i am trying to figure out if there is a reasonably easy way to extend NVD3's lineChart model to allow variable stroke widths along each line path in a chart.
specifically, i am dealing with a simple line chart where i need to show the year-on-year growth of employment in different sectors (for which NVD3's lineChart works perfectly), while also giving an idea of the relative weight of these sectors (i.e. agricolture might be growing while employing only a few hundred people overall, while retail might be struggling but still be employing a large percentage of the population) - this won't be a linear scale of course, but assuming that relative weight of each sector varies across time, a thicker line could represent a sector with more employees than one with a thin line.
obviously i could very easily change the stroke width for the whole line using i.e. an average weight of each sector across the whole timespan, but as far as i understand there is no way in SVG to specify a varying width of a single path element: would it make sense to create an NVD3 model that builds on top of lineChart but splits each line into discrete polygons (triangles?) for each year-on-year period?
Looking for an answer to this myself. It seems there is no easy way, but one possibility is to use the stroke-dasharray attribute.
http://owl3d.com/svg/vsw/articles/vsw_article.html
Essentially, you can create a series of cloned paths, covering a range of stroke widths. If you turn them into dash arrays, you can play with the spacing between dashes to control which paths are visible at each point.
Depending on the shape and width you are looking for, you may also be able to fudge it by adding a second path element with a varying offset from the first.
Perhaps generate a closed path and apply a pattern fill or regular fill on that path. The closed path is effectively a triangle shape, to mimic a line of varied width.
Related
I have a GeoJSON file with small details and features that I want to render using D3. Unfortunately, important details are lost because D3
removes polygon coordinate pairs that are closely spaced.
I've set up a small example to show this. Both links use the exact same GeoJSON data, rendered with both D3-geo and mapbox through github.
Specifically, notice the two areas marked by the red circles.
https://bl.ocks.org/alvra/eebb06be793bc06ff3ae01e6945298b6
https://gist.github.com/alvra/eebb06be793bc06ff3ae01e6945298b6
The top one one marks a part of polygon that is rounded using many closely spaced coordinate pairs, but D3 removes most points and just draws a rough square end.
The lower red circle marks a tiny triangle that is removed altogether. The adjacent polygons should touch exactly, but are also affected by D3's loss of precision.
I haven't found any documentation about D3's coordinate precision or a (configurable) feature size limit.
I've tried decreasing D3-geo's EPSILON and related EPSILON2 values and that removes this problem (for me), although I'm sure even smaller features will still be affected.
Assuming this is related to the fact that D3 uses proper geodesics for polygon segments, while the other mapping libraries just draw straight lines (in the output coordinate space),
I was hoping that this process can only introduce new points.
I haven't been able to find other users experiencing similar problems with small features, although I'm surprised this has never come up before.
Does anyone have an idea about the proper way to deal with this?
Through epsilon, I've narrowed the problem down to this use of pointEqual(). This indicates the problem is with clipCircle considering closely spaced coordinates equal and removes them.
Indeed, if I disable circular clipping projection.clipAngle(null), the problem disappears.
I have some labels arranged along the outside of a series of arcs (generated by pie charts). These labels are positioned along 'copies' of the pie arcs, which works to fit them nicely, but they unfortunately also cut them off prematurely, as seen in the screenshot below (in this case, an 'i' from the beginning and bracket contents at the end).
Is it possible to tell the text to extend beyond the path's limits? Or failing that, to extend the path itself along its existing course?
edit: The code I'm using to make the arcs is pretty much exactly what's found here: https://www.visualcinnamon.com/2015/09/placing-text-on-arcs.html.
I got a data set that where each sample has a size (0-1000) and a value (grade 1-5). I want to visualise the data with circles of different sizes along a line (domain axis), much like:
http://www.nytimes.com/interactive/2013/05/25/sunday-review/corporate-taxes.html?_r=1&
(note that circles even with the same effective taxrate do not overlap)
Example data:
sample 1: size 300 value 3.2
sample 2: size 45 value 3.8
sample 3: size 4400 value 4.0
sample 5: size 233 value 0.2
sample 6: size 4000 value 4.2
How can the data above be visualised using circles on a line (size decides diameter, value decides approximate position on the line) so that circles do not overlap?
I've been looking at D3's packing layout, but from what I can tell it doesn't support this out of the box. Anyone got any ideas on how to approach this?
