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

triangulation

triangulation — Delaunay and Voronoi triangulation and interpolation

Functions

GwyTriangulation *	gwy_triangulation_new ()
gboolean	gwy_triangulation_triangulate ()
gboolean	gwy_triangulation_triangulate_iterative ()
gboolean	gwy_triangulation_interpolate ()
void	gwy_triangulation_data_free ()
GwyTriangulationData *	gwy_triangulation_delaunay ()
GwyTriangulationData *	gwy_triangulation_boundary ()
GwyTriangulationData *	gwy_triangulation_voronoi ()

Types and Values

#define	GWY_TRIANGULATION_NONE
typedef	GwyTriangulationPointXY
typedef	GwyTriangulationPointXYZ
	GwyTriangulationData
struct	GwyTriangulation
struct	GwyTriangulationClass

Object Hierarchy

    GObject
    ╰── GwyTriangulation

Includes

#include <libprocess/gwyprocess.h>

Description

Functions

gwy_triangulation_new ()

GwyTriangulation *
gwy_triangulation_new (void);

Creates a new triangulation.

Returns

A new empty triangulation.

Since: 2.18

gwy_triangulation_triangulate ()

gboolean
gwy_triangulation_triangulate (GwyTriangulation *triangulation,
                               guint npoints,
                               gconstpointer points,
                               gsize point_size);

Finds Delaunay and Voronoi triangulations for a set of points in plane.

The triangulation might not work in numerically unstable cases. At present this includes various ambiguous cases with neighbour points on straight lines or circles. Also, no points in the input set may coincide.

It is possible to call this method successively on several different sets of points to triangulate each separately. Note that pointers in data returned by methods such as gwy_triangulation_delaunay() become invalid then.

Parameters

triangulation	Triangulation.
npoints	Number of points.
points	Array of points. They must be typecastable to GwyXY for triangulation and to GwyXYZ for interpolation. However, they can be larger than that. The actual struct size is indicated by `point_size` .
point_size	Size of point struct, in bytes.

Returns

TRUE on success, FALSE on failure. On failure the triangulation is empty.

Since: 2.18

gwy_triangulation_triangulate_iterative ()

gboolean
gwy_triangulation_triangulate_iterative
                               (GwyTriangulation *triangulation,
                                guint npoints,
                                gconstpointer points,
                                gsize point_size,
                                GwySetFractionFunc set_fraction,
                                GwySetMessageFunc set_message);

Finds Delaunay and Voronoi triangulations for a set of points in plane.

See gwy_triangulation_triangulate() for discussion. This function differs only by the optional set_fraction and set_message arguments that permit providing user feedback for large triangulations and cancelling the procedure upon request.

Parameters

triangulation	Triangulation.
npoints	Number of points.
points	Array of points. They must be typecastable to GwyXY for triangulation and to GwyXYZ for interpolation. However, they can be larger than that. The actual struct size is indicated by `point_size` .
point_size	Size of point struct, in bytes.
set_fraction	Function that sets fraction to output (or `NULL`).
set_message	Function that sets message to output (or `NULL`).

Returns

TRUE on success, FALSE on failure. On failure the triangulation is empty. Cancellation via set_fraction or set_message callback also counts as failure.

Since: 2.44

gwy_triangulation_interpolate ()

gboolean
gwy_triangulation_interpolate (GwyTriangulation *triangulation,
                               GwyInterpolationType interpolation,
                               GwyDataField *dfield);

Regularizes XYZ data to a grid, represented by a data field.

The area and resolution of the regular grid is given by the dimensions and offsets of dfield .

Parameters

triangulation	Triangulation.
interpolation	Interpolation to use. Only `GWY_INTERPOLATION_ROUND` and `GWY_INTERPOLATION_LINEAR` are implemented. Is is an error to pass any other interpolation type.
dfield	Data field to fill with interpolated values.

Returns

TRUE if the interpolation succeeds, FALSE on failure, e.g. due to numerical errors. In the latter case the contents of dfield is undefined.

Since: 2.18

gwy_triangulation_data_free ()

void
gwy_triangulation_data_free (GwyTriangulationData *triangulation_data);

Frees raw triangulation data.

This function should be used to free triangulation data returned by gwy_triangulation_delaunay() and similar. It does not free the array members as they are owned by the triangulation object.

