I have a list of around 1100 polygons to iterate through in $polygons (none of them overlapping each other) and I need to find to which polygon my point or circle with a 1 mile radius belongs/intersects. I used the function below and it takes about 1 second and a half, which is good, but I was wondering, is there is another better/faster approach to it?
I read about R/M-tree algorithms, but I don't have any rectangle hierarchies indexed inside the DB. I'm also trying cts:polygon-intersect to see if it is faster, but I doubt it.
cts:circle-intersects(cts:circle(1,cts:point(5.8864790,51.0006240)), $polygons)
You can use cts:bounding-boxes to get bounding boxes (of varying granularity in the case of the polygons) and check whether they overlap, and only go to the more expensive check if they do. Checking whether two boxes intersect is very quick.
So far, cts:circle-intersects is the fastest, iterates in 1.3 seconds between all the 1100+ polygons. I've tried cts:polygon-intersects and cts:region-intersects also. Since this is not a very critical task in order to apply some fancy and speedy algorithms I will leave it like this for the moment.
Related
I want to write a program with 'geometry automata'. I'd like it to be a companion to a book on artistic designs. There will be different units, like the 'four petal unit' and 'six petal unit' shown below, and users and choose rulesets to draw unique patterns onto the units:
I don't know what the best data structure to use for this project is. I also don't know if similar things have been done and if so, using what packages or languages. I'm willing to learn anything.
All I know right now is 2D arrays to represent a grid of units. I'm also having trouble mathematically partitioning the 'subunits'. I can see myself just overlapping a bunch of unit circle formulas and shrinking the x/y domains (cartesian system). I can also see myself representing the curve from one unit to another (radians).
Any help would be appreciated.
Thanks!!
I can't guarantee that this is the most efficient solution, but it is a solution so should get you started.
It seems that a graph (vertices with edges) is a natural way to encode this grid. Each node has 4 or 6 neighbours (the number of neighbours matches the number of petals). Each node has 8 or 12 edges, two for each neighbour.
Each vertex has an (x,y) co-ordinate, for example the first row in in the left image, starting from the left is at location (1,0), the next node to its right is (3,0). The first node on the second row is (0,1). This can let you make sure they get plotted correctly, but otherwise the co-ordinate doesn't have much to do with it.
The trouble comes from having two different edges to each neighbour, each aligned with a different circle. You could identify them with the centres of their circles, or you could just call one "upper" and the other "lower".
This structure lets you follow edges easily, and can be stored sparsely if necessary in a hash set (keyed by co-ordinate), or linked list.
Data structure:
The vertices can naturally be stored as a 2-dimensional array (row, column), with the special characteristic that every second column has a horizontal offset.
Each vertex has a set of possible connections to those vertices to its right (upper-right, right, or lower right). The set of possible connections depends on the grid. Whether a connection should be displayed as a thin or a thick line can be represented as a single bit, so all possible connections for the vertex could be packed into a single byte (more compact than a boolean array). For your 4-petal variant, only 4 bits need storing; for the 6-petal variant you need to store 6 bits.
That means your data structure should be a 2-dimensional array of bytes.
Package:
Anything you like that allows drawing and mouse/touch interaction. Drawing the connections is pretty straightforward; you could either draw arcs with SVG or you could even use a set of PNG sprites for different connection bit-patterns (the sprites having partial transparency so as not to obscure other connections).
Background: I have two tables containing geometries (polygons and multipolygons). One table contains large polygons that touch but do not overlap (they are actually administrative boundaries). The other contains smaller polygons (in this case, they are parcels of land).
In most cases, each smaller polygon from the second table will be wholly contained within one of the larger polygons from the first table. This is simple enough to determine with spatial queries (ST_WITHIN). Some, however, will overlap two (or, theoretically, more) admin area polygons.
The question is, for those smaller polygons which overlap two large ones, how can I tell which it is most in?
This image illustrates the situation. Land parcel A is wholly within Leftshire, and B is wholly within Rightshire. This is a simple ST_WITHIN spatial query. I can determine that C overlaps both Leftshire and Rightshire as ST_WITHIN will be false but ST_OVERLAP will be true for both of them. But how can I determine that C is more in Leftshire than it is in Rightshire?
