VTK
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vtkMath Class Reference

performs common math operations More...

#include <vtkMath.h>

Inheritance diagram for vtkMath:
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Collaboration diagram for vtkMath:
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Public Types

typedef vtkObject Superclass
 

Public Member Functions

virtual vtkTypeBool IsA (const char *type)
 Return 1 if this class is the same type of (or a subclass of) the named class. More...
 
vtkMathNewInstance () const
 
void PrintSelf (ostream &os, vtkIndent indent) override
 Methods invoked by print to print information about the object including superclasses. More...
 
template<class T1 , class T2 >
void TensorFromSymmetricTensor (const T1 symmTensor[9], T2 tensor[9])
 
- Public Member Functions inherited from vtkObject
 vtkBaseTypeMacro (vtkObject, vtkObjectBase)
 
virtual void DebugOn ()
 Turn debugging output on. More...
 
virtual void DebugOff ()
 Turn debugging output off. More...
 
bool GetDebug ()
 Get the value of the debug flag. More...
 
void SetDebug (bool debugFlag)
 Set the value of the debug flag. More...
 
virtual void Modified ()
 Update the modification time for this object. More...
 
virtual vtkMTimeType GetMTime ()
 Return this object's modified time. More...
 
void PrintSelf (ostream &os, vtkIndent indent) override
 Methods invoked by print to print information about the object including superclasses. More...
 
void RemoveObserver (unsigned long tag)
 
void RemoveObservers (unsigned long event)
 
void RemoveObservers (const char *event)
 
void RemoveAllObservers ()
 
vtkTypeBool HasObserver (unsigned long event)
 
vtkTypeBool HasObserver (const char *event)
 
int InvokeEvent (unsigned long event)
 
int InvokeEvent (const char *event)
 
unsigned long AddObserver (unsigned long event, vtkCommand *, float priority=0.0f)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
unsigned long AddObserver (const char *event, vtkCommand *, float priority=0.0f)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
vtkCommandGetCommand (unsigned long tag)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
void RemoveObserver (vtkCommand *)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
void RemoveObservers (unsigned long event, vtkCommand *)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
void RemoveObservers (const char *event, vtkCommand *)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
vtkTypeBool HasObserver (unsigned long event, vtkCommand *)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
vtkTypeBool HasObserver (const char *event, vtkCommand *)
 Allow people to add/remove/invoke observers (callbacks) to any VTK object. More...
 
template<class U , class T >
unsigned long AddObserver (unsigned long event, U observer, void(T::*callback)(), float priority=0.0f)
 Overloads to AddObserver that allow developers to add class member functions as callbacks for events. More...
 
template<class U , class T >
unsigned long AddObserver (unsigned long event, U observer, void(T::*callback)(vtkObject *, unsigned long, void *), float priority=0.0f)
 Overloads to AddObserver that allow developers to add class member functions as callbacks for events. More...
 
template<class U , class T >
unsigned long AddObserver (unsigned long event, U observer, bool(T::*callback)(vtkObject *, unsigned long, void *), float priority=0.0f)
 Allow user to set the AbortFlagOn() with the return value of the callback method. More...
 
int InvokeEvent (unsigned long event, void *callData)
 This method invokes an event and return whether the event was aborted or not. More...
 
int InvokeEvent (const char *event, void *callData)
 This method invokes an event and return whether the event was aborted or not. More...
 
- Public Member Functions inherited from vtkObjectBase
const char * GetClassName () const
 Return the class name as a string. More...
 
virtual void Delete ()
 Delete a VTK object. More...
 
virtual void FastDelete ()
 Delete a reference to this object. More...
 
void InitializeObjectBase ()
 
void Print (ostream &os)
 Print an object to an ostream. More...
 
virtual void Register (vtkObjectBase *o)
 Increase the reference count (mark as used by another object). More...
 
virtual void UnRegister (vtkObjectBase *o)
 Decrease the reference count (release by another object). More...
 
int GetReferenceCount ()
 Return the current reference count of this object. More...
 
void SetReferenceCount (int)
 Sets the reference count. More...
 
void PrintRevisions (ostream &)
 Legacy. More...
 
virtual void PrintHeader (ostream &os, vtkIndent indent)
 Methods invoked by print to print information about the object including superclasses. More...
 
virtual void PrintTrailer (ostream &os, vtkIndent indent)
 Methods invoked by print to print information about the object including superclasses. More...
 

Static Public Member Functions

static vtkMathNew ()
 
static vtkTypeBool IsTypeOf (const char *type)
 
static vtkMathSafeDownCast (vtkObjectBase *o)
 
static double Pi ()
 A mathematical constant. More...
 
static int Round (float f)
 Rounds a float to the nearest integer. More...
 
static int Round (double f)
 
template<typename OutT >
static void RoundDoubleToIntegralIfNecessary (double val, OutT *ret)
 Round a double to type OutT if OutT is integral, otherwise simply clamp the value to the output range. More...
 
static int Floor (double x)
 Rounds a double to the nearest integer not greater than itself. More...
 
static int Ceil (double x)
 Rounds a double to the nearest integer not less than itself. More...
 
static int CeilLog2 (vtkTypeUInt64 x)
 Gives the exponent of the lowest power of two not less than x. More...
 
template<class T >
static T Min (const T &a, const T &b)
 Returns the minimum of the two arguments provided. More...
 
template<class T >
static T Max (const T &a, const T &b)
 Returns the maximum of the two arguments provided. More...
 
static bool IsPowerOfTwo (vtkTypeUInt64 x)
 Returns true if integer is a power of two. More...
 
static int NearestPowerOfTwo (int x)
 Compute the nearest power of two that is not less than x. More...
 
static vtkTypeInt64 Factorial (int N)
 Compute N factorial, N! = N*(N-1) * (N-2)...*3*2*1. More...
 
static vtkTypeInt64 Binomial (int m, int n)
 The number of combinations of n objects from a pool of m objects (m>n). More...
 
static intBeginCombination (int m, int n)
 Start iterating over "m choose n" objects. More...
 
static int NextCombination (int m, int n, int *combination)
 Given m, n, and a valid combination of n integers in the range [0,m[, this function alters the integers into the next combination in a sequence of all combinations of n items from a pool of m. More...
 
static void FreeCombination (int *combination)
 Free the "iterator" array created by vtkMath::BeginCombination. More...
 
static void RandomSeed (int s)
 Initialize seed value. More...
 
