Go to content Go to navigation and search

Home

Current SQL Server Blog Articles

    SQL Server Spatial: STFlipVectors
    SQL Server Spatial: Extract LineStrings in GeometryCollection to create LineString
    SQL Server Spatial: Converting a LineString to COGO XML
    SQL Server Spatial: Creating (Multi)LineStrings geometries from COGO XML instructions
    New Version of Package of TSQL Spatial Functions
    Vectorize/Segmentize SQL Server 2012
    Coordinate Editing Functions for SQL Server Spatial
    Function to Scale a geometry object for SQL Server Spatial
    TSQL String Tokenizer Function for SQL Server
    geography/geometry to MBR helper functions
    generate_series for SQL Server 2008
    Extract Polygons from result of STIntersection in SQL Server Spatial
    Function to round ordinates of a SQL Server Spatial geometry object
    Extract elements of SQL Server Spatial geometry object
    Counting number of polygon rings SQL Server Spatial
    Filtering Polygon Rings in SQL Server Spatial
    Function to Move a geometry object in SQL Server Spatial
    Alternate Centroid Functions for SQL Server Spatial
    Function to Rotate geometry objects in SQL Server Spatial
    A GetVertices wrapper for DumpPoints in SQL Server 2008 Spatial
    Creating a Morton number Space Key generator for SQL Server
    Gridding a geometry or geography object (SQL Server Denali)
    On hinting spatial indexes
    Random Search Procedure (SQL Server 2008 Spatial)
    COGO: Converting (Google Earth) Formatted Longitude/Latitude points to decimal degrees (SQL Server)
    COGO: Convert Degrees, Minutes and Seconds values to Decimal Degrees
    COGO: DD2DMS Formatting a latitude/longitude decimal degree value
    COGO: Create point from bearing and distance
    COGO: Compute number of vertices required to stroke circle or circular arc
    COGO: Calculating the bearing between two points (SQL Server 2008 Spatial)
    COGO: Compute arc length subtended by angle centre of circle
    COGO: Compute chord length of segment of a circle (arc)
    COGO: Computing Arc To Chord (Arc2Chord) Separation
    COGO: Creating a stroked polygon from a circle's centre x,y and radius
    COGO: Finding centre and radius of a curve defined by three points: FindCircle function
    Identifying Tight Radius Curves sections within LineString geometry data
    Generating random point data for SQL Server 2008 Spatial
    New Presentation on Active (Searchable) Spatial Metadata for SQL Server 2008 Spatial and FreeText
    Checking is a column in a table or a view is of type geometry or geography
    Extracting geometry type string values from geometry/geography objects in SQL Server 2008 Spatial
    Vectorising geometry objects in SQL Server 2008
    MBR to geography/geometry helper functions
    Extracting geometry types from geometry/geography objects in SQL Server 2008
    Getting the number of coordinate dimensions of a geometry/geography object in SQL Server 2008
    A Dump Points Function for SQL Server 2008 Spatial
    toGeography and toGeography Conversion Functions for SQL Server 2008 Spatial
    Write text file with spatial data from SQL Server 2008
    Loading Shapefiles into Geography type column in SQL Server 2008
    Tip #6: Correcting invalid geometries
    Tip #5: Where or where has my little column gone
    Tip #4: What Coordinate System is that?
    Tip #3: What object is that?
    Tip #2: Spatial Indexing and Primary Keys
    Tip #1: SQL Server 2008 "Katmai" - Setting SRIDs

Search

    Browse

RSS / Atom

Email me

textpattern

Creative Commons License
All Blog Articles, Data Models and Free Source Code by Simon Greener, The SpatialDB Advisor is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

COGO: Creating a stroked polygon from a circle's centre x,y and radius

Thursday May 05 2011 at 00:55

The relevant standards covering spatial data types within databases provide functionality at many levels (and miss some that is required by pratitioners like myself) from object definition through to API specification.

One area within those standards that has limited support within commercial GIS software and database implementations is the case of circular arcs (line and polygon boundary) and circles. Oracle Spatial has always supported them (though they aren’t that easy to work with for the newcomer). Some database implementations, like PostGIS 1.x, support circular arcs though not comprehensively; Microsoft’s SQL Server’s “strict” implementation of OGC SFS 1.1 does not support them at all.

Why do we need circular arcs and circles you may ask?

Where man (or woman if the generic English noun grates) has engineered structures in the natural world, those structures (buildings, roads, railways etc) use many Euclidean geometric forms in the definition. Thus we most often see straight lines defining rectangles and squares (or combinations thereof) in buildings, and we have always seen circles in buildings (think of the unglazed circular opening at the top of the Pantheon in Rome). The Sydney Opera House initially tried to use parabolas and ellipsoids to define the pre-cast segments of its “sail” roof – impossible mathematics and construction in pre-computing Sydney – before finally settling on segments derived from a much simpler spheres). Horizontal and vertical curves in roads and railways are just that: curves! In forestry, circular plots are often used when conducting in statistical inventory in the field.

