# LineString

A **LineString** is a one-dimensional object representing a sequence of points and the line segments connecting them.

## LineString Instances

The illustration below shows examples of **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 may 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 will throw a `System.FormatException`

.

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

### Valid Instances

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

The

**LineString**instance must be accepted.If a

**LineString**instance is not empty then it must contain at least two distinct points.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

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);
```

Each point in the `LineString`

instance may contain Z (elevation) and M (measure) values. This example adds M values to the `LineString`

instance created in the example above. 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);
```

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 and a call to `MakeValid`

will convert 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
```

The above code snippet will return the following:

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

## See Also

STLength (geometry Data Type)

STStartPoint (geometry Data Type)

STEndpoint (geometry Data Type)

STPointN (geometry Data Type)

STNumPoints (geometry Data Type)

STIsRing (geometry Data Type)

STIsClosed (geometry Data Type)

STPointOnSurface (geometry Data Type)

Spatial Data (SQL Server)