Polygons

Rings, from the previous tutorials, are still strings; i.e. they have length, but no surface. To construct the surface you use polygons. A polygon defines a region of space. A polygon is constructed from one exterior bounding ring that defines the outside of the region and zero or more interior rings, which define holes in the region.

Open the SQL Editor of your choice (web or desktop based) connected to your SAP HANA database instance.

Type and execute the following SQL statement.

SELECT NEW ST_Polygon('Polygon ((0 0, 4 0, 0 3, 0 0), (0.5 0.5, 0.5 1.5, 1.5 1.5, 1 0.5, 0.5 0.5))').ST_asSVG() FROM dummy;

This query instantiates a surface in the 2-dimensional Euclidean space and returns its dimensions. In the example above it is a polygon defined by an external ring with the shape of a triangle connecting points (0, 0); i.e., X=0 and Y=0, with points (4, 0) and (4, 3) and an internal ring with the shape of a square. The constructor is using Well-known text (WKT). As explained in the previous tutorial, WKT is a text markup language for representing vector geometry objects defined by the Open Geospatial Consortium (OGC).

Below is an SVG modified to fill a geometry with the color using fill="yellow" to better illustrate the meaning of the external and internal rings of polygons.

Now, execute the following query.

SELECT NEW ST_Polygon('Polygon ((0 0, 4 0, 0 3, 0 0), (0.5 0.5, 0.5 1.5, 1.5 1.5, 1 0.5, 0.5 0.5))').ST_Dimension() FROM dummy;

The ST_Dimension() method will return 2. In the earlier point exercise the same method returned 0, and in the strings exercise it returned 1.

Unlike a string, a polygon has a surface, and therefore has an area. Use the ST_Area() method to calculate it.

SELECT NEW ST_Polygon('Polygon ((0 0, 4 0, 0 3, 0 0))').ST_Area() FROM dummy;

Please note the double round brackets, as this polygon consists of only an external ring.

This statement calculates the area of right triangle (also known as ‘right-angled triangle’), with catheti (also known as legs) having lengths of 3 and 4. Obviously the area is half of 3*4 and equals 6.

You can calculate the boundary of a polygon using the ST_Boundary() method. This method is one of Transformation Functions, which take one geometry as an input, and produce another geometry as an output.

Check the boundary of the first polygon from this tutorial; i.e., a triangle with a square inside.

SELECT NEW ST_Polygon('Polygon ((0 0, 4 0, 0 3, 0 0), (0.5 0.5, 0.5 1.5, 1.5 1.5, 1 0.5, 0.5 0.5))').ST_Boundary().ST_asWKT() FROM dummy;

The result is a MultiLineString containing two LineStrings, one representing a triangle and the another representing a square.

MultiLineString is another spatial type. It is a collection of line strings. There are two more spatial collection types supported by SAP HANA: MultiPoint and MultiPolygon. Their names describe what they represent.

Strings too have their boundaries, represented by their endpoints, except when they are rings. Rings - curves where the start point is the same as the end point and there are no self-intersections - have no boundaries.

Now, check the boundaries of a triangle string from the previous query.

SELECT NEW ST_LineString('LineString (0 0,4 0,0 3,0 0)').ST_Boundary().ST_asWKT() FROM dummy;

The result is an empty geometry.

Check the boundaries of a multi-segment line, where the end points are not the same.

SELECT NEW ST_LineString('LineString (0 0,4 0,0 3,1 0)').ST_Boundary().ST_asWKT() FROM dummy;

The result is a MultiPoint collection containing two end points.

Points do not have boundaries.

SELECT NEW ST_Point('Point (0 0)').ST_Boundary().ST_asWKT() FROM dummy;

A typical requirement in spatial calculations is to find relationships between different geometries. For example, you may need to determine if one geometry is covered by another geometry; if some particular point of interest is within a city’s boundaries, for instance.

ST_Within() is a method that will allow you to determine if one geometry is within another. It is one of the Spatial Predicates and as other methods from this group returns a result of 1 meaning ‘true’ or 0 meaning ‘false’.

SELECT NEW ST_Point (1,1).ST_Within(NEW ST_Polygon('Polygon ((0 0, 4 0, 0 3, 0 0), (0.5 0.5, 0.5 1.5, 1.5 1.5, 1 0.5, 0.5 0.5))')) FROM dummy;

Indeed the point (1, 1) is not within interior of your polygon from the earlier exercise, defined by the external ring in the shape of a triangle and an internal ring in the shape of a square. An area inside a square is the exterior of this particular geometry.

To check if a point is within a given disk you use another transformation functions: ST_Buffer(). This method applied to a point defines the circle area of a particular distance from that point.

SELECT NEW ST_Point (1,1).ST_Within(NEW ST_Point(0, 0).ST_Buffer(2)) FROM dummy;

The point (1, 1) is in the circle with the center point of (0, 0) and the radius of 2.