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LineString

  • Article
  • 11/22/2024

Applies to: SQL Server Azure SQL Database Azure SQL Managed Instance SQL analytics endpoint in Microsoft Fabric Warehouse in Microsoft Fabric SQL database in Microsoft Fabric

A LineString is a one-dimensional object representing a sequence of points and the line segments connecting them in SQL Database Engine spatial data.

LineString instances

The following illustration shows examples of LineString instances.

Diagram of examples of geometry LineString instances.

As shown in the illustration:

  • Figure 1 is a simple, nonclosed LineString instance.

  • Figure 2 is a nonsimple, nonclosed LineString instance.

  • Figure 3 is a closed, simple LineString instance, and therefore is a ring.

  • Figure 4 is a closed, nonsimple LineString instance, and therefore is not a ring.

Accepted instances

Accepted LineString instances can be input into a geometry variable, but they might not be valid LineString instances. The following criteria must be met for a LineString instance to be accepted. The instance must be formed of at least two points or it must be empty. The following LineString instances are accepted.

DECLARE @g1 geometry = 'LINESTRING EMPTY';  
DECLARE @g2 geometry = 'LINESTRING(1 1,2 3,4 8, -6 3)';  
DECLARE @g3 geometry = 'LINESTRING(1 1, 1 1)';

@g3 shows that a LineString instance can be accepted, but not valid.

The following LineString instance is not accepted. It throws a System.FormatException.

DECLARE @g geometry = 'LINESTRING(1 1)';

Valid instances

For a LineString instance to be valid, it must meet the following criteria.

  1. The LineString instance must be accepted.
  2. If a LineString instance is not empty, then it must contain at least two distinct points.
  3. The LineString instance cannot overlap itself over an interval of two or more consecutive points.

The following LineString instances are valid.

DECLARE @g1 geometry= 'LINESTRING EMPTY';  
DECLARE @g2 geometry= 'LINESTRING(1 1, 3 3)';  
DECLARE @g3 geometry= 'LINESTRING(1 1, 3 3, 2 4, 2 0)';  
DECLARE @g4 geometry= 'LINESTRING(1 1, 3 3, 2 4, 2 0, 1 1)';  
SELECT @g1.STIsValid(), @g2.STIsValid(), @g3.STIsValid(), @g4.STIsValid();

The following LineString instances are not valid.

DECLARE @g1 geometry = 'LINESTRING(1 4, 3 4, 2 4, 2 0)';  
DECLARE @g2 geometry = 'LINESTRING(1 1, 1 1)';  
SELECT @g1.STIsValid(), @g2.STIsValid();

Warning

The detection of LineString overlaps is based on floating-point calculations, which are not exact.

Examples

Example A.

The following example shows how to create a geometry LineString instance with three points and an SRID of 0:

DECLARE @g geometry;  
SET @g = geometry::STGeomFromText('LINESTRING(1 1, 2 4, 3 9)', 0);

Example B.

Each point in the LineString instance can contain Z (elevation) and M (measure) values. This example adds M values to the LineString instance created in the previous example. M and Z can be NULL values.

DECLARE @g geometry;  
SET @g = geometry::STGeomFromText('LINESTRING(1 1 NULL 0, 2 4 NULL 12.3, 3 9 NULL 24.5)', 0);

Example C.

The following example shows how to create a geometry LineString instance with two points that are the same. A call to IsValid indicates that the LineString instance is not valid. A call to MakeValid converts the LineString instance into a Point.

DECLARE @g geometry  
SET @g = geometry::STGeomFromText('LINESTRING(1 3, 1 3)',0);  
IF @g.STIsValid() = 1  
  BEGIN  
     SELECT @g.ToString() + ' is a valid LineString.';    
  END  
ELSE  
  BEGIN  
     SELECT @g.ToString() + ' is not a valid LineString.';  
     SET @g = @g.MakeValid();  
     SELECT @g.ToString() + ' is a valid Point.';    
  END

Here's the result set.

LINESTRING(1 3, 1 3) is not a valid LineString  
POINT(1 3) is a valid Point.

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