#include <vtkMath.h>
Inheritance diagram for vtkMath:
vtkMath is 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; and random number generation.
Definition at line 38 of file vtkMath.h.
| void | PrintSelf (ostream &os, vtkIndent indent) |
| static float | Pi () |
| static float | DegreesToRadians () |
| static float | RadiansToDegrees () |
Public Types | |
| typedef vtkObject | Superclass |
Public Member Functions | |
| virtual const char * | GetClassName () |
| virtual int | IsA (const char *type) |
Static Public Member Functions | |
| static vtkMath * | New () |
| static int | IsTypeOf (const char *type) |
| static vtkMath * | SafeDownCast (vtkObject *o) |
| static void | Cross (const float x[3], const float y[3], float z[3]) |
| static float | Normalize (float x[3]) |
| static float | Distance2BetweenPoints (const float x[3], const float y[3]) |
| static float | Normalize2D (float x[3]) |
| static int | SolveLinearSystem (double **A, double *x, int size) |
| static double | EstimateMatrixCondition (double **A, int size) |
| static void | RandomSeed (long s) |
| static double | Random () |
| static double * | SolveCubic (double c0, double c1, double c2, double c3) |
| static double * | SolveQuadratic (double c0, double c1, double c2) |
| static int | ExtentIsWithinOtherExtent (int extent1[6], int extent2[6]) |
| static int | BoundsIsWithinOtherBounds (double bounds1[6], double bounds2[6], double delta[3]) |
| static int | PointIsWithinBounds (double point[3], double bounds[6], double delta[3]) |
| static double | DoubleDegreesToRadians () |
| static double | DoublePi () |
| static double | DoubleRadiansToDegrees () |
| static int | Round (float f) |
| static int | Round (double f) |
| static int | Floor (double x) |
| static float | Dot (const float x[3], const float y[3]) |
| static double | Dot (const double x[3], const double y[3]) |
| static void | Cross (const double x[3], const double y[3], double z[3]) |
| static float | Norm (const float *x, int n) |
| static double | Norm (const double *x, int n) |
| static float | Norm (const float x[3]) |
| static double | Norm (const double x[3]) |
| static double | Normalize (double x[3]) |
| static void | Perpendiculars (const double x[3], double y[3], double z[3], double theta) |
| static void | Perpendiculars (const float x[3], float y[3], float z[3], double theta) |
| static double | Distance2BetweenPoints (const double x[3], const double y[3]) |
| static float | Dot2D (const float x[3], const float y[3]) |
| static double | Dot2D (const double x[3], const double y[3]) |
| static float | Norm2D (const float x[3]) |
| static double | Norm2D (const double x[3]) |
| static double | Normalize2D (double x[3]) |
| static float | Determinant2x2 (const float c1[2], const float c2[2]) |
| static double | Determinant2x2 (double a, double b, double c, double d) |
| static double | Determinant2x2 (const double c1[2], const double c2[2]) |
| static void | LUFactor3x3 (float A[3][3], int index[3]) |
| static void | LUFactor3x3 (double A[3][3], int index[3]) |
| static void | LUSolve3x3 (const float A[3][3], const int index[3], float x[3]) |
| static void | LUSolve3x3 (const double A[3][3], const int index[3], double x[3]) |
| static void | LinearSolve3x3 (const float A[3][3], const float x[3], float y[3]) |
| static void | LinearSolve3x3 (const double A[3][3], const double x[3], double y[3]) |
| static void | Multiply3x3 (const float A[3][3], const float in[3], float out[3]) |
| static void | Multiply3x3 (const double A[3][3], const double in[3], double out[3]) |
| static void | Multiply3x3 (const float A[3][3], const float B[3][3], float C[3][3]) |
| static void | Multiply3x3 (const double A[3][3], const double B[3][3], double C[3][3]) |
| static void | Transpose3x3 (const float A[3][3], float AT[3][3]) |
| static void | Transpose3x3 (const double A[3][3], double AT[3][3]) |
| static void | Invert3x3 (const float A[3][3], float AI[3][3]) |
| static void | Invert3x3 (const double A[3][3], double AI[3][3]) |
| static void | Identity3x3 (float A[3][3]) |
| static void | Identity3x3 (double A[3][3]) |
| static double | Determinant3x3 (float A[3][3]) |
| static double | Determinant3x3 (double A[3][3]) |
| static float | Determinant3x3 (const float c1[3], const float c2[3], const float c3[3]) |
| static double | Determinant3x3 (const double c1[3], const double c2[3], const double c3[3]) |
| static double | Determinant3x3 (double a1, double a2, double a3, double b1, double b2, double b3, double c1, double c2, double c3) |
| static void | QuaternionToMatrix3x3 (const float quat[4], float A[3][3]) |
| static void | QuaternionToMatrix3x3 (const double quat[4], double A[3][3]) |
| static void | Matrix3x3ToQuaternion (const float A[3][3], float quat[4]) |
| static void | Matrix3x3ToQuaternion (const double A[3][3], double quat[4]) |
| static void | Orthogonalize3x3 (const float A[3][3], float B[3][3]) |
| static void | Orthogonalize3x3 (const double A[3][3], double B[3][3]) |
| static void | Diagonalize3x3 (const float A[3][3], float w[3], float V[3][3]) |
| static void | Diagonalize3x3 (const double A[3][3], double w[3], double V[3][3]) |
| static void | SingularValueDecomposition3x3 (const float A[3][3], float U[3][3], float w[3], float VT[3][3]) |
| static void | SingularValueDecomposition3x3 (const double A[3][3], double U[3][3], double w[3], double VT[3][3]) |
| static int | InvertMatrix (double **A, double **AI, int size) |
| static int | InvertMatrix (double **A, double **AI, int size, int *tmp1Size, double *tmp2Size) |
| static int | LUFactorLinearSystem (double **A, int *index, int size) |
| static int | LUFactorLinearSystem (double **A, int *index, int size, double *tmpSize) |
| static void | LUSolveLinearSystem (double **A, int *index, double *x, int size) |
| static double | Random (double min, double max) |
| static int | Jacobi (float **a, float *w, float **v) |
| static int | Jacobi (double **a, double *w, double **v) |
| static int | JacobiN (float **a, int n, float *w, float **v) |
| static int | JacobiN (double **a, int n, double *w, double **v) |
| static double * | SolveLinear (double c0, double c1) |
| static int | SolveCubic (double c0, double c1, double c2, double c3, double *r1, double *r2, double *r3, int *num_roots) |