static int GetSeed ()
 Return the current seed used by the random number generator. More...
 
static double Random ()
 Generate pseudo-random numbers distributed according to the uniform distribution between 0.0 and 1.0. More...
 
static double Random (double min, double max)
 Generate pseudo-random numbers distributed according to the uniform distribution between min and max. More...
 
static double Gaussian ()
 Generate pseudo-random numbers distributed according to the standard normal distribution. More...
 
static double Gaussian (double mean, double std)
 Generate pseudo-random numbers distributed according to the Gaussian distribution with mean mean and standard deviation std. More...
 
static void Add (const float a[3], const float b[3], float c[3])
 Addition of two 3-vectors (float version). More...
 
static void Add (const double a[3], const double b[3], double c[3])
 Addition of two 3-vectors (double version). More...
 
static void Subtract (const float a[3], const float b[3], float c[3])
 Subtraction of two 3-vectors (float version). More...
 
static void Subtract (const double a[3], const double b[3], double c[3])
 Subtraction of two 3-vectors (double version). More...
 
static void MultiplyScalar (float a[3], float s)
 Multiplies a 3-vector by a scalar (float version). More...
 
static void MultiplyScalar2D (float a[2], float s)
 Multiplies a 2-vector by a scalar (float version). More...
 
static void MultiplyScalar (double a[3], double s)
 Multiplies a 3-vector by a scalar (double version). More...
 
static void MultiplyScalar2D (double a[2], double s)
 Multiplies a 2-vector by a scalar (double version). More...
 
static float Dot (const float a[3], const float b[3])
 Dot product of two 3-vectors (float version). More...
 
static double Dot (const double a[3], const double b[3])
 Dot product of two 3-vectors (double version). More...
 
static void Outer (const float a[3], const float b[3], float c[3][3])
 Outer product of two 3-vectors (float version). More...
 
static void Outer (const double a[3], const double b[3], double c[3][3])
 Outer product of two 3-vectors (double version). More...
 
static void Cross (const float a[3], const float b[3], float c[3])
 Cross product of two 3-vectors. More...
 
static void Cross (const double a[3], const double b[3], double c[3])
 Cross product of two 3-vectors. More...
 
static float Norm (const float v[3])
 Compute the norm of 3-vector (float version). More...
 
static double Norm (const double v[3])
 Compute the norm of 3-vector (double version). More...
 
static float Normalize (float v[3])
 Normalize (in place) a 3-vector. More...
 
static double Normalize (double v[3])
 Normalize (in place) a 3-vector. More...
 
static float Distance2BetweenPoints (const float p1[3], const float p2[3])
 Compute distance squared between two points p1 and p2. More...
 
static double Distance2BetweenPoints (const double p1[3], const double p2[3])
 Compute distance squared between two points p1 and p2. More...
 
static double AngleBetweenVectors (const double v1[3], const double v2[3])
 Compute angle in radians between two vectors. More...
 
static double GaussianAmplitude (const double variance, const double distanceFromMean)
 Compute the amplitude of a Gaussian function with mean=0 and specified variance. More...
 
static double GaussianAmplitude (const double mean, const double variance, const double position)
 Compute the amplitude of a Gaussian function with specified mean and variance. More...
 
static double GaussianWeight (const double variance, const double distanceFromMean)
 Compute the amplitude of an unnormalized Gaussian function with mean=0 and specified variance. More...
 
static double GaussianWeight (const double mean, const double variance, const double position)
 Compute the amplitude of an unnormalized Gaussian function with specified mean and variance. More...
 
static float Dot2D (const float x[2], const float y[2])
 Dot product of two 2-vectors. More...
 
static double Dot2D (const double x[2], const double y[2])
 Dot product of two 2-vectors. More...
 
static void Outer2D (const float x[2], const float y[2], float A[2][2])
 Outer product of two 2-vectors (float version). More...
 
static void Outer2D (const double x[2], const double y[2], double A[2][2])
 Outer product of two 2-vectors (double version). More...
 
static float Norm2D (const float x[2])
 Compute the norm of a 2-vector. More...
 
static double Norm2D (const double x[2])
 Compute the norm of a 2-vector. More...
 
static float Normalize2D (float v[2])
 Normalize (in place) a 2-vector. More...
 
static double Normalize2D (double v[2])
 Normalize (in place) a 2-vector. More...
 
static float Determinant2x2 (const float c1[2], const float c2[2])
 Compute determinant of 2x2 matrix. More...
 
static void MultiplyMatrix (const double *const *A, const double *const *B, unsigned int rowA, unsigned int colA, unsigned int rowB, unsigned int colB, double **C)
 General matrix multiplication. More...
 
static float Determinant3x3 (const float c1[3], const float c2[3], const float c3[3])
 Compute determinant of 3x3 matrix. More...
 
static double Determinant3x3 (const double c1[3], const double c2[3], const double c3[3])
 Compute determinant of 3x3 matrix. More...
 
static double Determinant3x3 (double a1, double a2, double a3, double b1, double b2, double b3, double c1, double c2, double c3)
 Calculate the determinant of a 3x3 matrix in the form: | a1, b1, c1 | | a2, b2, c2 | | a3, b3, c3 |. More...
 
static vtkTypeBool SolveLinearSystem (double **A, double *x, int size)
 Solve linear equations Ax = b using Crout's method. More...
 
static vtkTypeBool InvertMatrix (double **A, double **AI, int size)
 Invert input square matrix A into matrix AI. More...
 
static vtkTypeBool InvertMatrix (double **A, double **AI, int size, int *tmp1Size, double *tmp2Size)
 Thread safe version of InvertMatrix method. More...
 
static vtkTypeBool LUFactorLinearSystem (double **A, int *index, int size)
 Factor linear equations Ax = b using LU decomposition into the form A = LU where L is a unit lower triangular matrix and U is upper triangular matrix. More...
 
static vtkTypeBool LUFactorLinearSystem (double **A, int *index, int size, double *tmpSize)
 Thread safe version of LUFactorLinearSystem method. More...
 
static void LUSolveLinearSystem (double **A, int *index, double *x, int size)
 Solve linear equations Ax = b using LU decomposition A = LU where L is lower triangular matrix and U is upper triangular matrix. More...
 
static double EstimateMatrixCondition (const double *const *A, int size)
 Estimate the condition number of a LU factored matrix. More...
 