For reference, I am using MariaDB 5.5.64. If the problem is more easily solved using a different version (or even using a different DB), that would be an acceptable fallback, but I would ideally like to solve it using the tools I have to hand if possible.
[Edit: One simple solution would be to check which larger area the centroid of the smaller area falls into. This would work perfectly for rectangles, as in the example. However, it will not be reliable where the shapes are more complex, and I need this to work even for complex multipolygons as neither administrative areas nor land parcels are reliably simple in real life!]
I am working in aspnetcore using the most up to date GeoAPI and NetTopologySuite version for core. What I'm trying to do should be fairly simple but I can't seem to find the proper way to do it either through experimentation of googling. Or even what to call it, to be honest, which makes googling harder.
Hopefully someone can kick me in the right direction.
I have a multipolygon which may be made up of one or more polygons. I want to create a buffer around that multipolygon's points out to X distance. This is basically a map overlay with concentric areas of interest. A given point of interest may fall in the original multi polygon's shapes... or it might fall in the first or second buffer area. Kinda like an onion if the core of an onion had random shapes in it.
That first part is simple. Just iterate the multipolygon's points and apply a buffer to each point using the buffer method:
var bufferZonePoints = new List<IGeometry>();
foreach(var point in multiPolygon.Coordinates)
{
bufferZonePoints.Add(point.Buffer(x));
}
var bufferZone = this.geometryFactory.CreateMultiPolygon(bufferZonePoints);
That's fine. But it's giving me another multipolygon made up of thousands of points. When I use this as a map overlay, I get a hurricane of circles following the vague outlines of the original shape sort of looking like a spirograph drawing. All I want is basically the outer boundary of all the buffer circles without all the points in the center.
I tried doing a ConvexHull on the multipolygon and it looked correct at first until I realize that it was shaving off the angles on the outside in order to get the smallest polygon all those points fit into (which is what convex hulls do after all). But that causes problems in the stuff I'm overlaying. Some points of interest may be outside the actual buffer, but be inside if the convex hull decides to round off a bumpy area of the zone. (I hope that makes sense).
Basically what I'm trying to do is take that multipolygon made up of all those buffered points and squash it down into a single polygon made up all the outermost boundaries of the buffers. But without all the spirograph garbage in the middle. I don't really want a ConvexHull. I've also tried Union and the GeometryCombiner class, but none of these are doing what I want.
I don't know if this helps makes this mud any clearer but there is a setting in QGIS that when you plunk down two circles and the circles would overlap they combine into one big blob like soap bubbles and the boundaries in between vanish. That's kinda what I'm trying to do via code.
Does that make sense? Can anyone help?
After continuing to experiment with my mapping tool. It would appear that Union DOES actually give me the result I wanted.
I started with two polygons that were far enough apart to make it obvious what was going on, did a union on them and got back just the shell of the combination of them. As I added more of the buffered points to it, the shame became a bit more obvious.
That's pretty well what I wanted.
Thanks anyway though! Hopefully this will help someone else.
Ok, here is the thing. Recently i decided i wanted to understand how Random map generation works. I found some papers and some arguments. The most interesting one was "Diamond Square algorithm" and "Midpoint Displacement". I still have to try to apply those to a software, but other than that, i ran into this site: http://www-cs-students.stanford.edu/~amitp/game-programming/polygon-map-generation/
As you can see, the idea is to use polygons. But i have no idea how to apply that a Tile-Based map, not even how to create those polygons using the tools i have (c++ and sdl). I am assuming there is no way to do it ( please correct me if i am wrong.) But if i am not, how does a non-tile map works, and how are these polygons generated?
This answer will not give you directly the answers you're looking for, but hopefully will get you close enough!
The Problem
I think what blocks you is how to represent the data. You're probably used to a 2D grid that simply represent the type of each tile. As you know, this is fine to handle a tile-based map, but doesn't properly allow you to model worlds where tiles are of a different shape.
Graphs
What I suggest to you, is to see the problem a bit differently. A grid is nothing more than a graph (more info) with nodes that have 4 (or 8 if you allow diagonals) implicit neighbor nodes. So first, what I would do if I was you, would be to move from your strict standard 2D grid to a more "loose" graph, where each node has a position, a position, a list of neighbors (in most cases you'll have corners with 2 neighbors, borders with 3 and "middle" tiles with 4) and finally a rendering component which simply draws your tile on screen at the given position. Once this is done, you should be able to have the exact same results on screen that you currently have with your "2D Tile-Based" engine by simply calling the rendering component with each node who's bounding box (didn't touch it in what you should add to your node, but I'll get back to this later) intersects with the camera's frustum (in a 2D world, it would most likely if the position +/- the size intersects the RECT currently being drawn).
