v.generalize - Vector based generalization.
vector, generalization, simplification, smoothing, displacement, network generalization
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]
- Copy attributes
- Remove lines and areas smaller than threshold
- Allow output files to overwrite existing files
- Verbose module output
- Quiet module output
- Name of input vector map
- Name for output vector map
- Feature type(s)
- Options: line,boundary,area
- Default: line,boundary,area
- Generalization algorithm
- Options: douglas,douglas_reduction,lang,reduction,reumann,remove_small,boyle,sliding_averaging,distance_weighting,chaiken,hermite,snakes,network,displacement
- Default: douglas
- 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
- remove_small: Removes lines shorter than threshold and areas of area less than threshold
- 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
- Maximal tolerance value
- Options: 0-1000000000
- Default: 1.0
- Look-ahead parameter
- Default: 7
- Percentage of the points in the output of 'douglas_reduction' algorithm
- Options: 0-100
- Default: 50
- Slide of computed point toward the original point
- Options: 0-1
- Default: 0.5
- Minimum angle between two consecutive segments in Hermite method
- Options: 0-180
- Default: 3
- Degree threshold in network generalization
- Default: 0
- Closeness threshold in network generalization
- Options: 0-1
- Default: 0
- Betweeness threshold in network generalization
- Default: 0
- Snakes alpha parameter
- Default: 1.0
- Snakes beta parameter
- Default: 1.0
- Number of iterations
- Default: 1
- Layer number
- A single vector map can be connected to multiple database tables. This number determines which table to use.
- Default: 1
- Category values
- Example: 1,3,7-9,13
- WHERE conditions of SQL statement without 'where' keyword
- Example: income < 1000 and inhab >= 10000
is module for generalization of GRASS vector maps. This module
comprises a bunch of algortihms for line simplification, line smoothing,
network generalization and displacemet. (New methods may be added later)
Also, this document contains only the descriptions of module and implemented
methods. For more examples and nice pictures, check
(Line) simplification is a process of reducing the compexity of vector features.
It transforms a line into another line which consists of fewer vertices but
still approximates the original line. The most of the algorithms described below
selects a subset of points of the original line.
On the other hand, (line) smoothing is a "reverse" process which takes as an
input a line and produces smoother line which approximates the original line.
In some cases, this is achieved by inserting new vertices into the line.
Sometimes, the increase of the number of vertices is dramatical (4000%).
When this situation occurs, it is always a good idea to simplify the line after
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.
v.generalize contains following line simplification algorithms
Different algorithms require different parameters, but all the algorithms have
one parameter in common. It is threshold parameter. In general, the degree
of simplification increases with the increasing value of threshold.
- Douglas-Peucker Algorithm
- "Douglas-Peucker Reduction Algorithm"
- Lang Algorithm
- Vertex Reduction
- Reumann-Witkam Algorithm
- Remove Small Lines/Areas
The following happens if r flag is presented.
If some line is simplified and hence becomes shorter than threshold then it is
removed. Also, if type contains area and a simplification algorithm is selected,
the areas of area less than threshold are also removed.
- Douglas-Peucker - "Quicksort" of line simplification, the most widely used
algorithm. Input parameters: input, threshold. For more
information, please check: http://geometryalgorithms.com/Archive/algorithm_0205/algorithm_0205.htm.
- Douglas-Peucker Reduction Algorithm is essentially the same algorithm as the
algorithm above. The difference is that it takes additional parameter reduction
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,
- Lang - Another standard algorithm. Input parameters: input, threshold, look_ahead.
For an excellent description, check: http://www.sli.unimelb.edu.au/gisweb/LGmodule/LGLangVisualisation.htm.
- Vertex Reduction - Simplest among the algorithms. Input parameters: input, threshold.
Given line, this algorithm removes the points of this line which are closer to each other than threshold.
Precisely, if p1 and p2 are two consecutive points and 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
- Remove Small Lines/Areas - removes the lines (strictly) shorter than threshold and areas of area (strictly)less than threshold.
Other lines/areas/boundaries are left unchanged. Input parameters: input, threshold
Douglas-Peucker and Douglas-Peucker Reduction Algorithm use the same method
to simplify the lines. Note that
is equivalent to
v.generalize input=in output=out method=douglas threshold=eps
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=in output=out method=douglas_reduction threshold=eps reduction=100
is that 'out' contains approximately only X% of points of 'in'.
v.generalize input=in output=out method=douglas_reduction threshold=0 reduction=X
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. Paremeter slide
is used for linear interpolation between old and new position (see below).
- McMaster's Distance-Weighting Algorithm - Works by taking 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. And 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 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 approximatelly threshold apart.
This method has excellent results for the 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 outputed points. It denotes the minimal
angle (in degrees) between two consecutive segements of line.
- Snakes is the method of minimization of the "energy" of the line. This method preserves the
general characteristcs of the lines but smooths the "sharp corners" of the line. Input parameters input, alpha, beta.
This algorithm works very well for small values of alpha and beta (between 0 and 5). These
parameters affects 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 throught 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
the line which "circumsrcibes" given line. On the other hand, Chaiken's Algorithm outputs
the line which "inscribes" given line. Moreover this line always touches/intersects the centre
of the 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 these
two algorithm 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 sometime used in the signal processing to smooth the signals.
More importantly, these algorithms never change the number of points on the lines. i.e they only
translate the points, they 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.
The displacement is used when the lines (linear
features) interact (overlap and/or are close to each other) at the current
level of detail. In general, displacement methods, as name suggests, move the
conflicting features apart so that they do not interact and can be distinguished.
This module implements algorithm for displacement of linear features based on
the Snakes approach. This method has very good results. However, it
requires a lot of memory and is not very efficient.
Displacement is selected by method=displacement. It uses following parameters:
threshold - specifies critical distance. Two features interact iff they are
closer than threshold appart.
alpha, beta - These parameters define the rigidity of lines. For greater
values of alpha, beta (>=1), the algorithm better preserves the original
shape of the lines. On the other hand, the lines may not
be move enough. 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. Probably, 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. Mostly, good values of iterations lies
between 10 and 100.
The lines affected by the algorithm can be specified by the layer,
cats and where parameters.
Is 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 measure at least closeness_thresh are selcted.
The lines in the centre of a network have greater values of this measure then
the lines near the border of a network. This means,
that this parameters 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 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 great for the lines
which lie between other lines and lie on the paths between two parts of a network.
In the terminology of the road neworks, these are highways, bypasses, main roads/streets....
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.
Daniel Bundala, Google Summer of Code 2007, Student
Wolf Bergenheim, Mentor
Last changed: $Date: 2007-11-01 09:43:24 -0700 (Thu, 01 Nov 2007) $
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