath::QuaternionToMatrix3x3	(	const QuaternionT &	q,
		MatrixT &&	A
	)

inlinestatic

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

Definition at line 2020 of file vtkMath.h.

◆ Matrix3x3ToQuaternion() [1/3]

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

inlinestatic

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

Definition at line 2081 of file vtkMath.h.

◆ Matrix3x3ToQuaternion() [2/3]

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

inlinestatic

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

Definition at line 2087 of file vtkMath.h.

◆ Matrix3x3ToQuaternion() [3/3]

template<class MatrixT , class QuaternionT , class EnableT >

void vtkMath::Matrix3x3ToQuaternion	(	const MatrixT &	A,
		QuaternionT &&	q
	)

inlinestatic

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

Definition at line 2094 of file vtkMath.h.

◆ MultiplyQuaternion() [1/2]

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

◆ MultiplyQuaternion() [2/2]

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

◆ RotateVectorByNormalizedQuaternion() [1/2]

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

◆ RotateVectorByNormalizedQuaternion() [2/2]

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

◆ RotateVectorByWXYZ() [1/2]

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

◆ RotateVectorByWXYZ() [2/2]

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

◆ Orthogonalize3x3() [1/2]

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.

◆ Orthogonalize3x3() [2/2]

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.

◆ Diagonalize3x3() [1/2]

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.

◆ Diagonalize3x3() [2/2]

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.

◆ SingularValueDecomposition3x3() [1/2]

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.

◆ SingularValueDecomposition3x3() [2/2]

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.

◆ SolveLinearSystemGEPP2x2()

static vtkTypeBool vtkMath::SolveLinearSystemGEPP2x2	(	double	a00,
		double	a01,
		double	a10,
		double	a11,
		double	b0,
		double	b1,
		double &	x0,
		double &	x1
	)

static

Solve linear equation Ax = b using Gaussian Elimination with Partial Pivoting for a 2x2 system.

If the matrix is found to be singular within a small numerical tolerance close to machine precision then 0 is returned. Note: Even if method succeeded the matrix A could be close to singular. The solution should be checked against relevant tolerance criteria.

◆ SolveLinearSystem()

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 b. Solution x is written over load vector. The dimension of the matrix is specified in size. If error is found, method returns a 0. Note: Even if method succeeded the matrix A could be close to singular. The solution should be checked against relevant tolerance criteria.

◆ InvertMatrix() [2/3]

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.

◆ InvertMatrix() [3/3]

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.

◆ LUFactorLinearSystem() [1/2]

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.

◆ LUFactorLinearSystem() [2/2]

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.

◆ LUSolveLinearSystem()

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.

◆ EstimateMatrixCondition()

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.)

◆ Jacobi() [1/2]

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

◆ Jacobi() [2/2]

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

◆ JacobiN() [1/2]

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

◆ JacobiN() [2/2]

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

◆ SolveHomogeneousLeastSquares()

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

◆ SolveLeastSquares()

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.

◆ RGBToHSV() [1/4]

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).

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 1370 of file vtkMath.h.

◆ RGBToHSV() [2/4]

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].

◆ RGBToHSV() [3/4]

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

inlinestatic

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 1375 of file vtkMath.h.

◆ RGBToHSV() [4/4]

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].

◆ HSVToRGB() [1/4]

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

inlinestatic

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

The input color is not modified. The input 'hsv' must be float values in the range [0, 1]. The elements of each component of the output 'rgb' are in the range [0, 1].

Definition at line 1390 of file vtkMath.h.

◆ HSVToRGB() [2/4]

static void vtkMath::HSVToRGB	(	float	h,
		float	s,
		float	v,
		float *	r,
		float *	g,
		float *	b
	)

static

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

The input color is not modified. The input 'hsv' must be float values in the range [0, 1]. The elements of each component of the output 'rgb' are in the range [0, 1].

◆ HSVToRGB() [3/4]

static void vtkMath::HSVToRGB	(	const double	hsv[3],
		double	rgb[3]
	)

inlinestatic

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

The input color is not modified. The input 'hsv' must be float values in the range [0, 1]. The elements of each component of the output 'rgb' are in the range [0, 1].

Definition at line 1395 of file vtkMath.h.

◆ HSVToRGB() [4/4]

static void vtkMath::HSVToRGB	(	double	h,
		double	s,
		double	v,
		double *	r,
		double *	g,
		double *	b
	)

static

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

The input color is not modified. The input 'hsv' must be float values in the range [0, 1]. The elements of each component of the output 'rgb' are in the range [0, 1].