Search
The more generic approach will also help you doing stuff like pathfinding with generic algorithms that explore nodes until they find a valid path (see A* or Dijkstra). Even if you decided to stick to a good old 2D Tile Map game, these techniques would still be useful!
Yeah but I want Polygons
I hear you! So, if you want polygons, basically all you need to do, is add to your nodes a list of vertices and the appropriate data that you might need to render your polygons (either vertex color, textures and U/V maps, etc...) and update your rendering component to do the appropriate OpenGL (this for example should help) calls to draw your nodes. Once again, the first step to iteratively upgrade your 2D Tile Engine to a polygon map engine would be to, for each tile in your map, give each of your nodes two triangles, a texture resource (the tile), and U/V mappings (0,0 - 0,1 - 1,0 and 1,1). Once again, when this step is done, you should have a "generic" polygon based tile map engine. The creation of most of this data can be created procedurally by calculating coordinates based on tile position, tile size, etc...
Convex Polygons
If you decide that you ever might need NPCs to navigate on your map or want to allow your player to navigate by clicking the map, I would suggest that you always use convex polygons (the triangle being the simplest for of a convex polygon). This allows your code that assume that two different positions on the same polygon can be navigated to in straight line.
Complex Maps
Based on the link you provided, you want to have rather complex maps. In this case, the author used Voronoi Diagrams to generate the polygons of the map. There are already solutions to do triangulation like that, but you might also want to use other techniques that are easier to work with if you're just switching to 3D like this one for example. Once you have interesting results, you should consider implementing serialization to save/open your map data from the game. If you want to create an editor, be aware that it might be a lot of work but can be worth it if you want people to help you creating maps or to add elements to the maps (like geometry that's not part of the terrain).
I went all over the place with this answer, but hopefully it helps!
Just iterate over all the tiles, and do a hit-test from the centre of the tile to the polys. Turn the type of the tile into the type of the polygon. Did you need more than that?
EDIT: Sorry, I realize that probably isn't helpful. Playing with procedural algorithms can be fun and profitable. Start with a loop that iterates over all tiles and chooses randomly whether or not the tile is occupied. Then, iterate over them again and choose whether it is occupied or its neighbour is.
Also, check out the source code for this: http://dustinfreeman.org/toys/wall7-dustin.html
I've implemented a function to check the overlapping of two polygons, p1 and p2, to verify if p1 overlaps p2 the function takes every edge of p1 and test if one point of it is inside p2 and not on an edge of p2 (they can share an edge).
The function works just fine, the problem is that it's called a thousand times and it makes my program really slow since it have to iterate through each edge point by point and I'm only checking 4 cases of polygon overlapping, they are:
If a triangle overlaps a triangle.
If a triangle overlaps a rectangle.
If a triangle overlaps a parallelogram.
If a rectangle overlaps a parallelogram.
Is there any simpler and faster way to check if these cases of overlapping occur?
I'm thinking all you are really looking for is where line segment intersections. This can be done in O((N+k) log N), where N is the number of line segments (roughly the number of vertices) and k is the number of intersections. Using the Bentley-Ottmann algorithm. This would probably be best done using ALL of the polygons, instead of simply considering only two at a time.
The trouble is keeping track of which line segments belong to which polygon. There is also the matter that considering all line segments may be worst than simply considering only two polygons, in which case you stop as soon as you get one valid intersection (some intersections may not meet your requirements to be count as an overlap). This method is probably faster, although it may require that you try different combinations of polygons. In which case, it's probably better to simply consider all line segments.
You can speed up the intersection test by first check if the edge intersects the boundin box of the polygon. Look at Line2D.interSects(Rectangle2D rect).
If you have ten thousands of polygons, then you further can speed up, by storing the polygons in a spatial index (Region Quadtree). This then will limit the search to a view polygons instead of bruite force searching all. But this proably make only sense if you often have to search, not only once at program start up.