I have a road network shapefile as a polyline and I want to convert this to a polygon layer wherever the network forms a 'hole' or closes in on itself. The problem is a hole could be made from more than one road feature. (i.e. three connecting roads form a hole). This means that I cant just say "if the first feature vertext is equal to the last vertex form a polygon."
I only have access to open source modules (PySAL, shapely etc NOT ArcPy)
Any ideas? Been stuck on this one for way too long!
I think you can iterate through the points,
And at each point compare to all points examined so far.
If there's a match, close-off a polygon.
Not sure if you're going to get much better than O(n^2).
Related
I would like to know how best to generate a schematic diagram, something like this, from a graph (created using the Python NetworkX library) that contains the latitude and longitude of each node (city) and the lines connecting them in the Indian railway network.
The cities (nodes) should be located reasonably close to their actual position, but not necessarily exactly. I am OK with using the plate carrée projection that simply maps lat/long onto X/Y in the diagram.
The rail lines (edges) can be straight lines or even curves if it fits better.
On the diagram should be displayed the cities (preferably as dots) along with a short (max 4 characters) label for each, the lines connecting them, and a single label for each line (the given example has quite long labels for the lines).
Preferably the amount of manual tweaking of coordinates to get things to fit should be minimised.
Using Graphviz was my first idea. But I don't know how well neato/fdp (required for fixed positioning of nodes) will perform with large numbers of nodes/edges. Also, making Graphviz display labels separately outside the nodes (rather than inline) seems to need a lot of manual positioning of each label, which would be pretty boring. Is there any better way to get this kind of layout?
Doable (https://forum.graphviz.org/t/another-stupid-graphviz-trick-geographic-graphs/256), but does not seem to use many Graphviz features. In addition to tools mentioned in the link, maybe consider pikchr (https://pikchr.org/home/doc/trunk/homepage.md)
I split de world in X random polygons.
Then I am given a coordinate C1, for instance (-21.45, 7.10), and I want to attribute the right polygon to this coordinate.
The first solution is to apply my ‘point_in_polygon’ algorithm (given a set of coordinates that defines a polygon and a coordinate that defines a point, tell me if the point is inside or not) on each polygon until I find the right one.
But that is very expensive if I have a lot of points to put in a lot of polygons.
An improvement on that relies on the following idea:
To optimise the search, I create a grid (a collection) with a step n, k where I already attribute each pair of coordinates such that:
for i=-180 to 180 step n
for j = -90 to 90 step k
grid.add(i,j)
Then I create a dictionary, and for each pair in the collection I find the corresponding polygon
For each g in grid
For each p in polygons
If point_in_polygon(g,p) == True
my_dict(g) = p
Then, when I receive C1, I look for the closest coordinate in my grid, let’s say g1.
Thanks to my_dict, I can get quickly p1 = my_dict(g1)
Then I compute point_in_polygon(C1, p1) which is likely to be true. If it’s not, I find the closest g which is assigned to a different polygon, and I redo a test. Etc. until I have found the right polygon.
Now, the question is: what is the optimal n, k to create the grid?
So that I can find the right polygon in the minimum number of steps.
I don’t want it too low, because the search of the closest g which is assigned to a different polygon might be expensive.
I don’t want it too high as well, because then I might be missing some polygons and then the search never converges.
My intuition is that the smallest polygon is going to give the steps.
I am not sure if this is a programming problem, a maths problem, or just something I can find empirically, that's why I ask it here.
Any inputs appreciated!
Let me suggest a slight modification to your grid. Currently, you store for each cell the polygon that the cell's center belongs to. Instead, store all the polygons that overlap the cell. Then, whenever you see that a cell has only a single overlapping polygon, you don't need to do any inclusion testing. The grid can be built by methods of conservative rasterization (note that the referenced article is not focused on conservative but rather general rasterization).
The efficiency of your grid correlates with the ratio of single-polygon cells and total cells (because this is the probability of not having to perform polygon-inclusion tests). The storage itself is pretty cheap. You can use a dense array and get constant access to the cells. Hence, from a theoretical point of view, you should have as many cells as possible (because as you have more cells, the single-polygon cell ratio increases). In practice, you might find that cache and other memory effects might make large grids impractical. However, there is no good way to know other than test. So, just try with a couple of sizes on a few different machines and try to find a good fit.
If I had to guess, I would say that your cells should be square and have an area of about 1% - 5% of the average polygon area. Also, more compact polygons can be handled more efficiently than many long and thin polygons.
Pick any point and draw a line straight down from that point. The first polygon edge you hit tells you what polygon the point is in.
So, if you don't want to do polygon tests, then instead of dividing the space into a regular grid, first cut it into strips with vertical cuts that go through all polygon intersections.
Now, within each strip none of the polygon edges cross or end, so you can make an ordered list of all those edges from bottom to top.
If you want to find the polygon that contains a point, then, do a binary search using the x coordinate to find the proper strip. Then in the list of edges that span the strip, you can do a binary search using the y coordinate to find the closest one underneath the point, and that tells you what polygon the point is in.
Google 'trapezoidal decomposition' to find lots of information about similar techniques.
