Interpolation and Resampling dialog box

 

Use this dialog box to carry interpolations and resampling on selected series.

 

Input

Specifies the worksheet location of the input data for this operation.

 

Valid Input Range

Provides a reference to the extent of the data available in the currently active worksheet. Use this range as a guide for typing valid extents in the Input Range box.

 

Input Range

Type in this box the range of cells containing the data you want to use as input for this command.

 

Values Context

Specifies the context of the values indicated by the Input Range box.

 

Univariate Even

Select this option to specify that the data indicated by Input Range is spaced at equal intervals of an independent variable.

 

Univariate Arbitrary

Select this option to specify that the data indicated by the Input Range box is spaced at arbitrary intervals of an independent variable.

 

 

Grid Even

Select this option to specify that the data indicated by the Input Range box represents a two-dimensional grid, spaced at equal intervals of the independent variables.

 

Grid Arbitrary

Select this option to specify that the data indicated by the Input Range box represents a two-dimensional grid, spaced at arbitrary intervals of the independent variables.

 

 

Multivariate Arbitrary

Select this option to specify that the data indicated by the Input Range box is spaced at arbitrary intervals of an independent variable.

 

Refer to Ind. Values Range on this topic for additional information on this subject.

 

Values in Rows

Check this box to indicate that the data specified by the Input Range box is organized in rows as opposed to columns (the default).

 

Refer to Specifying Input Arguments for additional information on this subject.

 

Output

Specifies the worksheet location for placing the results of this operation.

 

New Workbook

Select this option to place the results of this operation in a new document workbook.

 

New Sheet

Select this option to place the results of this operation in a new worksheet.

 

Range Position

Select this option to place the results of this operation starting at the worksheet location specified in the box to the right of this option.

 

Plot

Check this box to plot the results of this operation.

 

Refer to Specifying Output Locations for additional information on this subject.

 

Options

 

Method

Specifies the method that will be used to carry out interpolation. Select one of the following:

 

 

Cubic Splines

Select this option to carry interpolation using cubic splines.

Refer to Cubic Spline Type and Spline End Conditions on this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

Fourier

Select this option to carry interpolation in the frequency domain using Fourier transforms.

 

Lagrange

Select this option to carry interpolation using Lagrange's method.

 

 

Linear

Select this option to carry linear interpolation using line segments between existing points.

 

Newton

Select this option to carry interpolation using Newton's method.

 

 

Rational

Select this option to carry interpolation using Werner & Schaback's rational method.

Refer to Werner & Schaback (1979) for additional information on this subject.

 

Rational CF

Select this option to carry interpolation using Stoer & Bulirsch's rational method.

Refer to Stoer & Bulirsch (2002) for additional information on this subject.

 

Global Shepard

Select this option to carry interpolation using the global Shepard method.

Refer to Grosse (1988), Renka (1988), Renka (1988a), Renka (1999), and Shepard (1968) for additional information on this subject.

 

Local Shepard

Select this option to carry interpolation using the local Shepard method.

Refer to Grosse (1988), Renka (1988), Renka (1988a), Renka (1999), and Shepard (1968) for additional information on this subject.

 

Local Shepard WLS

Select this option to carry interpolation using the local Shepard method with weighted least squares.

Refer to Grosse (1988), Renka (1988), Renka (1988a), Renka (1999), and Shepard (1968) for additional information on this subject.

 

 

Cubic Spline Type

Specifies the type of cubic spline that will be used to carry interpolation. Select one of the following:

 

Clamped Spline

Select this option to carry interpolation using splines where the end-point conditions refer to the value of the first derivative of the series at its extreme points.

Refer to Complete Cubic Splines for additional information on this subject.

 

Natural Spline

Select this option to carry interpolation using splines where the end-point conditions refer to the value of the second derivative of the series at its extreme points.

Refer to Natural Cubic Splines for additional information on this subject.

