Show HN: Smooth.js - Turn arrays into smooth functions | Hacker News Reader

Show HN: Smooth.js - Turn arrays into smooth functions

github.com

46 pointsmistercow27 comments

Beautiful. Will definitely use this for a project I'm working on - specifically to get around the common issue that many canvas based drawing tools run into. Im curious to see how it performs. Thanks!

I'd love any feedback you have. I haven't focused on performance much yet (although I think I've made reasonable design decisions in general). I think there's some caching I can do on cubic splines which might be beneficial, but I'll obviously need to do some benchmarks to see if they're worthwhile.

Neat looking library, but I have a little syntax question-- what's the reason for using ugly Cish constants like Smooth.METHOD_CUBIC? Surely it would work just as well (and be more JSish) to say something like

  Smooth points,
    method: 'cubic' 
    clip: 'periodic'
    cubicTension: 'catmull-rom'

I can't give any really strong justification, besides to say that C-style constants make me feel warm and safe. My weak justifications are that I find having my constants declared in one place helps me to remember to handle all of them, and that it helps slightly with auto-complete.

But there is a good reason in the case of the cubicTension constants: those aren't enums, but actual values. You can put any cubicTension parameter you want between 0 and 1.

Totally get that-- if it's the style you're comfortable with, go for it. Hope I didn't sound critical, just curious.

Although if I may, there is a potential benefit to using strings there in that it lets you get rid of the switch statement entirely:

  unless config.clip of ClipHelpers
    throw new Error "No clip mode '#{config.clip}'. Available modes are #{(k for k of ClipHelpers).join(', ')}"
  clipHelper = ClipHelpers[config.clip]

This could also make it easy for a user to add helpers at runtime. Maybe overkill for this, just something to keep in mind.

Very well done. Simple and effective. This will be useful on a surprising number of my projects.

Cool. You may want to add more interpolants, for instance a Fourier (for regularly spaced points) or (even better, but not regularly spaced) Chebyshev interpolation would be useful, highly accurate, and can be computed fast (N log(N))

I definitely want to add more interpolants. The only limitation really is that it has to be possible to do the calculation lazily. As I understand Fourier interpolation, this should be fine with that. I am less familiar with Chebyshev interpolation.

For Fourier, given an N-dim vector you would compute the N Fourier coefficients in Nlog(N) time, stored in memory, then whenever a new x-value is requested it takes linear time to evaluate the point (add up the basis vectors with the stored coefficients).

Chebyshev polynomials are more accurate than Fourier. In fact they are the most accurate interpolating polynomials in general. They're not as wildly known, but often used in numerical analysis. The problem with Fourier is that if your function is not periodic, the coefficients do not converge quickly, making the interpolant less accurate for a given number of nodes. Chebyshev gets around this problem, but instead of using equally spaced points, points are spaced out along the uneven "Chebyshev nodes". So to get an interpolated point, say 2.5, 2.5 no longer falls halfway between the 2nd and 3rd Cheb node, you would first have to figure out the value of 2.5 in the nonuniform Chebyshev distribution of points, and then compute the interpolating value in linear time at this point.[1]

Both Chebyshev and Fourier are "global" interpolants. As opposed to cubic splines and your other ones. If you change a single value in your vector, the entire interpolant is affected and needs to be recomputed.

[1] http://en.wikipedia.org/wiki/Chebyshev_polynomials

> For Fourier, given an N-dim vector you would compute the N Fourier coefficients in Nlog(N) time

But Nlog(N) only works for certain values of N, right (like powers of two)? I guess for other cases, we could use the clipping method to dictate behavior, but that doesn't feel great.

Here's a python version, if anyone wants it. I know that I've had to do interpolation in the past, and this would have been nice to have.

http://pastebin.com/fqNRNcBP

Sorry to nitpick, but it's not smooth if it has sharp corners (not differentiable).

Yes, that's true, but I feel that the nearest neighbor and linear modes are useful even if they do clash slightly with the name. You'll note that the default configuration does, in fact, produce a smooth function.

Even cubic splines are not smooth. "Smooth" has very well defined meaning in math -- it means precisely "infinitely many times differentiable". Cubic splines are differentiable only finitely many times (only twice, actually).

Yes, but "smooth" also has a well defined meaning in everyday language. The word "smooth" is commonly used when talking about splines and interpolation.

really cool. recently was frustrated doing similar interpolation- this is a cool api though, wish i had done it this way. would be fun to support other data as well, ie. hex math for gradients. thanks!

> hex math for gradients

Ooo that's a good idea. Of course, you can use 3D vectors for rgb values to get much the same effect.

Very cool, this reminds me of D3.scales https://github.com/mbostock/d3/wiki/Scales good work!

Nicely done. I have implemented the Linear part of this already but this will save me from having to do the rest. Thanks!

I feel like the .js suffix is meant to imply this is JavaScript code, but it is actually CoffeeScript. They are not the same.

Why is it not named Smooth.coffee?

Because it compiles to js and can run in either.

There's no such thing as "running CoffeeScript".

> The golden rule of CoffeeScript is: "It's just JavaScript".

You can always run coffee at the command line.

I considered naming it that, but ultimately decided that the fact that it's written in CoffeeScript is irrelevant. It's a JavaScript library; it's meant to be used with JavaScript (which of course implies that it's meant to be used with CoffeeScript), but it happens to be written in CoffeeScript.

And there is every possibility that it could get rewritten in JavaScript. Or it could be rewritten in something else that compiles to JS, if something comes along to which this task is well-suited. The implementation can change, and the name should remain appropriate. What will not certainly change, however, is the environment in which this is intended to be used.

Hope that makes sense.

I guess so. I wouldn't mind if it was smooth.coffee (maybe other people would?), but I can see your rationale.

It seems like saying something could be cross-compiled doesn't really mean it is in that other language, but again, people seem to think of CoffeeScript as different.

Also, sorry for forgetting, but thanks for making this! It looks pretty awesome.

Do you have any plans for extrapolation?

My first thought was "Awww, it's in CoffeeScript" :) It looks like there in fact is an issue with how people (at least me ;) ) react to CoffeeScript... I wonder if you have real control over the performance. Anyway - it's a great idea and I think the name is appropriate.

BTW. Yesterday I needed to mirror some sequence and I ended up using Math.sin()

> I wonder if you have real control over the performance.

In general, the mapping between CoffeeScript and JS is so trivial that it's hard to think of places where there could be a lack of control. Of course, if that were ever an issue, CoffeeScript lets you directly embed JS by surrounding it in backticks.

I also had a bad gut reaction to CoffeeScript initially, and I won't pretend it doesn't have drawbacks; the powerful, in-browser debugger that it desperately craves still hasn't yet been written, after all. But it really gets right what so many compile-to-javascript languages have gotten wrong in the past. At the very least, it is hands down the easiest way to sketch an idea for JavaScript. I just never end up feeling like I would gain anything significant by porting that sketch to native JS.

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