static vtkTypeBool SolveHomogeneousLeastSquares (int numberOfSamples, double **xt, int xOrder, double **mt)
 Solves for the least squares best fit matrix for the homogeneous equation X'M' = 0'. More...
 
static vtkTypeBool SolveLeastSquares (int numberOfSamples, double **xt, int xOrder, double **yt, int yOrder, double **mt, int checkHomogeneous=1)
 Solves for the least squares best fit matrix for the equation X'M' = Y'. More...
 
template<class T >
static T ClampValue (const T &value, const T &min, const T &max)
 Clamp some value against a range, return the result. More...
 
static double ClampAndNormalizeValue (double value, const double range[2])
 Clamp a value against a range and then normalize it between 0 and 1. More...
 
template<class T1 , class T2 >
static void TensorFromSymmetricTensor (const T1 symmTensor[6], T2 tensor[9])
 Convert a 6-Component symmetric tensor into a 9-Component tensor, no allocation performed. More...
 
template<class T >
static void TensorFromSymmetricTensor (T tensor[9])
 Convert a 6-Component symmetric tensor into a 9-Component tensor, overwriting the tensor input. More...
 
static int GetScalarTypeFittingRange (double range_min, double range_max, double scale=1.0, double shift=0.0)
 Return the scalar type that is most likely to have enough precision to store a given range of data once it has been scaled and shifted (i.e. More...
 
static vtkTypeBool GetAdjustedScalarRange (vtkDataArray *array, int comp, double range[2])
 Get a vtkDataArray's scalar range for a given component. More...
 
static vtkTypeBool ExtentIsWithinOtherExtent (const int extent1[6], const int extent2[6])
 Return true if first 3D extent is within second 3D extent Extent is x-min, x-max, y-min, y-max, z-min, z-max. More...
 
static vtkTypeBool BoundsIsWithinOtherBounds (const double bounds1[6], const double bounds2[6], const double delta[3])
 Return true if first 3D bounds is within the second 3D bounds Bounds is x-min, x-max, y-min, y-max, z-min, z-max Delta is the error margin along each axis (usually a small number) More...
 
static vtkTypeBool PointIsWithinBounds (const double point[3], const double bounds[6], const double delta[3])
 Return true if point is within the given 3D bounds Bounds is x-min, x-max, y-min, y-max, z-min, z-max Delta is the error margin along each axis (usually a small number) More...
 
static int PlaneIntersectsAABB (const double bounds[6], const double normal[3], const double point[3])
 Implements Plane / Axis-Aligned Bounding-Box intersection as described in Graphics Gems IV, Ned Greene; pp. More...
 
static double Solve3PointCircle (const double p1[3], const double p2[3], const double p3[3], double center[3])
 In Euclidean space, there is a unique circle passing through any given three non-collinear points P1, P2, and P3. More...
 
static double Inf ()
 Special IEEE-754 number used to represent positive infinity. More...
 
static double NegInf ()
 Special IEEE-754 number used to represent negative infinity. More...
 
static double Nan ()
 Special IEEE-754 number used to represent Not-A-Number (Nan). More...
 
static vtkTypeBool IsInf (double x)
 Test if a number is equal to the special floating point value infinity. More...
 
static vtkTypeBool IsNan (double x)
 Test if a number is equal to the special floating point value Not-A-Number (Nan). More...
 
static bool IsFinite (double x)
 Test if a number has finite value i.e. More...
 
static float RadiansFromDegrees (float degrees)
 Convert degrees into radians. More...
 
static double RadiansFromDegrees (double degrees)
 Convert degrees into radians. More...
 
static float DegreesFromRadians (float radians)
 Convert radians into degrees. More...
 
static double DegreesFromRadians (double radians)
 Convert radians into degrees. More...
 
static float Norm (const float *x, int n)
 Compute the norm of n-vector. More...
 
static double Norm (const double *x, int n)
 Compute the norm of n-vector. More...
 
static void Perpendiculars (const double v1[3], double v2[3], double v3[3], double theta)
 Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3 (i.e. More...
 
static void Perpendiculars (const float v1[3], float v2[3], float v3[3], double theta)
 Given a unit vector v1, find two unit vectors v2 and v3 such that v1 cross v2 = v3 (i.e. More...
 
static bool ProjectVector (const float a[3], const float b[3], float projection[3])
 Compute the projection of vector a on vector b and return it in projection[3]. More...
 
static bool ProjectVector (const double a[3], const double b[3], double projection[3])
 Compute the projection of vector a on vector b and return it in projection[3]. More...
 
static bool ProjectVector2D (const float a[2], const float b[2], float projection[2])
 Compute the projection of 2D vector a on 2D vector b and returns the result in projection[2]. More...
 
static bool ProjectVector2D (const double a[2], const double b[2], double projection[2])
 Compute the projection of 2D vector a on 2D vector b and returns the result in projection[2]. More...
 
static double Determinant2x2 (double a, double b, double c, double d)
 Calculate the determinant of a 2x2 matrix: | a b | | c d |. More...
 
static double Determinant2x2 (const double c1[2], const double c2[2])
 Calculate the determinant of a 2x2 matrix: | a b | | c d |. More...
 
static void LUFactor3x3 (float A[3][3], int index[3])
 LU Factorization of a 3x3 matrix. More...
 
static void LUFactor3x3 (double A[3][3], int index[3])
 LU Factorization of a 3x3 matrix. More...
 
static void LUSolve3x3 (const float A[3][3], const int index[3], float x[3])
 LU back substitution for a 3x3 matrix. More...
 
static void LUSolve3x3 (const double A[3][3], const int index[3], double x[3])
 LU back substitution for a 3x3 matrix. More...
 
static void LinearSolve3x3 (const float A[3][3], const float x[3], float y[3])
 Solve Ay = x for y and place the result in y. More...
 
static void LinearSolve3x3 (const double A[3][3], const double x[3], double y[3])
 Solve Ay = x for y and place the result in y. More...
 
static void Multiply3x3 (const float A[3][3], const float in[3], float out[3])
 Multiply a vector by a 3x3 matrix. More...
 
static void Multiply3x3 (const double A[3][3], const double in[3], double out[3])
 Multiply a vector by a 3x3 matrix. More...
 
static void Multiply3x3 (const float A[3][3], const float B[3][3], float C[3][3])
 Multiply one 3x3 matrix by another according to C = AB. More...
 
static void Multiply3x3 (const double A[3][3], const double B[3][3], double C[3][3])
 Multiply one 3x3 matrix by another according to C = AB. More...
 
