Develop Reference

Algorithm to decompose Polygons into lineStrings (Headlands from Plots)

Consider the following polygon (an agricultural plot)
From this polygon, I would like to extract the "headlands" of the plot, being the consecutive lines (sides) of the polygon (Wikipedia) used for turning on the field. While often only the rows running perpendicular to the lay of the field are considered, I need all sides of the polygon.
Here, a consecutive line means any set of coordinates, where the angle between any two coordinates of the set is not larger than a value X (e.g 30 degrees).
For the given example, the resulting headlands should look like the following:
I wrote a small algorithm trying to accomplish this, basically checking the angle between two coordinates and either pushing the given coordinate to the existing lineString if the angle is below X degrees or creating a new lineString (headland) if not.
Check out the following Gist
However, in some cases corners of a field are rounded, therefore may consist of many coordinates within small distances of each other. The relative angles then may be less than the value X, even though the corner is too sharp to actually be cultivated without turning.
In order to overcome that issue, I added an index that increases whenever a coordinate is too close for comparison, so that the next coordinate will be checked against the initial coordinate. Check out the following Gist.
This works for simple plots like the one in the example, however I am struggling with more complex ones as the following.
Here, the bottom headland is recognised as one lineString together with the headland on the right, even though optically a sharp corner is given. Also, two coordinates in the upper right corner were found to be a separate headland even though they should be connected to the right headland. The result should therefore yield in the following:
What I would like to know is if there is an approach that efficiently decomposes any polygon into it's headlands, given a specific turning angle. I set up a repo for the code here, and an online testing page with many examples here if that helps.

Position resizable circles near each other

I am working on this browser-based experiment where i am given N specific circles (let's say they have a unique picture in them) and need to position them together, leaving as little space between them as possible. It doesn't have to be arranged in a circle, but they should be "clustered" together.
The circle sizes are customizable and a user will be able to change the sizes by dragging a javascript slider, changing some circles' sizes (for example, in 10% of the slider the circle 4 will have radius of 20px, circle 2 10px, circle 5 stays the same, etc...). As you may have already guessed, i will try to "transition" the resizing-repositioning smoothly when the slider is being moved.
The approach i have tried tried so far: instead of manually trying to position them i've tried to use a physics engine-
The idea:
place some kind of gravitational pull in the center of the screen
use a physics engine to take care of the balls collision
during the "drag the time" slider event i would just set different
ball sizes and let the engine take care of the rest
For this task i have used "box2Dweb". i placed a gravitational pull to the center of the screen, however, it took a really long time until the balls were placed in the center and they floated around. Then i put a small static piece of ball in the center so they would hit it and then stop. It looked like this:
The results were a bit better, but the circles still moved for some time before they went static. Even after playing around with variables like the ball friction and different gravitational pulls, the whole thing just floated around and felt very "wobbly", while i wanted the balls move only when i drag the time slider (when they change sizes). Plus, box2d doesn't allow to change the sizes of the objects and i would have to hack my way for a workaround.
So, the box2d approach made me realize that maybe to leave a physics engine to handle this isn't the best solution for the problem. Or maybe i have to include some other force i haven't thought of. I have found this similar question to mine on StackOverflow. However, the very important difference is that it just generates some n unspecific circles "at once" and doesn't allow for additional specific ball size and position manipulation.
I am really stuck now, does anyone have any ideas how to approach this problem?
update: it's been almost a year now and i totally forgot about this thread. what i did in the end is to stick to the physics model and reset forces/stop in almost idle conditions. the result can be seen here http://stateofwealth.net/
the triangles you see are inside those circles. the remaining lines are connected via "delaunay triangulation algorithm"

I recall seeing a d3.js demo that is very similar to what you're describing. It's written by Mike Bostock himself: http://bl.ocks.org/mbostock/1747543
It uses quadtrees for fast collision detection and uses a force based graph, which are both d3.js utilities.
In the tick function, you should be able to add a .attr("r", function(d) { return d.radius; }) which will update the radius each tick for when you change the nodes data. Just for starters you can set it to return random and the circles should jitter around like crazy.

(Not a comment because it wouldn't fit)
I'm impressed that you've brought in Box2D to help with the heavy-lifting, but it's true that unfortunately it is probably not well-suited to your requirements, as Box2D is at its best when you are after simulating rigid objects and their collision dynamics.
I think if you really consider what it is that you need, it isn't quite so much a rigid body dynamics problem at all. You actually want none of the complexity of box2d as all of your geometry consists of spheres (which I assure you are vastly simpler to model than arbitrary convex polygons, which is what IMO Box2D's complexity arises from), and like you mention, Box2D's inability to smoothly change the geometric parameters isn't helping as it will bog down the browser with unnecessary geometry allocations and deallocations and fail to apply any sort of smooth animation.
What you are probably looking for is an algorithm or method to evolve the positions of a set of coordinates (each with a radius that is also potentially changing) so that they stay separated by their radii and also minimize their distance to the center position. If this has to be smooth, you can't just apply the minimal solution every time, as you may get "warping" as the optimal configuration might shift dramatically at particular points along your slider's movement. Suffice it to say there is a lot of tweaking for you to do, but not really anything scarier than what one must contend with inside of Box2D.
How important is it that your circles do not overlap? I think you should just do a simple iterative "solver" that first tries to bring the circles toward their target (center of screen?), and then tries to separate them based on radii.
I believe if you try to come up with a simplified mathematical model for the motion that you want, it will be better than trying to get Box2D to do it. Box2D is magical, but it's only good at what it's good at.

