---
title: "CircularString | Microsoft Docs"
ms.custom: ""
ms.date: 10/18/2019
ms.prod: "sql-server-2014"
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ms.topic: conceptual
ms.assetid: 9fe06b03-d98c-4337-9f89-54da98f49f9f
author: MladjoA
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---
# CircularString
  A `CircularString` is a collection of zero or more continuous circular arc segments. A circular arc segment is a curved segment defined by three points in a two-dimensional plane; the first point cannot be the same as the third point. If all three points of a circular arc segment are collinear, the arc segment is treated as a line segment.

> [!IMPORTANT]
>  For a detailed description and examples of the new spatial features introduced in [!INCLUDE[ssSQL11](../../includes/sssql11-md.md)], including the `CircularString` subtype, download the white paper, [New Spatial Features in SQL Server 2012](https://go.microsoft.com/fwlink/?LinkId=226407).

## CircularString instances
 The drawing below shows valid `CircularString` instances:

 ![](../../database-engine/media/5ff17e34-b578-4873-9d33-79500940d0bc.png "5ff17e34-b578-4873-9d33-79500940d0bc")

### Accepted instances
 A `CircularString` instance is accepted if it is either empty or contains an odd number of points, n, where n > 1. The following `CircularString` instances are accepted.

```sql
DECLARE @g1 geometry = 'CIRCULARSTRING EMPTY';
DECLARE @g2 geometry = 'CIRCULARSTRING(1 1, 2 0, -1 1)';
DECLARE @g3 geometry = 'CIRCULARSTRING(1 1, 2 0, 2 0, 2 0, 1 1)';
```

 `@g3` shows that `CircularString` instance may be accepted, but not valid. The following CircularString instance declaration is not accepted. This declaration throws a `System.FormatException`.

```sql
DECLARE @g geometry = 'CIRCULARSTRING(1 1, 2 0, 2 0, 1 1)';
```

### Valid instances
 A valid `CircularString` instance must be empty or have the following attributes:

-   It must contain at least one circular arc segment (that is, have a minimum of three points).

-   The last endpoint for each circular arc segment in the sequence, except for the last segment, must be the first endpoint for the next segment in the sequence.

-   It must have an odd number of points.

-   It cannot overlap itself over an interval.

-   Although `CircularString` instances may contain line segments, these line segments must be defined by three collinear points.

 The following example shows valid `CircularString` instances.

```sql
DECLARE @g1 geometry = 'CIRCULARSTRING EMPTY';
DECLARE @g2 geometry = 'CIRCULARSTRING(1 1, 2 0, -1 1)';
DECLARE @g3 geometry = 'CIRCULARSTRING(1 1, 2 0, 2 0, 1 1, 0 1)';
DECLARE @g4 geometry = 'CIRCULARSTRING(1 1, 2 2, 2 2)';
SELECT @g1.STIsValid(), @g2.STIsValid(), @g3.STIsValid(),@g4.STIsValid();
```

 A `CircularString` instance must contain at least two circular arc segments to define a complete circle. A `CircularString` instance cannot use a single circular arc segment (such as (1 1, 3 1, 1 1)) to define a complete circle. Use (1 1, 2 2, 3 1, 2 0, 1 1) to define the circle.

 The following example shows CircularString instances that are not valid.

```sql
DECLARE @g1 geometry = 'CIRCULARSTRING(1 1, 2 0, 1 1)';
DECLARE @g2 geometry = 'CIRCULARSTRING(0 0, 0 0, 0 0)';
SELECT @g1.STIsValid(), @g2.STIsValid();
```

### Instances with collinear points
 In the following cases a circular arc segment will be treated as a line segment:

-   When all three points are collinear (for example, (1 3, 4 4, 7 5)).

-   When the first and middle point are the same, but the third point is different (for example, (1 3, 1 3, 7 5)).

-   When the middle and last point are the same, but the first point is different (for example, (1 3, 4 4, 4 4)).