| static int | SolveQuadratic (double c0, double c1, double c2, double *r1, double *r2, int *num_roots) |
| static int | SolveLinear (double c0, double c1, double *r1, int *num_roots) |
| static int | SolveHomogeneousLeastSquares (int numberOfSamples, double **xt, int xOrder, double **mt) |
| static int | SolveLeastSquares (int numberOfSamples, double **xt, int xOrder, double **yt, int yOrder, double **mt, int checkHomogeneous=1) |
| static void | RGBToHSV (float rgb[3], float hsv[3]) |
| static void | RGBToHSV (float r, float g, float b, float *h, float *s, float *v) |
| static double * | RGBToHSV (double rgb[3]) |
| static double * | RGBToHSV (double r, double g, double b) |
| static void | RGBToHSV (double rgb[3], double hsv[3]) |
| static void | RGBToHSV (double r, double g, double b, double *h, double *s, double *v) |
| static void | HSVToRGB (float hsv[3], float rgb[3]) |
| static void | HSVToRGB (float h, float s, float v, float *r, float *g, float *b) |
| static double * | HSVToRGB (double hsv[3]) |
| static double * | HSVToRGB (double h, double s, double v) |
| static void | HSVToRGB (double hsv[3], double rgb[3]) |
| static void | HSVToRGB (double h, double s, double v, double *r, double *g, double *b) |
| static void | LabToXYZ (double lab[3], double xyz[3]) |
| static void | XYZToRGB (double xyz[3], double rgb[3]) |
| static void | UninitializeBounds (double bounds[6]) |
| static int | AreBoundsInitialized (double bounds[6]) |
| static void | ClampValue (double *value, const double range[2]) |
| static void | ClampValue (double value, const double range[2], double *clamped_value) |
| static void | ClampValues (double *values, int nb_values, const double range[2]) |
| static void | ClampValues (const double *values, int nb_values, const double range[2], double *clamped_values) |
| static int | GetScalarTypeFittingRange (double range_min, double range_max, double scale=1.0, double shift=0.0) |
| static int | GetAdjustedScalarRange (vtkDataArray *array, int comp, double range[2]) |
Protected Member Functions | |
| vtkMath () | |
| ~vtkMath () | |
Static Protected Attributes | |
| static long | Seed |
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Reimplemented from vtkObject. |
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Create an object with Debug turned off, modified time initialized to zero, and reference counting on. Reimplemented from vtkObject. |
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Reimplemented from vtkObject. |
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Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeRevisionMacro found in vtkSetGet.h. Reimplemented from vtkObject. |
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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 vtkTypeRevisionMacro found in vtkSetGet.h. Reimplemented from vtkObject. |
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Reimplemented from vtkObject. |
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Methods invoked by print to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes. Reimplemented from vtkObject. |
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Useful constants. |
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Useful constants. (double-precision version) |
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Useful constants. (double-precision version) |
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Useful constants. (double-precision version) |
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Rounds a float to the nearest integer. |
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Rounds a float to the nearest integer. |
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Definition at line 599 of file vtkMath.h. Referenced by vtkUnstructuredGridPartialPreIntegration::Psi(). |
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Dot product of two 3-vectors (float version). |
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Dot product of two 3-vectors (double-precision version). |
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Cross product of two 3-vectors. Result vector in z[3]. |
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Cross product of two 3-vectors. Result vector in z[3]. (double-precision version) |
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Compute the norm of n-vector. Referenced by Normalize(). |
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Cross product of two 3-vectors. Result vector in z[3]. (double-precision version) |
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Compute the norm of 3-vector. |
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Compute the norm of 3-vector (double-precision version). |
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Normalize (in place) a 3-vector. Returns norm of vector. Definition at line 617 of file vtkMath.h. References Norm(). |
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Normalize (in place) a 3-vector. Returns norm of vector (double-precision version). Definition at line 631 of file vtkMath.h. References Norm(). |
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Given a unit vector x, find two unit vectors y and z such that x cross y = z (i.e. the vectors are perpendicular to each other). There is an infinite number of such vectors, specify an angle theta to choose one set. If you want only one perpendicular vector, specify NULL for z. |
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Normalize (in place) a 3-vector. Returns norm of vector (double-precision version). |
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Compute distance squared between two points. Definition at line 701 of file vtkMath.h. Referenced by vtkTriangle::TriangleArea(). |
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Compute distance squared between two points (double precision version). |
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Dot product of two 2-vectors. The third (z) component is ignored. |
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Dot product of two 2-vectors. The third (z) component is ignored (double-precision version). |
