BivariateAkimaSpline Type

Namespace: Altaxo.Calc.Interpolation
Assembly: AltaxoCore.Redist.dll
Base Type: obj

Class to spline bivariate function data (in gridded form).

The source originates from:

Hiroshi Akima

"Algorithm 474: Bivariate Interpolation and smooth surface fitting based on local procedures"

Communications of the ACM, Vol.17 (Jan.1974), Number 1

and where translated to C# by D.Lellinger 2005.

Constructors

Constructor Description

BivariateAkimaSpline(x, y, z, copyDataLocally)

Full Usage: BivariateAkimaSpline(x, y, z, copyDataLocally)

Parameters:
    x : IReadOnlyList<float> - ARRAY OF DIMENSION LX STORING THE X COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)
    y : IReadOnlyList<float> - ARRAY OF DIMENSION LY STORING THE Y COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)
    z : IROMatrix<float> - DOUBLY-DIMENSIONED ARRAY OF DIMENSION (LX,LY) STORING THE VALUES OF THE FUNCTION (Z VALUES) AT INPUT GRID POINTS
    copyDataLocally : bool - If true, the data where cloned before stored here in this instance. If false, the data are stored directly. Make sure then, that the data are not changed outside.

Constructs an Akima bivariate spline.

x : IReadOnlyList<float>

ARRAY OF DIMENSION LX STORING THE X COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)

y : IReadOnlyList<float>

ARRAY OF DIMENSION LY STORING THE Y COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)

z : IROMatrix<float>

DOUBLY-DIMENSIONED ARRAY OF DIMENSION (LX,LY) STORING THE VALUES OF THE FUNCTION (Z VALUES) AT INPUT GRID POINTS

copyDataLocally : bool

If true, the data where cloned before stored here in this instance. If false, the data are stored directly. Make sure then, that the data are not changed outside.

Instance members

Instance member Description

this.Interpolate

Full Usage: this.Interpolate

Parameters:
    x : float
    y : float

Returns: float

x : float
y : float
Returns: float

Static members

Static member Description

BivariateAkimaSpline.Interpolate(x, y, z, u, v, w)

Full Usage: BivariateAkimaSpline.Interpolate(x, y, z, u, v, w)

Parameters:
    x : IReadOnlyList<float> - VECTOR OF DIMENSION LX STORING THE X COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)
    y : IReadOnlyList<float> - VECTOR OF DIMENSION LY STORING THE Y COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)
    z : IROMatrix<float> - MATRIX OF DIMENSION (LX,LY) STORING THE VALUES OF THE FUNCTION (Z VALUES) AT INPUT GRID POINTS
    u : IReadOnlyList<float> - VECTOR OF DIMENSION N STORING THE X COORDINATES OF DESIRED POINTS
    v : IReadOnlyList<float> - VECTOR OF DIMENSION N STORING THE Y COORDINATES OF DESIRED POINTS
    w : IVector<float> - VECTOR OF DIMENSION N WHERE THE INTERPOLATED Z VALUES AT DESIRED POINTS ARE TO BE DISPLAYED

THIS SUBROUTINE INTERPOLATES, FROM VALUES OF THE FUNCTION GIVEN AT INPUT GRID POINTS IN AN X-Y PLANE AND FOR A GIVEN SET OF POINTS IN THE PLANE, THE VALUES OF A SINGLE-VALUED BIVARIATE FUNCTION Z = Z(X,Y). THE METHOD IS BASED ON A PIECE-WISE FUNCTION COMPOSED OF A SET OF BICUBIC POLYNOMIALS IN X AND Y. EACH POLYNOMIAL IS APPLICABLE TO A RECTANGLE OF THE INPUT GRID IN THE X-Y PLANE. EACH POLYNOMIAL IS DETERMINED LOCALLY.

x : IReadOnlyList<float>

VECTOR OF DIMENSION LX STORING THE X COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)

y : IReadOnlyList<float>

VECTOR OF DIMENSION LY STORING THE Y COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)

z : IROMatrix<float>

MATRIX OF DIMENSION (LX,LY) STORING THE VALUES OF THE FUNCTION (Z VALUES) AT INPUT GRID POINTS

u : IReadOnlyList<float>

VECTOR OF DIMENSION N STORING THE X COORDINATES OF DESIRED POINTS

v : IReadOnlyList<float>

VECTOR OF DIMENSION N STORING THE Y COORDINATES OF DESIRED POINTS

w : IVector<float>

VECTOR OF DIMENSION N WHERE THE INTERPOLATED Z VALUES AT DESIRED POINTS ARE TO BE DISPLAYED

BivariateAkimaSpline.Interpolate(x, y, z, u, v, w)

Full Usage: BivariateAkimaSpline.Interpolate(x, y, z, u, v, w)

Parameters:
    x : float[] - ARRAY OF DIMENSION LX STORING THE X COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)
    y : float[] - ARRAY OF DIMENSION LY STORING THE Y COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)
    z : float[] - DOUBLY-DIMENSIONED ARRAY OF DIMENSION (LX,LY) STORING THE VALUES OF THE FUNCTION (Z VALUES) AT INPUT GRID POINTS
    u : float[] - ARRAY OF DIMENSION N STORING THE X COORDINATES OF DESIRED POINTS
    v : float[] - ARRAY OF DIMENSION N STORING THE Y COORDINATES OF DESIRED POINTS
    w : float[] - ARRAY OF DIMENSION N WHERE THE INTERPOLATED Z VALUES AT DESIRED POINTS ARE TO BE DISPLAYED

Old interface to the akima spline. Since all arrays are converted to IVector or IMatrix, avoid this interface if possible.

x : float[]

ARRAY OF DIMENSION LX STORING THE X COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)

y : float[]

ARRAY OF DIMENSION LY STORING THE Y COORDINATES OF INPUT GRID POINTS (IN ASCENDING ORDER)

z : float[]

DOUBLY-DIMENSIONED ARRAY OF DIMENSION (LX,LY) STORING THE VALUES OF THE FUNCTION (Z VALUES) AT INPUT GRID POINTS

u : float[]

ARRAY OF DIMENSION N STORING THE X COORDINATES OF DESIRED POINTS

v : float[]

ARRAY OF DIMENSION N STORING THE Y COORDINATES OF DESIRED POINTS

w : float[]

ARRAY OF DIMENSION N WHERE THE INTERPOLATED Z VALUES AT DESIRED POINTS ARE TO BE DISPLAYED