ay how many valid permutations exist.
But allow me to guesstimate a number for 20 components (no more, no less). Here are my starting assumptions:
Let's say the average input and output parameter count of any component is 2. So we have 20 components, each with 2 inputs and 2 outputs.
There are roughly 35 types of parameter, so the odds of connecting two parameters at random that have the same type are roughly 3%. However there are many conversions defined and often you want a parameter of type A to seed a parameter of type B. So let's say that 10% of random connections are in fact valid. (This assumption ignores the obvious fact that certain parameters (number, point, vector) are far more common than others, so the odds of connecting identical types are actually much higher than 3%)
Now even when data can be shared between two parameters, that doesn't mean that hooking them up will result in a valid operation (let's ignore for the time being that the far majority of combinations that are valid are also bullshit). So let's say that even when we manage to pick two parameters that can communicate, the odds of us ending up with a valid component combo are still only 1 in 2.
We will limit ourselves to only single connections between parameters. At no point will a single parameter seed more than one recipient and at no point will any parameter have more than one source. We do allow for parameters which do not share or receive data.
So let's start by creating the total number of permutations that are possible simply by positioning all 20 components from left to right. This is important because we're not allowed to make wires go from right to left. The left most component can be any one of 20. So we have 20 possible permutations for the first one. Then for each of those we have 19 options to fill the second-left-most slot. 20×19×18×17×...×3×2×1 = 20! ~2.5×1018.
We can now start drawing wires from the output of component #1 to the inputs of any of the other components. We can choose to share no outputs, output #1, output #2 or both with any of the downstream components (19 of them, with two inputs each). That's 2×(19×2) + (19×2)×(19×2-1) ~ 1500 possible connections we can make for the outputs of the first component. The second component is very similar, but it only has 18 possible targets and some of the inputs will already have been used. So now we have 2×(18×2-1) + (18×2-1)×(18×2-1) ~1300. If we very roughly (not to mention very incorrectly, but I'm too tired to do the math properly) extrapolate to the other 18 components where the number of possible connections decreases in a similar fashion thoughout, we end up with a total number of 1500×1300×1140×1007×891×789×697×...×83×51×24×1 which is roughly 6.5×1050. However note that only 10% of these wires connect compatible parameters and only 50% of those will connect compatible components. So the number of valid connections we can make is roughly 3×1049.
All we have to do now is multiply the total number of valid connection per permutation with the total number of possible permutations; 20! × 3×1049 which comes to 7×1067 or 72 unvigintillion as Wolfram|Alpha tells me.
Impressive as these numbers sound, remember that by far the most of these permutations result in utter nonsense. Nonsense that produces a result, but not a meaningful one.
EDIT: This computation is way off, see this response for an improved estimate.
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David Rutten
david@mcneel.com
Poprad, Slovakia…
Added by David Rutten at 12:06pm on March 15, 2013
t BBox will then be mapped relative to the UVW space of that box to the new target boxes.
Where your definition is slipping up is the data matching aspect of GH. You have two lists (that count). One list contains 100 items of target boxes and the other contains 2 items of geometry. GH defaults to the Longest List data matching
List A --> List B
Target Box A0 --> Cuboid
Target Box A1 --> Cylinder
Target Box A2 --> (Oops List B has run out of items. Now GH will repeat the last item = Cylinder)
Target Box A3 --> Cylinder
.....
Target Box J9 --> Cylinder
Solution
There are two approaches to rectify this the most logical would be to group the geometries into one object (What you had in mind with the bounding box) to do this use the Group Component on the Transform Tab > Utility Panel.
The other approach is far more common in GH mentality. Use the Graft, right click the G input of Morph and select Graft from the Context Menu. This places all of the items in the List on to separate branches. Creating a list of lists (although these new list only have one item). When GH now tries to data match them it will apply the whole of the first geometry list (Only the Cuboid) to all of the target boxes and all of the second list (Cylinder) to the target boxes again.
I hope this helps…
ther math and logic. i can usually conceptualise what i want to do and cobble some semi working thing together but don't know which components to use and how to patch it. so i'm super happy to have someone who knows what he's doing to find this interesting.
and i'm glad you mention the fanned frets again, there is one input parameter that's still missing for the multiscale frets to be fully parametric, it's the angle of the nut or which fret should be straight. it depends a bit on personal preferences and playing posture what is more comfortable. so being able to adjust this easily would be cool. again i have no idea how the maths for that work or if you can just rotate each fret the same amount around it's middle point. The input either as fret number (for the straight fret) or as a simple slider from bridge to nut should do as input setting.
Here are the two extremes and the middle ground:
i've been thinkin today while analysing your patches and cleaning up my mess what exactly the monster should do.
