Module 8: Circles

Mix.install([
  {:vega_lite, "~> 0.1.10"},
  {:kino_vega_lite, "~> 0.1.13"}
])

Preparation

Lets take a look at a definition of a circle type that covers the center point and radius:

defmodule Circle do
  defstruct [:x, :y, :r]
end

This allows us to create instances of circles:

circle = %Circle{x: 1, y: 2, r: 3}

We can access the fields as with any other struct:

"The circle has a radius of #{circle.r} and its center is at (#{circle.x}, #{circle.y})."

Exercise

Lets use this type to declare a number of circles:

circles = [
  %Circle{x: 0, y: 0, r: 1.13137},
  %Circle{x: -2, y: -3.5, r: -0.7071},
  %Circle{x: 2.5, y: 3, r: 1.4142},
  %Circle{x: -4, y: -2.5, r: 0.7071},
  %Circle{x: -2.5, y: 3, r: 1.4142},
  %Circle{x: 0, y: -4, r: -0.7071},
  %Circle{x: 2, y: -3.5, r: 0.7071},
  %Circle{x: 0, y: 0, r: -4.596},
  %Circle{x: 4, y: -2.5, r: 0.7071},
]

Some of these circles have a negative radiuses. That is no good. In the next cell, write code that flips the negative radiuses (by multiplying them by $-1$). Rebind the circles variable to the resulting data structure.

Write some code that calculates the total area of these circles.

The area of a circle with radius $r$ is:

$ \hspace{20mm} A(r) = \pi r^2 $

Write a function that takes a radius as a single input (lets call it $r{in}$) and returns another raidus (we will call that one $r{out}$). You decide whether to make the function anonymous or place it in a module. Make sure that the area of a circle with a radius of $r{out}$ is twice as large as one with a radius of $r{in}$. In other words, make sure that:

$ \hspace{20mm} A(r{out}) = 2 \cdot A(r{in}) $

For this, you may want to try out the built-in :math.sqrt function that calculates the square root of its parameter.

Use the function you have just defined to double the area of each of the circles in the variable circles and rebind this variable to the resulting data structure:

The distance $D$ between the points $P_1 : (x_1, y_1)$ and $P_2 : (x_2, y_2)$ can be calculated using the Pythagorean theorem:

$ \hspace{20mm} D = \sqrt{(x_2-x_1)^2 + (x_2-x_1)^2} $

Implement a function that takes two circles as parameters and returns the distance between their centers. You decide whether it be an anonymous function or one that recides in a module.

Now, calculate the largest distance between the centers of any two circles in circles.

Hints:

• In order to find all combinations of elements from two lists, one can place one call to Enum.map inside of another.
• The List.flatten function will convert a list of lists to simply a list of all the values.
• The Enum.max function will give you the largest element of a list.

The time has come to plot these circles. I have written some code that can plot data, but unfortunately this code doesn’t know how to work with structs. Instead, it needs a list of maps where alle keys are strings. So, your job is to preprocess the data in circles in such a way that it adheres to the format supported by my code. Bind a variable called data to the resulting data structure.

alias VegaLite, as: Vl

Vl.new(width: 400, height: 300)
|> Vl.data_from_values(data)
|> Vl.mark(:point)
|> Vl.encode_field(:x, "x", type: :quantitative)
|> Vl.encode_field(:y, "y", type: :quantitative)
|> Vl.encode_field(:size, "r", type: :nominal, title: "Radius")

Next step …

When you have completed this exercise you can continue here.