hat differ in shapes, sizes and height the facade would be a mess. Some spaces need some light while other can't have any. I would like to have full freedom of creation inside the building, to make it as functional as possible. Thats why i decided the parametric "skin" solution would be best. Since the location has industrial past (factories made of brick) i decided that brick would give interesting result.
I tried creating the definition on my own but since i lack skill in GH i got some problems (especially multiplication of bricks and the diffrence between each "level" (half a brick on y axis) caused problems for me.
I post my simple sketch explaining the idea of definition i would like to create (sorry about quality):
1 - Brep - I would like to use 25x12x6cm (classic brick) but as well experiment with diffrent shapes - like the one on the right with hole inside - that would give more light. Thats why i think the best solution would be using brep for this definition.
2- Multiplication - biggest problem for me - I don't know how tall the wall would be, what will be the final shape of Brep (brick) and that's why i would like to manipulate this with sliders as well. All the walls are flat (maybe it would be easier to use surface?). As i managed to multiply the bricks easy way i don't know how to gain control over height of the wall - for example that it is 30 bricks high, but has each second row moved on x axis by the distance of 1/2 brick. I tried using Series but with no success. Could you help me with that please?
3 - Rotation - i would like to use image sampler for that so i can "paint" where i want more sun and where i dont need it at all (black and white). The rotation has to be limited to 180 degrees as well. Obviously i didn't get here yet, but i never used image sampler so if you could give me some advice how to use component and how to create such images i would be really grateful.
4 - More of a concept thing - since the connection angles differ from 90 degrees i will have to figure out how to connect the parts of the wall at sides ;).
I would like to ask you for help with the defintion, since i am totally stuck at step 2. I post what i came up with so far. Thank you for your time and help!
PS. I post an image that is pretty similar to one of options i would like to check for my building.
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bi-directional link, the link is unidirectional (downflow only), because of the use of proxies.
Matrix transforms and persistent constraints: I don't think this is true. The parts can have mates to other parts that preserve geometric relationships like 'coincident' , 'aligned' etc. These are essentially bi-directional. GH's algorithmic approach does not do relationships in the same / flexible way. In GH, the 'relationship' has to be part of the generation method that dependent on the creation sequence. I.e. draw line 2 perpendicularly from the end of point of line 1. If you are thinking about parts or assemblies sharing, or referencing parameters as part of the regen process, this is also possible. iLogic does this, and adds scripting. So does Catia. Inventor/iLogic can also access Excel and have all the parameter processing done centrally, if required.
Consequently, scripting the placement of components is irrelevant in GH, unless you decide that each component needs to be contained in its own separate file.
I wouldn't be too hasty here. Yes, you are right about compartmentalisation. I think this needs to happen with GH, in order to deal with scalability/everyday interoperability requirements. Confining projects to one script is not sustainable. MCAD apps have been doing this for ages with 'Relational Modeling'.The Adaptive Components placement example illustrates that it is beneficial to be able to script some 'hints' that can be used on placement of the component. Say, if your component requires points as inputs, then its should be able to find the nearest points to the cursor as it moves around. I think Aish's D# / DesignScript demo'd this kind of behaviour a few years ago. Similarly, Modo Toolpipe reminds me how a lot of UI based transactions can be captured as scripts (macro recorder etc). Allowing this input to be mixed in and/or extended by GH I think will yield a lot of 'modeling efficiency' around the edges. This is a (mis)using GH as an user-programmable 'jig' for placing/manipulating 'dumb' elements in Rhino. It may even give the 'dumb elements' a bit more 'intelligence' by leaving behind embedded attributes, like links to particular construction planes etc.Even if we confine ourselves to scripting. GH is a visual or graphic programming interface. A lot of 'insert and connect' tasks can be done more easily using graphic methods. If we need to select certain vertices on a mesh as inputs for, say, a facade panel, its going to be quicker to do this 'graphically' (like the AC example), then ferreting out the relevant indices in the data tree et al. The 'facade panel' script would then have some coding to filter/prompt the user as to what inputs were acceptable, and so on.
