How to programmatically generate a ring/annulus with varying blocks of colors

Question

A picture is worth a thousand words...

I'd like to know how to be able to generate an image like that where (1) the two circles are obviously perfect circles, (2) I can define the beginning and ending parts of each region in terms of angles, e.g. section 1 starts at 0 radians from the vertical and ends at pi/2 radians from the vertical, etc., and (3) I can define the color of each region.

In fact the outside and inside of the ring should not have a black border; the border of each region should be the same color as each region.

How might I do this with, say, ImageMagick?

Answer 1

You can create annulus in vector graphics with the Arc command. See Mozilla's Path Document for details on parameter.

With ImageMagick, you could -draw any part of an vector-graphic. Example:

convert -size 100x100 xc:transparent -stroke black -strokewidth 1 \
        -fill blue  -draw 'path "M 10 50 A 40 40 0 0 1 50 10 L 50 20 A 30 30 0 0 0 20 50 Z"' \
        -fill red   -draw 'path "M 50 10 A 40 40 0 0 1 90 50 L 80 50 A 30 30 0 0 0 50 20 Z"' \
        -fill green -draw 'path "M 90 50 A 40 40 0 0 1 10 50 L 20 50 A 30 30 0 0 0 80 50 Z"' \
        annulus.png

Other great example here, and here

update

To create a more programmatic approach, use any OOP scripting language. Below is quick example with Python & Wand, but Ruby & RMagick are also highly recommended.

#!/usr/bin/env python3

import math

from wand.color import Color
from wand.drawing import Drawing
from wand.image import Image

class Annulus(Image):
  def __init__(self, inner, outer, padding=5):
    self.Ri = inner
    self.Ro = outer
    side = (outer + padding) * 2
    self.midpoint = side/2
    super(Annulus, self).__init__(width=side,
                                  height=side,
                                  background=Color("transparent"))
    self.format = 'PNG'

  def __iadd__(self, segment):
    cos_start, cos_end = math.cos(segment.As), math.cos(segment.Ae)
    sin_start, sin_end = math.sin(segment.As), math.sin(segment.Ae)
    SiX, SiY = self.midpoint + self.Ri * cos_start, self.midpoint + self.Ri * sin_start
    SoX, SoY = self.midpoint + self.Ro * cos_start, self.midpoint + self.Ro * sin_start
    EiX, EiY = self.midpoint + self.Ri * cos_end,   self.midpoint +  self.Ri * sin_end
    EoX, EoY = self.midpoint + self.Ro * cos_end,   self.midpoint + self.Ro * sin_end
    with Drawing() as draw:
      for key, value in segment.draw_args.items():
        setattr(draw, key, value)
      draw.path_start()
      draw.path_move(to=(SiX, SiY))
      draw.path_elliptic_arc(to=(EiX, EiY),
                             radius=(self.Ri, self.Ri),
                             clockwise=True)
      draw.path_line(to=(EoX, EoY))
      draw.path_elliptic_arc(to=(SoX, SoY),
                             radius=(self.Ro, self.Ro),
                             clockwise=False)
      draw.path_close()
      draw.path_finish()
      draw(self)
    return self

class Segment(object):
  def __init__(self, start=0.0, end=0.0, **kwargs):
    self.As = start
    self.Ae = end
    self.draw_args = kwargs

if __name__ == '__main__':
  from wand.display import display
  ring  = Annulus(20, 40)
  ring += Segment(start=0,
                  end=math.pi/2,
                  fill_color=Color("yellow"))
  ring += Segment(start=math.pi/2,
                  end=math.pi,
                  fill_color=Color("pink"),
                  stroke_color=Color("magenta"),
                  stroke_width=1)
  ring += Segment(start=math.pi,
                  end=0,
                  fill_color=Color("lime"),
                  stroke_color=Color("orange"),
                  stroke_width=4)
  display(ring)

Answer 2

I know little about gnuplot but think it probaby fits the bill here - my commands may be crude, but they seem pretty legible and effective. Someone cleverer than me may be able to improve them!

Anyway, here is the script I came up with:

set xrange [-1:1]
set yrange [-1:1]
set angles degrees
set size ratio -1
# r1 = annulus outer radius, r2 = annulus inner radius
r1=1.0
r2=0.8
unset border; unset tics; unset key; unset raxis
set terminal png size 1000,1000
set output 'output.png'
set style fill solid noborder
set object circle at first 0,0 front size r1 arc [0:60]    fillcolor rgb 'red'
set object circle at first 0,0 front size r1 arc [60:160]  fillcolor rgb 'green'
set object circle at first 0,0 front size r1 arc [160:360] fillcolor rgb 'blue'

# Splat a white circle on top to conceal central area
set object circle at first 0,0 front size r2 fillcolor rgb 'white'

plot -10 notitle

And here is the result:

So, if you save the above script as annulus.cmd you would run it and create the file output.png using the command

gnuplot annulus.cmd

Obviously the guts of the script are the 3 lines that start set object circle each of which creates a separate annulus segment in a different colour with a different set of start and end angles.

Noodling around and changing some things gives this:

set xrange [-1:1]
set yrange [-1:1]
set angles degrees
set size ratio -1
# r1 = annulus outer radius, r2 = annulus inner radius
r1=1.0
r2=0.4
unset border; unset tics; unset key; unset raxis
set terminal png size 1000,1000
set output 'output.png'
set style fill solid noborder
set object circle at first 0,0 front size r1 arc [0:60]    fillcolor rgb 'red'
set object circle at first 0,0 front size r1 arc [60:120]  fillcolor rgb 'green'
set object circle at first 0,0 front size r1 arc [120:180] fillcolor rgb 'blue'
set object circle at first 0,0 front size r1 arc [180:240] fillcolor rgb 'yellow'
set object circle at first 0,0 front size r1 arc [240:300] fillcolor rgb 'black'
set object circle at first 0,0 front size r1 arc [300:360] fillcolor rgb 'magenta'

# Splat a white circle on top to conceal central area
set object circle at first 0,0 front size r2 fillcolor rgb 'white'

plot -10 notitle

Answer 3

As I am better at thinking in straight lines than circles, I thought I would have another go at this, a totally different way...

First, draw our annulus out in a straight line like this:

convert -size 45x40 xc:red xc:lime -size 270x40 xc:blue +append line.png

I sneakily made the lengths of the line segments add up to 360, so that there is one pixel per degree - for my simple brain to cope with :-) So, there are 45 px (degrees) of red, 45 px (degrees) of lime and 270 pixels (degrees) of blue, and they are all appended together with +append to make the line. Note that the first -size 45x40 setting persists until later changed, so it applies to both the red and lime line segments before I change it ready to apply to the blue.

Now we bend that line around a circle, like this:

convert line.png -virtual-pixel White -distort arc 360 result.png

You can also do it all in one go when you get used to the concept, like this:

convert -size 60x40 xc:red xc:lime xc:blue xc:cyan xc:magenta xc:black +append -virtual-pixel White -distort arc 360 result.png

You can add grey borders to your annulus segments like this:

convert -size 600x400 xc:red xc:lime xc:blue xc:cyan xc:magenta xc:black -bordercolor "rgb(180,180,180)" -border 20 +append -virtual-pixel White -distort arc 360 result.png

If you want everything on a transparent background, change all the white above to none.