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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: Compute chord length of segment of a circle (arc)

Thursday May 05 2011 at 11:20

In working with circles one must be able to compute the arc2chord separation, the length of an arc and the length of the chord subtended by an angle subtended at the centre of a circle.

In particular this is important for converting circles to vertex-stroked polygons and vice versa.

Here is an encoding of the calculation of the length of a chord subtended by an angle at the centre of a circle for use in SQL Server 2008 spatial.

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

/* ----------------------------------------------------------------------------------------
* @function   : ComputeChordLength
* @precis     : Returns the length of the chord subtended by an angle of a circle.
* @version    : 1.0
* @usage      : FUNCTION ComputeChordLength( @p_dRadius Float,
*                                            @p_dAngle Float)
*                RETURNS FLOAT;
*               eg select cogo.ComputeChordLength(10,90.0) as chordLength;
* @param      : p_dRadius   : Radius of Circle
* @paramtype  : p_dRadius   : FLOAT
* @param      : p_dAngle    : Angle subtended at centre for which chord length is to be calculated (Value > 0 and <= 360
* @paramtype  : p_dAngle    : FLOAT
* @return     : ChordLength : The chord subtended by the angle
* @rtnType    : ChordLength : FLOAT
* @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 2008 
* @copyright  : Licensed under a Creative Commons Attribution-Share Alike 2.5 Australia License. (http://creativecommons.org/licenses/by-sa/2.5/au/)
TSQL
*/
Create Function ComputeChordLength( @p_dRadius Float,
                                    @p_dAngle  Float)
Returns Float
AS
BEGIN
  DECLARE
      @dChord    Float,
      @dAngleRad Float;
    BEGIN
      SET @dAngleRad = RADIANS(@p_dAngle);
      SET @dChord    = 2 * @p_dRadius * Sin(@dAngleRad / 2);
      Return @dChord;
    END;
END
GO

An example of how to execute this function is as follows:

select cogo.ComputeChordLength(10,90.0) as chordLength;

chordLength
14.1421356237309



I hope this helps someone.

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