# CompoundCurve

**SQL Server 2016**

A **CompoundCurve** is a collection of zero or more continuous **CircularString** or **LineString** instances of either geometry or geography types.

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An empty **CompoundCurve** instance can be instantiated, but for a **CompoundCurve** to be valid it must meet the following criteria:

It must contain at least one

**CircularString**or**LineString**instance.The sequence of

**CircularString**or**LineString**instances must be continuous.

If a **CompoundCurve** contains a sequence of multiple **CircularString** and **LineString **instances, the ending endpoint for every instance except for the last instance must be the starting endpoint for the next instance in the sequence. This means that if the ending point of a prior instance in the sequence is (4 3 7 2), the starting point for the next instance in the sequence must be (4 3 7 2). Note that Z(elevation) and M(measure) values for the point must also be the same. If there is a difference in the two points, a System.FormatException is thrown. Points in a **CircularString** do not have to have a Z or M value. If no Z or M values are given for the ending point of the prior instance, the starting point of the next instance cannot include Z or M values. If the ending point for the prior sequence is (4 3), the starting point for the next sequence must be (4 3); it cannot be (4 3 7 2). All points in a **CompoundCurve** instance must have either no Z value or the same Z value.

The following illustration shows valid **CompoundCurve** types.

**CompoundCurve** instance is accepted if it is an empty instance or meets the following criteria.

All the instances contained by

**CompoundCurve**instance are accepted circular arc segment instances. For more information on accepted circular arc segment instances, see LineString and CircularString.All of the circular arc segments in the

**CompoundCurve**instance are connected. The first point for each succeeding circular arc segment is the same as the last point on the preceeding circular arc segment.Note This includes the Z and M coordinates. So, all four coordinates X, Y, Z, and M must be the same.

None of the contained instances are empty instances.

The following example shows accepted **CompoundCurve** instances.

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

The following example shows **CompoundCurve** instances that are not accepted. These instances throw System.FormatException.

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

A **CompoundCurve** instance is valid if it meets the following criteria.

The

**CompoundCurve**instance is accepted.All circular arc segment instances contained by the

**CompoundCurve**instance are valid instances.

The following example shows valid **CompoundCurve** instances.

DECLARE @g1 geometry = 'COMPOUNDCURVE EMPTY'; DECLARE @g2 geometry = 'COMPOUNDCURVE(CIRCULARSTRING(1 0, 0 1, -1 0), (-1 0, 2 0))'; DECLARE @g3 geometry = 'COMPOUNDCURVE(CIRCULARSTRING(1 1, 1 1, 1 1), (1 1, 3 5, 5 4))'; SELECT @g1.STIsValid(), @g2.STIsValid(), @g3.STIsValid();

@g3 is valid because the **CircularString** instance is valid. For more information on the validity of the **CircularString** instance, see CircularString.

The following example shows **CompoundCurve** instances that are not valid.

DECLARE @g1 geometry = 'COMPOUNDCURVE(CIRCULARSTRING(1 1, 1 1, 1 1), (1 1, 3 5, 5 4, 3 5))'; DECLARE @g2 geometry = 'COMPOUNDCURVE((1 1, 1 1))'; DECLARE @g3 geometry = 'COMPOUNDCURVE(CIRCULARSTRING(1 1, 2 3, 1 1))'; SELECT @g1.STIsValid(), @g2.STIsValid(), @g3.STIsValid();

@g1 is not valid because the second instance is not a valid LineString instance. @g2 is not valid because the **LineString** instance is not valid. @g3 is not valid because the **CircularString** instance is not valid. For more information on valid **CircularString** and **LineString** instances, see CircularString and LineString.