This also brings up the point that generating components and assemblies in MCAD is not as straightforward. In iParts and iAssemblies, each configuration needs to be generated as a "child" (the individual file needs to be created for each child) before those children can be used elsewhere.
Not sure what you mean here. If the i-parts are built up using sketches /profiles or other more rudimentary features (like Revits' profile/face etc family templates) then reuse should be fairly straight forward. I suppose you could make it like GH scripting, if you cut and paste or include script snippets that generate the desired Inventor features.
One of the reasons why the distributed file approach makes perfect sense in MCAD, is that in industry you deal with a finite set of objects. Generative tools are usually not a requirement. Most mechanical engineers, product engineers and machinists would never have any use for that.
I don't think this is true. Look at the automotive body design apps, which are mostly Catia based. All of the body parts are pretty much 'generative' and generated from splines, in a procedural way, using very similar approaches to GH. Or sheet metal design. It's not always about configuration of off-the-shelf items like bolts. And, the constraints manager is available to arbitrate which bit of script fires first, and your mundane workaday associative dimensions etc can update without getting run over by the DAG(s) :-)
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m
-Area of blue line: min. 80% of the rectangel a x b
-Max. hight h of the top point: h,max = a
-Min. Volume between rectangel a x b and membrane: 500 m3
Can anyone help me?…
ou will see all of the available components on a ribbon at once so there is no need to keep clicking drop down menus.
It's all about discoverability with GH. What if you're a beginner and don't know about the Create Facility (dbl click canvas) how can you find Extr?
Even if you hover over every component or use the drop down lists you will not see the name Extr appear anywhere.
Sure it makes sense that Extr is short for Extrude but it's also the Nick Name of Extrude to Point component
So you can easily miss the fact that one has a Distance Input verses a Point Input.
I think I made the move to Icons around about the move from version 0.5 to 0.6, possibly before. I initially thought that I would go back to text because I loved the mono chromatic look of the text but I soon realised that Icons were the way forward. The greatest benefit is speed. You don't need to digest and decipher every component (which is written 90 degrees to the norm).
I'm not saying you should move to Icons forthwith but at least consider that once you have a better knowledge and understanding of GH, Icons will set you free.
My top ten tips that I would highly recommend to anyone wanting to better themselves with GH.
1) Turn on Draw Icons
2) Turn on Draw Fancy Wires
3) Turn on Obscure Components
4) Use the Create Facility like a Command Line eg "Slider=-1<0.75<2" or "Shiftlist=-1"
5) Use Component Aliases to customise your use of the Create Facility eg giving the Point XYZ component an alias of XYZ will bring it up as the first option on the Create Facility as opposed to the other possibilities.
6) Try to answer other people's questions even if it's not relevant to your own area. By looking into solving a problem outside of your comfort zone and then posting your results it is very rewarding but it also lets you see the other approaches that get posted in a new light.
7) Take the time to understand Data/Path structures.
8) Buy a second monitor - There is nothing that can compare to real estate when working in Grasshopper.
9) Read Rajaa Issa's Essential Mathematics
10) Pick a panel in a tab on the ribbon and get to know every component inside and out and then move on. Start with the Sets Tab > List Panel…
onents (radiation, sunlight-hours and view analysis) which let you study the effect of the orientation of your building and the analysis result. When you come to a question similar to "what is the orientation that the building receives the most/least amount of radiation?" is probably the right time to use this component.
HOW?
I'll try to explain the steps using a simple example. Here is my design geometries. The building in the center is the building to be designed and the rest of the buildings are context. I want to see the effect of orientation on the amount of the radiation on the test building surfaces from the start of Oct. to the end of Feb. for Chicago.
First I need to set up the normal radiation analysis and run it for the building as it is right now. [I'm not going to explain how you can set up this since you can find it in the sample file (Download the sample file from here)]
Now I need to set up the parameters for orientation study using orientationStudyPar component. You can find it under the Extra tab:
At minimum I need to input the divisionAngle, and the totalAngle and set runTheStudy to True. In this case I put 45 for divisionAngle and 180 for the totalAngle which means I want the study to be run for angles 0, 45, 90, 135 and 180.
[Note1: The divisionAngle should be divisible by totalAngle.]
