[pgrouting-dev] alphaShape

[Vicky Vergara]

Hi all, Regina,
working on removing CGAL as requisite for building pgRouting, so
aka rewriting pgr_alphaShape and pgr_pointsAsPolygon
using the example "S" found here:
http://www.bostongis.com/postgis_concavehull.snippet

As reminder, the alpha complexCαis a subcomplex of the Delaunaytriangulation
(DT)
So no curves on the result (ST_concaveHull has results with curves, so its
not an alpha shape)


This is the "face only" result I am getting using some alpha radius.
The yellow face are holes, and the red borders are the borders of the hole
The blue faces are "Singular" belong to alpha shape but there is no other
face belonging to the alpha complex
that is adjacent to any of the face edges
The purple line are the borders of the alpha shape.




[image: image.png]

Interesting thing is that the alpha shape is a collection of geometries
(polygon, line, point)
Its not just the border of the polygons.

This is the "face + line" result I get using that alpha,
(that alpha makes all points to be on a line and or triangle, So right now
there are not "lonely points")


[image: image.png]


So, currently pgRouting is returning things wrong, besides the fact that it
should not deal with geometries,
the pgr_alphashape is not really returning an alpha shape information:

in form of a sequence of (x, y) it is defining polygons borders either
external ring or internal rings of the polygons separated by NULL NULL
so its missing the lonely lines and the lonely points
and pgr_pointsAsPolygon is transforming that to a geometry.
So to keep the same functionality aka not returning the alpha shape with
lonely lines and lonely points, but only the polygon borders:
- The blue triangles are  polygons on the result,
-  Am I right on this statement?:
  - yellow selection is a polygon with a hole, it can not have the triangle
pointed by the arrow because it would be a self intersecting polygon,
   and the white area in the base of the arrow is really not a hole, looks
like, but that area is just surrounded by 3 individual polygons

etc...


[image: image.png]


I just want to make sure I am on the right track, and I have no concepts
wrong.
Regards
Vicky


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Vicky Vergara
Operations Research

eMail: vicky at georepublic.de
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