# SqlGeometry and Boxes

I wanted to write a blog about partitioning (calling an algorithm using an on-the-fly quadtree or octree) and how it is implemented in Boost.Geometry, and how it could also be used / implemented for the SqlGeometry type. But somehow that blog will be too large and I blog here just about a box/rectangle in SqlGeometry. It is not too difficult, but I just googled and did not find other blogs saying the same things, so I hope it adds something.

## STEnvelope

The OGC/ISO STEnvelope function, supported by spatial databases and many geometry libraries, returns the envelope of a geometry. An envelope is: a bounding box or bounding rectangle, also known as an axis aligned bounding box (aabb), a bbox, a minimum bounding rectangle (mbr) or an extent.

More in detail, STEnvelope returns a Geometry object describing a rectangle. OGC does not know the notion of a box. That is sometimes a bit inconvenient, but it is how it is. Boost.Geometry created a Box Concept, because Boost.Geometry is strongly typed, and envelopes returning polygons with always four or five points would confuse the non-OGC users of our library.

I blogged earlier about the spatial extent of a query in SQL Server, here.

A box is a simple geometry, with (in 2D) a minimum x and y and a maximum x and y. But how to get that from a geometry in a spatial database... I mean, the envelope returns a polygon containing five points (assuming it is closed), is the first point lower left? And is that guaranteed? The OGC specifications say: The minimum bounding box for this Geometry, returned as a Geometry. The polygon is defined by the corner points of the bounding box [(MINX, MINY), (MAXX, MINY), (MAXX, MAXY), (MINX, MAXY), (MINX, MINY)]. So yes, it should be guaranteed.

Let's look at it in more detail.

## SQL Server

In SQL Server it indeed seems the case that the first point of the polygon returned by STEnvelope is the lower left point. Then, the third point must be the upper right point. Because, if you consider the polygon clockwise, it is the third point, and if it is counterclockwise, it is also the third point.

We use this query:

`select geometry::STGeomFromText('POLYGON((0 0,2 5,4 1,0 0))',0).STEnvelope().STPointN(3).STAsText()`

... to get the third point (which should be upper right), and it indeed gives me: POINT(4 5)

## PostGIS

In PostGIS, the first point of the polygon returned by ST_Envelope is the lower left point as well. Great.

As you (maybe) know, SQLGeometry uses methods, PostGIS uses functions. So the corresponding nested function calls would be:

`select ST_AsText(ST_PointN((ST_Envelope(ST_GeomFromText('POLYGON((0 0,2 5,4 1,0 0))',0))), 3))`

But... no result, we get a null value back. Looking at the OGC specs, this is correct: NumPoints is defined for a LineString and not for a Polygon. SqlServer is somewhat more relaxed here (as is Boost.Geometry), returning the total number of points of a polygon (including interior rings, if any).

OK, behaviour is correct, so we try again, now inserting the ST_Boundary function (making a linestring of the boundary of a polygon). Our new function call is:

`select ST_AsText(ST_PointN(ST_Boundary((ST_Envelope(ST_GeomFromText('POLYGON((0 0,2 5,4 1,0 0))',0)))), 3))`

... and we have our upper right point. Using a 1 for the last value (the index of ST_PointN is one-based) would return the lower left point.

## Boost.Geometry

Boost.Geometry, as said, returns a box (conforming a Box Concept) for the envelope (or assigns one). So this is more or less outside the discussion... Having a box you can get the minimum-corner coordinates (might be 2D, might be 3D, or more) and the maximum-corner coordinates.

## SqlGeometry

I blogged about the useful SqlGeometry type here. The SqlGeometry type is polymorphic, it can be any OGC geometry. But, therefore, it cannot be a Rectangle (because, remember, a rectangle is not an OGC Geometry). So if it contains a Rectangle, it is a Polygon.

Using C#, it would be useful to get the coordinates from a Polygon returned by STEnvelope and that goes like this. Note that (in the light of defensive programming) we don't even assume that the first point is the lower left point. We add this code as a function (we could add it to a class GeometryExtensions, but for now we don't). It is called BoxToCoordinates, see the code below.

And, for symmetry, and because it is convenient, or often necessary (last reason most important ;-) ) we add a counterpart function as well, which creates a rectangle for you given four coordinate values. We call that one CoordinatesToBox, see code below.

## The code

OK, this was some preparation for next blog, not too difficult, and now we can convert an STEnvelope result to coordinate values, and back. The full code is displayed below. Between BoxToCoordinates and CoordinatesToBox, there will be some more interesting calculations in the next blog. Stay tuned.

`using System;using Microsoft.SqlServer.Types;namespace BlogSqlGeometryBox{    class Program    {        public static SqlGeometry FromWkt(string text, int srid)        {           return SqlGeometry.STGeomFromText(new System.Data.SqlTypes.SqlChars(text), srid);        }        public static SqlGeometry CoordinatesToBox(double x1, double y1, double x2, double y2, int srid)        {           SqlGeometryBuilder builder = new SqlGeometryBuilder();           builder.SetSrid(srid);           builder.BeginGeometry(OpenGisGeometryType.Polygon);           builder.BeginFigure(x1, y1);           builder.AddLine(x1, y2);           builder.AddLine(x2, y2);           builder.AddLine(x2, y1);           builder.AddLine(x1, y1); // Yes, we close it neatly           builder.EndFigure();           builder.EndGeometry();           return builder.ConstructedGeometry;        }        private static void MakeFirstSmaller<T>(ref T a, ref T b) where T : IComparable        {           if (a.CompareTo(b) > 0)           {               // Exchange the two values               T t = a;               a = b;               b = t;           }        }        public static void BoxToCoordinates(SqlGeometry box, out double x1, out double y1, out double x2, out double y2)        {           SqlGeometry lower_left = box.STPointN(1);           SqlGeometry upper_right = box.STPointN(3);           x1 = lower_left.STX.Value;           y1 = lower_left.STY.Value;           x2 = upper_right.STX.Value;           y2 = upper_right.STY.Value;           // Defensive programming:           MakeFirstSmaller(ref x1, ref x2);           MakeFirstSmaller(ref y1, ref y2);        }        static void Main(string[] args)        {           SqlGeometry triangle = FromWkt("POLYGON((0 0,2 5,4 1,0 0))", 0);           SqlGeometry box = triangle.STEnvelope();           double x1, y1, x2, y2;           BoxToCoordinates(box, out x1, out y1, out x2, out y2);           // Do something with these coordinates. Let's create a larger box           x1 -= 1;           y1 -= 1;           x2 += 1;           y2 += 1;           box = CoordinatesToBox(x1, y1, x2, y2, 0);           System.Console.WriteLine(box.STAsText().ToSqlString().ToString());        }    }}`

Writing:

`POLYGON ((-1 -1, -1 6, 5 6, 5 -1, -1 -1))`