Ubuntu Manpage: v.generalize - Vector based generalization.

NAME

       v.generalize  - Vector based generalization.

KEYWORDS

       vector, generalization, simplification, smoothing, displacement, network generalization

SYNOPSIS

       v.generalize
       v.generalize help
       v.generalize  [-cr]  input=name  output=name   [type=string[,string,...]]   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]    [layer=integer]    [cats=range]    [where=sql_query]   [--overwrite]  [--verbose]
       [--quiet]

   Flags:
       -c
           Copy attributes

       -r
           This does nothing. It is retained for backwards compatibility

       --overwrite
           Allow output files to overwrite existing files

       --verbose
           Verbose module output

       --quiet
           Quiet module output

   Parameters:
       input=name
           Name of input vector map

       output=name
           Name for output vector map

       type=string[,string,...]
           Feature type
           Options: line,boundary,area
           Default: line,boundary,area

       method=string
           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
           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

       layer=integer
           Layer number
           A single vector map can be connected to multiple database tables. This number determines which  table
           to use.
           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 = 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).  For more examples and nice pictures, see tutorial

       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. Also,
the first and the last point of each line is never translated and/or deleted.

SIMPLIFICATION
v.generalize contains following line simplification algorithms:

Douglas-Peucker Algorithm

Douglas-Peucker Reduction Algorithm

Lang Algorithm

Vertex Reduction

Reumann-Witkam Algorithm

Remove Small Lines/Areas
Different algorithms require different parameters, but all the algorithms have one parameter in common:
the threshold parameter. 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://geometryalgorithms.com/Archive/algorithm_0205/algorithm_0205.htm.

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.

Reuman-Witkam - Input parameters: input, threshold. This algorithm quite reasonably
preserves the global characteristics of the lines. For more information, see:

http://www.ifp.uni-stuttgart.de/lehre/vorlesungen/GIS1/Lernmodule/Lg/LG_de_6.html (german).
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.
One of the key advantages of 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.
The lines affected by the algorithm can be specified by the 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.
All three parameters above can be presented at the same time. In that case, the algorithm selects only
the lines which meet each criterion.

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

AUTHORS