static void Transpose3x3 (const float A[3][3], float AT[3][3])
 Transpose a 3x3 matrix. More...
 
static void Transpose3x3 (const double A[3][3], double AT[3][3])
 Transpose a 3x3 matrix. More...
 
static void Invert3x3 (const float A[3][3], float AI[3][3])
 Invert a 3x3 matrix. More...
 
static void Invert3x3 (const double A[3][3], double AI[3][3])
 Invert a 3x3 matrix. More...
 
static void Identity3x3 (float A[3][3])
 Set A to the identity matrix. More...
 
static void Identity3x3 (double A[3][3])
 Set A to the identity matrix. More...
 
static double Determinant3x3 (const float A[3][3])
 Return the determinant of a 3x3 matrix. More...
 
static double Determinant3x3 (const double A[3][3])
 Return the determinant of a 3x3 matrix. More...
 
static void QuaternionToMatrix3x3 (const float quat[4], float A[3][3])
 Convert a quaternion to a 3x3 rotation matrix. More...
 
static void QuaternionToMatrix3x3 (const double quat[4], double A[3][3])
 Convert a quaternion to a 3x3 rotation matrix. More...
 
static void Matrix3x3ToQuaternion (const float A[3][3], float quat[4])
 Convert a 3x3 matrix into a quaternion. More...
 
static void Matrix3x3ToQuaternion (const double A[3][3], double quat[4])
 Convert a 3x3 matrix into a quaternion. More...
 
static void MultiplyQuaternion (const float q1[4], const float q2[4], float q[4])
 Multiply two quaternions. More...
 
static void MultiplyQuaternion (const double q1[4], const double q2[4], double q[4])
 Multiply two quaternions. More...
 
static void RotateVectorByNormalizedQuaternion (const float v[3], const float q[4], float r[3])
 rotate a vector by a normalized quaternion using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula More...
 
static void RotateVectorByNormalizedQuaternion (const double v[3], const double q[4], double r[3])
 rotate a vector by a normalized quaternion using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula More...
 
static void RotateVectorByWXYZ (const float v[3], const float q[4], float r[3])
 rotate a vector by WXYZ using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula More...
 
static void RotateVectorByWXYZ (const double v[3], const double q[4], double r[3])
 rotate a vector by WXYZ using // https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula More...
 
static void Orthogonalize3x3 (const float A[3][3], float B[3][3])
 Orthogonalize a 3x3 matrix and put the result in B. More...
 
static void Orthogonalize3x3 (const double A[3][3], double B[3][3])
 Orthogonalize a 3x3 matrix and put the result in B. More...
 
static void Diagonalize3x3 (const float A[3][3], float w[3], float V[3][3])
 Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V. More...
 
static void Diagonalize3x3 (const double A[3][3], double w[3], double V[3][3])
 Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V. More...
 
static void SingularValueDecomposition3x3 (const float A[3][3], float U[3][3], float w[3], float VT[3][3])
 Perform singular value decomposition on a 3x3 matrix. More...
 
static void SingularValueDecomposition3x3 (const double A[3][3], double U[3][3], double w[3], double VT[3][3])
 Perform singular value decomposition on a 3x3 matrix. More...
 
static vtkTypeBool Jacobi (float **a, float *w, float **v)
 Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix. More...
 
static vtkTypeBool Jacobi (double **a, double *w, double **v)
 Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix. More...
 
static vtkTypeBool JacobiN (float **a, int n, float *w, float **v)
 JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. More...
 
static vtkTypeBool JacobiN (double **a, int n, double *w, double **v)
 JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. More...
 
static void RGBToHSV (const float rgb[3], float hsv[3])
 Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...
 
static void RGBToHSV (float r, float g, float b, float *h, float *s, float *v)
 Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...
 
static doubleRGBToHSV (const double rgb[3])
 Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...
 
static doubleRGBToHSV (double r, double g, double b)
 Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...
 
static void RGBToHSV (const double rgb[3], double hsv[3])
 Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...
 
static void RGBToHSV (double r, double g, double b, double *h, double *s, double *v)
 Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). More...
 
static void HSVToRGB (const float hsv[3], float rgb[3])
 Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...
 
static void HSVToRGB (float h, float s, float v, float *r, float *g, float *b)
 Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...
 
static doubleHSVToRGB (const double hsv[3])
 Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...
 
static doubleHSVToRGB (double h, double s, double v)
 Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...
 
static void HSVToRGB (const double hsv[3], double rgb[3])
 Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...
 
static void HSVToRGB (double h, double s, double v, double *r, double *g, double *b)
 Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). More...
 
static void LabToXYZ (const double lab[3], double xyz[3])
 Convert color from the CIE-L*ab system to CIE XYZ. More...
 
static void LabToXYZ (double L, double a, double b, double *x, double *y, double *z)
 Convert color from the CIE-L*ab system to CIE XYZ. More...
 
static doubleLabToXYZ (const double lab[3])
 Convert color from the CIE-L*ab system to CIE XYZ. More...
 
static void XYZToLab (const double xyz[3], double lab[3])
 Convert Color from the CIE XYZ system to CIE-L*ab. More...
 
static void XYZToLab (double x, double y, double z, double *L, double *a, double *b)
 Convert Color from the CIE XYZ system to CIE-L*ab. More...
 
static doubleXYZToLab (const double xyz[3])
 Convert Color from the CIE XYZ system to CIE-L*ab. More...
 
static void XYZToRGB (const double xyz[3], double rgb[3])
 Convert color from the CIE XYZ system to RGB. More...
 
static void XYZToRGB (double x, double y, double z, double *r, double *g, double *b)
 Convert color from the CIE XYZ system to RGB. More...
 
static doubleXYZToRGB (const double xyz[3])
 Convert color from the CIE XYZ system to RGB. More...
 
static void RGBToXYZ (const double rgb[3], double xyz[3])
 Convert color from the RGB system to CIE XYZ. More...
 
static void RGBToXYZ (double r, double g, double b, double *x, double *y, double *z)
 Convert color from the RGB system to CIE XYZ. More...
 
static doubleRGBToXYZ (const double rgb[3])
 Convert color from the RGB system to CIE XYZ. More...
 
static void RGBToLab (const double rgb[3], double lab[3])
 Convert color from the RGB system to CIE-L*ab. More...
 
static void RGBToLab (double red, double green, double blue, double *L, double *a, double *b)
 Convert color from the RGB system to CIE-L*ab. More...
 
