Quadtree | Quad Tree implementation in java | Dataset library

I'm following a tutorial by George Francis in the tutorial after some initial examples he shows how to use image data to create random layouts.

I'm trying to work out how to get the image data from a canvas created using paper.js, as I need to get the rgb values from each individual pixel on the canvas

Link to codepen

Unknowns:

• Do I need to use the rasterize() method on the shape I've created?

Currently I am attempting the following:

Currently I’m trying to implement different functions to realize operations on quadtrees using C language.

Context:

A quadtree (black and white picture) is:

• White
• Black
• Is broken down into 4 sub-images: top-left,top-right,bottom-left,bottom-right

Pictures are represented by the next struct:

I have a map that has some overlapping points. I'm using a quadtree and turf.js to determine, when I click on a point, how many other points are within a 30 mile radius.

What I'd like to do (if there's more than one point in that radius) is use d3.forceSimulation to equally spread out the overlapping points.

This is a pretty close example of what I want to do, but uses d3v3 and google maps: http://bl.ocks.org/cdmahoney/raw/9876525/?raw=true

I have included d3.forceSimulation and when I click on a place with more than one point within the 30 mile radius, the points do take on the force-- but they move up to the left hand corner of the page.

How can I get the points to push out in even distances from where I click on the map, like this:

Help very much appreciated!!

In physics simulations (for example n-body systems) it is sometimes necessary to keep track of which particles (points in 3D space) are close enough to interact (within some cutoff distance d) in some kind of index. However, particles can move around, so it is necessary to update the index, ideally on the fly without recomputing it entirely. Also, for efficiency in calculating interactions it is necessary to keep the list of interacting particles in the form of tiles: a tile is a fixed size array (eg 32x32) where the rows and columns are particles, and almost every row-particle is close enough to interact with almost every column particle (and the array keeps track of which ones actually do interact).

What algorithms may be used to do this?

Here is a more detailed description of the problem:

1. Initial construction: Given a list of points in 3D space (on the order of a few thousand to a few million, stored as array of floats), produce a list of tiles of a fixed size (NxN), where each tile has two lists of points (N row points and N column points), and a boolean array NxN which describes whether the interaction between each row and column particle should be calculated, and for which:

   a. every pair of points p1,p2 for which distance(p1,p2) < d is found in at least one tile and marked as being calculated (no missing interactions), and

   b. if any pair of points is in more than one tile, it is only marked as being calculated in the boolean array in at most one tile (no duplicates),

   and also the number of tiles is relatively small if possible (but this is less important than being able to update the tiles efficiently)

2. Update step: If the positions of the points change slightly (by much less than d), update the list of tiles in the fastest way possible so that they still meet the same conditions a and b (this step is repeated many times)

It is okay to keep any necessary data structures that help with this, for example the bounding boxes of each tile, or a spatial index like a quadtree. It is probably too slow to calculate all particle pairwise distances for every update step (and in any case we only care about particles which are close, so we can skip most possible pairs of distances just by sorting along a single dimension for example). Also it is probably too slow to keep a full (quadtree or similar) index of all particle positions. On the other hand is perfectly fine to construct the tiles on a regular grid of some kind. The density of particles per unit volume in 3D space is roughly constant, so the tiles can probably be built from (essentially) fixed size bounding boxes.

To give an example of the typical scale/properties of this kind of problem, suppose there is 1 million particles, which are arranged as a random packing of spheres of diameter 1 unit into a cube with of size roughly 100x100x100. Suppose the cutoff distance is 5 units, so typically each particle would be interacting with (2*5)**3 or ~1000 other particles or so. The tile size is 32x32. There are roughly 1e+9 interacting pairs of particles, so the minimum possible number of tiles is ~1e+6. Now assume each time the positions change, the particles move a distance around 0.0001 unit in a random direction, but always in a way such that they are at least 1 unit away from any other particle and the typical density of particles per unit volume stays the same. There would typically be many millions of position update steps like that. The number of newly created pairs of interactions per step due to the movement is (back of the envelope) (10**2 * 6 * 0.0001 / 10**3) * 1e+9 = 60000, so one update step can be handled in principle by marking 60000 particles as non-interacting in their original tiles, and adding at most 60000 new tiles (mostly empty - one per pair of newly interacting particles). This would rapidly get to a point where most tiles are empty, so it is definitely necessary to combine/merge tiles somehow pretty often - but how to do it without a full rebuild of the tile list?

P.S. It is probably useful to describe how this differs from the typical spatial index (eg octrees) scenario: a. we only care about grouping close by points together into tiles, not looking up which points are in an arbitrary bounding box or which points are closest to a query point - a bit closer to clustering that querying and b. the density of points in space is pretty constant and c. the index has to be updated very often, but most moves are tiny

I make a copy of crypto bubbles where I want the coins to float around like bubbles now I run into the problem that a squares are completely filled and some are not this is because of the shadow? How do I solve this?

I am doing a compuational geometric issue which uses TriangularMeshQuadtree from a C# library, and some of its constructors is written as follows (from metadata, so I cannot see the details of implementations):

constructor 1:

I'm looking for an algorithm that can find intersecting rectangles that overlap each other.

The catch is that my data structure is similar to a quadtree with bounding boxes instead of points. I'm doing a basic rectangle intersection check but the problem is as I zoom into the tree the child nodes get detected and the parents, I would like to exclude the parent if its fully occluded by a child for the given camera rectangle.

zoom animation

As you can see from the image above as the camera rectangle (black box) sits inside the green node the purple node is still highlighted (filled), consequently as I zoom more and more the parents are always highlighted, even though the camera rectangle can be fully filled with child nodes only.

This makes sense since the camera rectangle is still inside the parent but I have searched and thought about the problem for a while and can't seem to figure out an elegant solution. There seems to be several ways of doing this for 3D spaces but I can't find anything simple for 2D AABB rectangles.

A few solutions that I thought of:

• Subtract the child nodes from the parents resulting in concave polygons and then perform polygon intersection.
• Use the fill color to check which rectangles are visible, therefore occluding the ones behind.
• Perform raycasting or sub-division and check which is the smallest node for a given section.

Is there a better way to do this? Thank you

Update 1

I have solved the problem by subdividing the camera into smaller sections and for each section the smallest intersecting node is found. This works but there must be a more efficient and cleaner way of doing this.

Update 2

Thank you Trentium for your answer. I can clearly see that an algorithm like that would be a lot more performant than what I'm currently doing.

Eventually I will implement it as splitting a rectangle into smaller rectangles and not polygons sounds like a fun challenge.

Also, I did some very non scientific benchmarks on the current approach and it takes 0.5ms-1ms to both filter and draw everything, so for now performance is still not a concern.

I have a project where I'm trying to zoom to specific points. In d3v3, I could do that with this function

Any "W" refers to half-width and any "H" refers to half-height. Any "X" and "Y" refers to the center of a rectangle aligned with the co-ordinate axes.

I am attempting to write some general purpose quadtree code for use in physics simulations and game design. At first it was returning ALL points in the contents of a quadtree that was completely enclosed by the search region. After adding a bunch of print() statements to illuminate the process I managed to solve that problem but now I have a new one I can't seem to figure out. For some reason when I query the quadtree for the "Placeables" within a rectangular region I either get a totally correct result, but more often than not I get nothing returned at all. Placeables are defined as follows: