How can I calculate the length and with of polygons using open source tools? By "polygon length" I mean the length of the longest line within the polygon (update: to be correct, I just need the longest line within the polygon's convex hull) and the width as the longest measure perpendicular to the length measurement.
I'm trying to create a non-axis aligned minimum bounding rectangle for a polygon. The length of this minimum bounding rectangle would be the polygon's diameter.
FWIW, in Postgis is a function since 1.5, ST_Longestline that returns the longestline between two geometries. If you feed that function with the same geometry twice instead of two different, you will get the longest line in that geometry. http://postgis.net/docs/ST_LongestLine.html
@Whuber. you write above that the longest line doesn't have to start and end in the polygons vertexes. You use the letter I as example. I don't get it. If I is represented by a Line with two vertexes, then that line has to be the longest line itself, right?
If the I letter is represented by a thin polygon, the longestline will be a diagonal line from say left upper vertex to right lower vertex.
But I cannot understand how there could be a longest line that doesn't end and start in polygon vertexes.
Do I miss understand something?
/Nicklas
Ok, Whuber, I misunderstood you, I read your answer once more. I was talking about what you call the diameter and you were talking about something else. Sorry
/Nicklas
JTS provides a Minimum Bounding Circle (http://tsusiatsoftware.net/jts/javadoc/com/vividsolutions/jts/algorithm/MinimumBoundingCircle.html) and a Minimum Diameter (http://tsusiatsoftware.net/jts/javadoc/index.html) - once you have those the rectangle should be easy to calculate.
Use Postgis and use ST_envelope(geometry) to get the minimum bounding box coordinates (defined with four points). From this result, you just have to calculate now length and width
A solution using pure Postgis query. It does the job but I don't do test on speed, I use some wkb for quick debug, so this script can be improve.
SELECT line1,
line2,
CASE WHEN line1>line2 THEN line1
WHEN line1<=line2 THEN line2
END AS length,
CASE WHEN line2>line1 THEN line1
WHEN line2<=line1 THEN line2
END AS width FROM (
SELECT ST_length(ST_AsText(ST_MakeLine(ST_AsText(ST_PointN(ST_Boundary(ST_envelope(the_geom)),1)),
ST_AsText(ST_PointN(ST_Boundary(ST_envelope(the_geom)),2))))) AS line1,ST_length(ST_AsText(ST_MakeLine(ST_AsText(ST_PointN(ST_Boundary(ST_envelope(the_geom)),2)),ST_AsText(ST_PointN(ST_Boundary(ST_envelope(the_geom)),3))))) AS line2
from tm_world_borders) AS size;
If you can't find a specific tool to do it you could use pgSQL and PostGIS or get a developer to implement that algorithm for you.
Many ways to do it, but here is one broken into 2 stages:
1) For each vertex find the largest distance to each other vertex within the polygon which can be done with a simple little nested loop in a SISD environment such as .NET:
for(var i=0; i<count; i++)
for(var j=i; j<count; j++)
find the 2 vertices with the greatest distance
construct a segment from those two points
var length = Distance(segment.Begin,segment.End);
2) for the width there are a few ways, the easiest to implement I think would be this:
// make the longest segment horizontal
transform the polygon with a rotation of the negative angle of the longest segment
for each vertex in the polygon find the highest and lowest y-coord values
// the "width" would be the max y-coord minus the min y-coord
var width = maxy-miny
This solves the problem in PostGIS - tested and it's working. Thanks to Mapbox for this great and elegant solution. Please note their license of use!
https://raw.githubusercontent.com/mapbox/postgis-vt-util/master/postgis-vt-util.sql
