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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: Finding centre and radius of a curve defined by three points: FindCircle function

Wednesday May 04 2011 at 12:32

KeywordsCOGO find centre radius center circle three 3 points

This article describes a T-Sql function that, given three points, will return the centre and radius of the circle circumscribed. This works only for projected data.

Recently I had need to convert a PL/SQL Oracle Spatial function I created years ago called FindCircle to SQL Server 2008 for use in another project. That function was original work already released to the public domain as part of my free COGO package for Oracle. Here is that function
for SQL Server.

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

  1. /** ----------------------------------------------------------------------------------------
  2.   * @function   : FindCircle
  3.   * @precis     : Function that determines if three points form a circle. If so a table containing
  4.   *               centre and radius is returned. If not, a null table is returned.
  5.   * @version    : 1.0
  6.   * @usage      : Function FindCircle(@p_X1 float, @p_Y1 float,
  7.   *                                   @p_X2 float, @p_Y2 float,
  8.   *                                   @p_X3 float, @p_Y3 float )
  9.   *                Returns @circle table ([cx]     float,
  10.   *                                       [cy]     float,
  11.   *                                       [radius] float )
  12.   *               eg select c.cx, c.cy, c.radius
  13.   *                    from [FindCircle](0.0,0.0,10.0,0.0,10.0,10.0) c;
  14.   * @param      : p_X1/p_Y1    : First point in curve
  15.   * @param      : p_X2/p_Y2    : Second point in curve
  16.   * @param      : p_X3/p_Y3    : Third point in curve
  17.   * @return     : cx/cy/radius : Centre X, Y and radius of found circle or NULL if three points do not form a circle.
  18.   * @history    : Simon Greener - May 2011 - Original coding.
  19.   * @copyright  : Licensed under a Creative Commons Attribution-Share Alike 2.5 Australia License. (http://creativecommons.org/licenses/by-sa/2.5/au/)
  20. **/
  21. CREATE FUNCTION cogo.FindCircle(@p_X1 FLOAT, @p_Y1 FLOAT,
  22.                                 @p_X2 FLOAT, @p_Y2 FLOAT,
  23.                                 @p_X3 FLOAT, @p_Y3 FLOAT )
  24. RETURNS @circle TABLE (
  25.       [cx]     FLOAT,
  26.       [cy]     FLOAT,
  27.       [radius] FLOAT
  28. )
  29. etc
The function can be used as follows:
  1. SELECT c.cx, c.cy, c.radius
  2.   FROM cogo.FindCircle(0.0,0.0,10.0,0.0,10.0,10.0) c;
|_. cx|_. cy|_. radius| |5|5|7.07106781186548| If anyone would like the source code for this function, please contact me directly. Simon

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Comment [3]

I have to solve the same problem in postgis postgresql 9. Can you please forward the code.

thanks in advance…

— Kedar Tambade · 28 June 2011, 15:54 · #

I would like to write a similar function for 10 points in T-SQL. Could you please send me the code?

Thanks a lot!


— Kate · 5 July 2011, 11:08 · #

This function only finds the circle when given 3 points. Why do you want to write one for 10 points?

Simon Greener · 6 July 2011, 01:08 · #