Superformula | Hacker News Reader

Superformula

en.wikipedia.org

176 pointsGuiA65 comments

Aw, they're concave.

Many years ago, when Symbolics LISP machines roamed the earth, Alex Pentland wrote the first animation physics engine. Everything was a deformed superellipse, or rather the solid of rotation of one. You could apply a bend and a taper to a superellipse-generated solid. These were called "superquadrics".[1] I spent much time trying to come up with an analytical formula for the closest distance between two such objects, for collision detection. This was a dead end; polyhedra and meshes, although they required much more bookkeeping, were more useful in programs. Interest in superquadrics died out.

Did you intended to leave a reference for note [1]?

Sorry. [1]

[1] http://www.cs.toronto.edu/~dt/papers/pami91/pami91.pdf

Interesting. I'm still wondering about why we should use analytical solutions for shapes rather than meshes? What all is the general advantage? It seems like now we have enough computational power to not have to worry about such analytical solutions.

Also, what is the advantage of using the 'Superformula' to create most shapes as opposed to using some simple parametrization of meshes and enforcing symmetry or something of the like?

I am guessing this is being posted in relation to the new PS4 game coming out, "No Man's Sky". See controversial article about it here (published yesterday): http://www.pcgamer.com/company-claims-no-mans-sky-uses-its-p...

According to the Wikipedia page (which links to https://register.epo.org/application?number=EP05100648&lng=e...), the patent on the superformula was withdrawn in 2006 because the renewal fees stopped being paid. Seems pretty strange that Genicap could assert ownership of the formula when they let the patent expire.

It was transferred in early 2015 and the new owner started paying properly: https://register.epo.org/application?number=EP05100648&lng=e...

No Man's Sky was first publicly demoed in 2013. Seems suspect, this might be an opportunistic renewal hoping to collect rent.

It is obviously rent seeking.

How is that possible?

In that case, it feels like a loophole there people could just skip the annual fees until an opertunity to sue someone occurs and then pay for all the years at ones.

Feels also strange a patent that have been withdrawn could be sold.

just to point out, NMS isn't PS4 exclusive, it is releasing on PC as well.

Oh, I actually didn't realize that! Good to know! :)

Wait, mathematical functions are patentable!?

May not survive, but it's really their application that's patented. You can patent inventions and processes (how software patents came into being, and also how someone patented a "method for exercising cats" - a laser pointer mounted to a platform that moved it randomly).

In some countries you can't patent formulas or processes or even ideas...

And, IMO, that's how it should be in the US. But it's not, not yet at least.

In which countries? Seems like this particular patent is in the EU so that rules out the EU countries...

In India you can't patent software. It has to be hardware related. Indian Patent Office issued it this year.

Except that system can be counteracted by describing a CPU and then describing an algorithm. Richard Stallman had a talk about patents and mentioned the Indian system.

Can you please link the video?

It's this one I believe. I don't have a timestamp (and don't have 2 hours to go through it to find it), though I believe it is a response to a question at the very end. https://www.youtube.com/watch?v=aiKRt3-FbM0

Ideas aren't patentable at all.

In no country I guess. You have to transform your idea in something more concrete first. A piece of hardware, a process, a composition of matter you name it.

Imagine all those stupid ideas from just lying in the bed and thinking about being patented. Nothing would have been created but everything would have been patented. That's worse than patenting a formula or a piece of software.

One can argue that that thought requires effort as well as a number of other preconditions which are not guaranteed to occur without heavy investment. Not all ideas are equal. Some ideas may be just a mindless combination that can be otherwise obtained from a machinal set up, whereas others can be the result of years of work or of some genius visionary. What I consider necessary is a rating system and a qualification threshold for what is worth to be considered a thing that can be claimed and what can not. I'm aware that a deep rabbit hole is opening here around this issue, but the question is if it's worth having it nevertheless compared to what we have now.

