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@rreusser

Hi Ricky: I really enjoy the notebooks you have shared on Observablehq. They are beautifully designed and your explanations are fantastic. Thank you for generously sharing your knowledge!

Recently, I have been studying your notebook Locally Scaled Domain Coloring Part 1: Contour Plots. However, there are some parts that I don't quite understand, so I was hoping to ask for your help.

I know that opening an issue to ask questions in your personal project may not be the most appropriate approach, but mathstodon has a limitation on the words I can send, and your twitter account seems has been deleted. If that is indeed the case, please allow me to extend my apologies to you.

Below are my questions:

The first part that I'm having trouble with is the following:

I can understand that both sides are using values in pixels, but I don't quite understand why it can be used to draw contours with uniform width. I understand that for a function f, (0.5-abs(fract(f)-0.5)) gives the distance between a pixel and contour lines $\{ f(x)=k\mid k\in\mathbb{Z} \}$. But it seems difficult to predict the change of (0.5-abs(fract(f) - 0.5))/fwidth(f) between different pixels? (Did I miss something?) So I don't quite understand why doing it as below can give contours with uniform width.

Another aspect that I don't quite understand is how the value of N_octave below is derived:

It seems in the code below this paragraph, $\nabla f$ is calculated using screen-space derivatives, while $f$ is a standard unit. I don't quite understand why this is being done. I apologize if these questions were explained in your article or if they are self-evident. My level of expertise in shaders is limited, and I have been unable to understand it for some time. So I hope you can provide some help and answer my questions. I'm sorry to bother you and thank you very much!