Parameters

triangulation_data

Raw triangulation data.

Since: 2.18

gwy_triangulation_delaunay ()

GwyTriangulationData *
gwy_triangulation_delaunay (GwyTriangulation *triangulation);

Obtains the Delaunay triangulation data.

Notes to the fields in the returned struct:

npoints equals to the number of points passed to gwy_triangulation_triangulate().

Parameters

triangulation

Triangulation.

Returns

Newly clreated GwyTriangulationData that must be freed with gwy_triangulation_data_free() when no longer used. The data within is owned by triangulation , see GwyTriangulationData.

Since: 2.18

gwy_triangulation_boundary ()

GwyTriangulationData *
gwy_triangulation_boundary (GwyTriangulation *triangulation);

Obtains the boundary, i.e. convex hull, of Delaunay triangulation.

Notes to the fields in the returned struct:

npoints equals to the number of points passed to gwy_triangulation_triangulate().

size is the boundary length.

index [] contains point indices in the boundary for points on the boundary; and GWY_TRIANGULATION_NONE for points not on the boundary.

neighbours [] lists sequentially the boundary points.

Parameters

triangulation

Triangulation.

Returns

Newly clreated GwyTriangulationData that must be freed with gwy_triangulation_data_free() when no longer used. The data within is owned by triangulation , see GwyTriangulationData.

Since: 2.18

gwy_triangulation_voronoi ()

GwyTriangulationData *
gwy_triangulation_voronoi (GwyTriangulation *triangulation,
                           guint *nvpoints,
                           const GwyXY **vpoints);

Obtains the Voronoi triangulation data.

Notes to the fields in the returned struct:

npoints equals to the number of Delaunay triangulation points passed to gwy_triangulation_triangulate() plus the number of points in the Voronoi triangulation, nvpoints . Voronoi triangulation points are the vertices of Voronoi cells. So each triangle has one original (Delaunay) point and two cell vertices (Voronoi points).

index [] is the usual index of blocks in neighbours , however, point indices smaller than the number of Delaunay points correspond to the Delaunay points, point indices equal or larger correspond to points in vpoints (it is necessary to subtract the number of original points to obtain the real position in vpoints ).

neighbours [] contains the neighbour blocks, with above caveats about point numbering.

Parameters

triangulation	Triangulation.
nvpoints	Location to store the number of new Voronoi triangulation points, or `NULL`.
vpoints	Location to store pointer to the Voronoi triangulation points, or `NULL`.

Returns

Newly clreated GwyTriangulationData that must be freed with gwy_triangulation_data_free() when no longer used. The data within is owned by triangulation , see GwyTriangulationData.

Since: 2.18

Types and Values

GWY_TRIANGULATION_NONE

#define GWY_TRIANGULATION_NONE G_MAXUINT

Point index value representing no point.

Since: 2.18

GwyTriangulationPointXY

typedef GwyXY GwyTriangulationPointXY;

GwyTriangulationPointXYZ

typedef GwyXYZ GwyTriangulationPointXYZ;

Representation of a point in plane with associated value for interpolation.

Note this is an alias for GwyXYZ since 2.45.

Since: 2.18

GwyTriangulationData

typedef struct {
    guint npoints;
    guint size;
    const guint *index;
    const guint *neighbours;
} GwyTriangulationData;

Representation of raw triangulation data.

Members index and neighbours are owned by the GwyTriangulation object that provided this data and remain valid only until this object is destroyed or used to perform another triangulation.

The exact interpretation of individual parts depends on what kind of triangulation data it is and may differ a bit from the general description provided here. See the descriptions of individual methods returning GwyTriangulationData.

Members

guint `npoints`;	Number of points in the set, also detrmines the size of `index` .
guint `size`;	The length of `neighbours` .
const guint *`index`;	Array of size `npoints` +1 defining the blocks of neighbours in `neighbours` . The block for point `i` starts at `index` [`i` ] and ends one element before `index` [`i` +1]. Hence the last of `index` is equal to `size` .
const guint *`neighbours`;	Neighbours of each point, represented as indices into some array (which array, that depends on what kind of data it is). The points in each block are sorted counter-clockwise.

Since: 2.18

struct GwyTriangulation

struct GwyTriangulation;

struct GwyTriangulationClass

struct GwyTriangulationClass {
    GObjectClass parent_class;
};