They seem to use a wide range to techniques depending on the image type and the maths is hidden inside the Wolfram language.
The HSF is used to limit the parts of individual curves to include in the calculation so is useful if you are trying to describe the shape using a single pair of parametric curves i.e. x=f(t) and y=g(t) which is what they have in the Einstein face drawing.
In your code you are creating the twitter outline using a series of arcs and using the ca array to control the portion of the circle to draw so you don’t have a need for the HSF.
The approach you take from here depends on whether you want to
- create a single pair of parametric equations . x=f(t) and y=g(t) to describe the whole contour
- describe the contour as a collection of circular arcs
If you want (1) then you need to modify the data so that the contour is roughly centred about the coordinates [0,0]. If the contour is offset from the origin then most values of the parametric parameter t would cause the HSV to output 0 which is hugely wasteful.
If you want (2) I suggest that you create a class that represents an arc it would have fields for the centre, radius and angle limits. Then have an array of arcs, this is better than having separate arrays for centre, angle limits and radii.
Personally I would go for (2) because it is easy to create a small sketch that takes an image and with some user input calculate the arc values need for the contour.
When drawing the arcs instead of translating the graphics matrix you calculate the arc cartesian values with
x = cx + radius * sin(t) and
y = cy + radius * cos(t)
it should be possible to generate the parametric equations for method (1), though I would need to think more on the actual algorithm.