static doubleRGBToLab (const double rgb[3])
 Convert color from the RGB system to CIE-L*ab. More...
 
static void LabToRGB (const double lab[3], double rgb[3])
 Convert color from the CIE-L*ab system to RGB. More...
 
static void LabToRGB (double L, double a, double b, double *red, double *green, double *blue)
 Convert color from the CIE-L*ab system to RGB. More...
 
static doubleLabToRGB (const double lab[3])
 Convert color from the CIE-L*ab system to RGB. More...
 
static void UninitializeBounds (double bounds[6])
 Set the bounds to an uninitialized state. More...
 
static vtkTypeBool AreBoundsInitialized (const double bounds[6])
 Are the bounds initialized? More...
 
static void ClampValue (double *value, const double range[2])
 Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. More...
 
static void ClampValue (double value, const double range[2], double *clamped_value)
 Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. More...
 
static void ClampValues (double *values, int nb_values, const double range[2])
 Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. More...
 
static void ClampValues (const double *values, int nb_values, const double range[2], double *clamped_values)
 Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. More...
 
- Static Public Member Functions inherited from vtkObject
static vtkObjectNew ()
 Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More...
 
static void BreakOnError ()
 This method is called when vtkErrorMacro executes. More...
 
static void SetGlobalWarningDisplay (int val)
 This is a global flag that controls whether any debug, warning or error messages are displayed. More...
 
static void GlobalWarningDisplayOn ()
 This is a global flag that controls whether any debug, warning or error messages are displayed. More...
 
static void GlobalWarningDisplayOff ()
 This is a global flag that controls whether any debug, warning or error messages are displayed. More...
 
static int GetGlobalWarningDisplay ()
 This is a global flag that controls whether any debug, warning or error messages are displayed. More...
 
- Static Public Member Functions inherited from vtkObjectBase
static vtkTypeBool IsTypeOf (const char *name)
 Return 1 if this class type is the same type of (or a subclass of) the named class. More...
 
static vtkObjectBaseNew ()
 Create an object with Debug turned off, modified time initialized to zero, and reference counting on. More...
 

Protected Member Functions

virtual vtkObjectBaseNewInstanceInternal () const
 
 vtkMath ()
 
 ~vtkMath () override
 
- Protected Member Functions inherited from vtkObject
 vtkObject ()
 
 ~vtkObject () override
 
void RegisterInternal (vtkObjectBase *, vtkTypeBool check) override
 
void UnRegisterInternal (vtkObjectBase *, vtkTypeBool check) override
 
void InternalGrabFocus (vtkCommand *mouseEvents, vtkCommand *keypressEvents=nullptr)
 These methods allow a command to exclusively grab all events. More...
 
void InternalReleaseFocus ()
 These methods allow a command to exclusively grab all events. More...
 
- Protected Member Functions inherited from vtkObjectBase
 vtkObjectBase ()
 
virtual ~vtkObjectBase ()
 
virtual void CollectRevisions (ostream &)
 
virtual void ReportReferences (vtkGarbageCollector *)
 
 vtkObjectBase (const vtkObjectBase &)
 
void operator= (const vtkObjectBase &)
 

Static Protected Attributes

static vtkSmartPointer< vtkMathInternal > Internal
 

Additional Inherited Members

- Protected Attributes inherited from vtkObject
bool Debug
 
vtkTimeStamp MTime
 
vtkSubjectHelper * SubjectHelper
 
- Protected Attributes inherited from vtkObjectBase
vtkAtomicInt32 ReferenceCount
 
vtkWeakPointerBase ** WeakPointers
 

Detailed Description

performs common math operations

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

See also
vtkMinimalStandardRandomSequence, vtkBoxMuellerRandomSequence, vtkQuaternion
Examples:
vtkMath (Examples)
Tests:
vtkMath (Tests)

Definition at line 90 of file vtkMath.h.

Member Typedef Documentation

Definition at line 94 of file vtkMath.h.

Constructor & Destructor Documentation

vtkMath::vtkMath ( )
inlineprotected

Definition at line 1288 of file vtkMath.h.

vtkMath::~vtkMath ( )
inlineoverrideprotected

Definition at line 1289 of file vtkMath.h.

Member Function Documentation

static vtkMath* vtkMath::New ( )
static
static vtkTypeBool vtkMath::IsTypeOf ( const char *  type)
static
virtual vtkTypeBool vtkMath::IsA ( const char *  name)
virtual

Return 1 if this class is the same type of (or a subclass of) the named class.

Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkObjectBase.

static vtkMath* vtkMath::SafeDownCast ( vtkObjectBase o)
static
virtual vtkObjectBase* vtkMath::NewInstanceInternal ( ) const
protectedvirtual
vtkMath* vtkMath::NewInstance ( ) const
void vtkMath::PrintSelf ( ostream &  os,
vtkIndent  indent 
)
overridevirtual

Methods invoked by print to print information about the object including superclasses.

Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from vtkObjectBase.

static double vtkMath::Pi ( )
inlinestatic

A mathematical constant.

This version is atan(1.0) * 4.0

Definition at line 100 of file vtkMath.h.

float vtkMath::RadiansFromDegrees ( float  degrees)
inlinestatic

Convert degrees into radians.

Definition at line 1298 of file vtkMath.h.

double vtkMath::RadiansFromDegrees ( double  degrees)
inlinestatic

Convert degrees into radians.

Definition at line 1304 of file vtkMath.h.

float vtkMath::DegreesFromRadians ( float  radians)
inlinestatic

Convert radians into degrees.

Definition at line 1310 of file vtkMath.h.

double vtkMath::DegreesFromRadians ( double  radians)
inlinestatic

Convert radians into degrees.

Definition at line 1316 of file vtkMath.h.

static int vtkMath::Round ( float  f)
inlinestatic

Rounds a float to the nearest integer.

Definition at line 122 of file vtkMath.h.

static int vtkMath::Round ( double  f)
inlinestatic

Definition at line 124 of file vtkMath.h.

template<typename OutT >
static void vtkMath::RoundDoubleToIntegralIfNecessary ( double  val,
OutT *  ret 
)
inlinestatic

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

Definition at line 133 of file vtkMath.h.

int vtkMath::Floor ( double  x)
inlinestatic

Rounds a double to the nearest integer not greater than itself.

This is faster than floor() but provides undefined output on overflow.

Definition at line 1343 of file vtkMath.h.

int vtkMath::Ceil ( double  x)
inlinestatic

Rounds a double to the nearest integer not less than itself.