Here are the input parameters needed, i think it's the complete list
scale length low E string
scale length high e string
fret angle/straight fret
string width at nut
string width at bridge
number of frets
fretboard overhang at nut (distance from string to fretboard bounds)
fretboard overhang at last fret
string gauges
string tensions
fretboard radius at nut (for compound radius fretboard radius at bridge is calculated with the stewmac formula)
fretwire crown width
fretwire crown height
action height at nut (distance between bottom of string and fretwire crown top)
action height at last fret
pickup 1 neck position
pickup 2 middle position
pickup 3 bridge position
nut width
the pickup positions should be used to draw circles for the magnet poles on each string so they are perfectly aligned and can be used for the pickup flatwork construction. ideally they would need a rotation control aligning the center line of the pickup so it's somewher between the last fret angle and bridge angle. personally i do this visually depending on the design i'm looking for, some people have huge theories on pickup positioning but personally i don't believe in it.
that should result in everything needed to quickly generate all the necessary construction curves or geometry for nut/fingerboard/frets/pickups. this is the core of what makes a guitar work, the more precise this dynamic system is the better the guitar plays and sounds.
i posted another thread trying to understand how i could use datasets form spreadsheets,databse, csv to organize the input parameters. What would make sense for the strings for example is hook into a spreadsheet with the different string sets, i attached one for the d'Addario NYXL string line which basically covers all combos that make sense.
The string tension is an interesting one, and implmenting it would sure be overkill albeit super interesting to try. it should be possible to extrapolate from the scale length of each string what the tension for a given string gauge of that string would be so that you could say 'i want a fully balanced set' or 'heavy top light bottom) and it would calculate which SKU from d'addario would best match the required tension. All the strings listed in the spreadsheet are available as single strings to buy.
i'm trying to reorganize everything which helps me understand it. i just discovered the 'hidden wires' feature which is great since once i understood what a certain block does or have finished one of my own, i can get the wires out of the way to carry on undistracted. a bit risky to hide so many wires but it makes it so much easier not to get completely lost :-)
btw, the 'fanned fret' term is trademarked, some guy tried to patent it in the 80's which is a bit silly since it has been done for centuries. there is a level of sophistication above this as well, check out http://www.truetemperament.com/ and that really is something else. it really is astounding how superior the tuning is on those wigglefrets, the problem is that it's rather awkward for string bending and also you can't easily recrown or level the frets when they are used. …
e matching with a dedicated component which creates combinations of items. You can find the [Cross Reference] component in the Sets.List panel.
When Grasshopper iterates over lists of items, it will match the first item in list A with the first item in list B. Then the second item in list A with the second item in list B and so on and so forth. Sometimes however you want all items in list A to combine with all items in list B, the [Cross Reference] component allows you to do this.
Here we have two input lists {A,B,C} and {X,Y,Z}. Normally Grasshopper would iterate over these lists and only consider the combinations {A,X}, {B,Y} and {C,Z}. There are however six more combinations that are not typically considered, to wit: {A,Y}, {A,Z}, {B,X}, {B,Z}, {C,X} and {C,Y}. As you can see the output of the [Cross Reference] component is such that all nine permutations are indeed present.
We can denote the behaviour of data cross referencing using a table. The rows represent the first list of items, the columns the second. If we create all possible permutations, the table will have a dot in every single cell, as every cell represents a unique combination of two source list indices:
Sometimes however you don't want all possible permutations. Sometimes you wish to exclude certain areas because they would result in meaningless or invalid computations. A common exclusion principle is to ignore all cells that are on the diagonal of the table. The image above shows a 'holistic' matching, whereas the 'diagonal' option (available from the [Cross Reference] component menu) has gaps for {0,0}, {1,1}, {2,2} and {3,3}:
If we apply this to our {A,B,C}, {X,Y,Z} example, we should expect to not see the combinations for {A,X}, {B,Y} and {C,Z}:
The rule that is applied to 'diagonal' matching is: "Skip all permutations where all items have the same list index". 'Coincident' matching is the same as 'diagonal' matching in the case of two input lists which is why I won't show an example of it here (since we are only dealing with 2-list examples), but the rule is subtly different: "Skip all permutations where any two items have the same list index".
The four remaining matching algorithms are all variations on the same theme. 'Lower triangle' matching applies the rule: "Skip all permutations where the index of an item is less than the index of the item in the next list", resulting in an empty triangle but with items on the diagonal.
'Lower triangle (strict)' matching goes one step further and also eliminates the items on the diagonal:
'Upper Triangle' and 'Upper Triangle (strict)' are mirror images of the previous two algorithms, resulting in empty triangles on the other side of the diagonal line:
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