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Compute the norm of a 2-vector. Ignores z-component. Definition at line 147 of file vtkMath.h. Referenced by Normalize2D(). |
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Compute the norm of a 2-vector. Ignores z-component (double-precision version). |
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Normalize (in place) a 2-vector. Returns norm of vector. Ignores z-component. Definition at line 645 of file vtkMath.h. References Norm2D(). |
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Normalize (in place) a 2-vector. Returns norm of vector. Ignores z-component (double-precision version). Definition at line 659 of file vtkMath.h. References Norm2D(). |
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Compute determinant of 2x2 matrix. Two columns of matrix are input. Definition at line 168 of file vtkMath.h. Referenced by Determinant3x3(). |
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Calculate the determinant of a 2x2 matrix: | a b | | c d | |
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Calculate the determinant of a 2x2 matrix: | a b | | c d | |
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LU Factorization of a 3x3 matrix. The diagonal elements are the multiplicative inverse of those in the standard LU factorization. |
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LU Factorization of a 3x3 matrix. The diagonal elements are the multiplicative inverse of those in the standard LU factorization. |
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LU back substitution for a 3x3 matrix. The diagonal elements are the multiplicative inverse of those in the standard LU factorization. |
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LU back substitution for a 3x3 matrix. The diagonal elements are the multiplicative inverse of those in the standard LU factorization. |
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Solve Ay = x for y and place the result in y. The matrix A is destroyed in the process. |
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Solve Ay = x for y and place the result in y. The matrix A is destroyed in the process. |
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Multiply a vector by a 3x3 matrix. The result is placed in out. |
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Multiply a vector by a 3x3 matrix. The result is placed in out. |
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Multiply one 3x3 matrix by another according to C = AB. |
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Multiply one 3x3 matrix by another according to C = AB. |
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Transpose a 3x3 matrix. |
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Transpose a 3x3 matrix. |
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Invert a 3x3 matrix. |
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Invert a 3x3 matrix. |
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Set A to the identity matrix. |
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Set A to the identity matrix. |
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Return the determinant of a 3x3 matrix. Definition at line 754 of file vtkMath.h. References vtkDeterminant3x3(). |
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Return the determinant of a 3x3 matrix. Definition at line 760 of file vtkMath.h. References vtkDeterminant3x3(). |
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Compute determinant of 3x3 matrix. Three columns of matrix are input. |
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Compute determinant of 3x3 matrix. Three columns of matrix are input. |
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Calculate the determinant of a 3x3 matrix in the form: | a1, b1, c1 | | a2, b2, c2 | | a3, b3, c3 | Definition at line 691 of file vtkMath.h. References Determinant2x2(). |
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Convert a quaternion to a 3x3 rotation matrix. The quaternion does not have to be normalized beforehand. |
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Convert a quaternion to a 3x3 rotation matrix. The quaternion does not have to be normalized beforehand. |
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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 method used is that of B.K.P. Horn. |
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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 method used is that of B.K.P. Horn. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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Thread safe version of InvertMatrix method. Working memory arrays tmp1SIze and tmp2Size of length size must be passed in. |
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Factor linear equations Ax = b using LU decomposition A = LU where L is lower triangular matrix and U is upper triangular matrix. Input is square matrix A, integer array of pivot indices index[0->n-1], and size of square matrix n. Output factorization LU is in matrix A. If error is found, method returns 0. |
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Thread safe version of LUFactorLinearSystem method. Working memory array tmpSize of length size must be passed in. |
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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. |
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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.) |
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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(). |
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Generate random numbers between 0.0 and 1.0. This is used to provide portability across different systems. Referenced by Random(). |
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Generate random number between (min,max). Definition at line 717 of file vtkMath.h. References Random(). |
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Jacobi iteration for the solution of eigenvectors/eigenvalues of a 3x3 real symmetric matrix. Square 3x3 matrix a; output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized. |
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Generate random number between (min,max). |
