algorithmic modeling for Rhino

Dear Users,

I've been working on data tree selection rules this weekend and when 0.9.0063 is released (hopefully tomorrow, 4th November) the [Path Compare], [Tree Split] and [Replace Path] components will work slightly different from before. Sorry about breaking this, but it proved impossible to improve the selection logic with the fairly ambiguous notation that was implemented already.

Not every change is breaking though and I hope that most simple matching rules will work as before. There will be a McNeel webinar on Wednesday the 6th of November where I discuss the new selection rules (as well as path mapping syntax and relative offsets within one or more data trees). This will be a pretty hard-core webinar aimed at expert users. The event will be recorded so you can always go and watch it later. I figured I'd briefly explain the new selection rules on Ning before I release the update though.


Imagine we have the following data tree, containing a bunch of textual characters:

{0;0} = [a,e,i,o,u,y]
{0;1} = [ä,ë,ê,ï,î,ö,ô,õ,ü,û,ÿ,ý]
{1;0} = [b,c,d,f,g,h,j,k,l,m,n,p,q,r,s,t,v,w,x,z]
{1;1} = [ç,ĉ,č,ĝ,ř,š,ş,ž]

There are a total of four branches {0;0}, {0;1}, {1;0} and {1;1}. The first branch contains all the vowels that are part of the standard English alphabet. The second branch contains all non-standard vowels and branches three and four contain the standard and non-standard consonants respectively.

So what if we want to select from this tree only the standard vowels? Basically include everything in the first branch and disregard everything else. We can use the [Tree Split] component with a selection rule to achieve this:


This selection rule hard-codes the number zero in both tree path locations. It doesn't define an item index rule, so all items in {0;0} will be selected.

If we want all the vowels (both standard and non-standard), then we have several options:

{0;?}         = select all branches that start with 0

{0;(0,1)}    = select all branches that start with 0 and end in either 0 or 1

{0;(0 to 1)} =    ......................................... and end in the range 0 to 1.

Conversely, selecting all standard vowels and consonants while disregarding all non-standard character can be achieved with rules as follows:



{(0 to 1);0}

It is also possible to select items from each branch in addition to limiting the selection to specific branches. In this case another rule stated in square brackets needs to be appended:

{0;?}[0 to 2]

The above rule will select the first three vowels from the standard and the non-standard lists.

Basically, rules work in a very consistent way, but there are some syntax conventions you need to know. The first thing to realize is that every individual piece of data in a data-tree can be uniquely and unambiguously identified by a collection of integers. One integer describes its index within the branch and the others are used to identify the branch within the tree. As a result a rule for selection items always looks the same:

{A;B;C;...;Z}[i]              where A, B, C, Z and i represent rules.

It's very similar to the Path Mapper syntax except it uses square brackets instead of parenthesis for the index (the Path Mapper will follow suit soon, but that won't be a breaking change). You always have to define the path selector rule in between curly brackets. You can supply any number of rules as long as you separate them with semi-colons.

The index rule is optional, but -when provided- it has to be encased in square brackets after the path selection rule(s).

The following rule notations are allowed:

*  Any number of integers in a path

?  Any single integer

6  Any specific integer

!6  Anything except a specific integer

(2,6,7)  Any one of the specific integers in this group.

!(2,6,7)  Anything except one of the integers in this group.

(2 to 20)  Any integer in this range (including both 2 and 20).

!(2 to 20) Any integer outside this range.

(0,2,...)  Any integer part of this infinite sequence. Sequences have to be at least two integers long, and every subsequent integer has to be bigger than the previous one (sorry, that may be a temporary limitation, don't know yet).

(0,2,...,48)  Any integer part of this finite sequence. You can optionally provide a single sequence limit after the three dots.

!(3,5,...)  Any integer not part of this infinite sequence. The sequence doesn't extend to the left, only towards the right. So this rule would select the numbers 0, 1, 2, 4, 6, 8, 10, 12 and all remaining even numbers.

!(7,10,21,...,425)  Any integer not part of this finite sequence.

Furthermore, it is possible to combine two or more rules using the boolean and/or operators. If you want to select the first five items in every list of a datatree and also the items 7, 12 and 42, then the selection rule would look as follows:

{*}[(0 to 4) or (6,11,41)]

The asterisk allows you to include all branches, no matter what their paths looks like.

It is at present not possible to use the parenthesis to define rule precedence, rules are always evaluated from left to right. It is at present also not possible to use negative integers to identify items from the end of a list.

If you want to know more, join the Webinar on Wednesday!


David Rutten

Seattle, WA

Tags: cull, datatree, filter, rule, selection, tree

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Ah, I forgot to mention 4 shorthand rules for range notation:

< 4  Any number smaller than X. This notation is shorthand for [0 to 3]

<= 8  Any number equal to or smaller than X. This notation is shorthand for [0 to 8].

> 10  Any number larger than X. This notation is shorthand for [11 to infinity].

>= 5  Any number larger than or equal to X. This notation is shorthand for [5 to infinity].


David Rutten

Seattle, WA

Any chance of a % notation that allows for the selection of a modulo pattern of branchs/items i.e. {0;1}[%3] gets b,f,j,m,q,t,x

And {0;1}[%!3] gets you the flip side 

You can do that already using sequence notation though. But I can create a shortcut for sequence using a % symbol.


David Rutten

Seattle, WA

Ah.. I didn't fully appreciate what the sequence syntax was showing. The % as a shortcut would be good. 

Yup, all positive even numbers can be encoded as


All even numbers in between 100 and 1000000 are encoded by


I suppose there's no reason to not allow sequence notation 'to the left of' the numbers, but my parser can't handle that yet. When (if) I add support, you could encode all even numbers (positive and negative) with



David Rutten

Seattle, WA

{*}[(0 to 4) or (6,11,41)]

Is this the reason for changing to square brackets?

It is more in line with notation used elsewhere (i.e. mathematics and programming).


David Rutten

Seattle, WA

Oh, I though you asked "Is there a reason for changing....". My bad.

I did a few tests with people who know nothing of data-tree notation and they invariably wanted to use parenthesis for visually grouping rules together. Logically it makes no difference whether you always use '[ ]' instead of '( )' and vice versa, or indeed 'µ «'.  The change was made purely because it seemed humans were more comfortable with the new notation.


David Rutten

Seattle, WA

So will old grasshopper files which used these components still work?

The way I see it if you only used the paths selection rules in curly brackets then it will continue to work.

Yes, it was not possible before to have item index rules anyway, but if you were using square brackets before you'll have to switch to parenthesis now.


David Rutten

Seattle, WA

Also ranges were defined with hyphens before, but this clashes a bit with the ability to write negative numbers, so now you have to use the ' to ' notation similar to the way domains are written in Grasshopper elsewhere.

I used to allow both commas and colons as group separators, now I don't. There is no more room for ambiguity in my New World Order!


David Rutten

Seattle, WA



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