Oooh, this one was a puzzle...
If you look at the code for the NYTimes graphic, it uses pre-computed coordinates in the data file, so that's not much use.
However, there's an unused variable declaration at the top of the script that hints that the original version used d3.geom.quadtree to lay out the circles. The quadtree isn't actually a layout method; it is used to create a search tree of adjacent nodes, so that when you need to find a node in a given area you don't have to search through the whole set. Example here.
The quadtree can therefore be used to identify which of your datapoints might be overlapping each other on the x-axis. Then you have to figure out how much you need to offset them in order to avoid that overlap. The variable radii complicate both functions...
I've got a test case implemented here:
http://fiddle.jshell.net/6cW9u/5/
The packing algorithm isn't perfect: I always add new circles to the outside of existing circles, without testing whether they could possibly fit closer in, so sometimes you get significant extra whitespace when it is just the far edges of circles bumping into each other. (Run it a few times to get an idea of the possibilities -- note that I've got x-variables distributed as random normal and r-variables distributed as random uniform.) I also got a stack overflow on the recursive methods during one iteration with N=100 -- the random distribution clearly wasn't distributed well enough for the quadtree optimization.
But it's got the basic functionality. Leave a comment here if you can't follow the logic of my code comments.
--ABR
Update
New fiddle here: http://fiddle.jshell.net/6cW9u/8/
After a lot of re-arranging, I got the packing algorithm to search for gaps between existing bubbles. I've got the sort order switched (so that biggest circles get added first) to show off how little circles can get added in the gaps -- although as I mention in the code comments, this reduces the efficiency of the quadtree search.
Also added various decoration and transition so you can clearly see how the circles are being positioned, and set the r-scale to be square root, so the area (not radius) is proportional to the value in the data (which is more realistic, and what the O.P. asked for).
D3's packing layout is not the answer here. It places circles in a spiral fashion around the existing group. Here's me reverse-engineering the algorithm behind packing layout:
I would suggest a force layout-based approach. That way, you can give your nodes force towards a gravitational center, and then let gravity do its thing.
Force layouts (e.g. Clustered Force Layout I) are usually animations, so you'll want to apply a static force layout.
I've wrapped up this approach in an example block, which looks like this:
I am currently working on OCR software and my idea is to use templates to try to recognize data inside invoices.
However scanned invoices can have several 'flaws' with them:
Not all invoices, based on a single template, are correctly aligned under the scanner.
People can write on invoices
etc.
Example of invoice: (Have to google it, sadly cannot add a more concrete version as client data is confidential obviously)
I find my data in the invoices based on the x-values of the text.
However I need to know the scale of the invoice and the offset from left/right, before I can do any real calculations with all data that I have retrieved.
What have I tried so far?
1) Making the image monochrome and use the left and right bounds of the first appearance of a black pixel. This fails due to the fact that people can write on invoices.
2) Divide the invoice up in vertical sections, use the sections that have the highest amount of black pixels. Fails due to the fact that the distribution is not always uniform amongst similar templates.
I could really use your help on (1) how to identify important points in invoices and (2) on what I should focus as the important points.
I hope the question is clear enough as it is quite hard to explain.
Detecting rotation
I would suggest you start by detecting straight lines.
Look (perhaps randomly) for small areas with high contrast, i.e. mostly white but a fair amount of very black pixels as well. Then try to fit a line to these black pixels, e.g. using least squares method. Drop the outliers, and fit another line to the remaining points. Iterate this as required. Evaluate how good that fit is, i.e. how many of the pixels in the observed area are really close to the line, and how far that line extends beyond the observed area. Do this process for a number of regions, and you should get a weighted list of lines.
For each line, you can compute the direction of the line itself and the direction orthogonal to that. One of these numbers can be chosen from an interval [0°, 90°), the other will be 90° plus that value, so storing one is enough. Take all these directions, and find one angle which best matches all of them. You can do that using a sliding window of e.g. 5°: slide accross that (cyclic) region and find a value where the maximal number of lines are within the window, then compute the average or median of the angles within that window. All of this computation can be done taking the weights of the lines into account.
Once you have found the direction of lines, you can rotate your image so that the lines are perfectly aligned to the coordinate axes.