 

Third Derivative

Select this option to carry interpolation using splines where the end-point conditions refer to the value of the third derivative of the series at its extreme points.

Refer to Splines With Specified End-Point Third Derivatives for additional information on this subject.

 

Not-a-Knot Spline

Select this option to carry interpolation using splines where where the third derivative of the spline function is continuous at the second and second-to-last nodes.

Refer to Not-a-knot Splines for additional information on this subject.

 

Refer to Spline End Conditions in this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

Numerator Degree

Specifies the degree of the numerator polynomial in rational interpolations. Type in this box the degree you want for the numerator polynomial.

 

 

Initial x

Type in this box the initial x-coordinate value of the input series.

 

 

Delta x

Type in this box the increment of successive x-coordinate values.

 

 

Initial y

Type in this box the increment of successive y-coordinate values.

 

 

Delta y

This value indicates the increment between successive y-values. Type in this box the y-increment between successive points in the series.

 

 

x-Values Range

Specifies a worksheet range containing the x-values related to the functional values of the input range.

Refer to Arbitrarily Spaced on this topic for additional information on this subject.

 

y-Values Range

Specifies a worksheet range containing the y-values related to the functional values of the input range.

Refer to Arbitrarily Spaced on this topic for additional information on this subject.

 

Ind. Values Range

Specifies a worksheet range containing the independent variable values related to the functional values of the input range for multi-variate arbitrary input series.

Refer to Multivariate Arbitrary on this topic for additional information on this subject

 

Shepard and Local Options

 

Weight Exponent

An arbitrary exponent used on the weight functions of Sheppard methods.

 

Weight Radius

Select this option to specify a radius of influence. This is the region from which all kNN neighbors are selected around points of interest when solving weighted local Shepard methods.

 

 

Weight Neighbors

Select this option to specify a number of nearest neighbors instead of a weight radius that may contain no neighbors. Selecting this option guarantees finding nearest neighbors around the points of interest when solving weighted local Shepard methods.

 

Functional Radius

Select this option to specify a radius of influence. This is the region from which all kNN neighbors are selected around points of interest when solving weighted local least squares Shepard methods.

 

 

Functional Neighbors

Select this option to specify a number of nearest neighbors instead of an influence radius that may contain no neighbors. Selecting this option guarantees finding enough nearest neighbors around the points of interest to solve weighted least squares local Shepard methods.

 

Polynomial Degree

The degree of the polynomial used to solve the system of linear equations for weighted least squares Shepard methods.

 

Refer to Grosse (1988), Renka (1988), Renka (1988a), Renka (1999), and Shepard (1968) for additional information on this subject.

 

Interpolation and Resampling Values

 

Interval Points

Select this option to interpolate the selected series for the number of points specified in the box to the right of this option, these points are selected equidistantly between the smallest and largest coordinate values of the independent variables.

 

 

Values Range

Select this option to interpolate the selected series at particular coordinate values, as specified by the worksheet range in the box to the right of this option.

 

 

Spline End Conditions

Specifies the conditions at the first and last points of the series.  These boxes will have different meanings depending on the type of selected spline (Cubic Spline).

 

Start Point Condition

Type in this box the value of the condition of the first or start point of the series. For example, you could type a value of zero (0) for the first derivative of the first point of the series in relation to clamped splines to make the series appear as having extrema at this point.

 

End Point Condition

Type in this box the value of the condition of the last or end point of the series. For example, you could type a value of one (1) for the first derivative of the last point of the series in relation to clamped splines to make the series appear as increasing at this point.

 

Refer to Cubic Spline Type in this topic, or to Interpolating Cubic Splines for additional information on this subject.

 

OK

Closes the dialog box and carries out this operation.

 

Cancel

Closes the dialog box without carrying out this operation.

 

 

Fig. Sample 3-dimensional interpolation of a 10x10 mesh to 37x37 using Not-a-Knot cubic splines.