◆ LabToXYZ() [1/2]

static void vtkMath::LabToXYZ	(	const double	lab[3],
		double	xyz[3]
	)

inlinestatic

Convert color from the CIE-L*ab system to CIE XYZ.

Definition at line 1406 of file vtkMath.h.

◆ LabToXYZ() [2/2]

static void vtkMath::LabToXYZ	(	double	L,
		double	a,
		double	b,
		double *	x,
		double *	y,
		double *	z
	)

static

Convert color from the CIE-L*ab system to CIE XYZ.

◆ XYZToLab() [1/2]

static void vtkMath::XYZToLab	(	const double	xyz[3],
		double	lab[3]
	)

inlinestatic

Convert Color from the CIE XYZ system to CIE-L*ab.

Definition at line 1417 of file vtkMath.h.

◆ XYZToLab() [2/2]

static void vtkMath::XYZToLab	(	double	x,
		double	y,
		double	z,
		double *	L,
		double *	a,
		double *	b
	)

static

Convert Color from the CIE XYZ system to CIE-L*ab.

◆ XYZToRGB() [1/2]

static void vtkMath::XYZToRGB	(	const double	xyz[3],
		double	rgb[3]
	)

inlinestatic

Convert color from the CIE XYZ system to RGB.

Definition at line 1428 of file vtkMath.h.

◆ XYZToRGB() [2/2]

static void vtkMath::XYZToRGB	(	double	x,
		double	y,
		double	z,
		double *	r,
		double *	g,
		double *	b
	)

static

Convert color from the CIE XYZ system to RGB.

◆ RGBToXYZ() [1/2]

static void vtkMath::RGBToXYZ	(	const double	rgb[3],
		double	xyz[3]
	)

inlinestatic

Convert color from the RGB system to CIE XYZ.

Definition at line 1439 of file vtkMath.h.

◆ RGBToXYZ() [2/2]

static void vtkMath::RGBToXYZ	(	double	r,
		double	g,
		double	b,
		double *	x,
		double *	y,
		double *	z
	)

static

Convert color from the RGB system to CIE XYZ.

◆ RGBToLab() [1/2]

static void vtkMath::RGBToLab	(	const double	rgb[3],
		double	lab[3]
	)

inlinestatic

Convert color from the RGB system to CIE-L*ab.

The input RGB must be values in the range [0, 1]. The output ranges of 'L' is [0, 100]. The output range of 'a' and 'b' are approximately [-110, 110].

Definition at line 1453 of file vtkMath.h.

◆ RGBToLab() [2/2]

static void vtkMath::RGBToLab	(	double	red,
		double	green,
		double	blue,
		double *	L,
		double *	a,
		double *	b
	)

static

Convert color from the RGB system to CIE-L*ab.

The input RGB must be values in the range [0, 1]. The output ranges of 'L' is [0, 100]. The output range of 'a' and 'b' are approximately [-110, 110].

◆ LabToRGB() [1/2]

static void vtkMath::LabToRGB	(	const double	lab[3],
		double	rgb[3]
	)

inlinestatic

Convert color from the CIE-L*ab system to RGB.

Definition at line 1464 of file vtkMath.h.

◆ LabToRGB() [2/2]

static void vtkMath::LabToRGB	(	double	L,
		double	a,
		double	b,
		double *	red,
		double *	green,
		double *	blue
	)

static

Convert color from the CIE-L*ab system to RGB.

◆ UninitializeBounds()

static void vtkMath::UninitializeBounds ( double bounds[6] )

inlinestatic

Set the bounds to an uninitialized state.

Definition at line 1475 of file vtkMath.h.

◆ AreBoundsInitialized()

static vtkTypeBool vtkMath::AreBoundsInitialized ( const double bounds[6] )

inlinestatic

Are the bounds initialized?

Definition at line 1490 of file vtkMath.h.

◆ ClampValue() [1/3]

template<class T >

T vtkMath::ClampValue	(	const T &	value,
		const T &	min,
		const T &	max
	)

inlinestatic

Clamp some value against a range, return the result.

min must be less than or equal to max. Semantics the same as std::clamp.

Definition at line 1878 of file vtkMath.h.

◆ ClampValue() [2/3]

void vtkMath::ClampValue	(	double *	value,
		const double	range[2]
	)

inlinestatic

Clamp some values against a range The method without 'clamped_values' will perform in-place clamping.

