I have centroids for polygon shapefiles. I know QGIS has a native joinbynearest algorithm, but I need a radial that extends to the farthest distance from the centroid (point), bound by the polygon.
If there's no known '''join by farthest''' option, perhaps someone knows the location of the algorithm source code, so I can try build something new.
Related
Context: I want to create an interactive heatmap with areas separated by a ZIP code. I've found no way of displaying it directly (i.e. using Google Maps or OSM), so I want to create curves or lines that are separating those areas, and visualize it in maps.
I have a set of points, represented by their coordinates and their according class (ZIP code). I want to get a curve separating them. The problem is that these points are not linearly separable.
I tried to use softmax regression, but that doesn't work well with non-linearly separable classes. The only methods I know which are able to separate non-linearly are nearest neighbors and neural networks. But such classifiers only classify, they don't tell me the borders between classes.
Is there a way to get the borders somehow?
If you have a dense cloud of known points within each Zip code with coordinates [latitude. longitude, zip code], using machine learning to find the boundary enclosing those points sounds like overkill.
You could probably get a good approximation of the boundary by using computational geometry, e.g finding the 2D convex hull of each Zip code's set of points using the Matlab convhull function
K = convhull(X,Y)
The result K would be a vector of points enclosing the input X, Y vector of points, that could be used to draw a polygon.
The only complication would be what coordinate system to work in, you might need to do a bit of work going between (lat, lon) and map (x,y) coordinates. If you do not have the Matlab Mapping Toolbox, you could look at the third party library M_Map M_Map home page, which offers some of the same functionality.
Edit: If the cloud of points for Zip codes has a bounding region that is non convex, you may need a more general computational geometry technique to find a better approximation to the bounding region. Performing a Voronoi tesselation of the region, as suggested in the comments, is one such possibility.
In part of an Artificial Neural Network matlab code, I want to find nearest points of two convex polygons.
I saw
dsearchn(X,T,XI)
command's description here, but that finds closest points between two sets of points, and polygons (like convexs) have infinites points.
So can you suggest any way/idea?
Notice: I'm using MATLAB 2014a. I have the coordinate of each convex's vertex point.
If you are not happy with what is provided by dsearchn, then, If I were you, I would do one of two following:
Find Nearest Neighbours on the vertices (for example which vertex of
polygon A is the NN of a given vertex of polygon B).
Pick a random point inside polygon A (you may want to compute the
convex hull of A, but you may skip that and take into account only
the vertices you know already). That random point is the query. Find
an NN of that point from the vertices of polygon B.
You may want to ask in Software recommendations for more.
Edit:
Another approach is this:
Create a representative dataset of polygon A. Set the size of the dataset yourself and fill it with samples of points that lie inside the polygon. Choose them uniformly randomly inside the polygon.
Then take a point of polygon B (either a vertex or a random point inside polygon B) and that's the query point, for which you will seek Nearest Neighbour(s) inside the representative dataset of polygon A.
Of course that's just an approximation, but I can't think of something else now.
Notice that you can of course do the same for polygon B.
With This File in File Exchange, I've find the solution.
With a little code modification, I have drawn a perpendicular bisector which I wanted. Of course, this way is time consuming.
I have made a 3D delaunay triangulation in matlab with some defined points. Considering it a consistent triangulation (I mean with fixed edges and angles) I want to move this triangulatoin in the space and then compute the location of one point by giving other points' location.
I have searched a lot on the net but I couldn't find a proper solution for this problem. Actually there isn't any similar example.
Using CGAL, I have a 3D Delaunay Triangulation of a set of random points on the unit sphere, that I obtained via:
Delaunay T(points.begin(), points.end());
Now, what I would like to be able to do is query T (using locate() or something like that) to find the three vertices of the surface facet that an arbitrary point (also on the unit sphere) is contained inside.
When I use locate(), I get interior cells as results sometimes, which include the infinite vertex. I don't want any of these. I just want the surface facets and to be able to do this for any arbitrary point I try to find that is also on the unit sphere. Trying to figure this out has taken a lot longer than I thought it would.
Any help would be much obliged. Thanks.
So I would use find_conflit(), with CGAL::Emptyset_iterator for cit because you don't need these.
In bfit, you will get the facets of the boundary of the "hole", and the hole is all tetrahedra in conflict with your point (whose circumscribing sphere contains the point, with a natural extension to the infinite vertex).
So, for bfit, put them in a standard container using std::back_inserter for example. Then, iterate over these, tests if they are finite facets. The finite facets you get are those that separate your point from the rest of the triangulation, so, you can then do orientation() tests with the center of the sphere to get the one you are interested in.
I have a 3D point cloud that I've transformed into a Delaunay triangulation using Matlab's function DelaunayTri. Now I have a test point in 3D and want to compute, in Matlab, the smallest distance between this point and the triangulation.
So far, I've thought of using the nearestNeighbor(...) member function of the DelaunayTri class in Matlab to find the point in the triangulation closest to my test point and then computing the distance between them. That is something but it is not what I really want.
The closest point on the triangulation to my test point is, in general, not a vertex of the triangulation but somewhere on the face of a triangle. How can I find this point?
Thank you!!!
I've written codes for these things, but they are not on the File Exchange. I can be convinced to give them out by direct mail though.
It is relatively easy to find the distance to a convex hull, but not trivial. A delaunay tessellation is bounded by the convex hull anyway. So you can convert that tessellation into the convex hull easily enough, or just use the convex hull. Note that a convex hull is often a terribly poor approximation for many purposes, especially if you are using this for color mapping, which is perhaps the most common thing I see this used for. In that case, an alpha shape is a far better choice. Alpha shapes also will have a triangulated boundary surface, though in general it will not be convex.
So, to find the nearest point on a convex triangulation:
Convert to the convex boundary surface, i.e., the convex hull. This reduces to finding those triangles which are not shared between pairs of tetrahedra. Internal facets will always appear exactly twice in the list of all facets. This trick also works for non-convex tessellations of course, so for alpha shapes.
Compute a bounding circumcircle for each triangular surface facet. This allows you to know when to stop checking facets.
Get the distances to each point on the surface. Sort each facet by the distance to the nearest point in that facet. Start by looking at the nearest facet in that list.
Compute the distance to the apparently nearest facet found in step 3. A simple solution is found by least distance programming (LDP), which can be converted to a constrained linear least squares. Lawson & Hanson have an algorithm for this.
Repeat step 4 until the current best distance found is less than the distance, comparing it to any of the circumcircles from step 2. This loop will be quite short really, at least for a convex hull. For a more general non-convex hull from an alpha shape, it may take more time.
You can also reduce the search space a bit by excluding the facets from your search that point AWAY from the point in question. Use those facet normals for this test.
I wrote the tool point2trimesh for this problem. It's kind of a "brute force" solution which works also for non-convex surfaces.