[Note 2: If you don't provide any point for the basePoint, the component will use the center of the geometry as the center of the rotation.]
[Note 3: You can also rotate the context with the geometry! Normally you don't have the chance to change the context to make your design work but if you got lucky the rotateContext input is for you! Set it to True. The default is set to False.]
You're all set for the orientation study, just connect the orientationStudyPar output to OrientationStudyP input in the component and wait for the result!
The component will run the study for all the orientations and preview the latest geometry. To see the result just grab a quick graph and connect it to totalRadiation. As you can see in the graph 135 is the orientation that I receive the maximum radiation. Dang!
If you want to see all the result geometries set bakeIt to True, and the result will be baked under LadyBug> RadaitionStudy>[projectname]> . The layer name starts with a number which is the totalRadiation.
Mostapha…
her people) a tremendous amount of time creating them by hand. Dog Treat was far from perfect, however it was good enough to use almost daily.
Three years is a long time. Since 2016 my Gh knowledge has expanded and I’ve seen how dodgy some of the scripting is. With this in mind I started work on a new build. Many things have been tweaked and some things have been rebuilt from the ground up.
Everything has been designed to be leaner and be a general solution to the problem of creating dog bone corners on geometry for quick, efficient and safe CNC fabrication.
Some of these things are:
Adding prompts about user geometry to make them aware about open curves, varying curve heights and if their geometry had been altered (mostly removing unnecessary points on curves).
Smooth Transfers. If you’re in a rush and need to speed through cutting, smooth transfers mean that a lead in geometry is now created alongside the actual dog bone arc. This means the router bit doesn’t have to come to a minute stop at every corner. This is turned on by default.
Acute Angle Condition If the angle between the two curves adjacent to a dog bone point is acute, previously the dog bone corner was useless. This was because the distance between the end points of the dog bone arc were less than the diameter of the router bit. There are many ways this condition could be addressed. I chose to circumscribe a larger arc based on the original angle between the adjacent curves. While it removes more material from the corner, it minimises tool wear and any potential for material to burn.
Single Curve A single curve can now be input into Dog Treat. It will be output with both internal and external treatments.
I’ll continue to update Dog Treat as the need arises, it’s become somewhat of a hobby now. Maybe one day it will become part of a Plug-in… once I learn to code it though!
Happy Treating!
Hi Everyone,
Here's a tool I've been working on for the past 4 months or so in my free time. It's a dog bone corner generator, however it's a little different to some of the existing ones. It's designed to be used for large amounts of geometry and as such, it avoids using any curve boolean operations that are computationally taxing. You don't have to split your curves up into internal and external lots either, it works it all out so you can be lazy. I've also incorporated Lunch Box's Object Bake Component for a one click operation that bakes geometry back out to Internal and External profile layers.
Let me know how it goes, will update where necessary.
Best,
Darcy
Change Log
06/11/19 - Version 2.0 SECOND DINNER - Rebuild
29/09/17 - Version 1.3 - Now with smooth corners option, True for smooth default/False for original
18/05/17 - Version 1.2 - Now includes variable angle domain input (defaults at 90°) for angled corners
13/11/16 - slight change to enable acceptance of very large interior curves
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Added by Darcy Zelenko at 8:44pm on November 9, 2016
lly it should not make much of a difference - random number generation is not affected, mutation also is not. crossover is a bit more tricky, I use Simulated Binary Crossover (SBX-20) which was introduced already in 1194:
Deb K., Agrawal R. B.: Simulated Binary Crossover for Continuous Search Space, inIITK/ME/SMD-94027, Convenor, Technical Reports, Indian Institue of Technology, Kanpur, India,November 1994