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JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. Square nxn matrix a; size of matrix in n; output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized. w and v need to be allocated previously |
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JacobiN iteration for the solution of eigenvectors/eigenvalues of a nxn real symmetric matrix. Square nxn matrix a; size of matrix in n; output eigenvalues in w; and output eigenvectors in v. Resulting eigenvalues/vectors are sorted in decreasing order; eigenvectors are normalized. w and v need to be allocated previously |
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Solves a cubic equation c0*t^3 + c1*t^2 + c2*t + c3 = 0 when c0, c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of (real) roots (counting multiple roots as one) followed by roots themselves. The value in roots[4] is a integer giving further information about the roots (see return codes for int SolveCubic()). |
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Solves a quadratic equation c1*t^2 + c2*t + c3 = 0 when c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of (real) roots (counting multiple roots as one) followed by roots themselves. Note that roots[3] contains a return code further describing solution - see documentation for SolveCubic() for meaning of return codes. |
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Solves a linear equation c2*t + c3 = 0 when c2 and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Return array contains number of roots followed by roots themselves. |
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Solves a cubic equation when c0, c1, c2, And c3 Are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Roots and number of real roots are stored in user provided variables r1, r2, r3, and num_roots. Note that the function can return the following integer values describing the roots: (0)-no solution; (-1)-infinite number of solutions; (1)-one distinct real root of multiplicity 3 (stored in r1); (2)-two distinct real roots, one of multiplicity 2 (stored in r1 & r2); (3)-three distinct real roots; (-2)-quadratic equation with complex conjugate solution (real part of root returned in r1, imaginary in r2); (-3)-one real root and a complex conjugate pair (real root in r1 and real part of pair in r2 and imaginary in r3). |
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Solves A Quadratic Equation c1*t^2 + c2*t + c3 = 0 when c1, c2, and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Roots and number of roots are stored in user provided variables r1, r2, num_roots |
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Solves a linear equation c2*t + c3 = 0 when c2 and c3 are REAL. Solution is motivated by Numerical Recipes In C 2nd Ed. Root and number of (real) roots are stored in user provided variables r2 and num_roots. |
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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 |
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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. |
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Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. |
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Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. |
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Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. |
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Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. |
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Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. |
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Convert color in RGB format (Red, Green, Blue) to HSV format (Hue, Saturation, Value). The input color is not modified. |
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Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). The input color is not modified. |
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Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). The input color is not modified. |
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Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). The input color is not modified. |
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Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). The input color is not modified. |
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Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). The input color is not modified. |
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Convert color in HSV format (Hue, Saturation, Value) to RGB format (Red, Green, Blue). The input color is not modified. |
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Convert color from Lab to XYZ system, and vice-versa |
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Convert color from Lab to XYZ system, and vice-versa |
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Set the bounds to an uninitialized state |
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Are the bounds initialized? |
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Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. |
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Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. |
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Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. |
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Clamp some values against a range The method without 'clamped_values' will perform in-place clamping. |
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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. |
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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. |
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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 |
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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) |
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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) |
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1.4.3-20050530