Detecting translation
Assuming the image wasn't scaled at any point, you can then try to use a FFT-based correlation of the image to match it to the template. Convert both images to gray, pad them with zeros till the originals take up at most 1/2 the edge length of the padded image, which preferrably should be a power of two. FFT both images in both directions, multiply them element-wise and iFFT back. The resulting image will encode how much the two images would agree for a given shift relative to one another. Simply find the maximum, and you know how to make them match.
Added text will cause no problems at all. This method will work best for large areas, like the company logo and gray background boxes. Thin lines will provide a poorer match, so in those cases you might have to blur the picture before doing the correlation, to broaden the features. You don't have to use the blurred image for further processing; once you know the offset you can return to the rotated but unblurred version.
Now you know both rotation and translation, and assumed no scaling or shearing, so you know exactly which portion of the template corresponds to which portion of the scan. Proceed.
If rotation is solved already, I'd just sum up all pixel color values horizontally and vertically to a single horizontal / vertical "line". This should provide clear spikes where you have horizontal and vertical lines in the form.
p.s. Generated a corresponding horizontal image with Gimp's scaling capabilities, attached below (it's a bit hard to see because it's only one pixel high and may get scaled down because it's > 700 px wide; the url is http://i.stack.imgur.com/Zy8zO.png ).
To give you some background as to what I'm doing: I'm trying to quantitatively record variations in flow of a compressible fluid via image analysis. One way to do this is to exploit the fact that the index of refraction of the fluid is directly related to its density. If you set up some kind of image behind the flow, the distortion in the image due to refractive index changes throughout the fluid field leads you to a density gradient, which helps to characterize the flow pattern.
I have a set of routines that do this successfully with a regular 2D pattern of dots. The dot pattern is slightly distorted, and by comparing the position of the dots in the distorted image with that in the non-distorted image, I get a displacement field, which is exactly what I need. The problem with this method is resolution. The resolution is limited to the number of dots in the field, and I'm exploring methods that give me more data.
One idea I've had is to use a regular grid of horizontal and vertical lines. This image will distort the same way, but instead of getting only the displacement of a dot, I'll have the continuous distortion of a grid. It seems like there must be some standard algorithm or procedure to compare one geometric grid to another and infer some kind of displacement field. Nonetheless, I haven't found anything like this in my research.
Does anyone have some ideas that might point me in the right direction? FYI, I am not a computer scientist -- I'm an engineer. I say that only because there may be some obvious approach I'm neglecting due to coming from a different field. But I can program. I'm using MATLAB, but I can read Python, C/C++, etc.
Here are examples of the type of images I'm working with:
Regular: Distorted:
--------
I think you are looking for the Digital Image Correlation algorithm.
Here you can see a demo.
Here is a Matlab Implementation.
From Wikipedia:
Digital Image Correlation and Tracking (DIC/DDIT) is an optical method that employs tracking & image registration techniques for accurate 2D and 3D measurements of changes in images. This is often used to measure deformation (engineering), displacement, and strain, but it is widely applied in many areas of science and engineering.
Edit
Here I applied the DIC algorithm to your distorted image using Mathematica, showing the relative displacements.
Edit
You may also easily identify the maximum displacement zone:
Edit
After some work (quite a bit, frankly) you can come up to something like this, representing the "displacement field", showing clearly that you are dealing with a vortex:
(Darker and bigger arrows means more displacement (velocity))
Post me a comment if you are interested in the Mathematica code for this one. I think my code is not going to help anybody else, so I omit posting it.
I would also suggest a line tracking algorithm would work well.
Simply start at the first pixel line of the image and start following each of the vertical lines downwards (You just need to start this at the first line to get the starting points. This can be done by a simple pattern that moves orthogonally to the gradient of that line, ergo follows a line. When you reach a crossing of a horizontal line you can measure that point (in x,y coordinates) and compare it to the corresponding crossing point in your distorted image.
Since your grid is regular you know that the n'th measured crossing point on the m'th vertical black line are corresponding in both images. Then you simply compare both points by computing their distance. Do this for each line on your grid and you will get, by how far each crossing point of the grid is distorted.
This following a line algorithm is also used in basic Edge linking algorithms or the Canny Edge detector.
(All this are just theoretic ideas and I cannot provide you with an algorithm to it. But I guess it should work easily on distorted images like you have there... but maybe it is helpful for you)