## table of contents

v.generalize(1grass) | GRASS GIS User's Manual | v.generalize(1grass) |

# NAME¶

**v.generalize** - Performs vector based
generalization.

# KEYWORDS¶

vector, generalization, simplification, smoothing, displacement, network generalization, topology, geometry

# SYNOPSIS¶

**v.generalize**

**v.generalize --help**

**v.generalize** [-**lt**] **input**=*name*
[**layer**=*string*] [**type**=*string*[,*string*,...]]
**output**=*name* [**error**=*name*]
**method**=*string* **threshold**=*float*
[**look_ahead**=*integer*] [**reduction**=*float*]
[**slide**=*float*] [**angle_thresh**=*float*]
[**degree_thresh**=*integer*] [**closeness_thresh**=*float*]
[**betweeness_thresh**=*float*] [**alpha**=*float*]
[**beta**=*float*] [**iterations**=*integer*]
[**cats**=*range*] [**where**=*sql_query*]
[--**overwrite**] [--**help**] [--**verbose**] [--**quiet**]
[--**ui**]

## Flags:¶

## Parameters:¶

**input**=*name***[required]**-

Name of input vector map

Or data source for direct OGR access **layer**=*string*-

Layer number or name (’-1’ for all layers)

A single vector map can be connected to multiple database tables. This number determines which table to use. When used with direct OGR access this is the layer name.

Default:*-1* **type**=*string[,**string*,...]-

Input feature type

Options:*line, boundary, area*

Default:*line,boundary,area* **output**=*name***[required]**-

Name for output vector map **error**=*name*-

Error map with failed generalizations

Lines and boundaries causing errors (collapsed to a point or topology errors) **method**=*string***[required]**-

Generalization algorithm

Options:*douglas, douglas_reduction, lang, reduction, reumann, boyle, sliding_averaging, distance_weighting, chaiken, hermite, snakes, network, displacement*

**douglas**: Douglas-Peucker Algorithm

**douglas_reduction**: Douglas-Peucker Algorithm with reduction parameter

**lang**: Lang Simplification Algorithm

**reduction**: Vertex Reduction Algorithm eliminates points close to each other

**reumann**: Reumann-Witkam Algorithm

**boyle**: Boyle’s Forward-Looking Algorithm

**sliding_averaging**: McMaster’s Sliding Averaging Algorithm

**distance_weighting**: McMaster’s Distance-Weighting Algorithm

**chaiken**: Chaiken’s Algorithm

**hermite**: Interpolation by Cubic Hermite Splines

**snakes**: Snakes method for line smoothing

**network**: Network generalization

**displacement**: Displacement of lines close to each other **threshold**=*float***[required]**-

Maximal tolerance value

Options:*0-1000000000* **look_ahead**=*integer*-

Look-ahead parameter

Default:*7* **reduction**=*float*-

Percentage of the points in the output of ’douglas_reduction’ algorithm

Options:*0-100*

Default:*50* **slide**=*float*-

Slide of computed point toward the original point

Options:*0-1*

Default:*0.5* **angle_thresh**=*float*-

Minimum angle between two consecutive segments in Hermite method

Options:*0-180*

Default:*3* **degree_thresh**=*integer*-

Degree threshold in network generalization

Default:*0* **closeness_thresh**=*float*-

Closeness threshold in network generalization

Options:*0-1*

Default:*0* **betweeness_thresh**=*float*-

Betweeness threshold in network generalization

Default:*0* **alpha**=*float*-

Snakes alpha parameter

Default:*1.0* **beta**=*float*-

Snakes beta parameter

Default:*1.0* **iterations**=*integer*-

Number of iterations

Default:*1* **cats**=*range*-

Category values

Example: 1,3,7-9,13 **where**=*sql_query*-

WHERE conditions of SQL statement without ’where’ keyword

Example: income < 1000 and population >= 10000

# DESCRIPTION¶

*v.generalize* is a module for the generalization of GRASS
vector maps. This module consists of algorithms for line simplification,
line smoothing, network generalization and displacement (new methods may be
added later).

The **cats** and **where** options are used only if a
**layer** > 0 is specified, otherwise, those options are ignored. Be
aware that the default is *layer=-1*, meaning that all layers are
processed, ignoring the **cats** and **where** options.

If **type=area** is selected, boundaries of selected areas will
be generalized, and the options **cats**, **where**, and **layer**
will be used to select areas.

# NOTES¶

(Line) simplification is a process of reducing the complexity of vector features. The module transforms a line into another line consisting of fewer vertices, that still approximate the original line. Most of the algorithms described below select a subset of points on the original line.

(Line) smoothing is a "reverse" process which takes as input a line and produces a smoother approximate of the original. In some cases, this is achieved by inserting new vertices into the original line, and can total up to 4000% of the number of vertices in the original. In such an instance, it is always a good idea to simplify the line after smoothing.