The following example shows how to create an empty CompoundCurve instance:

DECLARE @g geometry; SET @g = geometry::Parse('COMPOUNDCURVE EMPTY');

The following example shows how to declare and initialize a geometry instance with a CompoundCurve** **in the same statement:

DECLARE @g geometry = 'COMPOUNDCURVE ((2 2, 0 0),CIRCULARSTRING (0 0, 1 2.1082, 3 6.3246, 0 7, -3 6.3246, -1 2.1082, 0 0))';

The following example shows how to declare and initialize a **geography** instance with a CompoundCurve:

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

The following example uses two different ways to use a CompoundCurve instance to store a square.

DECLARE @g1 geometry, @g2 geometry; SET @g1 = geometry::Parse('COMPOUNDCURVE((1 1, 1 3), (1 3, 3 3),(3 3, 3 1), (3 1, 1 1))'); SET @g2 = geometry::Parse('COMPOUNDCURVE((1 1, 1 3, 3 3, 3 1, 1 1))'); SELECT @g1.STLength(), @g2.STLength();

The lengths for both @g1 and @g2 are the same. Notice from the example that a **CompoundCurve** instance can store one or more instances of LineString.

The following example shows how to use two different CircularString instances to initialize a CompoundCurve.

DECLARE @g geometry; SET @g = geometry::Parse('COMPOUNDCURVE(CIRCULARSTRING(0 2, 2 0, 4 2), CIRCULARSTRING(4 2, 2 4, 0 2))'); SELECT @g.STLength();

This produces the following output: 12.566370… which is the equivalent of 4∏. The CompoundCurve instance in the example stores a circle with a radius of 2. Both of the previous code examples did not have to use a CompoundCurve. For the first example a LineString instance would have been simpler, and a CircularString instance would have been simpler for the second example. However, the next example shows where a CompoundCurve provides a better alternative.

The following example uses a CompoundCurve instance to store a semicircle.

DECLARE @g geometry; SET @g = geometry::Parse('COMPOUNDCURVE(CIRCULARSTRING(0 2, 2 0, 4 2), (4 2, 0 2))'); SELECT @g.STLength();

The following example shows how multiple CircularString and LineString instances can be stored by using a CompoundCurve.

DECLARE @g geometry SET @g = geometry::Parse('COMPOUNDCURVE((3 5, 3 3), CIRCULARSTRING(3 3, 5 1, 7 3), (7 3, 7 5), CIRCULARSTRING(7 5, 5 7, 3 5))'); SELECT @g.STLength();

The following example shows how to use a CompoundCurve instance to store a sequence of CircularString and LineString instances with both Z and M values.

SET @g = geometry::Parse('COMPOUNDCURVE(CIRCULARSTRING(7 5 4 2, 5 7 4 2, 3 5 4 2), (3 5 4 2, 8 7 4 2))');

The following example shows why CircularString instances must be explicitly declared. The programmer is trying to store a circle in a CompoundCurve instance.

DECLARE @g1 geometry; DECLARE @g2 geometry; SET @g1 = geometry::Parse('COMPOUNDCURVE(CIRCULARSTRING(0 2, 2 0, 4 2), (4 2, 2 4, 0 2))'); SELECT 'Circle One', @g1.STLength() AS Perimeter; -- gives an inaccurate amount SET @g2 = geometry::Parse('COMPOUNDCURVE(CIRCULARSTRING(0 2, 2 0, 4 2), CIRCULARSTRING(4 2, 2 4, 0 2))'); SELECT 'Circle Two', @g2.STLength() AS Perimeter; -- now we get an accurate amount

The output is as follows:

Circle One11.940039… Circle Two12.566370…

The perimeter for Circle Two is approximately 4∏, which is the actual value for the perimeter. However, the perimeter for Circle One is significantly inaccurate. Circle One's CompoundCurve instance stores one circular arc segment (ABC) and two line segments (CD, DA). The CompoundCurve instance has to store two circular arc segments (ABC, CDA) to define a circle. A LineString instance defines the second set of points (4 2, 2 4, 0 2) in Circle One's CompoundCurve instance. You have to explicitly declare a CircularString instance inside a CompoundCurve.