Given a set of surfaces in three-dimensional space, I am attempting to assign each surface to a zone referring to the smallest 3D region the set encloses, or no zone if this is not applicable. I also want to determine if a surface is an interface between two zones. So, for example, if we had 11 surfaces representing two cubes stacked on top of each other, the surfaces in the top cube would be in the same zone and the surfaces in the bottom would be in a different zone (with the interface surface being in both zones).
As an example, I want to take in a set of surfaces such as this and turn it in to this. Each color here represents a zone, with gray being no zone associated (as in the flap at the bottom).
I have done some searching around trying to find if someone has already come up with an algorithm to do this, but I have not found anything (most seem to identify regions rather than link surfaces to the region they enclose). As such I am trying to come up with my own algorithm and am wondering if there are any other alternatives or if my method would work.
I am assuming all surfaces are connected.
My idea is the following:
Select a random surface whose sides each touch exactly one other surface, and add this to zone 1.
Add each connected surface to zone 1 provided each of its sides touch exactly one other surface.
For those connected surfaces that touch more than one surface on at least one of its sides, add it to the "maybe" list.
For each new surface in zone 1, repeat steps 2-3.
Once a surface has been added to the "maybe" list twice, add it to zone 1 and remove from the "maybe" list. Mark this surface as a zone interface.
Add the zone interface to zone 2.
Select one random surface from the "maybe" list and assign it to zone 2 and clear the "maybe" list.
Repeat steps 2-7 (updating the zone number of course) until there are no surfaces that are unassigned.
This seems to work for simple scenarios (e.g., two cubes stacked on top of one another), but I am not sure if there are any tricky conditions I need to watch out for, or if it falls apart once there are more than two zones that share a side.
Any improvement on my rough algorithm/alternate ideas for implementation would be appreciated. Thanks!
EDIT: Here are some more details in response to some comments.
A zone by my definition is simply a group of surfaces that completely bound a 3D region with no gaps. So if I had two cubes, A and B, that do not touch, I would have two zones: one consisting of all the surfaces of cube A and the other of all the surfaces for cube B. If I had a cube that was missing one side, there would be no zone associated with those surfaces.
My end goal is to make an automated process for grouping surfaces in a modeling tool I am creating. The specifics are classified, but essentially I am dealing with models where certain properties are common only between surfaces in the same "zone" as described above. I want to make an automated process that creates these zones so that the user can apply these properties to all surfaces in the zone at once instead of doing it manually.
Essentially the problem boils down to finding the smallest 3D regions that are completely enclosed by an arbitrary set of surfaces, and keeping track of which surfaces belong to which regions. I hope this makes my question more clear.
What you are interested in, then, would be discovering closed surface (volume) mesh topology from a set of input polygons; in other words - polytopes. This is common to pretty much every 3d modeling package. I would guess that Blender has code that does that. There are different ways of doing this, commonly however, some version of half-edge graph is used. See wiki link here: Doubly Linked half edge graph. The idea is to walk your input polies, and build these graphs. Once done, you can easily query each graph to see if there are holes (edges missing, etc).
I attached a picture explaining how to use a half-edge structure to get what you want: Say you are given a soup of five rectangles (they make up a cube with out a top. U process your first rectangle say ABCD, this creates your first graph, say G1. Now you process second polygon, say FEHG, none of these vertices you have seen yet, so you create second graph, G2. Now say you process polygon CDGH. You have seen these vertices before, so instead of creating a new graph, you merge(connect) existing graphs that share these nodes. Proceed until you process all polygons. You get graph in picture.
Now, to query the graph to get your information. Once you walk the graph, you will see that there are exactly four vertices (nodes) that are missing edges. Those verts correspond to the missing top of the box (the edges are red in the illustration). Hence you know that this graph is not a closed manifold. If you had another box, that did not share nodes with this one, you would have another graph. So each graph, once you done processing your polygons, is a "zone" for you.
Note, if you have two say intersecting shapes, you can track those too using these graphs, but its much more complicated. Basically when processing a new polygon, you would not only have to see if any of its verts belong to already processed graphs, but also see if this polygon intersects any of the previously processed polygons, if so, split this polygon and add all this to the intersected graph.
i'm developing a Gtk Program with Python. I have to display a map and some nodes on this map, which walking around on streets. To achieve this I am using libchamplain.
Displaying the map was quite easy. But is there a way to check if a Coordinate (lat, lon) points on a street? Or any other solution to put some walking markers on the map?
Thank you.
I solved my problem.
I created a PathLayer and calculated a very, very simple route for a randomly chosen Point on the Map based on this algorithm. Then i use Object to print that Point on the route. Every second the Point removes and get plotted on the next position.
I am working on an OpenGL project where I need to be able to click on stuff in 3D space. As far as I can tell gluUnproject() will do that job. But I have heard unexpected things might happen, and the accuracy will be thrown off. It could just be that these people used it wrong, or something else. Is there anything unusual I should know about gluUnproject()?
I once asked a question, which contains what you seem to be searching, click here to see my question.
But basically what you can use gluUnproject() for is to calculate 2D Screen Coordinates (Probably Mouse Coordinates) to 3D World Space Coordinates.
Then you can calculate two points. The first point could be the point on the near plane and the second point could be at the far plane, thereby you can create a line which you then can use to perform collision detection with.
The above images comes from a post (click here to see the post), the post actually describes and tells about probably what you seem to be seeking.