Gwyddion – Free SPM (AFM, SNOM/NSOM, STM, MFM, …) data analysis software

interpolation

interpolation — General interpolation functions

Functions

gdouble gwy_interpolation_get_dval ()
gdouble gwy_interpolation_get_dval_of_equidists ()
gdouble gwy_interpolation_interpolate_1d ()
gdouble gwy_interpolation_interpolate_2d ()
gboolean gwy_interpolation_has_interpolating_basis ()
gint gwy_interpolation_get_support_size ()
void gwy_interpolation_resolve_coeffs_1d ()
void gwy_interpolation_resolve_coeffs_2d ()
void gwy_interpolation_resample_block_1d ()
void gwy_interpolation_resample_block_2d ()
void gwy_interpolation_shift_block_1d ()

Includes

#include <libprocess/gwyprocess.h>

Description

Data interpolation is usually pixel-like in Gwyddion, not function-like. That means the contribution of individual data saples is preserved on scaling (the area that “belongs” to all values is the same, it is not reduced to half for edge pixels).

Most of the functions listed here are quite low-level and typically one would use GwyDataField or GwyDataLine methods instead of these functions.

Functions

gwy_interpolation_get_dval ()

gdouble
gwy_interpolation_get_dval (gdouble x,
                            gdouble x1_,
                            gdouble y1_,
                            gdouble x2_,
                            gdouble y2_,
                            GwyInterpolationType interpolation);

This function uses two-point interpolation methods to get interpolated value between two arbitrary data points.

Parameters

x

requested value coordinate

 

x1_

x coordinate of first value

 

y1_

y coordinate of first value

 

x2_

x coordinate of second value

 

y2_

y coordinate of second value

 

interpolation

interpolation type

 

Returns

interpolated value

gwy_interpolation_get_dval_of_equidists ()

gdouble
gwy_interpolation_get_dval_of_equidists
                               (gdouble x,
                                gdouble *data,
                                GwyInterpolationType interpolation);

Computes interpolated value from 2 or 4 equidistant values.

For GWY_INTERPOLATION_NONE no data value is actually used, and zero is returned.

For GWY_INTERPOLATION_ROUND or GWY_INTERPOLATION_LINEAR it is enough to set middle two data values, that to use data in format {0, data[i], data[i+1], 0} and function computes value at data[i+x] (the outer values are not used).

For four value interpolations you have to prepare data as {data[i-1], data[i], data[i+1], data[i+2]} and function again returns value at data[i+x].

Interpolation with non-interpolating bases are silently replaced with an interpolating function with the same support size. See gwy_interpolation_interpolate_1d() for a function interpolating from interpolation coefficients.

Parameters

x

Possibily noninteger position in data to get value at.

 

data

Array of 4 values to interpolate between (see below).

 

interpolation

Interpolation type to use.

 

Returns

Interpolated value.

gwy_interpolation_interpolate_1d ()

gdouble
gwy_interpolation_interpolate_1d (gdouble x,
                                  const gdouble *coeff,
                                  GwyInterpolationType interpolation);

Interpolates a signle data point in one dimension.

The interpolation basis support size can be obtained generically with gwy_interpolation_get_support_size().

Parameters

x

Position in interval [0,1) to get value at.

 

coeff

Array of support-length size with interpolation coefficients (that are equal to data values for an interpolating basis).

 

interpolation

Interpolation type to use.

 

Returns

Interpolated value.

Since: 2.2

gwy_interpolation_interpolate_2d ()

gdouble
gwy_interpolation_interpolate_2d (gdouble x,
                                  gdouble y,
                                  gint rowstride,
                                  const gdouble *coeff,
                                  GwyInterpolationType interpolation);

Interpolates a signle data point in two dimensions.

Parameters

x

X-position in interval [0,1) to get value at.

 

y

Y-position in interval [0,1) to get value at.

 

rowstride

Row stride of coeff .

 

coeff

Array of support-length-squared size with interpolation coefficients (that are equal to data values for an interpolating basis).

 

interpolation

Interpolation type to use.

 

Returns

Interpolated value.

Since: 2.2

gwy_interpolation_has_interpolating_basis ()

gboolean
gwy_interpolation_has_interpolating_basis
                               (GwyInterpolationType interpolation);

Obtains the interpolating basis property of an inteprolation type.

Interpolation types with inteprolating basis directly use data values for interpolation. For these types gwy_interpolation_resolve_coeffs_1d() and gwy_interpolation_resolve_coeffs_2d() are no-op.

Generalized interpolation types (with non-interpolation basis) require to preprocess the data values to obtain interpolation coefficients first. On the ohter hand they typically offer much higher interpolation quality.

