---
parser: v2
author_name: Markus Fath
author_profile: https://github.com/fath-markus
auto_validation: true
time: 15
primary_tag: products>sap-hana
tags: [ tutorial>beginner, programming-tool>sql, products>sap-hana-cloud, products>sap-hana\,-express-edition, software-product-function>sap-hana-spatial, software-product-function>sap-hana-multi-model-processing ]
slug: hana-spatial-methods-compute
canonical_url: https://developers.sap.com/tutorials/hana-spatial-methods-compute
---
# Computation methods
Computation methods help you calculating characteristics of geometries
## Prerequisites
- **Tutorial:** [Access methods](hana-spatial-methods-access)
- You must have the table `"TUTORIAL_GEO"."SPATIALSHAPES"` from previous tutorials already created and loaded in your system to be able to run examples from this tutorial.
## Next Steps
- [Transformation methods](hana-spatial-methods-transform)
## You will learn
You will learn about a number of computation methods and how to apply them to different geometries.
---
### Compute methods
You must have seen some of the spatial compute methods already in previous tutorials.
E.g. `ST_Length()` calculated the length of the line string, and `ST_Area()` calculated the area of a polygon.
Some other were used to calculate characteristics of geometries, like `ST_IsRing()` and `ST_IsClosed()` in examples with strings.
### Area and perimeter of polygons
Polygons have a few more useful methods. They can be applied to a collection of polygons (multi-polygon)too.
Besides area you can calculate as well perimeter of surfaces. The perimeter of a polygon includes the length of all rings (exterior and interior).
```sql
SELECT "SHAPE".ST_asWKT() AS "WKT",
"SHAPE".ST_Area() AS "AREA",
ROUND("SHAPE".ST_Perimeter(), 4) AS "PERIMETER"
FROM "TUTORIAL_GEO"."SPATIALSHAPES"
WHERE "SHAPE".ST_GeometryType() in ('ST_Polygon');
```
As mentioned, you can calculate area and perimeter of multi-polygons as well. Below is the example of computations of the multi-polygon, which is a result of union aggregation of individual polygons in the table.
```sql
SELECT
"AGGRSHAPE".ST_asWKT() AS "WKT",
"AGGRSHAPE".ST_Area() AS "AREA",
ROUND("AGGRSHAPE".ST_Perimeter(), 2) AS "PERIMETER"
FROM (
SELECT ST_UnionAggr("SHAPE") as "AGGRSHAPE"
FROM "TUTORIAL_GEO"."SPATIALSHAPES"
WHERE "SHAPE".ST_GeometryType() in ('ST_Polygon')
)
```
### Centroid of polygons
The method `ST_Centroid()` returns the point that is the mathematical centroid of a polygon or multi-polygon.
```sql
SELECT
"SHAPE".ST_asWKT() AS "WKT",
"SHAPE".ST_Centroid().ST_asWKT() AS "CENTROID_WKT"
FROM "TUTORIAL_GEO"."SPATIALSHAPES"
WHERE "SHAPE".ST_GeometryType() IN ('ST_Polygon');
```
And another example where all individual polygons are combined into one multi-polygon.
```sql
SELECT
"AGGRSHAPE".ST_asWKT() AS "WKT",
"AGGRSHAPE".ST_Centroid().ST_asWKT() AS "CENTROID_WKT"
FROM (
SELECT ST_UnionAggr("SHAPE") as "AGGRSHAPE"
FROM "TUTORIAL_GEO"."SPATIALSHAPES"
WHERE "SHAPE".ST_GeometryType() in ('ST_Polygon')
);
```
### Point on a surface
Centroid of a polygon is not always at the surface of that polygon. Consider the following example.
```sql
SELECT
"PolygonWithInnerRing".ST_asSVG() AS "SVG",
"PolygonWithInnerRing".ST_Centroid().ST_asSVG() AS "CENTROID_SVG"
FROM (
SELECT NEW ST_Polygon('Polygon ((-5 -5, 5 -5, 0 5, -5 -5), (-2 -2, -2 0, 2 0, 2 -2, -2 -2))') as "PolygonWithInnerRing"
FROM "DUMMY"
);
```
Slightly modified SVG for better visualization, like the one below:
```xml
```
shows that the centroid (the red dot) is located inside of the inner ring, and therefore not f the surface of the polygon.
In some cases you will need to have a point (like some sort of marker on the map) that lays somewhere on the surface of a given polygon. That's the purpose of a method `ST_PointOnSurface()`.
Update the example above to include the calculation of the point-on-surface.
```sql
SELECT
"PolygonWithInnerRing".ST_asSVG() AS "SVG",
"PolygonWithInnerRing".ST_PointOnSurface().ST_asSVG() AS "CENTROID_SVG"
FROM (
SELECT NEW ST_Polygon('Polygon ((-5 -5, 5 -5, 0 5, -5 -5), (-2 -2, -2 0, 2 0, 2 -2, -2 -2))') as "PolygonWithInnerRing"
FROM "DUMMY"
);
```
Again slightly modify styling of SVG objects, to have the centroid in red and the point-on-surface in blue.
```xml
```
You can see on the visualization that the blue dot is indeed located on the yellow surface.
### Distance
The `ST_Distance` method computes the shortest distance between two geometries.
>In a round-Earth spatial reference system this method can only be used with geometries for point to point calculations.
The statement below will return five geometries from the table `SPATIALSHAPES` that are closest to the point `(0,0)`.
```sql
SELECT TOP 5
"SHAPEID",
"SHAPE".ST_asWKT() AS "WKT",
ROUND("SHAPE".ST_Distance(NEW ST_Point('POINT (0 0)')), 4) AS "DISTANCE"
FROM "TUTORIAL_GEO"."SPATIALSHAPES"
WHERE "SHAPE".ST_isEmpty() = 0
ORDER BY 3 ASC;
```
### Optional
- Blog post [Markers for geographical areas (with SAP HANA SQL)](https://blogs.sap.com/2020/07/10/markers-for-geographical-areas-with-sap-hana-sql/),
- You can find all available methods in [SAP HANA Spatial Reference](https://help.sap.com/viewer/bc9e455fe75541b8a248b4c09b086cf5/2020_04_QRC/en-US/7a13f280787c10148dc893063dfed1c4.html).