I have an array of about 100-400 points, and I want to find the shortest path around all of them. Yes, I know this is a classic case of travelling salesman, but here's some stuff that may simplify it:
Most points are adjacent to other points, since they form the edges of a transparent-background image.
So I programmed a simple "pathfinder" that picks a point, then looks for adjacent points to try and navigate around the shape. It works, but only if the image is simple enough. Here's an example:
As you can see, the Pikachu outline was calculated perfectly into a single path. However, the Raichu features some narrow areas that completely fail to connect suitably. This algorithm would also fail on more complex sprites such as this one:
Shedinja http://static.pokefarm.org/_img/pkmn_m/292.png Where the two parts aren't even connected. In a best case I'd have two paths.
So basically, I need to know how to trace single shapes more reliably, and how to join two paths by their closest points into a single path.
Related
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.
How can I draw a Bezier Line between two non-static DOM elements, like this:
The two lines should be drawn between the
<div class="brick small">Line starts here</div>
and the
<div class="brick small">Line ends here</div>
of this CodePen: https://codepen.io/anon/pen/XeamWe
Note that the boxes can be dragged. If one of the elements changes its position, the line should be updated accordingly.
If I'm not wrong I can't use a canvas, right? What can I use instead?
Let me point you toward the answer I beleve you're looking for, it's a dom element type called 'SVG' which is supported by most if not all web browsers of today (so you won't need to plug in anything external), in which you can draw lines, shapes, apply graphical filters much like in Photoshop and many other useful things, but the one to be pointed out here is the so called 'path', a shape that can consist of both straight lines with sharp corners, or curved lines (bezier) or both combined.
The easiest way to create such paths is to first draw them in for example Illustrator, save the shape in the SVG format, open that file in a text editor and pretty much just copy the generated markup code and paste it into your html, as it is supported there. This will result in the drawn shape to be displayed on your site. But in your case, you won't come around the a little bit complex structuring of the paths, because you wish to have control of it using javascript, so I would suggest first making a few simple paths in this way by exporting from Illustrator, study these in code, then manipulate their bezier values in javascript until you get the hang of how they work, once you've done that you will be able to create the accurate bezier shape you have in mind and (knowing the positions of the elements you want to connect) position them so that they connect your boxes.
Paths can even be decorated with markers, like an arrowhead in the end or beginning of the path, you can even design your own markers as you like them to look and much more if you would dig deeper into it.
Good luck! :)
My case is that I am dynamically positioning a bunch of icons on a static map image, each by CSS, positioned absolutely. Now it often happens, that two or even more points are too near to each other, so the icons overlap and they are not anymore distinguishable.
I am looking for an algorithm to find these "too near to each other" points, and then spread their icons out in a manner that they do not overlap each other anymore.
I am thinking of a radial spread, like finding the average middle point of all points that are too near and then spread them out relatively to that point.
Is there any pattern for such a problem of which you may know?
Thanks a lot in advance.
Here are a few solutions that might solve your problem:
Use a solution to the closest pair of points problem to find the two icons that are closest to one another. If the closest pair is "too close" by your definition, you can move them apart from one another and repeat this process.
Use a spatial data structure like a k-d tree or R-tree to store all the points. You can then execute fast nearest-neighbor searches to find points that are close to one another and move them apart.
Use a force-directed layout algorithm to find a layout for the points that globally minimizes some energy function. Algorithms like Fruchterman-Reingold are pretty straightforward to code up and produce good results.
Hope this helps!
i'm learning Html5 Canvas for some weeks, but the problem above baffle me a long time.
An irregular shape, possible is a circle, Rect, ellipse, polygon , or a path which constructed by some lines and bezier curve...
I found some algorithm for some shape, like circle, rect, and polygon,but , if i used them in canvas, it will be so complex for those many many shape.
I also view some canvas libary,such as Kinetic.js, paper.js, fabric.js,etc, they all do this work well, but the code of they is so much and blend here to there, so I can't get main point...
but i found,all of them don't use the 'isPointInPath' method to do this work. why? if use this, I can do this work too!
kinetic.js , i knew him use the getImageData to determine, but strange, the imagedata its got is no alpha(alpha is always 255), but the shape its drew is semitransparent, oh no my brain is out of thought.
so i'm here want to know how determine a point is in a irregular shape(possibly it's semitransparent) in canvas, even a think way can help me.
and , is some preblem with the 'isPointInPath' method? thus no one use it?
I see no reason why you can't use the built-in functions:
var isInPath = context.isPointInPath(x, y)
For strokes you can use - strokes are separate as a path can be an open line or you can have stroke widths that expands outside the actual polygon:
var isInStroke = context.isPointInStroke(x, y)
Note that this will only work for the last path (after using beginPath()). If you need to iterate several paths (ie. shapes) you need to re-construct the paths (no need to stroke or fill though). This is perhaps a reason why some don't use it.
Transparency is not an issue as checking paths involves the vectors, not the rendered output of those (color information is not part of the check).
In the future you will be able to use the Path object directly. Currently this is not implemented in any browser which otherwise would make iterating a breeze; so re-constructing last path is the only way for now. As you don't actually have to draw anything when checking, the performance is acceptable unless there are a zillion objects to iterate.
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)).