This is faster than ceil() but provides undefined output on overflow.

Definition at line 1352 of file vtkMath.h.

static int vtkMath::CeilLog2 ( vtkTypeUInt64  x)
static

Gives the exponent of the lowest power of two not less than x.

Or in mathspeak, return the smallest "i" for which 2^i >= x. If x is zero, then the return value will be zero.

template<class T >
T vtkMath::Min ( const T &  a,
const T &  b 
)
inlinestatic

Returns the minimum of the two arguments provided.

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

Definition at line 1360 of file vtkMath.h.

template<class T >
T vtkMath::Max ( const T &  a,
const T &  b 
)
inlinestatic

Returns the maximum of the two arguments provided.

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

Definition at line 1367 of file vtkMath.h.

bool vtkMath::IsPowerOfTwo ( vtkTypeUInt64  x)
inlinestatic

Returns true if integer is a power of two.

Definition at line 1322 of file vtkMath.h.

int vtkMath::NearestPowerOfTwo ( int  x)
inlinestatic

Compute the nearest power of two that is not less than x.

The return value is 1 if x is less than or equal to zero, and is VTK_INT_MIN if result is too large to fit in an int.

Definition at line 1329 of file vtkMath.h.

static vtkTypeInt64 vtkMath::Factorial ( int  N)
static

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

0! is taken to be 1.

static vtkTypeInt64 vtkMath::Binomial ( int  m,
int  n 
)
static

The number of combinations of n objects from a pool of m objects (m>n).

This is commonly known as "m choose n" and sometimes denoted $_mC_n$ or $\left(\begin{array}{c}m \\ n\end{array}\right)$.

static int* vtkMath::BeginCombination ( int  m,
int  n 
)
static

Start iterating over "m choose n" objects.

This function returns an array of n integers, each from 0 to m-1. These integers represent the n items chosen from the set [0,m[.

You are responsible for calling vtkMath::FreeCombination() once the iterator is no longer needed.

Warning: this gets large very quickly, especially when n nears m/2! (Hint: think of Pascal's triangle.)

static int vtkMath::NextCombination ( int  m,
int  n,
int combination 
)
static

Given m, n, and a valid combination of n integers in the range [0,m[, this function alters the integers into the next combination in a sequence of all combinations of n items from a pool of m.

If the combination is the last item in the sequence on input, then combination is unaltered and 0 is returned. Otherwise, 1 is returned and combination is updated.

static void vtkMath::FreeCombination ( int combination)
static

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

static void vtkMath::RandomSeed ( int  s)
static

Initialize seed value.

NOTE: Random() has the bad property that the first random number returned after RandomSeed() is called is proportional to the seed value! To help solve this, call RandomSeed() a few times inside seed. This doesn't ruin the repeatability of Random().

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

static int vtkMath::GetSeed ( )
static

Return the current seed used by the random number generator.

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

static double vtkMath::Random ( )
static

Generate pseudo-random numbers distributed according to the uniform distribution between 0.0 and 1.0.

This is used to provide portability across different systems.

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

static double vtkMath::Random ( double  min,
double  max 
)
static

Generate pseudo-random numbers distributed according to the uniform distribution between min and max.

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

static double vtkMath::Gaussian ( )
static

Generate pseudo-random numbers distributed according to the standard normal distribution.

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

static double vtkMath::Gaussian ( double  mean,
double  std 
)
static

Generate pseudo-random numbers distributed according to the Gaussian distribution with mean mean and standard deviation std.

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

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

Addition of two 3-vectors (float version).

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

Definition at line 319 of file vtkMath.h.

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

Addition of two 3-vectors (double version).

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

Definition at line 329 of file vtkMath.h.

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

Subtraction of two 3-vectors (float version).

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

Definition at line 339 of file vtkMath.h.

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

Subtraction of two 3-vectors (double version).

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

Definition at line 349 of file vtkMath.h.

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

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

This modifies the input 3-vector.

Definition at line 360 of file vtkMath.h.

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

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

This modifies the input 2-vector.

Definition at line 371 of file vtkMath.h.

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

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

This modifies the input 3-vector.

Definition at line 382 of file vtkMath.h.

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

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

This modifies the input 2-vector.

Definition at line 393 of file vtkMath.h.

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

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

Definition at line 403 of file vtkMath.h.

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

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

Definition at line 410 of file vtkMath.h.

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

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

Definition at line 417 of file vtkMath.h.

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

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

Definition at line 430 of file vtkMath.h.

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

Cross product of two 3-vectors.

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

Definition at line 1476 of file vtkMath.h.

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

Cross product of two 3-vectors.

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

Definition at line 1486 of file vtkMath.h.

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

Compute the norm of n-vector.

x is the vector, n is its length.

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

Compute the norm of n-vector.

x is the vector, n is its length.

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

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

Definition at line 463 of file vtkMath.h.

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

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

Definition at line 470 of file vtkMath.h.

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

Normalize (in place) a 3-vector.

Returns norm of vector. (float version)

Definition at line 1373 of file vtkMath.h.

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

Normalize (in place) a 3-vector.

Returns norm of vector (double version).

Definition at line 1387 of file vtkMath.h.

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

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

the vectors are perpendicular to each other). There is an infinite number of such vectors, specify an angle theta to choose one set. If you want only one perpendicular vector, specify nullptr for v3.

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

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

the vectors are perpendicular to each other). There is an infinite number of such vectors, specify an angle theta to choose one set. If you want only one perpendicular vector, specify nullptr for v3.

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

Compute the projection of vector a on vector b and return it in projection[3].

If b is a zero vector, the function returns false and 'projection' is invalid. Otherwise, it returns true.

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

Compute the projection of vector a on vector b and return it in projection[3].

If b is a zero vector, the function returns false and 'projection' is invalid. Otherwise, it returns true.

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

Compute the projection of 2D vector a on 2D vector b and returns the result in projection[2].

If b is a zero vector, the function returns false and 'projection' is invalid. Otherwise, it returns true.

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

Compute the projection of 2D vector a on 2D vector b and returns the result in projection[2].

If b is a zero vector, the function returns false and 'projection' is invalid. Otherwise, it returns true.

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

Compute distance squared between two points p1 and p2.

(float version).

Definition at line 1457 of file vtkMath.h.

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

Compute distance squared between two points p1 and p2.

(double version).

Definition at line 1466 of file vtkMath.h.

