Finding the intersection of two great circles on the Earth - c#

I'm trying to find the intersection between two great circles on a map. As an example, I tried to find where the route from San Francisco to Barcelona intersects with the route from Los Angeles to Paris.
I was able to find the answer by querying a postGIS database:
select
st_astext(st_intersection(
st_segmentize(ST_GeographyFromText('LINESTRING(-122.4194 37.7749, 2.1686 41.3874)'),10)
,st_segmentize(ST_GeographyFromText('LINESTRING(-118.4079 35.9434, 2.3522 48.8566)'),10)));
This gives me the point
POINT(-81.92999062964206 58.49293500104545)
Which seems reasonable.
The problem is that I am only able to do this calculation by querying a database. I'm looking for a way to do this same calculation directly in a program, preferably using C# or C++.
All the libraries I've tried does the calculation using 2D lines and so the intersection will be placed much further south-west.

Related

Polygon to line string coverage path

I hope that this is not the wrong place for my question, however, when I don't have anywhere else to go, SO never lets me down.
I am looking for a way to convert any given polygon on a map, to a serpentine line string. I would like to pass the polygon as a geography data type (it could be a poly string) which then takes the polygon, and generates a line string covering the entire area of the polygon.
The below images illustrates perfectly what I want to achieve in the sense that I want to provide the blue polygon and I want the green path to be returned either as a collection of points or a geography data type:
Taken from https://robotics.stackexchange.com/questions/14539/generate-a-coverage-path-given-a-polygon-region
I have scoured the internet and cannot seem to find any code examples around how to get this done. I would like to do this in C# preferable but I am not too fussy about the language. Second to C# I can look at using SQL too or even Python as a last resort.
I have read countless articles on Path planning but they all seem to be overkill in terms of what I want to achieve.
Could anybody point me in any direction as to how I can achieve this? Any information or samples will be highly appreciated.
I have thought about breaking the polygon down to its boundary lines and draw a serpentine line string across it by manually checking if a given point is within the bounds of the polygon. Surely there has to be a more efficient way to achieve this? Maybe a ready made API of some sort?

C#: How to determine if a coordinates is in the continental United States?

I am getting coordinates - lat/lon and I want to check if these coordinates are in the continental United States or not. Is there a easy way to do it in C#? I can convert the coordinates into MGRS or UTM.
Thanks!
Oh wow, they have it just for you:
http://econym.org.uk/gmap/states.xml
All the coords of the US states!
Build up a polygon and apply any polygon-contains-point algorithm.
The classic algorithm is ray-casting, and its even pretty simple. Let me know if you have any trouble with it.
Now, you have two options:
Use the data to build a polygon for each state, and check a point with each one of them. If none match, it is not in the US.
However, there is a problem with that approach - I don't know how the data was gathered, but its possible that there are very little gaps between states, or even slight overlaps. So if you only care if its generally in the US or not, I suggest the second approach:
Use the data to build a polygon for each state, and an algorithm to combine those polygons to one (like union). Save that polygon and use that as with the 1st approach.

Convert shape to polygons

Is there any simple (or not) algorithm that is capable of creating polygons from closed path?
Assume w have following path:
0,0; 2,0, 2,1; 1,1;
1,2; 2,2; 2,3; 0,3;
I need to be able to create polygon indexes for OpenGL vertex buffer. Language I'm using is C#.
Someone suggested me Convex Hull, but it's not the thing I'm looking for, cause I have a shape already. I know that this could be a trivial issue, but seriously, I can't find any description or something to point mi in the right direction.
Edit:
Answer 1 suggest to select a point and connect it to other not connected points, this works fine for presented in answer shape but it will not work for shape i posted, shape above looks like this:
Converting to triangles is either easy or hard, depending on what your requirements are and how well you want to do it.
If your polygon is convex, the easiest way is to use GL_TRIANGLES with the indicies
0, 1, 2, 0, 2, 3, 0, 3, 4, ...
It will look like this:
The situation for concave is more work. An algorithm that also works for concave polygons (not ones with holes!) is the Ear-clipping method, described on wikipedia (there is more on that page.)
Things get really interesting when you want a "good" triangulation: avoid skinny or small triangles, reduce number of triangles etc., and then you can trade off quality for speed. I won't go into any advanced algorithms here; searching for polygon triangulation on Google will get you lots of info.
As for normals, if your polygon is planar (it most likely "should" be) then take two non co-incident edges and cross product them (there are two normals and you probably only want one: you need to choose the order in which you cross product (clockwise or anticlockwise) based on the right hand rule.

Check if coordinate is within area

I got a real-estate facing problem.
I've got a real-world address that I'm converting to earth coordinates (such as "London Eye" to "-0.119543;51.503324").
I also got a perimeter or area within I'm going to search (for example "10" is "10 km").
Now I got a bunch of coordinates (totally random around the earth) and I want to check if the current coordinate is within 10km of the coordinates of the london eye.
Is there any solution to this or maybe am I even facing a x-y-problem?
You could use the Haversine Formula to calculate the distance between two points:
http://www.stormconsultancy.co.uk/blog/development/code-snippets/the-haversine-formula-in-c-and-sql/
Nearest GPS coordinate based on distance from a given point
However for speed I think you need to calculate max/min longitude and latitude values (i.e a square around the London Eye) as this will be a lot quicker to calculate if there are lots of points to check. Then use the Haversine formula on this small subset of points (within your square) to find those within 10km.
It seems like this could help you:
http://www.doogal.co.uk/dotnetcoords.php
It is based on http://www.jstott.me.uk/jcoord, which allows distance calculation between points. Don't take my word for it though, haven't used either.
There is a well known solution to the problem. Haversine_formula
I think you can also search for C# code for the same. Hope it helps.