Given all this, the reasons why there is such patchy support is perplexing. But that is for another day. But what is important to note is that some spatial software (not just SQL Server 2008) simply do not support them.

Many years ago I was required to expose circular forest inventory plots, stored in an Oracle database as as three columns in a table (long,lat and radius) into something the enterprise GIS mapping software could use to produce maps. That software did not support Oracle circles so we had to find a method for representation. We ended up using synchronized materialized views and a function I wrote in PL/SQL called CIRCLE2POLYGON (this is available in my free COGO package). Here is a version of that function for SQL Server 2008.

Note that I have a schema call cogo in which I create functions like this. You can use anything you like.

/**
* @function   : Circle2Polygon
* @precis     : Returns 2003 Polygon shape from Circle Centre XY and Radius
* @version    : 1.0
* @usage      : FUNCTION Circle2Polygon ( @p_dCentreX  float,
*                                         @p_dCentreY  float,
*                                         @p_dRadius   float,
*                                         @p_iSegments integer,
*                                         @p_srid      integer,
*                                         @p_precision integer)
*                RETURNS GEOMETRY
*               eg select cogo.circle2polygon(100,100,5.0,12,0,3);
* @param      : p_dCentreX    : X Ordinate of centre of Circle
* @paramtype  : p_dCentreX    : FLOAT
* @param      : p_dCentreY    : Y Ordinate of centre of Circle
* @paramtype  : p_dCentreY    : FLOAT
* @param      : p_dRadius     : Radius of Circle
* @paramtype  : p_dRadius     : FLOAT
* @param      : p_iSegments   : Number of arc (chord) segments in circle (+ve clockwise, -ve anti-clockwise)
* @paramtype  : p_iSegments   : INTEGER
* @param      : p_srid        : SRID of output shape
* @paramtype  : p_srid        : INTEGER
* @param      : p_precision   : Precision of any XY value ie number of significant digits. If null then 3 is assumed (ie 1 mm): 3456.2345245 -> 3456.235 
* @paramtype  : p_precision   : INTEGER
* @return     : geometry      : Polyon geometry with required rotation of outer shell.
* @rtnType    : geometry      : GEOMETRY
* @note       : Does not throw exceptions
* @note       : Assumes planar projection eg UTM.
* @history    : Simon Greener  - Feb 2005 - Original coding.
* @history    : Simon Greener  - May 2011 - Converted to SQL Server
* @copyright  : Licensed under a Creative Commons Attribution-Share Alike 2.5 Australia License. (http://creativecommons.org/licenses/by-sa/2.5/au/)
*/
Create
Function cogo.Circle2Polygon( @p_dCentreX  float,
                              @p_dCentreY  float,
                              @p_dRadius   float,
                              @p_iSegments integer,
                              @p_srid      integer,
                              @p_precision integer)
Returns geometry
etc

The function can be used to generate a coarse circle of 3 segments per 90 degree slice (4 quarters of circle to give 3 * 4 = 12 segments or slices) as follows:

select cogo.circle2polygon(100,100,5.0,12,0,3);

Which looks like this:

Or, having a bit of fun:

select cogo.circle2polygon(100,100,
                           a.intValue/6 + 5.0,
                           a.intValue,
                           0,3)
  from dbo.generate_series(144,0,-12) a;

select b.Radius,
       cogo.circle2polygon(100 + b.Radius/2,
                           100 + b.Radius/2,
                           b.Radius,
                           b.segments,
                           0,3)
  from (select (a.intValue/6 + 5.0) as Radius,
                a.intValue as segments 
          from dbo.generate_series(144,0,-12) a 
        ) b;

If anyone is interested in this function or would like me to create custom TSQL functions to meet your spatial business requirements, please contact me.

Creative Commons License

post this at del.icio.uspost this at Diggpost this at Technoratipost this at Redditpost this at Farkpost this at Yahoo! my webpost this at Windows Livepost this at Google Bookmarkspost this to Twitter

Comment [2]

Dear sir,

I do appriciate the knowledge you share here but i do wonder. Is there a specific reason why you implemented your own circle construction function? i would love to know if there is a performance hit accompanied with your implementation.

The native function to draw a circle provided by microsoft is following:
declare g Geometry set g = ‘Point(10 10)’
select @g.STBuffer(5)

As you can see, we do specify a point as centre. then we add a buffer of n meter which will be the radius of the circle.

Kind regards
Kevin Bosteels

— Kevin Bosteels · 29 May 2012, 11:06 · #

Kevin,

Two reasons.

1. 2008 did not have Circular arcs and circles and methods for segmenting them.
2. Control over the number of segments in the circle: there is no control over things like arc to chord separation in your method.

(2012 has 1 and some control of 2 – but that’s what happens in software: things change with versions.)

Of course, the performance of your approach will be better as it is core to the product. Performance was never the reason I did what I did. It was mainly a learning exercise in which I ported stuff I had done in Oracle to SQL Server.

Another reason why my approach is not so good: if the data is geodetic/geographic.

regards
Simon

— Simon Greener · 29 May 2012, 11:40 · #