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

Compute angle in radians between two vectors.

static double vtkMath::GaussianAmplitude ( const double  variance,
const double  distanceFromMean 
)
static

Compute the amplitude of a Gaussian function with mean=0 and specified variance.

That is, 1./(sqrt(2 Pi * variance)) * exp(-distanceFromMean^2/(2.*variance)).

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

Compute the amplitude of a Gaussian function with specified mean and variance.

That is, 1./(sqrt(2 Pi * variance)) * exp(-(position - mean)^2/(2.*variance)).

static double vtkMath::GaussianWeight ( const double  variance,
const double  distanceFromMean 
)
static

Compute the amplitude of an unnormalized Gaussian function with mean=0 and specified variance.

That is, exp(-distanceFromMean^2/(2.*variance)). When distanceFromMean = 0, this function returns 1.

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

Compute the amplitude of an unnormalized Gaussian function with specified mean and variance.

That is, exp(-(position - mean)^2/(2.*variance)). When the distance from 'position' to 'mean' is 0, this function returns 1.

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

Dot product of two 2-vectors.

(float version).

Definition at line 567 of file vtkMath.h.

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

Dot product of two 2-vectors.

(double version).

Definition at line 574 of file vtkMath.h.

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

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

Definition at line 581 of file vtkMath.h.

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

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

Definition at line 595 of file vtkMath.h.

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

Compute the norm of a 2-vector.

(float version).

Definition at line 610 of file vtkMath.h.

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

Compute the norm of a 2-vector.

(double version).

Definition at line 618 of file vtkMath.h.

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

Normalize (in place) a 2-vector.

Returns norm of vector. (float version).

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

Normalize (in place) a 2-vector.

Returns norm of vector. (double version).

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

Compute determinant of 2x2 matrix.

Two columns of matrix are input.

Definition at line 637 of file vtkMath.h.

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

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

Definition at line 645 of file vtkMath.h.

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

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

Definition at line 648 of file vtkMath.h.

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

LU Factorization of a 3x3 matrix.

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

LU Factorization of a 3x3 matrix.

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

LU back substitution for a 3x3 matrix.

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

LU back substitution for a 3x3 matrix.

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

Solve Ay = x for y and place the result in y.

The matrix A is destroyed in the process.

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

Solve Ay = x for y and place the result in y.

The matrix A is destroyed in the process.

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

Multiply a vector by a 3x3 matrix.

The result is placed in out.

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

Multiply a vector by a 3x3 matrix.

The result is placed in out.

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

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

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

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

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

General matrix multiplication.

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

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

Transpose a 3x3 matrix.

The input matrix is A. The output is stored in AT.

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

Transpose a 3x3 matrix.

The input matrix is A. The output is stored in AT.

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

Invert a 3x3 matrix.

The input matrix is A. The output is stored in AI.

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

Invert a 3x3 matrix.

The input matrix is A. The output is stored in AI.

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

Set A to the identity matrix.

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

Set A to the identity matrix.

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

Return the determinant of a 3x3 matrix.

Definition at line 1504 of file vtkMath.h.

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

Return the determinant of a 3x3 matrix.

Definition at line 1510 of file vtkMath.h.

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

Compute determinant of 3x3 matrix.

Three columns of matrix are input.

Definition at line 1429 of file vtkMath.h.

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

Compute determinant of 3x3 matrix.

Three columns of matrix are input.

Definition at line 1438 of file vtkMath.h.

double vtkMath::Determinant3x3 ( double  a1,
double  a2,
double  a3,
double  b1,
double  b2,
double  b3,
double  c1,
double  c2,
double  c3 
)
inlinestatic

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

Definition at line 1447 of file vtkMath.h.

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

Convert a quaternion to a 3x3 rotation matrix.

The quaternion does not have to be normalized beforehand. The quaternion must be in the form [w, x, y, z].

See also
Matrix3x3ToQuaternion() MultiplyQuaternion()
vtkQuaternion
static void vtkMath::QuaternionToMatrix3x3 ( const double  quat[4],
double  A[3][3] 
)
static

Convert a quaternion to a 3x3 rotation matrix.

The quaternion does not have to be normalized beforehand. The quaternion must be in the form [w, x, y, z].

See also
Matrix3x3ToQuaternion() MultiplyQuaternion()
vtkQuaternion
static void vtkMath::Matrix3x3ToQuaternion ( const float  A[3][3],
float  quat[4] 
)
static

Convert a 3x3 matrix into a quaternion.

This will provide the best possible answer even if the matrix is not a pure rotation matrix. The quaternion is in the form [w, x, y, z]. The method used is that of B.K.P. Horn. See: https://people.csail.mit.edu/bkph/articles/Quaternions.pdf

See also
QuaternionToMatrix3x3() MultiplyQuaternion()
vtkQuaternion
static void vtkMath::Matrix3x3ToQuaternion ( const double  A[3][3],
double  quat[4] 
)
static

Convert a 3x3 matrix into a quaternion.

This will provide the best possible answer even if the matrix is not a pure rotation matrix. The quaternion is in the form [w, x, y, z]. The method used is that of B.K.P. Horn. See: https://people.csail.mit.edu/bkph/articles/Quaternions.pdf

See also
QuaternionToMatrix3x3() MultiplyQuaternion()
vtkQuaternion
static void vtkMath::MultiplyQuaternion ( const float  q1[4],
const float  q2[4],
float  q[4] 
)
static

Multiply two quaternions.

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

See also
Matrix3x3ToQuaternion() QuaternionToMatrix3x3()
vtkQuaternion
static void vtkMath::MultiplyQuaternion ( const double  q1[4],
const double  q2[4],
double  q[4] 
)
static

Multiply two quaternions.

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

See also
Matrix3x3ToQuaternion() QuaternionToMatrix3x3()
vtkQuaternion
static void vtkMath::RotateVectorByNormalizedQuaternion ( const float  v[3],
const float  q[4],
float  r[3] 
)
static

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

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

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

static void vtkMath::RotateVectorByWXYZ ( const float  v[3],
const float  q[4],
float  r[3] 
)
static
static void vtkMath::RotateVectorByWXYZ ( const double  v[3],
const double  q[4],
double  r[3] 
)
static
static void vtkMath::Orthogonalize3x3 ( const float  A[3][3],
float  B[3][3] 
)
static

Orthogonalize a 3x3 matrix and put the result in B.

