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

interpolation (HEAD)

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