#include <vtkMath.h>
Inheritance diagram for vtkMath:
Public Methods | |
| virtual const char * | GetClassName () |
| virtual int | IsA (const char *type) |
Static Public Methods | |
| vtkMath * | New () |
| int | IsTypeOf (const char *type) |
| vtkMath * | SafeDownCast (vtkObject *o) |
| double | DoubleDegreesToRadians () |
| void | Cross (const float x[3], const float y[3], float z[3]) |
| void | Cross (const double x[3], const double y[3], double z[3]) |
| float | Norm (const float *x, int n) |
| float | Normalize (float x[3]) |
| double | Normalize (double x[3]) |
| float | Distance2BetweenPoints (const float x[3], const float y[3]) |
| double | Distance2BetweenPoints (const double x[3], const double y[3]) |
| float | Normalize2D (float x[3]) |
| double | Normalize2D (double x[3]) |
| int | SolveLinearSystem (double **A, double *x, int size) |
| int | InvertMatrix (double **A, double **AI, int size) |
| int | LUFactorLinearSystem (double **A, int *index, int size) |
| double | EstimateMatrixCondition (double **A, int size) |
| void | RandomSeed (long s) |
| float | Random () |
| float | Random (float min, float max) |
| double * | SolveCubic (double c0, double c1, double c2, double c3) |
| double * | SolveQuadratic (double c0, double c1, double c2) |
| double * | SolveLinear (double c0, double c1) |
| int | SolveLinear (double c0, double c1, double *r1, int *num_roots) |
| float | Pi () |
| float | DegreesToRadians () |
| float | Dot (const float x[3], const float y[3]) |
| double | Dot (const double x[3], const double y[3]) |
| float | Norm (const float x[3]) |
| double | Norm (const double x[3]) |
| void | Perpendiculars (const double x[3], double y[3], double z[3], double theta) |
| void | Perpendiculars (const float x[3], float y[3], float z[3], double theta) |
| float | Dot2D (const float x[3], const float y[3]) |
| double | Dot2D (const double x[3], const double y[3]) |
| float | Norm2D (const float x[3]) |
| double | Norm2D (const double x[3]) |
| float | Determinant2x2 (const float c1[2], const float c2[2]) |
| double | Determinant2x2 (double a, double b, double c, double d) |
| void | LUFactor3x3 (float A[3][3], int index[3]) |
| void | LUFactor3x3 (double A[3][3], int index[3]) |
| void | LUSolve3x3 (const float A[3][3], const int index[3], float x[3]) |
| void | LUSolve3x3 (const double A[3][3], const int index[3], double x[3]) |
| void | LinearSolve3x3 (const float A[3][3], const float x[3], float y[3]) |
| void | LinearSolve3x3 (const double A[3][3], const double x[3], double y[3]) |
| void | Multiply3x3 (const float A[3][3], const float in[3], float out[3]) |
| void | Multiply3x3 (const double A[3][3], const double in[3], double out[3]) |
| void | Multiply3x3 (const float A[3][3], const float B[3][3], float C[3][3]) |
| void | Multiply3x3 (const double A[3][3], const double B[3][3], double C[3][3]) |
| void | Transpose3x3 (const float A[3][3], float AT[3][3]) |
| void | Transpose3x3 (const double A[3][3], double AT[3][3]) |
| void | Invert3x3 (const float A[3][3], float AI[3][3]) |
| void | Invert3x3 (const double A[3][3], double AI[3][3]) |
| void | Identity3x3 (float A[3][3]) |
| void | Identity3x3 (double A[3][3]) |
| double | Determinant3x3 (float A[3][3]) |
| double | Determinant3x3 (double A[3][3]) |
| float | Determinant3x3 (const float c1[3], const float c2[3], const float c3[3]) |
| double | Determinant3x3 (double a1, double a2, double a3, double b1, double b2, double b3, double c1, double c2, double c3) |
| void | QuaternionToMatrix3x3 (const float quat[4], float A[3][3]) |
| void | QuaternionToMatrix3x3 (const double quat[4], double A[3][3]) |
| void | Matrix3x3ToQuaternion (const float A[3][3], float quat[4]) |
| void | Matrix3x3ToQuaternion (const double A[3][3], double quat[4]) |
| void | Orthogonalize3x3 (const float A[3][3], float B[3][3]) |
| void | Orthogonalize3x3 (const double A[3][3], double B[3][3]) |
| void | Diagonalize3x3 (const float A[3][3], float w[3], float V[3][3]) |
| void | Diagonalize3x3 (const double A[3][3], double w[3], double V[3][3]) |
| void | SingularValueDecomposition3x3 (const float A[3][3], float U[3][3], float w[3], float VT[3][3]) |
| void | SingularValueDecomposition3x3 (const double A[3][3], double U[3][3], double w[3], double VT[3][3]) |
| int | InvertMatrix (double **A, double **AI, int size, int *tmp1Size, double *tmp2Size) |
| int | LUFactorLinearSystem (double **A, int *index, int size, double *tmpSize) |
| void | LUSolveLinearSystem (double **A, int *index, double *x, int size) |
| int | Jacobi (float **a, float *w, float **v) |
| int | Jacobi (double **a, double *w, double **v) |
| int | JacobiN (float **a, int n, float *w, float **v) |
| int | JacobiN (double **a, int n, double *w, double **v) |
| int | SolveCubic (double c0, double c1, double c2, double c3, double *r1, double *r2, double *r3, int *num_roots) |
| int | SolveQuadratic (double c0, double c1, double c2, double *r1, double *r2, int *num_roots) |
| int | SolveLeastSquares (int numberOfSamples, double **xt, int xOrder, double **yt, int yOrder, double **mt) |
Protected Methods | |
| vtkMath () | |
| ~vtkMath () | |
Static Protected Attributes | |
| long | Seed |
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 64 of file vtkMath.h.
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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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Return the class name as a string. This method is defined in all subclasses of vtkObject with the vtkTypeMacro found in vtkSetGet.h. 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 vtkTypeMacro 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 vtkTypeMacro found in vtkSetGet.h. Reimplemented from vtkObject. |
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Will cast the supplied object to vtkObject* is this is a safe operation (i.e., a safe downcast); otherwise NULL is returned. This method is defined in all subclasses of vtkObject with the vtkTypeMacro found in vtkSetGet.h. Reimplemented from vtkObject. |
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Useful constants. |
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Useful constants. |
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Useful constants. (double-precision version) |
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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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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. |
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Normalize (in place) a 3-vector. Returns norm of vector (double-precision version). |
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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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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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Compute distance squared between two points. Definition at line 541 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 154 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. |
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Normalize (in place) a 2-vector. Returns norm of vector. Ignores z-component (double-precision version). |
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Compute determinant of 2x2 matrix. Two columns of matrix are input. Definition at line 175 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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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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Mutltiply one 3x3 matrix by another according to C = AB. |
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Mutltiply 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. |
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Return the determinant of a 3x3 matrix. |
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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 | |
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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). |
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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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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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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 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 |
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1.2.11.1 written by Dimitri van Heesch,
© 1997-2001