Definition at line 1893 of file vtkMath.h.

◆ ClampValue() [3/3]

void vtkMath::ClampValue	(	double	value,
		const double	range[2],
		double *	clamped_value
	)

inlinestatic

Clamp some values against a range The method without 'clamped_values' will perform in-place clamping.

Definition at line 1904 of file vtkMath.h.

◆ ClampValues() [1/2]

static void vtkMath::ClampValues	(	double *	values,
		int	nb_values,
		const double	range[2]
	)

static

Clamp some values against a range The method without 'clamped_values' will perform in-place clamping.

◆ ClampValues() [2/2]

static void vtkMath::ClampValues	(	const double *	values,
		int	nb_values,
		const double	range[2],
		double *	clamped_values
	)

static

Clamp some values against a range The method without 'clamped_values' will perform in-place clamping.

◆ ClampAndNormalizeValue()

double vtkMath::ClampAndNormalizeValue	(	double	value,
		const double	range[2]
	)

inlinestatic

Clamp a value against a range and then normalize it between 0 and 1.

If range[0]==range[1], the result is 0.

Precondition: valid_range: range[0]<=range[1]

Postcondition: valid_result: result>=0.0 && result<=1.0

Definition at line 1915 of file vtkMath.h.

◆ TensorFromSymmetricTensor() [1/3]

template<class T1 , class T2 >

static void vtkMath::TensorFromSymmetricTensor	(	const T1	symmTensor[6],
		T2	tensor[9]
	)

static

Convert a 6-Component symmetric tensor into a 9-Component tensor, no allocation performed.

Symmetric tensor is expected to have the following order : XX, YY, ZZ, XY, YZ, XZ

◆ TensorFromSymmetricTensor() [2/3]

template<class T >

void vtkMath::TensorFromSymmetricTensor ( T tensor[9] )

inlinestatic

Convert a 6-Component symmetric tensor into a 9-Component tensor, overwriting the tensor input.

Symmetric tensor is expected to have the following order : XX, YY, ZZ, XY, YZ, XZ

Definition at line 1953 of file vtkMath.h.

◆ GetScalarTypeFittingRange()

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

static

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.

[range_min * scale + shift, range_max * scale + shift]. If any one of the parameters is not an integer number (decimal part != 0), the search will default to float types only (float or double) Return -1 on error or no scalar type found.

◆ GetAdjustedScalarRange()

static vtkTypeBool vtkMath::GetAdjustedScalarRange	(	vtkDataArray *	array,
		int	comp,
		double	range[2]
	)

static

Get a vtkDataArray's scalar range for a given component.

If the vtkDataArray's data type is unsigned char (VTK_UNSIGNED_CHAR) the range is adjusted to the whole data type range [0, 255.0]. Same goes for unsigned short (VTK_UNSIGNED_SHORT) but the upper bound is also adjusted down to 4095.0 if was between ]255, 4095.0]. Return 1 on success, 0 otherwise.

◆ ExtentIsWithinOtherExtent()

static vtkTypeBool vtkMath::ExtentIsWithinOtherExtent	(	const int	extent1[6],
		const int	extent2[6]
	)

static

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.

◆ BoundsIsWithinOtherBounds()

static vtkTypeBool vtkMath::BoundsIsWithinOtherBounds	(	const double	bounds1[6],
		const double	bounds2[6],
		const double	delta[3]
	)

static

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)

◆ PointIsWithinBounds()

static vtkTypeBool vtkMath::PointIsWithinBounds	(	const double	point[3],
		const double	bounds[6],
		const double	delta[3]
	)

static

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)

◆ PlaneIntersectsAABB()

static int vtkMath::PlaneIntersectsAABB	(	const double	bounds[6],
		const double	normal[3],
		const double	point[3]
	)

static

Implements Plane / Axis-Aligned Bounding-Box intersection as described in Graphics Gems IV, Ned Greene; pp.

75-76. Variable names are based on the description in the book. This function returns +1 if the box lies fully in the positive side of the plane (by convention, the side to which the plane's normal points to), -1 if the box fully lies in the negative side and 0 if the plane intersects the box. -2 is returned if any of the arguments is invalid.

◆ Solve3PointCircle()

static double vtkMath::Solve3PointCircle	(	const double	p1[3],
		const double	p2[3],
		const double	p3[3],
		double	center[3]
	)

static

In Euclidean space, there is a unique circle passing through any given three non-collinear points P1, P2, and P3.

