# LineString

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

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.

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();

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

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);