Behavior at jump discontinuities

[hazelnb]

Consider the plot <Plot.OfX y={(x: number) => math.mod(x, 1)}/>. This of course has a number of jump discontinuities, but by default mafs joins discontinuities with a vertical line. Personally, I find this behavior unexpected and undesirable and would like to at least have the option to configure the discontinutiy behavior. Something like Mathematica's Exclusions and ExclusionsStyle seem appropriate for the existing Mafs API. I.e., the user provides Plot.OfX with a parameter which tells it where the discontinuities are and how they should be drawn.

To my mind, this should either be:

1. an array of x values of discontinuities
2. a function (x: number): boolean

I think the "jump" style that I'm hoping for can be accomplished by modifying the onPoint callback in sampleParametric to output an M command rather than an L command if the t value of the point is a discontiuity.

Let me know what you think! I love the library, and I'm using it to make companion interactive visualizations for my dissertation :)

[stevenpetryk]

Totally agreed. I think the function approach might be required for cases where there are infinite discontinuities, but instead of accepting a number and returning a boolean, it should accept a range and return a list (with the option to pass a static list, no function).

Mafs could use those values and:

• Evaluate continuity (or the user can explicitly specify)
• Ensure additional points are plotted near these important points (whether continuous or not)

In other words, a way to indicate important regions to plot.

[stevenpetryk]

Agreed also on the approach for jump discontinuities.

For holes, the best approach would probably just be a two <circle>s: one to mask off the function, and one to show the classic circular outline.

This means adding a mask to some functions which may have an effect on perf, but I doubt it.

[stevenpetryk]

Got a nice API for holes I think (not jumps yet, because the sample function scares me after not working with it for over a year).

I think this could be a bit more automated (like, in this case, it might be more convenient to pass in x = -0.5 and let Mafs figure out that it's NaN). However, I'm worried about imprecise computer math making that infeasible.

[stevenpetryk]

I think JavaScript's stupidity IEEE-754's limitations will prevent a lot of ergonomics here. But I'm okay with devs having to do the math to tell Mafs where to display these indicators.

[hazelnb]

Wow thanks for starting working on this so quickly, this looks great! I think your modifications for the "jump" api make sense, and if you're open to doing code review I would be happy to take a crack at implementing it.

As a mathematician, I swear Javascript makes some truly odd choices for built in operators that have caused some surprising and sneaky bugs for my viz. I have certainly not come to expect ergonomics haha.