Parameters

interpolation

Interpolation type.

 

Returns

TRUE if the inteprolation type has interpolating basis, FALSE if data values cannot be directly used for interpolation of this type.

Since: 2.2

gwy_interpolation_get_support_size ()

gint
gwy_interpolation_get_support_size (GwyInterpolationType interpolation);

Obtains the basis support size for an interpolation type.

Parameters

interpolation

Interpolation type.

 

Returns

The length of the support interval of the interpolation basis.

Since: 2.2

gwy_interpolation_resolve_coeffs_1d ()

void
gwy_interpolation_resolve_coeffs_1d (gint n,
                                     gdouble *data,
                                     GwyInterpolationType interpolation);

Transforms data values in a one-dimensional array to interpolation coefficients.

This function is no-op for interpolation types with finite-support interpolating function. Therefore you can also omit it and use the data array directly for these interpolation types.

Parameters

n

Number of points in data .

 

data

An array of data values. It will be rewritten with the coefficients.

 

interpolation

Interpolation type to prepare data for.

 

Since: 2.2

gwy_interpolation_resolve_coeffs_2d ()

void
gwy_interpolation_resolve_coeffs_2d (gint width,
                                     gint height,
                                     gint rowstride,
                                     gdouble *data,
                                     GwyInterpolationType interpolation);

Transforms data values in a two-dimensional array to interpolation coefficients.

This function is no-op for interpolation types with finite-support interpolating function. Therefore you can also omit it and use the data array directly for these interpolation types.

Parameters

width

Number of columns in data .

 

height

Number of rows in data .

 

rowstride

Total row length (including width ).

 

data

An array of data values. It will be rewritten with the coefficients.

 

interpolation

Interpolation type to prepare data for.

 

Since: 2.2

gwy_interpolation_resample_block_1d ()

void
gwy_interpolation_resample_block_1d (gint length,
                                     gdouble *data,
                                     gint newlength,
                                     gdouble *newdata,
                                     GwyInterpolationType interpolation,
                                     gboolean preserve);

Resamples a one-dimensional data array.

This is a primitive operation, in most cases methods such as gwy_data_line_new_resampled() provide more convenient interface.

Parameters

length

Data block length.

 

data

Data block to resample.

 

newlength

Requested length after resampling.

 

newdata

Array to put the resampled data to.

 

interpolation

Interpolation type to use.

 

preserve

TRUE to preserve the content of data , FALSE to permit its overwriting with temporary data.

 

Since: 2.2

gwy_interpolation_resample_block_2d ()

void
gwy_interpolation_resample_block_2d (gint width,
                                     gint height,
                                     gint rowstride,
                                     gdouble *data,
                                     gint newwidth,
                                     gint newheight,
                                     gint newrowstride,
                                     gdouble *newdata,
                                     GwyInterpolationType interpolation,
                                     gboolean preserve);

Resamples a two-dimensional data array.

This is a primitive operation, in most cases methods such as gwy_data_field_new_resampled() provide more convenient interface.

Parameters

width

Number of columns in data .

 

height

Number of rows in data .

 

rowstride

Total row length (including width ).

 

data

Data block to resample.

 

newwidth

Requested number of columns after resampling.

 

newheight

Requested number of rows after resampling.

 

newrowstride

Requested total row length after resampling (including newwidth ).

 

newdata

Array to put the resampled data to.

 

interpolation

Interpolation type to use.

 

preserve

TRUE to preserve the content of data , FALSE to permit its overwriting with temporary data.

 

Since: 2.2

gwy_interpolation_shift_block_1d ()

void
gwy_interpolation_shift_block_1d (gint length,
                                  gdouble *data,
                                  gdouble offset,
                                  gdouble *newdata,
                                  GwyInterpolationType interpolation,
                                  GwyExteriorType exterior,
                                  gdouble fill_value,
                                  gboolean preserve);

Shifts a one-dimensional data block by a possibly non-integer offset.

The GWY_EXTERIOR_LAPLACE exterior type cannot be used with this function.

Parameters

length

Data block length.

 

data

Data block to shift.

 

offset

The shift, in corrective sense. Shift value of 1.0 means the zeroth value of newdata will be set to the first value of data .

 

newdata

Array to put the shifted data to.

 

interpolation

Interpolation type to use.

 

exterior

Exterior pixels handling.

 

fill_value

The value to use with GWY_EXTERIOR_FIXED_VALUE .

 

preserve

TRUE to preserve the content of data , FALSE to permit its overwriting with temporary data.

 

Since: 2.2

© David Nečas and Petr Klapetek

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