If matrix A has a negative determinant, then B will be a rotation plus a flip i.e. it will have a determinant of -1.

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

Orthogonalize a 3x3 matrix and put the result in B.

If matrix A has a negative determinant, then B will be a rotation plus a flip i.e. it will have a determinant of -1.

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

Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V.

The matrix V will have a positive determinant, and the three eigenvectors will be aligned as closely as possible with the x, y, and z axes.

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

Diagonalize a symmetric 3x3 matrix and return the eigenvalues in w and the eigenvectors in the columns of V.

The matrix V will have a positive determinant, and the three eigenvectors will be aligned as closely as possible with the x, y, and z axes.

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

Perform singular value decomposition on a 3x3 matrix.

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

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

Perform singular value decomposition on a 3x3 matrix.

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

static vtkTypeBool vtkMath::SolveLinearSystem ( double **  A,
double x,
int  size 
)
static

Solve linear equations Ax = b using Crout's method.

Input is square matrix A and load vector x. Solution x is written over load vector. The dimension of the matrix is specified in size. If error is found, method returns a 0.

static vtkTypeBool vtkMath::InvertMatrix ( double **  A,
double **  AI,
int  size 
)
static

Invert input square matrix A into matrix AI.

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

static vtkTypeBool vtkMath::InvertMatrix ( double **  A,
double **  AI,
int  size,
int tmp1Size,
double tmp2Size 
)
static

Thread safe version of InvertMatrix method.

Working memory arrays tmp1SIze and tmp2Size of length size must be passed in.

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

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

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

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

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

Thread safe version of LUFactorLinearSystem method.

Working memory array tmpSize of length size must be passed in.

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

Solve linear equations Ax = b using LU decomposition A = LU where L is lower triangular matrix and U is upper triangular matrix.

Input is factored matrix A=LU, integer array of pivot indices index[0->n-1], load vector x[0->n-1], and size of square matrix n. Note that A=LU and index[] are generated from method LUFactorLinearSystem). Also, solution vector is written directly over input load vector.

static double vtkMath::EstimateMatrixCondition ( const double *const *  A,
int  size 
)
static

Estimate the condition number of a LU factored matrix.

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

static vtkTypeBool vtkMath::Jacobi ( float **  a,
float w,
float **  v 
)
static

Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix.

Square 3x3 matrix a; output eigenvalues in w; and output eigenvectors in v arranged column-wise. Resulting eigenvalues/vectors are sorted in decreasing order; the most positive eigenvectors are selected for consistency; eigenvectors are normalized. NOTE: the input matrix a is modified during the solution

static vtkTypeBool vtkMath::Jacobi ( double **  a,
double w,
double **  v 
)
static

Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix.

Square 3x3 matrix a; output eigenvalues in w; and output eigenvectors in v arranged column-wise. Resulting eigenvalues/vectors are sorted in decreasing order; the most positive eigenvectors are selected for consistency; eigenvectors are normalized. NOTE: the input matrix a is modified during the solution

static vtkTypeBool vtkMath::JacobiN ( float **  a,
int  n,
float w,
float **  v 
)
static

JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix.

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

static vtkTypeBool vtkMath::JacobiN ( double **  a,
int  n,
double w,
double **  v 
)
static

JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix.

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

static vtkTypeBool vtkMath::SolveHomogeneousLeastSquares ( int  numberOfSamples,
double **  xt,
int  xOrder,
double **  mt 
)
static

Solves for the least squares best fit matrix for the homogeneous equation X'M' = 0'.

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

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

Solves for the least squares best fit matrix for the equation X'M' = Y'.

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

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

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

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 1009 of file vtkMath.h.

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

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

The input color is not modified. The input RGB must be float values in the range [0, 1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

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

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

The input color is not modified. The input RGB must be float values in the range [0, 1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

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

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

The input color is not modified. The input RGB must be float values in the range [0, 1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

static void vtkMath::RGBToHSV ( const double  rgb[3],
double  hsv[3] 
)
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 1015 of file vtkMath.h.

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

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

The input color is not modified. The input RGB must be float values in the range [0, 1]. The output ranges are hue [0, 1], saturation [0, 1], and value [0, 1].

static void vtkMath::HSVToRGB ( const float  hsv[3],
float  rgb[3] 
)
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 1029 of file vtkMath.h.

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].

static double* vtkMath::HSVToRGB ( const double  hsv[3])
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].

static double* vtkMath::HSVToRGB ( double  h,
double  s,
double  v 
)
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].

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 1035 of file vtkMath.h.

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].

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 1044 of file vtkMath.h.

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.

static double* vtkMath::LabToXYZ ( const double  lab[3])
static

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

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 1056 of file vtkMath.h.

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.

static double* vtkMath::XYZToLab ( const double  xyz[3])
static

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

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

Convert color from the CIE XYZ system to RGB.

Definition at line 1068 of file vtkMath.h.

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.

static double* vtkMath::XYZToRGB ( const double  xyz[3])
static

Convert color from the CIE XYZ system to RGB.

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

Convert color from the RGB system to CIE XYZ.

Definition at line 1080 of file vtkMath.h.

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.

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

Convert color from the RGB system to CIE XYZ.

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 1095 of file vtkMath.h.

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].

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

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 1107 of file vtkMath.h.

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.

static double* vtkMath::LabToRGB ( const double  lab[3])
static

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

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

Set the bounds to an uninitialized state.

Definition at line 1119 of file vtkMath.h.

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

Are the bounds initialized?

Definition at line 1133 of file vtkMath.h.

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 1517 of file vtkMath.h.

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 1532 of file vtkMath.h.

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 1543 of file vtkMath.h.

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.

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.

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 1555 of file vtkMath.h.

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

template<class T >
void vtkMath::TensorFromSymmetricTensor ( 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 1594 of file vtkMath.h.

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.

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.

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.

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)

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)

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.

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

static double vtkMath::Inf ( )
static

Special IEEE-754 number used to represent positive infinity.

static double vtkMath::NegInf ( )
static

Special IEEE-754 number used to represent negative infinity.

static double vtkMath::Nan ( )
static

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

static vtkTypeBool vtkMath::IsInf ( double  x)
static

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

static vtkTypeBool vtkMath::IsNan ( double  x)
static

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

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.

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

Definition at line 1581 of file vtkMath.h.

Member Data Documentation

vtkSmartPointer<vtkMathInternal> vtkMath::Internal
staticprotected

Definition at line 1291 of file vtkMath.h.


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