At least for me, seems like the easiest solution is to first set up the circles in a cluster. So first set the largest circle in the center, put the second circle next to the first one. For the third one you can just put it next to the first circle, and then move it along the edge until it hits the second circle.
All the other circles can follow the same method: place it next to an arbitrary circle, and move it along the edge until it is touching, but not intersecting, another circle. Note that this won't make it the most efficient clustering, but it works. After that, when you expand, say, circle 1, you'd move all the adjacent circles outward, and shift them around to re-cluster.

Merge two svg path elements programmatically

I am rendering a map out of SVG paths (using jVectormap).
There are cases where one region has to be merged with the neighboring region.
Unfortunately both regions don't touch each other and I have to interpolate to fill the space in between.
jVectormap uses very simple SVG paths with M to set the the absolute startpoint and l to connect relative points.
Does any of the SVG libraries cover such an operation?

I haven't tried this, but you may get around it by running the converter at jVectormap with the following parameters:
--buffer_distance=0
--where="ISO='region_1' OR ISO='region_2'"
Where region_1 and region_2 are the two regions that you need to merge.
Solving the problem this way also means that the generated SVG paths are true to the original coordinates, whereas a following fix may lead to some (probably minor) inconsistencies.

This might not be the kind of answer you're looking for, but using Raphael.js you could loop over the entire length of the path of one region getPointAtLength(), comparing it with all points of the second region. If the coordinates are closer than n pixels from any coordinates on the second region and the previous coordinates weren't, than that could be regarded a "glue" point. You would then jump to the second regio and start looping over it, if the next point is still closer than n points, than go in the opposite direction, if still closer change direction and go farther along the path till finding a point that's farther away from the original region than n pixels. Continue looping in that direction till once again finding a new "glue" point, where once again you will switch to the original region in the manner described and all points which weren't covered in this final loop could be discarded (or you could simply create a new shape based on the points you came across whilst looping over the length of the original region.
True enough, it's not the easiest script to make, but it should be quite do-able I believe, especially when you can use a function like getPointAtLength to find the points between the defined svg points (though you need to only 'record' the defined points, and that's sort of the hard path as Raphael.js doesn't excitedly have any functions which would help with this, still even that shouldn't be too hard to match up by hand (in code of course)).

how to make an infinite map with html and js

I'm trying to implement a seemingly dynamic infinite map of divs.
My main issues are how to generate new tiles in any direction when the user drag the board
and then what/how should the map be stored in the database .
Here is the quick start I have.

I suspect the grid is just large as opposed to truly infinite.
You only store the tiles that are placed.
The 'view' of the board is limited, even the minimap version is only about 256x256.
The 'empty' board can be just draw, derived from the top left( or other single point ) and width and depth of the screen.
You could also use a pseudo random number to procedurally vary the appearance of each blank square.

One way of doing it would be to store the coordinates of each word in an R-Tree. You would then use the R-Tree to find all the words within the coordinate boundaries you like to see. This could be done in your backend (many database systems support indexing spatial coordinates).

How to create jigsaw puzzle from an image using javascript

I googled it but didn't find a good answer. Specifically, I want to learn:
to slice an image into curved pieces
to create individual objects from those pieces (i assume that i need
this to reassemble)
thanks.

There are several pieces to this puzzle. :)
The first piece is SVG and its Canvas. That's what you'll need to draw, because otherwise you can't make a curved piece out of a picture. Only rectangles are possible with standard HTML/CSS.
The second piece is an algorithm for generating jigsaw pieces from the picture. Google should help you with that if you can't figure one out by yourself (though it doesn't seem very complicated).
The rest should be straightforward.
Added: A quick Google search gave just such a jigsaw engine in the first result. Check out the source of that.

I'll assume the image you want to saw to pieces is a raster image with a resolution that you will use for the puzzle pieces, call that /picture/. Also, I assume you have the edges along which you wish to saw in a second raster image with the same dimensions, call that /raster/. Then your problem amounts to determining all connected areas in the raster. Each pixel of the raster gets annotated with the id of the jigsaw piece it belongs to, initially 'none', -1 or whatever. Then your algorithm scans across all pixels in the raster, skipping pixels that already belong to a piece. For each unassigned piece it executes a flood fill, "coloring" the pixels with the pieces id (e.g. number). In a second scan, after allocating an image for each piece, you add the corresponding pixels of the image to the piece. As part of your first pass you can maintain for each piece id the bounding box. That allows you to allocate the the images for the pieces to their proper dimensions.
You need a suitable convention to deal with border pixels: e.g. border pixels to the right belong to the piece if they have the same x-position, but are above they also belong to the piece.