Smoothing and simplification algorithms implemented in this module
work line by line, i.e. simplification/smoothing of one line does not affect
the other lines; they are treated separately. For isolated loops formed by a
single line/boundary, he first and the last point of each line/boundary can
be translated and/or deleted, unless the *-l* flag is used to disable
loop support.

Lines and boundaries are not translated if they would collapse to
a single point. Boundaries are not translated if they would intersect with
themselves or other boundaries. Such erroneous features are written to an
optional *error* vector map. Overlaying the *error* map over the
generalized map indicates the kind of error. Lines/boundaries collapsing to
a point are written out as points, boundaries violating topology are written
out as boundaries. The *error* map can be overlaid over the generalized
map to understand why some features were not generalized.

## SIMPLIFICATION¶

Simplification can fail for many boundaries if the simplification parameters would result in a large reduction of vertices. If many lines/boundaries could not be simplified, try different parameters that would cause a lower degree of simplification.

*v.generalize* contains following line simplification
algorithms:

- Douglas-Peucker Algorithm
- Douglas-Peucker Reduction Algorithm
- Lang Algorithm
- Vertex Reduction
- Reumann-Witkam Algorithm

**threshold**parameter, given in map units (for latitude-longitude locations: in decimal degree). In general, the degree of simplification increases with the increasing value of

**threshold**.

## ALGORITHM DESCRIPTIONS¶

*Douglas-Peucker*- "Quicksort" of line simplification, the most widely used algorithm. Input parameters:**input**,**threshold**. For more information, see:

http://geomalgorithms.com/a16-_decimate-1.html.*Douglas-Peucker Reduction Algorithm*is essentially the same algorithm as the algorithm above, the difference being that it takes an additional**reduction**parameter which denotes the percentage of the number of points on the new line with respect to the number of points on the original line. Input parameters:**input**,**threshold**,**reduction**.*Lang*- Another standard algorithm. Input parameters:**input**,**threshold**,**look_ahead**. For an excellent description, see:

http://www.sli.unimelb.edu.au/gisweb/LGmodule/LGLangVisualisation.htm.*Vertex Reduction*- Simplest among the algorithms. Input parameters:**input**,**threshold**. Given a line, this algorithm removes the points of this line which are closer to each other than**threshold**. More precisely, if p1 and p2 are two consecutive points, and the distance between p2 and p1 is less than**threshold**, it removes p2 and repeats the same process on the remaining points.*Reumann-Witkam*- Input parameters:**input**,**threshold**. This algorithm quite reasonably preserves the global characteristics of the lines. For more information, see for example:

http://psimpl.sourceforge.net/reumann-witkam.html.

*Douglas-Peucker* and *Douglas-Peucker Reduction
Algorithm* use the same method to simplify the lines. Note that

v.generalize input=boundary_county output=boundary_county_dp20 method=douglas threshold=20

is equivalent to

v.generalize input=boundary_county output=boundary_county_dp_red20_100 \

method=douglas_reduction threshold=20 reduction=100

However, in this case, the first method is faster. Also observe
that *douglas_reduction* never outputs more vertices than
*douglas*, and that, in general, *douglas* is more efficient than
*douglas_reduction*. More importantly, the effect of

v.generalize input=boundary_county output=boundary_county_dp_red0_30 \

method=douglas_reduction threshold=0 reduction=30

is that ’out’ contains approximately only 30% of points of ’in’.

## SMOOTHING¶

The following smoothing algorithms are implemented in
*v.generalize*:

*Boyle’s Forward-Looking Algorithm*- The position of each point depends on the position of the previous points and the point**look_ahead**ahead.**look_ahead**consecutive points. Input parameters:**input**,**look_ahead**.*McMaster’s Sliding Averaging Algorithm*- Input Parameters:**input**,**slide**,**look_ahead**. The new position of each point is the average of the**look_ahead**points around. Parameter**slide**is used for linear interpolation between old and new position (see below).*McMaster’s Distance-Weighting Algorithm*- Takes the weighted average of**look_ahead**consecutive points where the weight is the reciprocal of the distance from the point to the currently smoothed point. The parameter**slide**is used for linear interpolation between the original position of the point and newly computed position where value 0 means the original position. Input parameters:**input**,**slide**,**look_ahead**.*Chaiken’s Algorithm*- "Inscribes" a line touching the original line such that the points on this new line are at least*threshold*apart. Input parameters:**input**,**threshold**. This algorithm approximates the given line very well.*Hermite Interpolation*- This algorithm takes the points of the given line as the control points of hermite cubic spline and approximates this spline by the points approximately**threshold**apart. This method has excellent results for small values of**threshold**, but in this case it produces a huge number of new points and some simplification is usually needed. Input parameters:**input**,**threshold**,**angle_thresh**.**Angle_thresh**is used for reducing the number of the points. It denotes the minimal angle (in degrees) between two consecutive segments of a line.*Snakes*is the method of minimisation of the "energy" of a line. This method preserves the general characteristics of the lines but smooths the "sharp corners" of a line. Input parameters**input**,**alpha**,**beta**. This algorithm works very well for small values of**alpha**and**beta**(between 0 and 5). These parameters affect the "sharpness" and the curvature of the computed line.

*Hermite Interpolation*is the fact that the computed line always passes through the points of the original line, whereas the lines produced by the remaining algorithms never pass through these points. In some sense, this algorithm outputs a line which "circumscribes" the input line.

On the other hand, *Chaiken’s Algorithm* outputs a
line which "inscribes" a given line. The output line always
touches/intersects the centre of the input line segment between two
consecutive points. For more iterations, the property above does not hold,
but the computed lines are very similar to the Bezier Splines. The
disadvantage of the two algorithms given above is that they increase the
number of points. However, *Hermite Interpolation* can be used as
another simplification algorithm. To achieve this, it is necessary to set
*angle_thresh* to higher values (15 or so).

One restriction on both McMasters’ Algorithms is that
*look_ahead* parameter must be odd. Also note that these algorithms
have no effect if *look_ahead = 1*.

Note that *Boyle’s*, *McMasters’* and
*Snakes* algorithm are sometimes used in the signal processing to
smooth the signals. More importantly, these algorithms never change the
number of points on the lines; they only translate the points, and do not
insert any new points.

*Snakes* Algorithm is (asymptotically) the slowest among the
algorithms presented above. Also, it requires quite a lot of memory. This
means that it is not very efficient for maps with the lines consisting of
many segments.

## DISPLACEMENT¶

The displacement is used when the lines overlap and/or are close to each other at the current level of detail. In general, displacement methods move the conflicting features apart so that they do not interact and can be distinguished.

This module implements an algorithm for displacement of linear
features based on the *Snakes* approach. This method generally yields
very good results; however, it requires a lot of memory and is not very
efficient.

Displacement is selected by **method=displacement**. It uses
the following parameters:

**threshold**- specifies critical distance. Two features interact if they are closer than**threshold**apart.**alpha**,**beta**- These parameters define the rigidity of lines. For larger values of**alpha**,**beta**(>=1), the algorithm does a better job at retaining the original shape of the lines, possibly at the expense of displacement distance. If the values of**alpha**,**beta**are too small (<=0.001), then the lines are moved sufficiently, but the geometry and topology of lines can be destroyed. Most likely the best way to find the good values of**alpha**,**beta**is by trial and error.**iterations**- denotes the number of iterations the interactions between the lines are resolved. Good starting points for values of**iterations**are between 10 and 100.

**layer**,

**cats**and

**where**parameters.

## NETWORK GENERALIZATION¶

Used for selecting "the most important" part of the network. This is based on the graph algorithms. Network generalization is applied if method=network. The algorithm calculates three centrality measures for each line in the network and only the lines with the values greater than thresholds are selected. The behaviour of algorithm can be altered by the following parameters:

**degree_thresh**- algorithm selects only the lines which share a point with at least**degree_thresh**different lines.**closeness_thresh**- is always in the range (0, 1]. Only the lines with the closeness centrality value at least**closeness_thresh**apart are selected. The lines in the centre of a network have greater values of this measure than the lines near the border of a network. This means that this parameter can be used for selecting the centre(s) of a network. Note that if closeness_thresh=0 then everything is selected.**betweeness_thresh**- Again, only the lines with a betweeness centrality measure at least**betweeness_thresh**are selected. This value is always positive and is larger for large networks. It denotes to what extent a line is in between the other lines in the network. This value is large for the lines which lie between other lines and lie on the paths between two parts of a network. In the terminology of road networks, these are highways, bypasses, main roads/streets, etc.

Also, the outputed network may not be connected if the value of
**betweeness_thresh** is too large.

# EXAMPLES¶

## SIMPLIFICATION EXAMPLE¶

Simplification of county boundaries with DP method (North Carolina
sample dataset), threshold given in mapset units (here: meters):

v.generalize input=boundary_county output=boundary_county_dp20 \

method=douglas threshold=20 error=boundary_county_dp20_leftover

*Figure: Vector simplification example (spatial subset:*
*original map shown in black, simplified map with 26% remaining vertices
shown in red)*

## SMOOTHING EXAMPLE¶

Smoothing of road network with Chaiken method (North Carolina
sample dataset), threshold given in mapset units (here: meters):

v.generalize input=roads output=roads_chaiken method=chaiken \

threshold=1 error=roads_chaiken_leftover

*Figure: Vector smoothing example (spatial subset:*
*original map shown in black, smoothed map with 500% increased number of
vertices shown in red)*

# SEE ALSO¶

*v.clean,* *v.dissolve*

v.generalize Tutorial (GRASS-Wiki)

# AUTHORS¶

Daniel Bundala, Google Summer of Code 2007, Student

Wolf Bergenheim, Mentor

Partial rewrite: Markus Metz

# SOURCE CODE¶

Available at: v.generalize source code (history)

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GRASS 7.8.5 |