Infinity

Replies to This Discussion

Permalink Reply by David Rutten on July 11, 2013 at 9:54am

Infinity is not a valid number and you cannot do any math with it. It's just there as a slightly more meaningful version of the NaN constant.

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David Rutten

david@mcneel.com

Tirol, Austria

Permalink Reply by Richard Schaffranek on July 11, 2013 at 10:21am

At the moment I am outputting -1 for non reachable nodes when preforming Dijkstra's algorithm on a graph, but +infinity would be more meaningful. 

So for me the question is how Grasshopper deals with infinity (Galapagos seams to have a problem but beyond that?). 

e.g.:

0 < Double.PositiveInfinity  =  ?

Double.MaxValue < Double.PositiveInfinity  =  ?

x = new Grasshopper.Kernel.Types.GH_Number(Double.PositiveInfinity) 

sorry for all the strange questions lately.  As summer is starting and all the students are gone, I spend my time reworking/adding new components/improving the SpiderWeb plugin. Hopefully making it better and maybe easier to understand.

thx

Richard

Permalink Reply by David Rutten on July 11, 2013 at 11:09am

The rules regarding Double.PositiveInfinity and Double.NegativeInfinity are .NET rules. If you want to know how infinities behave in equality and smaller/larger than operators, just try them:

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David Rutten

david@mcneel.com

Tirol, Austria

Permalink Reply by Richard Schaffranek on July 12, 2013 at 3:09am

Did start testing +/-Infinity:

Found a few things that are inconsistent to msdn / Rhino.Geometry. .... .

Attached a file with things I tried. 

Some outcome:

1. The subdivision by 0 would be nice if it would return +/- infinity instead of <null>.

2. As +Infinity <= +Infinity results in TRUE, I don't see why the "Include" component returns false when checking if +infinity is within the boundaries of the domain -Infinity to + Infinity

3. I do not understand why Galapagos has problems dealing with infinity. I do understand that as return value of a fitness function, infinity is rather unfeasible but as it can be used in comparing two numbers it shouldn't be a problem? 

Attachments:

• Infinity Test.gh, 32 KB

Permalink Reply by David Rutten on July 12, 2013 at 7:05am

Compared to infinity everything else might as well be zero. That is probably why Galapagos can't handle it. Infinity really isn't a number and trying to treat it like one will result in all kinds of paradoxes and weird arithmetic exceptions.

If a domain or a point or vector contain an infinity they are considered to be invalid. This is a RhinoCommon enforced rule.

Also note that x/0 where x > 0 does not equal +infinity. This operation has no solution. The best you can say is that x/y where y approaches zero tends to infinity.

If you have a fitness function which sometimes awards +infinity or -infinity to a certain phase-state then you'll need to improve your function to return an actual number.

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David Rutten

david@mcneel.com

Tirol, Austria

Permalink Reply by Richard Schaffranek on July 12, 2013 at 8:34am

Do know that infinity is a little tricky in and brings a lot of problems. But e.g.:

"Also note that x/0 where x > 0 does not equal +infinity. This operation has no solution. The best you can say is that x/y where y approaches zero tendsto infinity." 

Yes, mathematically speaking a division by 0 is not defined but the .NET environment handles it differently as pointed out on the linked page above.

"If a domain or a point or vector contain an infinity they are considered to be invalid. This is a RhinoCommon enforced rule."

As shown in the sample I attached I can e.g. create a valid domain from -infinity to +infinity but +infinity is not in the list. This is a little odd.

So I guess to answer the question from the beginning, there are a lot of problems with infinity such as inconsistencies between .NET and GH, and general difficulties with the value itself.

Permalink Reply by David Rutten on July 12, 2013 at 9:42am

I do agree that as long as I support -infinity and +infinity I should make the comparison and smaller/larger than logic work and maybe even look into the stuff to do with Interval inclusion. 

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David Rutten

david@mcneel.com

Tirol, Austria

Permalink Reply by Richard Schaffranek on May 23, 2014 at 9:49am

I don't want to start the discussion about the meaning of infinity again  but I noticed something more that if using a number parameter to store (+Infinity)  and making this parameter part of a cluster -> Rhino crashes.

However it would be great if the issues with infinity could be dealt with,

thx Richard

Permalink Reply by David Rutten on June 6, 2014 at 4:53am

Adjusted the Smaller Than, Larger Than and Equals components to take infinities into account:

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David Rutten

david@mcneel.com