## DESCRIPTION

v.net.visibility computes the visibility graph of a vector map containing lines, areas (boundaries) and points. The visibility graph is the graph where the nodes are the end point of the lines, boundaries or simply points. There is an edge between two nodes if they are 'visible' to each other. Two nodes are visibible if there are no segments in between of them, i.e. the edge does not intersect any line or boundary in the vector map. This is useful to compute the shortest path in a vector map from any two points. To do this, first you need to compute the visibility graph and from that to compute the shortest path using v.net.path or d.path.

IMPORTANT: the algorithm doesn't work well with intersecting lines (that includes overlapping)

## NOTES

If you compute a shortest path after computing the visibility graph you will notice that this path might go through a vertex of a line. If this is not what you wanted you might need to process the map in v.buffer, initially whith a small value. Example:

    v.buffer input=map output=bufferedmap buffer=1 type=point,line,area,boundary

The first argument is the input map. It supports lines, boundaries (so, areas) and points. For the algorithm was written to work with lines and boundaries not intersecting each other (that includes overlapping).
The resulting map containing the visibility graph is given in the output map.

If you need to add additional points to compute a shortest path between them afterwards you can use the coordinates parameter, e.g.:

    coordinates=25556200,6686400,25556400,6686600

where 25556200,6686400 are the coordinate of the first point and 25556400,6686600 are the coordinates of the second point. Of course you can give as many points as you need. They will be added to the visibility graph and edges from them will be computed. You can always add those points after computing the visibility graph. Simply use the visibility parameter. The input will be the original vector map, the vis will be the computed visibility graph and the output the new visibility graph which will be the vis + the new points given with coordinate (edges will be computed as well).

    v.net.visibility input=map visibility=vis_map output=new_vis_map \
          coordinates=25556200,6686400,25556400,6686600

## EXAMPLES

### Example 1

A simple example (North Carolina sample data) showing how to use the module:

    v.extract input=zipcodes_wake output=areas_7_11_25 cats=7,11,25
    g.region vector=zipcodes_wake
    d.mon wx0
    d.vect areas_7_11_25
    v.net.visibility input=areas_7_11_25 output=graph
    d.vect graph
    d.vect areas_7_11_25 color=red type=boundary

### Example 2

d.er An example on how to use v.buffer along with the module:

    v.buffer input=lines output=buffered_lines buffer=1
    v.net.visibility input=buffered_lines output=graph
    d.vect graph
    d.vect lines col=red

### Example 3

An example on how to use the coordinate parameter. This will compute the visibility graph of the vector map lines with the point 2555678,6686343:

    v.net.visibility input=lines output=graph coordinates=2555678,6686343
    d.vect graph
    d.vect lines col=red

### Example 4

An example (North Carolina sample data) on how to use the coordinate parameter with the vis parameter. Here the vector map graph is computed then a new visibility graph is computed from it with the point 669547.97,208348.20 extra:

    v.extract input=zipcodes_wake output=areas_7_11_25 cats=7,11,25
    g.region vector=zipcodes_wake
    d.mon wx0
    d.vect areas_7_11_25
    v.net.visibility input=zipcodes_wake output=graph
    v.net.visibility input=zipcodes_wake visibility=graph output=new_graph \
          coordinates=669547.97,208348.20
    d.erase
    d.vect areas_7_11_25
    echo "symbol basic/star 20 669547.97 208348.20 black red" | d.graph -m
    d.vect new_graph
    d.vect areas_7_11_25 color=red type=boundary

### Example 5

An example for connections of points (Spearfish):

    v.net.visibility input=archsites output=graph
    g.region vector=archsites
    d.mon wx0
    d.vect graph
    d.vect archsites col=red

## KNOWN ISSUES

In some cases when 3 points or nodes are collinear, some wrong edges are added. This happens only really rarly and shouldn't be a big problem. When two points have the exact same x coordinate and are visible, some wrong edges are added.

## SEE ALSO

d.path, v.net, v.net.alloc, v.net.iso, v.net.salesman, v.net.steiner, v.to.db

## AUTHOR

Maximilian Maldacker
Mentor: Wolf Bergenheim

Last changed: $Date: 2015-05-11 02:16:13 +0200 (Mon, 11 May 2015) $