Abst ract. The success of binary-coded gene t ic algorithms (GA s) inproblems having discrete sear ch sp ace largely depends on the codingused to represent the prob lem variables and on the crossover ope ratorthat propagates buildin g blocks from pare nt strings to childrenst rings . In solving optimization problems having continuous searchspace, binary-co ded GAs discr et ize the search space by using a codingof the problem var iables in binary st rings. However , t he coding of realvaluedvari ables in finit e-length st rings causes a number of difficulties:inability to achieve arbit rary pr ecision in the obtained solution , fixedmapping of problem var iab les, inh eren t Hamming cliff problem associatedwit h binary coding, and processing of Holland 's schemata incont inuous search space. Although a number of real-coded GAs aredevelop ed to solve optimization problems having a cont inuous searchspace, the search powers of these crossover operators are not adequate .In t his paper , t he search power of a crossover operator is defined int erms of the probability of creating an arbitrary child solut ion froma given pair of parent solutions . Motivated by t he success of binarycodedGAs in discret e search space problems , we develop a real-codedcrossover (which we call the simulated binar y crossover , or SBX) operatorwhose search power is similar to that of the single-point crossoverused in binary-coded GAs . Simulation results on a number of realvaluedt est problems of varying difficulty and dimensionality suggestt hat the real-cod ed GAs with t he SBX operator ar e ab le to perform asgood or bet t er than binary-cod ed GAs wit h t he single-po int crossover.SBX is found to be particularly useful in problems having mult ip le optimalsolutions with a narrow global basin an d in prob lems where thelower and upper bo unds of the global optimum are not known a priori.Further , a simulation on a two-var iable blocked function showsthat the real-coded GA with SBX work s as suggested by Goldberg
and in most cases t he performance of real-coded GA with SBX is similarto that of binary GAs with a single-point crossover. Based onth ese encouraging results, this paper suggests a number of extensionsto the present study.
7. ConclusionsIn this paper, a real-coded crossover operator has been develop ed bas ed ont he search characte rist ics of a single-point crossover used in binary -codedGAs. In ord er to define the search power of a crossover operator, a spreadfactor has been introduced as the ratio of the absolute differences of thechildren points to that of the parent points. Thereaft er , the probabilityof creat ing a child point for two given parent points has been derived forthe single-point crossover. Motivat ed by the success of binary-coded GAsin problems wit h discrete sear ch space, a simul ated bin ary crossover (SBX)operator has been develop ed to solve problems having cont inuous searchspace. The SBX operator has search power similar to that of the single-po intcrossover.On a number of t est fun ctions, including De Jong's five te st fun ct ions, ithas been found that real-coded GAs with the SBX operator can overcome anumb er of difficult ies inherent with binary-coded GAs in solving cont inuoussearch space problems-Hamming cliff problem, arbitrary pr ecision problem,and fixed mapped coding problem. In the comparison of real-coded GAs wit ha SBX operator and binary-coded GAs with a single-point crossover ope rat or ,it has been observed that the performance of the former is better than thelatt er on continuous functions and the performance of the former is similarto the lat ter in solving discret e and difficult functions. In comparison withanother real-coded crossover operator (i.e. , BLX-0 .5) suggested elsewhere ,SBX performs better in difficult test functions. It has also been observedthat SBX is particularly useful in problems where the bounds of the optimum
point is not known a priori and wher e there are multi ple optima, of whichone is global.Real-coded GAs wit h t he SBX op erator have also been tried in solvinga two-variab le blocked function (the concept of blocked fun ctions was introducedin [10]). Blocked fun ct ions are difficult for real-coded GAs , becauselocal optimal points block t he progress of search to continue towards t heglobal optimal point . The simulat ion results on t he two-var iable blockedfunction have shown that in most occasions , the sea rch proceeds the way aspr edicted in [10]. Most importantly, it has been observed that the real-codedGAs wit h SBX work similar to that of t he binary-coded GAs wit h single-pointcrossover in overcoming t he barrier of the local peaks and converging to t heglobal bas in. However , it is premature to conclude whether real-coded GAswit h SBX op erator can overcome t he local barriers in higher-dimensionalblocked fun ct ions.These results are encour aging and suggest avenues for further research.Because the SBX ope rat or uses a probability distribut ion for choosing a childpo int , the real-coded GAs wit h SBX are one st ep ahead of the binary-codedGAs in te rms of ach ieving a convergence proof for GAs. With a direct probabilist ic relationship between children and parent points used in t his paper,cues from t he clas sical stochast ic optimization methods can be borrowed toachieve a convergence proof of GAs , or a much closer tie between the classicaloptimization methods and GAs is on t he horizon.