> also how someone patented a "method for exercising cats"

It appears that USPTO has issued it several times [0]:

  6505576 Pet Toy
  6557495 Laser Pet Toy
  6651591 Automatic laser pet toy and exerciser
  6701872 Method and apparatus for automatically exercising a curious animal

[0] http://www.freepatentsonline.com/crazy.html

Idea, which is 50/50 art and political action: we patent a method for submitting patents, involving computers and the internet. It acts to block people from submitting new patents and so bring the whole irrationality of the US patent system to the foreground.

Ducking Genius!

You could probably patent a reddit comment in the US...

Whether it'll stick once someone challenges it is another question.

This particular patent is European...

If it were developed today, even the numeral system [0] would be patented.

[0] https://en.wikipedia.org/wiki/Numeral_system

Software is patentable, genes are patentable, so why not?

> Currently, the superformula is patented by Gielis, [2] but the patent was withdrawn in 2006 because of the patent fees not being paid.[3]

I did not know you could patent a mathematical formula.

no doubt it was something like "a system and method for generating natural shapes"

"Method and apparatus for synthesizing patterns"

https://www.google.com/patents/EP1177529B1?cl=en

You can't, only its application. Genicap's patent does cover application in software though.

Even patenting a formula's application is becoming more restricted. In Australia and the US, the two relevant tests seem to be whether the formula does something a human can't, and whether the formula is used to 'improve' the operations of a computer or machine (e.g. if it made your hard drive faster or controlled a robotic arm).

I had to look into this regarding an algorithm we're building and whether it's patentable. If your formula is a mere scheme or method implemented in a computer, it's likely to be rejected. The following links add detail:

http://www.fisheradamskelly.com.au/2015/12/full-federal-cour...

https://en.wikipedia.org/wiki/Alice_Corp._v._CLS_Bank_Intern...

http://www.ipwatchdog.com/2016/05/13/federal-circuit-says-so...

In most jurisdictions you can't really patent the use of an abstract mathematical formula on a computer with no gain, but that's something the law has only caught up to in the last decade. The patent is most likely invalid in the EU and US but was approved way back when those standards for invalidity didn't exist in their current forms. Of course, a court wouldn't need to be bound by the original decision of the examiner and would determine validity based on current case law and practice.

You can't. On one, Gielis even put the equation in claim 1 but somehow they got the village idiot for an examiner.

http://www.google.com/patents/US7620527

Patent 5533051 [0] is a classic. Some quotes:

  A second aspect of the present invention which further enhances
  its ability to achieve high compression percentages, is its
  ability to be applied to data recursively. Specifically, the
  methods of the present invention are able to make multiple
  passes over a file, each time further compressing the
  file. Thus, a series of recursions are repeated until the
  desired compression level is achieved.

  ...

  Thus, one skilled in the art can see that by keeping the
  appropriate counters, the direct bit encode method of the
  present invention is effective for reducing an input string by
  one bit regardless of the bit pattern of the input string.

What would one say about the examiner now?

[0] https://www.google.com/patents/US5533051

Especially one that is obvious. I remember drawing similar things using a TI-84 in high school math, probably when we learned about polar coordinates.

And let's not forget there's an implementation on Wikipedia.

Well in this case the developer of NMS specifically said he was struggling with planet generation until he discovered that exact formula, so you can understand why there is _some_ (not a lot mind) reasoning for the company who owns this patent (who are making a game involving it iirc) are making this claim. Judging by their statement though it seems they want more of a 'partnership' type thing (knowledge sharing, ride on NMS coattails for a bit etc)

Not in EU. Such a patent is invalid, but if they managed to get it approved by the EU patent bureau (which is known for accepting such baseless claims) then they have a patent that needs a court action to be invalidated. In the meantime, it is assumed to be valid.

But it seems to be an EU patent based on this link (on the Wikipedia page) https://worldwide.espacenet.com/publicationDetails/biblio?CC...

Yes, this patent is supposed valid but any court would invalidate it. The EU patent bureau has produced a lot of these "method and apparatus". Turns out that one can't patent algorithms, but one can patent the machine composed of a computer running such an algorithm. It is a known loophole and I don't think any of these patents hold up in court.