How to intersect two polygons?

This seems non-trivial (it gets asked quite a lot on various forums), but I absolutely need this as a building block for a more complex algorithm.
Input: 2 polygons (A and B) in 2D, given as a list of edges [(x0, y0, x1, y2), ...] each. The points are represented by pairs of doubles. I do not know if they are given clockwise, counter-clockwise or in any direction at all. I do know that they are not necessarily convex.
Output: 3 polygons representing A, B and the intersecting polygon AB. Either of which may be an empty (?) polygon, e.g. null.
Hint for optimization: These polygons represent room and floor boundaries. So the room boundary will normally fully intersect with the floor boundary, unless it belongs to another floor on the same plane (argh!).
I'm kind of hoping someone has already done this in c# and will let me use their strategy/code, as what I have found so far on this problem is rather daunting.
EDIT: So it seems I'm not entirely chicken for feiling faint at the prospect of doing this. I would like to restate the desired output here, as this is a special case and might make computation simpler:
Output: First polygon minus all the intersecting bits, intersection polygons (plural is ok). I'm not really interested in the second polygon, just its intersection with the first.
EDIT2: I am currently using the GPC (General Polygon Clipper) library that makes this really easy!
Arash Partow's FastGEO library contains implementations of many interesting algorithms in computational geometry. Polygon intersection is one of them. It's written in Pascal, but it's only implementing math so it's pretty readable. Note that you will certainly need to preprocess your edges a little, to get them into clockwise or counterclockwise order.
ETA: But really, the best way to do this is to not do this. Find another way to approach your problem that doesn't involve arbitrary polygon intersections.
If you are programming in .NET Framework, you may want to take a look at SqlGeometry class available in .NET assemblies shipped as Microsoft SQL Server System CLR Types
The SqlGeometry class provides STIntersection method
SqlGeometry g1 = SqlGeometry.Parse("POLYGON ((...))");
SqlGeometry g2 = SqlGeometry.Parse("POLYGON ((...))");
SqlGeometry intersection = g1.STIntersection(g2);
What I think you should do
Do not attempt to do this yourself if you can possibly help it. Instead, use one of the many available polygon intersection algorithms that already exist.
I was strongly considering the following codebase on the strength of their demonstration code and the fact that they mentioned their handling of most/all of the weird cases. You would need to donate an amount (of you/your company's choice) if you use it commercially, but it's worth it to get a robust version of this kind of code.
http://www.cs.man.ac.uk/~toby/gpc/
What I actually did was to use a polygon-intersection algorithm that is part of the Java2D libraries. You can possibly find something similar in MS's own C# libraries to use.
There are other options out there as well; look for "polygon clipper" or "polygon clipping", since the same basic algorithms that handle polygon intersection also tend to be usable for the general clipping cases.
Once you actually have a polygon clipping library, you just need to subtract polygon B from polygon A to get your first piece of output, and intersect polygons A and B to get your second piece of output.
How to roll your own, for the hopelessly masochistic
When I was considering rolling my own, I found the Weiler-Atherton algorithm to have the most potential for general polygon-cutting. I used the following as a reference:
http://cs1.bradley.edu/public/jcm/weileratherton.html
http://en.wikipedia.org/wiki/Weiler-Atherton
The details, as they say, are too dense to include here, but I have no doubt that you'll be able to find references on Weiler-Atherton for years to come. Essentially, you split all the points into those that are entering the final polygon or exiting the final polygon, then you form a graph out of all the points, and then walk the graph in the appropriate directions in order to extract all the polygon pieces you want. By changing the way you define and treat the "entering" and "exiting" polygons, you can achieve several possible polygon intersections (AND, OR, XOR, etc.).
It's actually fairly implementable, but like with any computational geometry code, the devil is in the degeneracies.
You may also want to have a look at the NetTopologySuite or even try importing it into Sql server 2008 & it's spatial tools.
Clipper is an open source freeware polygon clipping library (written in Delphi and C++) that does exactly what you're asking - http://sourceforge.net/projects/polyclipping/
In my testing, Clipper is both significantly faster and far less prone to error than GPC (see more detailed comparisons here - http://www.angusj.com/delphi/clipper.php#features). Also, while there's source code for both Delphi and C++, the Clipper library also includes a compiled DLL to make it very easy to use the clipping functions in other (Windows) languages too.
A polygon is fully described by an ordered list of points (P1, P2, ..., Pn). The edges are (P1 - P2), (P2 - P3), ..., (Pn - P1). If you have two polygons A and B which overlaps, there will be a point An (from the list on points describing polygon A) which lies within the area surrounded by polygon B or vice versa (a point of B lies in A). If no such point is found, then the polygons does not overlap. If such a point is found (i.e. Ai) check the adjacent points of the polygon A(i-1) and A(i+1). Repeat until you find a point outside the area or all points are checked (then the first polygon lies completly within the second polygon). If you found a point outside then you can calculate the crossing point. Find the corresponding edge of polygon B and follow it with resersed roles = now check if the points of polygon B lie within polygon A. This way you can build a list of points which describe the overlapping polygon. If needed you should check if the polygons are identical, (P1, P2, P3) === (P2, P3, P1).
This is just an idea and there maybe better ways. If you find a working and tested solution I would recommend that you use it...
narozed
Try to use GIS tools for that, such as ArcObjects, TopologySuite, GEOS, OGR, etc. I'm not sure if all of these distributions are availuable to .net, but they all do the same.
This academic paper explains how to do this.
If you dare to take a look to other people's GPL C++ code, you can see how do they do it in Inkscape:
http://bazaar.launchpad.net/~inkscape.dev/inkscape/trunk/view/head:/src/2geom/shape.cpp (line 126)

Categories

Resources