[postgis-users] Is CIRCULARLINESTRING ready for use?

[Mark Leslie]

Bruce Rindahl wrote:
> Mark Leslie wrote:
>> Support for CIRCULARSTRING is there.  Loading and retrieving of the 
>> supported curved geometries should scale to large numbers perfectly 
>> well, but not all the SQL-MM geometries are currently supported.  In 
>> particular, PostGIS was choking when I attempted to implement curved 
>> polygons.  Index support is complete, but I don't recall any heavy 
>> testing to ensure it's solid.  It does manage to calculate a fairly 
>> tight bounding box based on the curvature of the segment, not just 
>> the defining points, so I would consider it ready for substantial 
>> testing.  If only we had a volunteer with a large number of circular 
>> string geometries ;)
> How about the states of Delaware and Pennsylvania?
>
>  http://en.wikipedia.org/wiki/Twelve-Mile_Circle
> I also have numerous parcels with circular arcs for testing but you 
> must tell me what the syntax is.  The documentation gives 
> CIRCULARSTRING(0 0, 1 1, 1 0) but does not tell you what the points 0 
> 0 , 1 1  and 1 0 mean.  Three point arc?  Start, end, center?  Let me 
> know and I will send you lots of shapes.
>
> See:
> http://postgis.refractions.net/pipermail/postgis-devel/2007-September/002778.html 
>
>
> I don't think this post was ever answered.
>
> Finally I have to question the support of circularstrings if we don't 
> support ellipses.  The circle of Delaware is an ellipse in every 
> projection except geodetic (?).  We can't correctly project a 
> circularstring to anything and maintain the spatial relationship.  For 
> example in SVG there is no circle command in paths - only ellipses.  A 
> circular arc is defined as an ellipse with both radii the same.
>
> Comments??
>
> Bruce
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You're correct, that post seems to have gone unanswered, for which I'm 
somewhat embarrassed.  I'll answer it here for posterity.

1)  CIRCULARSTRING(0 0, 1 1, 1 0)
Frank defined this well, quoted here for completeness.

  Start, End and any other point on the arc that isn't the start or end.
  Note necessarily the center.  In the case of a circle the start and
  end are the same, but the intermediate point *is* required to be the
  arc center (ie. the opposite side of the circle).

I will add the a circular string need not define only one circular arc.  In the case of multiple arcs
in a string, the last point of the preceding arc is the first point of the succeeding arc.  An example 
would be CIRCULARSTRING(0 0, 1 1, 1 0, 4 3, 9 8)  This means that a valid circular string must have an 
odd number of points greater than 1 ( n > 1 && n % 2 == 1)

2)  COMPOUNDCURVE(CIRCULARSTRING(0 0, 1 1, 1 0),(1 0, 0 1))
A compound curve is a single, continuous curve that has both curved (circular) segments and 
linear segments.  That means that in addition to having well-formed components, the end point 
every component except the last must be coincident with the start point of the following component.

3)  CURVEPOLYGON(CIRCULARSTRING(0 0, 4 0, 4 4, 0 4, 0 0),(1 1, 3 3, 3 1, 
1 1))
A curved polygon is just like a polygon, with an outer ring and zero or more inner rings.  The difference
is a ring can take the form of a circular string, linear string or compound string.  This is where PostGIS
currently falls down.  The way we internally represent a compound string causes problems when embedding 
within curve polygons.

4)  MULTICURVE((0 0, 5 5),CIRCULARSTRING(4 0, 4 4, 8 4))
This is a collection of curves, which can include linear strings, circular string or compound strings.

5)  MULTISURFACE(CURVEPOLYGON(CIRCULARSTRING(0 0, 4 0, 4 4, 0 4, 0 0),(1 
1, 3 3, 3 1, 1 1)),((10 10, 14 12, 11 10, 10 10),(11 11, 11.5 11, 11 
11.5, 11 11)))
This is a collection of polygons, which can include curve polygons or linear polygons.

-- 
Mark Leslie
Geospatial Software Architect
LISAsoft

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