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Applies to: 
SQL Server
Azure SQL Database
Azure SQL Managed Instance
SQL database in Microsoft Fabric Preview
Returns a polygonal approximation of a geometry instance that contains circular arc segments.
Syntax
.CurveToLineWithTolerance ( tolerance, relative )
Arguments
tolerance
Is a double expression that defines the maximum error between the original circular arc segment and its linear approximation.
relative
Is a bool expression that indicates whether to use a relative maximum for the deviation. When relative is set to false (0), then an absolute maximum is set for the deviation that a linear approximate can have. When relative is set to true (1) then the tolerance is calculated as a product of the tolerance parameter and the diameter of the bounding box for the spatial object.
Return Types
SQL Server return type: geometry
CLR return type: SqlGeometry
Exceptions
Setting tolerance <= 0 throws an ArgumentOutOfRange exception.
Remarks
This method can specify an error tolerance amount for the resultant LineString.
The following table shows the instance type returned by CurveToLineWithTolerance()for various types.
| Invoking Instance Type | Spatial Type Returned |
|---|---|
| Empty geometry instance | Empty GeometryCollection instance |
| Point and MultiPoint | Point instance |
| MultiPoint | Point or MultiPoint instance |
| CircularString, CompoundCurve, or LineString | LineString instance |
| MultiLineString | LineString or MultiLineString instance |
| CurvePolygon and Polygon | Polygon instance |
| MultiPolygon | Polygon or MultiPolygon instance |
| GeometryCollection with a single instance that does not contain a circular arc segment | The instance that is contained in the GeometryCollection determines the type of instance returned. |
| GeometryCollection with a single one-dimensional circular arc segment instance (CircularString, CompoundCurve) | LineString instance |
| GeometryCollection with a single two-dimensional circular arc segment instance (CurvePolygon) | Polygon instance |
| GeometryCollection with multiple one dimensional instances | MultiLineString instance |
| GeometryCollection with multiple two dimensional instances | MultiPolygon instance |
| GeometryCollection with multiple instances of different dimensions | GeometryCollection instance |
Examples
A. Using different tolerance values on a CircularString instance
The following example shows how setting the tolerance affects the LineString instance returned from a CircularString instance:
DECLARE @g geometry;
SET @g = geometry::Parse('CIRCULARSTRING(0 0, 1 2.1082, 3 6.3246, 0 7, -3 6.3246, -1 2.1082, 0 0)');
SELECT @g.CurveToLineWithTolerance(0.1,0).STNumPoints(), @g.CurveToLineWithTolerance(0.01, 0).STNumPoints();
B. Using the method on a MultiLineString instance containing one LineString
The following example shows what is returned from a MultiLineString instance that only contains one LineString instance:
DECLARE @g geometry;
SET @g = geometry::Parse('MULTILINESTRING((1 3, 4 8, 6 9))');
SELECT @g.CurveToLineWithTolerance(0.1,0).ToString();
C. Using the method on a MultiLineString instance containing multiple LineStrings
The following example shows what is returned from a MultiLineString instance that contains more than one LineString instance:
DECLARE @g geometry;
SET @g = geometry::Parse('MULTILINESTRING((1 3, 4 8, 6 9),(4 4, 9 18))');
SELECT @g.CurveToLineWithTolerance(0.1,0).ToString();
D. Setting relative to true for an invoking CurvePolygon instance
The following example uses a CurvePolygon instance to call CurveToLineWithTolerance() with relative set to true:
DECLARE @g geometry = 'CURVEPOLYGON(COMPOUNDCURVE(CIRCULARSTRING(0 4, 4 0, 8 4), (8 4, 0 4)))';
SELECT @g.CurveToLineWithTolerance(.5,1).ToString();
E. Using the method on a GeometryCollection instance
The following example calls CurveToLineWithTolerance() on a GeometryCollection that contains a two-dimensional CurvePolygon instance and a one-dimensional CircularString instance. CurveToLineWithTolerance() converts both circular arc segment types to line segment types and returns them in a GeometryCollection type.
DECLARE @g geometry;
SET @g = geometry::Parse('GEOMETRYCOLLECTION(CURVEPOLYGON( COMPOUNDCURVE(CIRCULARSTRING(0 2, 2 0, 4 2), (4 2, 0 2))), CIRCULARSTRING(4 4, 8 6, 9 5))');
SELECT @g.CurveToLineWithTolerance(0.1,0).STNumPoints(), @g.CurveToLineWithTolerance(0.1, 0).ToString();
See Also
CurveToLineWithTolerance (geography Data Type)
STCurveToLine (geometry Data Type)