Using Cartesian coordinates to represent these points as spatial vectors, it is possible to use the dot product and cross product to calculate the radius and center of the circle. See: http://en.wikipedia.org/wiki/Circumscribed_circle and more specifically the section Barycentric coordinates from cross- and dot-products

◆ Inf()

static double vtkMath::Inf ( )

static

Special IEEE-754 number used to represent positive infinity.

◆ NegInf()

static double vtkMath::NegInf ( )

static

Special IEEE-754 number used to represent negative infinity.

◆ Nan()

static double vtkMath::Nan ( )

static

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

◆ IsInf()

static vtkTypeBool vtkMath::IsInf ( double x )

static

Test if a number is equal to the special floating point value infinity.

◆ IsNan()

static vtkTypeBool vtkMath::IsNan ( double x )

static

Test if a number is equal to the special floating point value Not-A-Number (Nan).

◆ IsFinite()

static bool vtkMath::IsFinite ( double x )

static

Test if a number has finite value i.e.

it is normal, subnormal or zero, but not infinite or Nan.

◆ QuadraticRoot()

static int vtkMath::QuadraticRoot	(	double	a,
		double	b,
		double	c,
		double	min,
		double	max,
		double *	u
	)

static

find roots of ax^2+bx+c=0 in the interval min,max.

place the roots in u[2] and return how many roots found

◆ TensorFromSymmetricTensor() [3/3]

template<class T1 , class T2 >

void vtkMath::TensorFromSymmetricTensor	(	const T1	symmTensor[9],
		T2	tensor[9]
	)

inline

Definition at line 1940 of file vtkMath.h.

Member Data Documentation

◆ Internal

vtkSmartPointer<vtkMathInternal> vtkMath::Internal

staticprotected

Definition at line 1650 of file vtkMath.h.

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

Common/Core/vtkMath.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Static Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Superclass

Constructor & Destructor Documentation

◆ vtkMath()

◆ ~vtkMath()

Member Function Documentation

◆ New()

◆ IsTypeOf()

◆ IsA()

◆ SafeDownCast()

◆ NewInstanceInternal()

◆ NewInstance()

◆ PrintSelf()

◆ Pi()

◆ RadiansFromDegrees() [1/2]

◆ RadiansFromDegrees() [2/2]

◆ DegreesFromRadians() [1/2]

◆ DegreesFromRadians() [2/2]

◆ Round() [1/2]

◆ Round() [2/2]

◆ RoundDoubleToIntegralIfNecessary()

◆ Floor()

◆ Ceil()

◆ CeilLog2()

◆ Min()

◆ Max()

◆ IsPowerOfTwo()

◆ NearestPowerOfTwo()

◆ Factorial()

◆ Binomial()

◆ BeginCombination()

◆ NextCombination()

◆ FreeCombination()

◆ RandomSeed()

◆ GetSeed()

◆ Random() [1/2]

◆ Random() [2/2]

◆ Gaussian() [1/2]

◆ Gaussian() [2/2]

◆ Assign() [1/2]

◆ Assign() [2/2]

◆ Add() [1/2]

◆ Add() [2/2]

◆ Subtract() [1/3]

◆ Subtract() [2/3]

◆ Subtract() [3/3]

◆ MultiplyScalar() [1/2]

◆ MultiplyScalar2D() [1/2]

◆ MultiplyScalar() [2/2]

◆ MultiplyScalar2D() [2/2]

◆ Dot() [1/5]

◆ Dot() [2/5]

◆ Dot() [3/5]

◆ Outer() [1/2]

◆ Outer() [2/2]

◆ Cross() [1/2]

◆ Cross() [2/2]

◆ Norm() [1/4]

◆ Norm() [2/4]

◆ Norm() [3/4]

◆ Norm() [4/4]

◆ SquaredNorm()

◆ Normalize() [1/2]

◆ Normalize() [2/2]

◆ Perpendiculars() [1/2]

◆ Perpendiculars() [2/2]

◆ ProjectVector() [1/2]

◆ ProjectVector() [2/2]

◆ ProjectVector2D() [1/2]

◆ ProjectVector2D() [2/2]

◆ Distance2BetweenPoints() [1/3]

◆ Distance2BetweenPoints() [2/3]

◆ Distance2BetweenPoints() [3/3]