Reduce (geometry Data Type)
Applies to: 
SQL Server
Azure SQL Database
Azure SQL Managed Instance
Returns an approximation of the given geometry instance. The approximation is produced by running an extension of the Douglas-Peucker algorithm on the instance with the given tolerance.
Syntax
.Reduce ( tolerance )
Arguments
tolerance
Is a value of type float. tolerance is the tolerance to input for the approximation algorithm.
Return Types
SQL Server return type: geometry
CLR return type: SqlGeometry
Remarks
For collection types, this algorithm operates independently on each geometry contained in the instance.
This algorithm doesn't modify Point instances.
On LineString, CircularString, and CompoundCurve instances, the approximation algorithm keeps the original start and end points of the instance. The algorithm next iteratively adds back the point from the original instance that most deviates from the result. This process continues until no point deviates more than the given tolerance.
Reduce() returns a LineString, CircularString, or CompoundCurve instance for CircularString instances. Reduce() returns either a CompoundCurve or LineString instance for CompoundCurve instances.
On Polygon instances, the approximation algorithm is applied independently to each ring. The method will produce a FormatException if the returned Polygon instance isn't valid; for example, a non-valid MultiPolygon instance is created if Reduce() is applied to simplify each ring in the instance and the resulting rings overlap. On CurvePolygon instances with an exterior ring and no interior rings, Reduce() returns a CurvePolygon, LineString, or Point instance. If the CurvePolygon has interior rings then a CurvePolygon or MultiPoint instance is returned.
When a circular arc segment is found, the approximation algorithm checks whether the arc can be approximated by its chord within half the given tolerance. Chords meeting this criteria have the circular arc replaced in the calculations by the chord. If a chord doesn't meet this criteria, then the circular arc is kept and the approximation algorithm is applied to the remaining segments.
Examples
A. Using Reduce() to simplify a LineString
The following example creates a LineString instance and uses Reduce() to simplify the instance.
DECLARE @g geometry;
SET @g = geometry::STGeomFromText('LINESTRING(0 0, 0 1, 1 0, 2 1, 3 0, 4 1)', 0);
SELECT @g.Reduce(.75).ToString();
B. Using Reduce() with varying tolerance levels on a CircularString
The following example uses Reduce() with three tolerance levels on a CircularString instance:
DECLARE @g geometry = 'CIRCULARSTRING(0 0, 8 8, 16 0, 20 -4, 24 0)';
SELECT @g.Reduce(5).ToString();
SELECT @g.Reduce(15).ToString();
SELECT @g.Reduce(16).ToString();
This example produces the following output:
CIRCULARSTRING (0 0, 8 8, 16 0, 20 -4, 24 0)
COMPOUNDCURVE (CIRCULARSTRING (0 0, 8 8, 16 0), (16 0, 24 0))
LINESTRING (0 0, 24 0)
Each of the instances returned contain the endpoints (0 0) and (24 0).
C. Using Reduce() with varying tolerance levels on a CompoundCurve
The following example uses Reduce() with two tolerance levels on a CompoundCurve instance:
DECLARE @g geometry = 'COMPOUNDCURVE(CIRCULARSTRING(0 0, 8 8, 16 0, 20 -4, 24 0),(24 0, 20 4, 16 0))';
SELECT @g.Reduce(15).ToString();
SELECT @g.Reduce(16).ToString();
In this example notice that the second SELECT statement returns the LineString instance: LineString(0 0, 16 0).
Showing an example where the original start and end points are lost
The following example shows how the original start and endpoints may not be retained by the resulting instance. This behavior occurs because keeping the original start and end points would result in an invalid LineString instance.
DECLARE @g geometry = 'LINESTRING(0 0, 4 0, 2 .01, 1 0)';
DECLARE @h geometry = @g.Reduce(1);
SELECT @g.STIsValid() AS Valid
SELECT @g.ToString() AS Original, @h.ToString() AS Reduced;