I'm trying to create this in Gamemaker. I already know the Voronoi vertices but i'm stuck with how to create polygons for each seed object. I need them to be independent so i can split it up later to apply texture mapping to them.
I've tried delaunay already but it doesn't seem as accurate as my voronoi generation. But being that the cicrumradius is the voronoi vertices anyways i feel like i don't need it. The problem with the Delaunay is that it only returns the points near the center of the diagram and doesn't return any points towards the Borders of the Box. The only good thing is that delaunay did skip an extra step and made it easier to return if the the seeds x and y are within the circumradius then just add them to the list of vertices
Is there any way to make a polygon from a plot of points from a data structure?
Pick the midpoint of each edge and the distance to each site then sort the result and pick the first and second (when they are equal) and save them into polygons. For the borders there is of course only 1 edge.
Duplicate:Getting polygons from voronoi edges
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I have a question. I am trying to calculate the area of the following layer (see picture)
intersect area
I used the intersection tool to find the intersection between the layer of 4 overlapping buffers with another polygon (transformed from raster and therefore consists of many other polygons). This layers now consists of more than 200 polygons and most of them on top of each other. I actually want to calculate the 2D area of this layer, so I actually want to transform this layer of many polygons into one polygon so that you are able to calculate the area of this one polygon. My question is therefore, is there a possibility to transform this layer into polygons that are adjacent of each other and that there are no overlapping polygons anymore so I can calculate the area? Maybe there is another way to do this?
If understand your question correctly, you should be able to use the Dissolve Boundaries tool in ArcGIS; dissolve into one polygon; then calculate the area of that polygon.
I'm starting with a single 2D triangle that I want to clip with a (potentially) convex 2D polygon. It's not self-intersecting, but may 'keep' or 'discard' the intersecting area based on the winding order.
I want to end up with a triangulation, i.e. a list of n vertices and m triangles, defined by 3 vertices each, of the clipped region in 2D space.
What would be the easiest (for me as a developer), and what the fastest (in terms of computation) way to achieve this?
If I a right, you want to clip inside the polygon, i.e. get the intersection between the triangle and the polygon.
As the triangle is a convex shape, the Sutherland-Hodgman algorithm is appropriate and no too difficult to implement (https://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman_algorithm).
Notice that if the intersection is not simply connected, the resulting polygon will be connected, with double edges joining the would-be parts. Some cleanup might be required.
After finding the intersection, you re-triangulate using the ear-clipping method or a more efficient one (https://en.wikipedia.org/wiki/Polygon_triangulation).
Alternatively, you can triangulate the polygon and perform the clipping of every triangle with the original one.
The triangle-triangle clipping problem is again solved with Sutherland-Hodgman, somewhat simplified as the input polygons have a constant size, and their intersection is convex and at worse an hexagon. Trigulation of a convex polygon is immediate.
I am trying to compute a Voronoi tesselation in 2D with the Manhattan distance in R.
Ideally this would be a function that takes a set of two-dimensional points and outputs a list of polygons that partition the space. I am not certain what representations of Voronoi tesselations are standard.
There are of course many ways to do this with the Euclidean metric (packages like deldir and qhull make this very easy), but I haven't found a way to do this for the manhattan distance. A search using sos's findFn('voronoi') also yielded no results.
Info: taxicabgeometry.net
Interactive: Manhattan-metric Voronoi diagram(Click version)
I've been rolling my own in python, and can sum up the basics here:
Between neighboring centroids is a perpendicular line, in manhattan metric - two rays and a 45 degree diagonal most likely, if the centroids are randomly generated, but a straight horizontal, vertical, or 45 degree diagonal line may also occur. Given a set of such lines for every centroid pair, the edges separating the regions are among them. Collect intersect points of each pair of lines which are equal-distant (within an epsilon), in manhattan metric, to it's 3 nearest centroids. Also collect the two mid points of the 45 degree diagonal which are similarly equal-distant to their nearest two centroids. The outer polies won't be closed. How to deal with them depends on what you need. The poly borders and border verts will need sorting, so your polies aren't a zigzagged mess. Winding order can be determined if they should be clockwise or other. More can be done, just depends on what you need.
Unfortunately, this gets exponentially slower the more points are involved. The intersecting of every bisector to every other bisector is the bottleneck. I've been attempting an insertion method, with some success, but . Now I'm thinking to try first creating a nearest-neighbor linkage between the centroids. If the neighbors are known, the bisectors to intersect will be minimal, and many centroids can be computed quickly.
Anyway, the brute-force approach does work:
The point near the cursor is actually 2 points of a tiny diagonal. It's a precise method, but more complicated than it first seems. The java code from the interactive link above may be faster, but was difficult to get solid and precise geometry from.
Sorry, I dont know R.
Maybe the question is about finding the maximum area of a square that match inside a circumcircle (of a triangle). The equation for such a square abs(x)+abs(y)=r (www.mathematische-basteleien.de/taxicabgeometry.htm). When you have a mesh of triangles the voronoi diagram is the dual.
I have a set of dense, irregurarly distributed 2D points ("scattered all over the place"). They can be stored in a single MULTIPOINT WKT object including "holes" or - if needed - as delaunay triangles.
How would you convert this into a polygon, i.e. one outer boundary and zero, one or more inner boundaries?
P.S. It's not the largest enclosing polygon I'm looking for (that would be solved by ConvexHull or ConcaveHull). I'm looking for a true polygon with the same shape as the scattered point set (including inner boundary).
Your question reads to me like “find a polygon which has a given set of points as vertices.” Is that interpretation correct?
If so, you can do the following: Create the convex hull of your points. Remove those points from consideration, and take the convex hull of the remaining points. Proceed in this fashion until there are no more remaining points. The intermediate result will be a sequence of convex polygones nested inside one another. You can turn them into a single polygon by connecting each subsequent pair of polygons. You connect two polygons by removing an edge from each, and connecting the resulting endpoints ”the other way round”. Some care has to be taken that these connections don't overlap anything else, but that shouldn't be too hard.
Note that there are many possible results fulfilling the specification as I read it. If you need a specific one, you'll have to give details on the criteria for that choice.
Use QHull: http://www.qhull.org/
It is the de facto standard for this sort of thing.
I want to create a Voronoi diagram on several pairs of
latitudes/longitudes, but want to use the great circle distance
between them, not the (inaccurate) Pythagorean distance.
Can I make qhull/qvoronoi or some other Linux program do this?
I considered mapping the points to 3D, having qvoronoi create a 3D
Voronoi diagram[1], and intersecting the result with the unit sphere, but
I'm not sure that's easy.
[1] I realize the 3D distance between two latitudes/longitudes (the
"through the Earth" path) isn't the same as the great circle distance,
but it's easy to prove that this transformation preserves relative
distances, which is all that matters for a Voronoi diagram.
I assume you've found this article. From that, it seems like you have the right idea by using a 3D embedding. Your question is then how to intersect the result with the sphere.
First of all you need to consider how you're going to represent the voronoi diagram. If you want to work in lat/long coordinates in a 2D plane, then your voronoi diagram will contain curved edges, so maybe it is best to just use a 3D representation.
If you use a program like qvoronoi, you should in theory only need the inifinite hyperplane data (generated by Fo). This gives you the equation of the plane and the two points it corresponds to. Usually you only need to use the voronoi diagram to test for inclusion within regions, and the hyperplanes should be enough for that.
See also this question: Algorithm to compute a Voronoi diagram on a sphere?