What is the most direct way to draw a pie chart using ImageMagick in an existing image. For example, how would I draw a single slice given the following inputs?
- A center point (x,y)
- Radius
- Percent
drawinggeometryimagemagick
What is the most direct way to draw a pie chart using ImageMagick in an existing image. For example, how would I draw a single slice given the following inputs?
My own favorites are these two:
compare image1 image2 -compose src diff.png
compare image1 image2 -compose src diff.pdf
The only difference between the 2 commands above: the first one shows the visual difference between the two images as a PNG file, the second one as a PDF.
The resulting diff file displays all pixels which are different in red color. The ones which are unchanged appear white.
Short and sweet.
Note, your images need not be the same type. You can even mix JPEG, TIFF, PNG -- under one condition: the images should be of the same size (image dimension in pixels). The output format is determined by the output filename's extension.
Should you, for some reason, need a higher resolution than the default one (72 dpi) -- then just add an appropriate -density
parameter:
compare -density 300 image1 image2 -compose src diff.jpeg
Here are a few illustrations of results for variations of the above command. Note: the two files compared were even PDF files, so it works with these too (as long as they are 1-pagers)!
Left: Image with text Center: Original image Right: Differences (=text) in red pixels.
compare \
porsche-with-scratch.pdf porsche-original.pdf \
-compose src \
diff-compose-default.pdf
This is the same command I suggested earlier above.
Left: Image with text Center: Original image Right: Differences in 'seagreen' pixels.
compare \
porsche-with-scratch.pdf porsche-original.pdf \
-compose src \
-highlight-color seagreen \
diff-compose-default.pdf
This command adds a parameter to make the difference pixels 'seagreen' instead of the default red.
Left: Image with text Center: Original image Right: Blue diffs (but w. some context background) l
compare \
porsche-with-scratch.pdf porsche-original.pdf \
-highlight-color blue \
diff-compose-default.pdf
This command removes the -compose src
part -- the result is the default behavior of compare
which keeps as a lightened background the first one of the 2 diffed images. (This time with added parameter to make the diff pixels appear in blue.)
r = R * sqrt(random())
theta = random() * 2 * PI
(Assuming random()
gives a value between 0 and 1 uniformly)
If you want to convert this to Cartesian coordinates, you can do
x = centerX + r * cos(theta)
y = centerY + r * sin(theta)
sqrt(random())
?Let's look at the math that leads up to sqrt(random())
. Assume for simplicity that we're working with the unit circle, i.e. R = 1.
The average distance between points should be the same regardless of how far from the center we look. This means for example, that looking on the perimeter of a circle with circumference 2 we should find twice as many points as the number of points on the perimeter of a circle with circumference 1.
Since the circumference of a circle (2πr) grows linearly with r, it follows that the number of random points should grow linearly with r. In other words, the desired probability density function (PDF) grows linearly. Since a PDF should have an area equal to 1 and the maximum radius is 1, we have
So we know how the desired density of our random values should look like. Now: How do we generate such a random value when all we have is a uniform random value between 0 and 1?
We use a trick called inverse transform sampling
Sounds complicated? Let me insert a blockquote with a little side track that conveys the intuition:
Suppose we want to generate a random point with the following distribution:
That is
- 1/5 of the points uniformly between 1 and 2, and
- 4/5 of the points uniformly between 2 and 3.
The CDF is, as the name suggests, the cumulative version of the PDF. Intuitively: While PDF(x) describes the number of random values at x, CDF(x) describes the number of random values less than x.
In this case the CDF would look like:
To see how this is useful, imagine that we shoot bullets from left to right at uniformly distributed heights. As the bullets hit the line, they drop down to the ground:
See how the density of the bullets on the ground correspond to our desired distribution! We're almost there!
The problem is that for this function, the y axis is the output and the x axis is the input. We can only "shoot bullets from the ground straight up"! We need the inverse function!
This is why we mirror the whole thing; x becomes y and y becomes x:
We call this CDF-1. To get values according to the desired distribution, we use CDF-1(random()).
…so, back to generating random radius values where our PDF equals 2x.
Step 1: Create the CDF:
Since we're working with reals, the CDF is expressed as the integral of the PDF.
CDF(x) = ∫ 2x = x2
Step 2: Mirror the CDF along y = x:
Mathematically this boils down to swapping x and y and solving for y:
CDF: y = x2
Swap: x = y2
Solve: y = √x
CDF-1: y = √x
Step 3: Apply the resulting function to a uniform value between 0 and 1
CDF-1(random()) = √random()
Which is what we set out to derive :-)
Best Answer
Create your pie wedge using SVG; I got my example from here:
Then, overlay that image using ImageMagick to your background image.
Note that you have to define your arcs with cartesian coordinates instead of radius, but the conversion should be fairly straightforward.