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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: Create point from bearing and distance

Friday May 06 2011 at 03:15

Sometimes the definition of an object can be as a bearing and distance from a known point. This often happens in unbiased statistical sampling, or when creating polygons describing land titles from coordinate geometry (COGO) measurements.

Here is a version of the PointFromBearingAndDistance PL/SQL function I wrote for Oracle Spatial many years ago 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   : PointFromBearingAndDistance
* @precis     : Returns a point geometry given a starting point, bearing and distance.
* @version    : 1.0
* @usage      : FUNCTION PointFromBearingAndDistance(@p_dStartE   float,
*                                                    @p_dStartN   float,
*                                                    @p_dBearing  float,
*                                                    @p_dDistance float,
*                                                    @p_precision int = 3,
*                                                    @p_srid      int = 0 )
*                 RETURNS GEOMETRY
*               eg select cogo.PointFromBearingAndDistance(0,0,45,100,3,0).STAsText();
* @param      : p_dStartE     : X Ordinate of start point of bearing
* @paramtype  : p_dStartE     : FLOAT
* @param      : p_dStartN     : Y Ordinate of start point of bearing
* @paramtype  : p_dStartN     : FLOAT
* @param      : p_dBearing    : Whole circle bearing (ie 0 North to 360 degree clockwise rotation)
* @paramtype  : p_dBearing    : FLOAT
* @param      : p_dDistance   : Distance in projection units from point along bearing
* @paramtype  : p_dDistance   : FLOAT
* @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
* @param      : p_srid        : SRID of output shape
* @paramtype  : p_srid        : INTEGER
* @return     : geometry      : Point geometry 
* @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
*/
CREATE FUNCTION 
[cogo].[PointFromBearingAndDistance] (@p_dStartE   Float,
                                      @p_dStartN   Float,
                                      @p_dBearing  Float,
                                      @p_dDistance Float,
                                      @p_precision int = 3,
                                      @p_srid      int = 0 )
RETURNS geometry
AS
Begin
  Declare
      @dAngle1    Float,
      @dAngle1Rad Float,
      @dDeltaN    Float,
      @dDeltaE    Float,
      @dEndE      Float,
      @dEndN      Float,
      @precision  int = CASE WHEN @p_precision IS NULL THEN  3 ELSE @p_precision END,
      @srid       int = CASE WHEN @p_srid      IS NULL THEN  0 ELSE @p_srid      END;
  BEGIN
      IF ( @p_dStartE   IS NULL OR
           @p_dStartN   IS NULL OR
           @p_dBearing  IS NULL OR
           @p_dDistance IS NULL )
      RETURN NULL;
 
      -- First calculate dDeltaE and dDeltaN
      IF ( @p_dBearing < 90 )
      BEGIN
          SET @dAngle1    = 90 - @p_dBearing;
          SET @dAngle1Rad = @dAngle1 * PI() / 180;
          SET @dDeltaE    = Cos(@dAngle1Rad) * @p_dDistance;
          SET @dDeltaN    = Sin(@dAngle1Rad) * @p_dDistance;
      END
      IF ( @p_dBearing < 180 )
      BEGIN
          SET @dAngle1    = @p_dBearing - 90;
          SET @dAngle1Rad = @dAngle1 * PI() / 180;
          SET @dDeltaE    = Cos(@dAngle1Rad) * @p_dDistance;
          SET @dDeltaN    = Sin(@dAngle1Rad) * @p_dDistance * -1;
      END
      IF ( @p_dBearing < 270 )
      BEGIN
          SET @dAngle1    = 270 - @p_dBearing;
          SET @dAngle1Rad = @dAngle1 * PI() / 180;
          SET @dDeltaE    = Cos(@dAngle1Rad) * @p_dDistance * -1;
          SET @dDeltaN    = Sin(@dAngle1Rad) * @p_dDistance * -1;
      END
      IF ( @p_dBearing <= 360 )
      BEGIN
          SET @dAngle1    = @p_dBearing - 270;
          SET @dAngle1Rad = @dAngle1 * PI() / 180;
          SET @dDeltaE    = Cos(@dAngle1Rad) * @p_dDistance * -1;
          SET @dDeltaN    = Sin(@dAngle1Rad) * @p_dDistance;
      End 
      -- Calculate the easting and northing of the end point
      SET @dEndE = @dDeltaE + @p_dStartE;
      SET @dEndN = @dDeltaN + @p_dStartn;
      RETURN geometry::Point(ROUND(@dEndE, @precision),ROUND(@dEndN, @precision), @srid);
    END;
END
GO

Here is an example of how to generate the geometry::Point object at the end of a bearing of 45 degrees and distance of 100 meters from ( 0,0 ) .

select cogo.PointFromBearingAndDistance(0,0,45,100,3,0).STAsText() as NewPoint;

NewPoint
POINT (70.711 70.711)


Or more visually:

DECLARE
  @XY Float = SQRT(POWER(100,2)/2);
select geometry::STGeomFromText('POINT(0 0)',0).STBuffer(10) as geom
union all
select geometry::STGeomFromText('LINESTRING(0 0,' + STR(@XY,10,5) + ' ' + STR(@XY,10,5) + ')',0) as geom
union all
select cogo.PointFromBearingAndDistance(0,0,45,100,3,0).STBuffer(10) as geom;

I hope this is helpful to someone.

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