Actually, I am not even sure that they can enforce anything against a software company with this patent. Someone who distributes a software does not produce an "apparatus" so I am not sure if they can even launch a procedure based on that patent.

Play with the superformula in d3.js: http://bl.ocks.org/mbostock/1021103

Also, tweening between superformula shapes in d3.js: http://bl.ocks.org/mbostock/1020902

If the superformula itself is patented, what protection does that give to a generalization of it, like replacing m with y & z as presented in the article?

None really, it is just prior art. The modification is substantial enough.

Caveat: not a patent lawyer.

> You can, however, patent the practical application of a mathematical formula

> Genicap's patent calls out the formula's potential use in "graphics programs (e.g., 2D, 3D, etc.); CAD software; finite element analysis programs; wave generation programs; or other software," it doesn't specifically mention game design (procedurally generated or otherwise).

http://arstechnica.com/gaming/2016/07/no-mans-sky-faces-pote...

How hard is it to invert? e.g. given a set of points along a particular curve, how difficult is it to find the values of the 6 parameters that generated it?

If you know a,b,m,n1,n2,n3, and use sufficient points, you may be able to get an interpolated approximation.

In general, one can fit many such curves through a finite set of points. http://math.stackexchange.com/questions/65970/can-a-function...

A question originally asked by Leibniz to determine the measure of usefulness of a law. https://plus.maths.org/content/omega-and-why-maths-has-no-to....

If you don't have the 6 parameters, good luck. A unique inverse is defined only for injective functions.

Someone experimented with this. See the links at the bottom of the Wikipedia article. This seems misguided to me -- why use a curve family when fitting is so hard -- but it has been done.

For even more gielis visualization pleasure, check this out: https://www.thregr.org/~wavexx/software/gte/

This reminds me of the polygon tool of Inkscape .

Video : https://www.youtube.com/watch?v=pBLy9KDPMHk

> While the above equation, dubbed the "superformula" by Gielis (2003), is clearly capable of describing a number of diverse biological shapes having a variety of symmetries, it seems unlikely that this formula has any particularly fundamental biological significance (Peterson 2002, Whitfield 2003) beyond as a possibly convenient parametrization. [1]

I'm not a huge fan of these random parametrizations; overall, it seems like they have no physical significance (yay! it can describe a bunch of things! I can do that anyways by picking a linear space with enough dimensions or a nice non-linear kernel and projecting into the first few principal components, and best of all, it's going to be fit directly to my problem). I'd like to be enlightened as to why this is such a big deal and why anyone would do this instead of parametrization of meshes for procedural generation? It seems a few comments here are referencing NMS, hence the question.

[1] http://mathworld.wolfram.com/Superellipse.html

Seems kind of like taking the fourier transform to the polar space.

If I made a formula that is more generalized, patents still apply?

Here it is in complex numbers:

    p = (r1*cos(ph1 + th) + 1.0*I*r2*sin(ph2 + th))*
   (Abs(cos(m*th/4)/a)**n2 + Abs(sin(m*th/4)/b)**n3)**(-1/n1)

This can produce a number of interesting shapes that original Gielis transforms can't.

I wonder if there is a distance function to it, so you can render it in 3D using sphere tracing.

This Shadertoy (https://www.shadertoy.com/view/4llGWM) uses sphere tracing it but doesn't use a real distance function, the author asks the same question.

For any D3 users, there is a superformula plugin. Very handy. http://bl.ocks.org/mbostock/1020902

The variations are interesting in relation to the approach and recession of the point on the line from the origin.

This is my take away:

PolarPlot[(Abs[Cos[2(t - Pi/2)/4]] + Abs[Sin[44(t - Pi/2)/4]])^(-1/(-0.2)), {t, 0, 2*Pi}, PlotRange -> {{-20, 20}, {-5, 32}}, PlotStyle -> Darker[Green, 0.2], PlotTheme -> "Marketing"]

Can we formulate Mobius Strip using this?

very cool

Bang !

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