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java.lang.Objectplugins.big.bigsnakeutils.process.process1D.BSplineBasis
public class BSplineBasis
Implements several basis B-spline basis functions.
Nested Class Summary | |
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static class |
BSplineBasis.BSplineBasisType
Type of B-spline basis functions. |
Field Summary | |
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static int |
ASPLINESUPPORT
Length of the support of the A-spline. |
static int |
CUBICBSPLINESUPPORT
Length of the support of the cubic B-spline. |
static int |
ESPLINE3SUPPORT
Length of the support of the exponential B-spline basis function with three roots. |
static int |
ESPLINE4SUPPORT
Length of the support of the exponential B-spline basis function with four roots. |
static int |
LINEARBSPLINESUPPORT
Length of the support of the linear B-spline. |
static int |
MSPLINESUPPORT
Length of the support of the M-spline. |
static int |
QUADRATICBSPLINESUPPORT
Length of the support of the quadratic B-spline. |
Constructor Summary | |
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BSplineBasis()
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Method Summary | |
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static double |
ASpline(double t,
double alpha)
Causal A-Spline. |
static double |
ASplinePrime(double t,
double alpha)
Derivative of causal A-Spline. |
static double |
autocorrelationESpline(int l,
double alpha)
Sampled autocorrelation of the exponential B-spline of order three. |
static double |
autocorrelationESpline3(int l,
int M)
Sampled autocorrelation of the exponential B-spline of order three. |
static double[] |
computeBSplineFilter(int N)
This function compute the B-Spline Filter B(z). |
static double[] |
computeESplineDerivativeMask(int N,
double alphaSub,
int M)
This function compute the derivative mask of a ESpline3 |
static double[] |
computeMultinomialCoef(int[] index,
int m,
int N,
double[] h)
This function compute the multinomial coefficient corresponding of the combination of the ki done by the function multinomial() . |
static double |
computePolynomialDerivative(double index,
int N)
This function compute the derivative mask of a B-Spline |
static double[] |
computePolynomialDerivativeMask(int N)
This function compute the derivative mask of a B-Spline |
static double |
ConstantBSpline(double t)
Causal constant B-spline. |
static double |
convolutedGreenFunctionESpline(double l,
double alpha1,
double alpha2,
double M1,
double M2)
The Green function corresponding to the convolution of two exponential splines with parameters alpha1 and alpha2 which have been scaled M1 and M2 times respectively. |
static double |
correlationESpline(int l,
double alpha)
Sampled correlation of the exponential B-spline of order three with a filter. |
static double |
correlationMSplineMSplinePrime(int p,
int M)
Sampled correlation of the MSpline with MSplinePrime, i.e. |
static double |
correlationOfTwoESpline(double l,
double alpha1,
double alpha2,
double M1,
double M2)
Correlation function of two exponential B-splines of order three with parameters alpha1 and alpha2 which have been scaled M1 and M2 times respectively. |
static double |
cot(double arg)
Cotangent. |
static double |
csc(double arg)
Cosecant. |
static double |
CubicBSpline(double t)
Causal cubic B-spline. |
static double |
ESpline3_Prime(double t,
double alpha)
Derivative of the causal exponential B-Spline with parameters (0,-j alpha, j alpha). |
static double |
ESpline3_PrimeBis(double t,
double alpha,
int M)
Derivative of the causal exponential B-Spline with parameters (0,-j alpha, j alpha) for a alpha which is non constant. |
static double |
ESpline3_PrimePrime(double t,
double alpha)
Second derivative of the causal exponential B-Spline with parameters (0,-j alpha, j alpha). |
static double |
ESpline3(double t,
double alpha)
Causal exponential B-Spline with parameters (0,-j alpha, j alpha). |
static double |
ESpline3Bis(double t,
double alpha,
int M)
Causal exponential B-Spline with parameters (0,-j alpha, j alpha) for a alpha which is non constant. |
static double |
ESpline4(double t,
double alpha)
Causal exponential B-Spline with parameters (0, 0,-j alpha, j alpha). |
static int |
factorial(int n)
This function compute the factorial function |
static double |
Keys_Prime(double t)
First Derivative of Keys |
static double |
Keys_PrimePrime(double t)
Second derivative of Keys |
static double |
Keys(double t)
Causal Keys interpolator. |
static double |