## Examples

### A. Instantiating a Geometry Instance with an Empty CircularString
 This example shows how to create an empty `CircularString` instance:

```sql
DECLARE @g geometry;
SET @g = geometry::Parse('CIRCULARSTRING EMPTY');
```

### B. Instantiating a Geometry Instance Using a CircularString with One Circular Arc Segment
 The following example shows how to create a `CircularString` instance with a single circular arc segment (half-circle):

```sql
DECLARE @g geometry;
SET @g = geometry:: STGeomFromText('CIRCULARSTRING(2 0, 1 1, 0 0)', 0);
SELECT @g.ToString();
```

### C. Instantiating a Geometry Instance Using a CircularString with Multiple Circular Arc Segments
 The following example shows how to create a `CircularString` instance with more than one circular arc segment (full circle):

```sql
DECLARE @g geometry;
SET @g = geometry::Parse('CIRCULARSTRING(2 1, 1 2, 0 1, 1 0, 2 1)');
SELECT 'Circumference = ' + CAST(@g.STLength() AS NVARCHAR(10));  
```

 This produces the following output:

```
Circumference = 6.28319
```

 Compare the output when `LineString` is used instead of `CircularString`:

```sql
DECLARE @g geometry;
SET @g = geometry::STGeomFromText('LINESTRING(2 1, 1 2, 0 1, 1 0, 2 1)', 0);
SELECT 'Perimeter = ' + CAST(@g.STLength() AS NVARCHAR(10));
```

 This produces the following output:

```
Perimeter = 5.65685
```

 Notice that the value for the `CircularString` example is close to 2π (2 * pi), which is the actual circumference of the circle.

### D. Declaring and Instantiating a Geometry Instance with a CircularString in the Same Statement
 This snippet shows how to declare and instantiate a `geometry` instance with a `CircularString` in the same statement:

```sql
DECLARE @g geometry = 'CIRCULARSTRING(0 0, 1 2.1082, 3 6.3246, 0 7, -3 6.3246, -1 2.1082, 0 0)';
```

### E. Instantiating a Geography Instance with a CircularString
 The following example shows how to declare and instantiate a `geography` instance with a `CircularString`:

```sql
DECLARE @g geography = 'CIRCULARSTRING(-122.358 47.653, -122.348 47.649, -122.348 47.658, -122.358 47.658, -122.358 47.653)';
```

### F. Instantiating a Geometry Instance with a CircularString that is a Straight Line
 The following example shows how to create a `CircularString` instance that is a straight line:

```sql
DECLARE @g geometry;
SET @g = geometry::STGeomFromText('CIRCULARSTRING(0 0, 1 2, 2 4)', 0);
```

## See Also
 [Spatial Data Types Overview](spatial-data-types-overview.md) 
 [CompoundCurve](compoundcurve.md) 
 [MakeValid (geography Data Type)](/sql/t-sql/spatial-geography/makevalid-geography-data-type) 
 [MakeValid (geometry Data Type)](/sql/t-sql/spatial-geometry/makevalid-geometry-data-type) 
 [STIsValid (geometry Data Type)](/sql/t-sql/spatial-geometry/stisvalid-geometry-data-type) 
 [STIsValid (geography Data Type)](/sql/t-sql/spatial-geography/stisvalid-geography-data-type) 
 [STLength (geometry Data Type)](/sql/t-sql/spatial-geometry/stlength-geometry-data-type) 
 [STStartPoint (geometry Data Type)](/sql/t-sql/spatial-geometry/ststartpoint-geometry-data-type) 
 [STEndpoint (geometry Data Type)](/sql/t-sql/spatial-geometry/stendpoint-geometry-data-type) 
 [STPointN (geometry Data Type)](/sql/t-sql/spatial-geometry/stpointn-geometry-data-type) 
 [STNumPoints (geometry Data Type)](/sql/t-sql/spatial-geometry/stnumpoints-geometry-data-type) 
 [STIsRing (geometry Data Type)](/sql/t-sql/spatial-geometry/stisring-geometry-data-type) 
 [STIsClosed (geometry Data Type)](/sql/t-sql/spatial-geometry/stisclosed-geometry-data-type) 
 [STPointOnSurface (geometry Data Type)](/sql/t-sql/spatial-geometry/stpointonsurface-geometry-data-type) 
 [LineString](linestring.md)