In short, according to the authors my SBX operator using real gene values is as good as older ones specially designed for discrete searches, and better in continuous searches. SBX as far as i know meanwhile is a standard general crossover operator.
But:
- there might be better ones out there i just havent seen yet. please tell me.
- besides tournament selection and mutation, crossover is just one part of the breeding pipeline. also there is the elite management for MOEA which is AT LEAST as important as the breeding itself.
- depending on the problem, there are almost always better specific ways of how to code the mutation and the crossover operators. but octopus is meant to keep it general for the moment - maybe there's a way for an interface to code those things yourself..!?
2) elite size = SPEA-2 archive size, yes. the rate depends on your convergence behaviour i would say. i usually start off with at least half the size of the population, but mostly the same size (as it is hard-coded in the new version, i just realize) is big enough.
4) the non-dominated front is always put into the archive first. if the archive size is exceeded, the least important individual (the significant strategy in SPEA-2) are truncated one by one until the size is reached. if it is smaller, the fittest dominated individuals are put into the elite. the latter happens in the beginning of the run, when the front wasn't discovered well yet.
3) yes it is. this is a custom implementation i figured out myself. however i'm close to have the HypE algorithm working in the new version, which natively has got the possibility to articulate perference relations on sets of solutions.
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he example file to this file so you can give it a try with any version of Honeybee that you're already using. The only requirement is to have OpenStudio installed as the component is using OpenStudio libraries to parse gbXML files. If you're using the latest version available on github the component is also available under WIP tab.
Why?
The main purpose of developing this component is to save time and effort for importing Revit models for energy and daylight analysis. It bothers me to see a lot of smart people spend a lot of time to just come up with solutions just to get the geometry from Revit to Honeybee for analysis. This component is not solving all the issue but is a first step forward. In an ideal world, the future version of Honeybee, which works both under DynamoBIM and Grasshopper should address this issue but that can take some time to be fully ready!
How?
To use this component you need to Export your Revit model as gbXML and then use the file path to load the file into Grasshopper. There are several resources available online on how to prepare the analytical model in Revit and export the gbXML file. Here is an image for importing the Revit 2017 sample model using the default settings. As you can see the model will be just as good as what your original gbXML file from Revit is.
What can be improved?
Well, there are several items that can be improved and they are mostly not on us. To get it started I add what I think are the 3 main shortcomings and my thoughts on how they can be addressed in the future. Feel free to add what you think needs to be added to this list in the comments section.
1. Revit analytical models and as the results gbXML files, by design, are not intended to be clean. Watch this presentation from the Autodesk University to see the logic behind this approach which in short is it doesn't matter for a large scale early stage energy model. Well, This will be quite a problem for studies that you can do with Honeybee. Included but not limited to daylight and comfort analysis.
The best solution that I can think of, until Autodesk fixes their exporter, is to use Revit Rooms and Spaces and generate a clean model from the scratch. We have already tried this approach in Revit but since the Revit API doesn't provide access to Room openings we had a very hard time to get it to work.
That's why that I opened an idea on Revit ideas to get over this issue. With your support we already have 81 votes, but it hasn't been enough to make them to consider the idea for an official review. If you haven't voted already and you think this will be a helpful feature take a moment and vote so we can have it implemented at some point in the future.
2. There is no way (that I know) to export only part of the model. The way export gbXML is set up in Revit is to export the whole model once together. As a result, if you have a huge model with 100 rooms and you want to get one of the rooms into Honeybee using this component you have to export the whole model, which can take some time, and then import them all back into Grasshopper. To partially address this issue I added an input to the component that allows you input a list of names for rooms that you're interested to be loaded into Grasshopper. You can use the name of the room/space in Revit as an input for the component.
3. The component doesn't import adjacencies, loads, schedules and HVAC systems. I wasn't able to export a gbXML file from Revit with any of this data except for the adjacency, but even if you can do that, the component currently can only import geometries and constructions. I hope we get access to 1 and so we don't have to use the xml file approach at all, but if that takes a very long time then we will add these features to the component.
Happy 2017!
Mostapha…
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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