LinearBSpline_Prime(double t)
Derivative of the linear B-spline. |
static double |
LinearBSpline(double t)
Causal linear B-spline. |
static double[] |
MaskESpline(int m,
int N,
double alphaSub)
Refinement mask of Espline3 for a m scaling parameters: m = dilation factor, N= order of the basis function |
static double[] |
MaskPolynomialSpline(int m,
int N)
Refinement mask of causal B-spline (Quadratic and cubic) for a m scaling parameters: m = dilation factor, N= order of the basis function |
static double |
MSpline_Prime(double t,
double alpha)
Derivative of the causal M-Spline |
static double |
MSpline_PrimePrime(double t,
double alpha)
Second derivative of the causal M-Spline |
static double |
MSpline(double t,
double alpha)
Causal M-Spline. |
static int |
multinomial(int coefMax,
int size,
int[] index,
int it,
int m,
int N,
double[] h)
This is a recursive function to compute the multinomial coefficient of (x0+x1+...+xm-1)^N The goal of this function is to find every {k0,...,km-1} as k0+...+km-1=N (cf multinomial theorem on Wikipedia for more understanding the formula) parameters : index= array of the ki, size= number f coefficient ki, coefMax= the maximum value that a ki can take, it= the iteration of the recursive function, m= dilation factor, N=order of the spline, h=mask |
static double |
Order5BSpline(double t)
Causal B-spline of order 5. |
static double |
Order6BSpline(double t)
Causal B-spline of order 6. |
static double |
Order7BSpline(double t)
Causal B-spline of order 7. |
static double |
QuadraticSpline(double t)
Causal quadratic B-spline. |
static double |
sec(double arg)
Secant. |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
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public static int LINEARBSPLINESUPPORT
public static int QUADRATICBSPLINESUPPORT
public static int CUBICBSPLINESUPPORT
public static int ESPLINE3SUPPORT
public static int ESPLINE4SUPPORT
public static int MSPLINESUPPORT
public static int ASPLINESUPPORT
Constructor Detail |
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public BSplineBasis()
Method Detail |
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public static double ConstantBSpline(double t)
public static double LinearBSpline(double t)
public static double QuadraticSpline(double t)
public static double[] MaskPolynomialSpline(int m, int N)
public static double[] MaskESpline(int m, int N, double alphaSub)
public static double CubicBSpline(double t)
public static double Order5BSpline(double t)
public static double Order6BSpline(double t)
public static double Order7BSpline(double t)
public static double ESpline3(double t, double alpha)
public static double ESpline3Bis(double t, double alpha, int M)
public static double ESpline4(double t, double alpha)
public static double Keys(double t)
public static double MSpline(double t, double alpha)
public static double ASpline(double t, double alpha)
public static double ASplinePrime(double t, double alpha)
public static double MSpline_Prime(double t, double alpha)
public static double MSpline_PrimePrime(double t, double alpha)
public static double Keys_Prime(double t)
public static double Keys_PrimePrime(double t)
public static double csc(double arg)
public static double sec(double arg)
public static double cot(double arg)
public static double LinearBSpline_Prime(double t)
public static double ESpline3_Prime(double t, double alpha)
public static double ESpline3_PrimeBis(double t, double alpha, int M)
public static double ESpline3_PrimePrime(double t, double alpha)
public static double correlationESpline(int l, double alpha)
public static double correlationMSplineMSplinePrime(int p, int M)
public static double convolutedGreenFunctionESpline(double l, double alpha1, double alpha2, double M1, double M2)
public static double correlationOfTwoESpline(double l, double alpha1, double alpha2, double M1, double M2)
public static double autocorrelationESpline(int l, double alpha)
public static double autocorrelationESpline3(int l, int M)
public static int factorial(int n)
public static int multinomial(int coefMax, int size, int[] index, int it, int m, int N, double[] h)
public static double[] computeMultinomialCoef(int[] index, int m, int N, double[] h)
multinomial()
.
public static double[] computeBSplineFilter(int N)
public static double[] computePolynomialDerivativeMask(int N)
public static double[] computeESplineDerivativeMask(int N, double alphaSub, int M)
public static double computePolynomialDerivative(double index, int N)
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