ctor. I do not dispose of any IGH_Goo instances, mostly because I have no idea when an instance is truly no longer needed. If any of your fields need to be disposed, you may have to implement a destructor, but I have no experience with this.
2) should I pass those classes to other parameters by DA(0, MotherClass.Duplicate?) or it is already there by GH_Goo ?
IGH_Goo is not duplicated by default. If you use DA.GetData() and ask for IGH_Goo types, you'll get a reference to the same instance as exists. Thus, if you take in an instance of your type, modify and output it, you should duplicate it yourself. But you only need to do this if you change the state of an instance.
MyGooType data = null;
if (!DA.GetData(0, ref data)) return;
data = data.Duplicate() as MyGooType;
data.Property = newValue;
DA.SetData(0, data);
3) should I create ChildClass and MotherClass in SolveInstance, or create it once as a component's field and then change theirs properties and pass it to DA (as duplicate ?)....
It's almost always better to use variables with the lowest possible scope. So method variables are preferred to class variables, class variables are preferred to static variables.
4) if I create those classes in SolveInstance, is it necessary to Dispose them there ?
NO! Do not dispose of instances that are passed on to output parameters. Disposing objects typically makes them invalid, so if you share instances with anyone else, you should not dispose them or the other code may well crash. However I don't think your types need to be disposable so this is a moot point now.
In general, if you're dealing with disposable types, and the instances aren't shared, then you dispose them as quickly as possible. But if they are shared it's a lot more complicated.
5) finally - maybe it would be better if MotherClass inherits the ChildClass ?
Maybe. Not necessarily. Depends on the classes. …
Added by David Rutten at 12:08pm on December 31, 2014
rk and I will just clarify some of the details. I will also note that I do not know what the shadings output of the decomposeByType component is supposed to do as Mostapha put it there a long time ago and I was not sure what his intentions were. Going down a list of clarification points:
1) You are right that you should either connect up the shade breps to the EPContext component or just plug the HBObjwShades into the RunSimulation component (never do both). However, connecting the breps to the EPContext component is greatly undesirable for two reasons: It will make the simulation run much longer and the energyPlus calculation will not account for the surface temperatures of the blinds (it will assume they are the same temperature as the outdoor air, which is very wrong in a lot of cases). When you connect up the HBObjwShades to run the simulation, EnergyPlus will understand the blinds as abstract objects defined only by a numeric parameterization and not as actual geometry. This enables the calculation to run fast and is also enough of a description that E+ can calculate the temperature of the blinds, thereby accounting for the heat that can be re-radiated from the blinds to the indoors when they get hot in the sun. This more desirable way of running the blinds was how I imagined the component being run most of the time and I mostly included the shadeBreps so that you have a visual of what you are simulating.
2) When you use the more desirable HBObjWShades to approximate your blinds, you should use the blindsSchedule input in order to tell E+ when the shades are pulled (this is instead of the transShcedule on the EPContext component).
3) The zoneData inputs on the EPWindowShade component are meant to help in an entirely different workflow, which evaluates shade benefit based on energy simulation results. I apologize if it seems confusing to have two major uses of the component in one but we have so many Honeybee components right now and I did not want to make 2 separate ones when they seemed so similar. See this example file to see how to do energy shade benefit (https://app.box.com/s/oi64zoj5u1slz494grzhgmdkx7yie9jo).
Ok. I think that clears up everything that I know. Now to the part that I do not. As I said, Mostapha put in the shadings input there a long time ago and I do not know what his intentions were. Abraham, as you know, I am about to do a major revision of the EPWindowShade component to make it compatible with OpenStudio, include drapes/generic shades in addition to blinds, and I also should figure out how to do electrochromic glazing. I can easily include all of the visualized shades as output from the decomposeByType component when I do this. However, I do not want to interfere with other intentions Mostapha had when he put the input in. If he could confirm that this was in-line with his vision for the shadings output, I will implement it soon.
-Chris
…
e point in each pair that has the lowest Z value (then later the highest Z)... The problem is the intersections are not returned sorted by Z, sometimes the lower point is first in the list, sometimes last. So I need to sort those pairs of points by Z value.I noticed the sort points component does not have any inputs for sort criteria... RhinoScript SortPoints allows you to sort by:
blnOrder
Optional. Number. The component sort order, where:
Value
Component Sort Order
0 (default)
X, Y, Z
1
X, Z, Y
2
Y, X, Z
3
Y, Z, X
4
Z, X, Y
5
Z, Y, X
Will we get something like this in GH? For now I think I can manage to analyze the Z for each and re-order the points, but a more comprehensive point sorting tool might be nice... no? Or did I miss something obvious? --Thx, --Mitch…
works joyfully if you want to change parameters and generate screen captures and planning to do a lot of them. You can of course generate the file name dynamically referring to the parameters you gave to the script, so that you have meaningful file names.
The example below will generate two captures at J:\Temp\001_top,jpg and J:\Temp\001_front,jpg both at 600X600 px in ghosted mode.
The instructions are as follows: (if you open the VB code by double clicking you will see it)
' Note1: The script is actually calling Rhino commands.
' Note2: Remember you have to draw something and is selectable for the script to function. The script uses _SelAll then _Zoom _Selected
' Note3: After you toggle blnSave to True, a new viewport will popup, be patient while Rhino work, and wait for that viewport to disappear befor clicking on anything.
' Note4: The component is not stable if you try to mouse click on anywhere while the saving process is running. Some stupid move may crash your programme, save RH and GH files before using this component.
' FileName : String Input = Supply with the path and file name without ".jpg" extension : e.g.: "C:\Temp\001" (Without the quotes)
' blnSave : Boolean Input = Saves when toggles to True (Remember to toggle back to False after use, otherwise the script will re-run itself during next update)
' Resolution_width : Integer Input = Resolution for the captured image
' Resolution_height : Integer Input = well...
' TopYea : Boolean Input = Toggles if the Top View is captured (Default is False if not connected)
' FrontYea : Boolean Input = Toggles if the Front View is captured (Default is False if not connected)
' ...Yea : Boolean Input = Toggles if the corresponding View is captured (Default is False if not connected)
' DisplayMode : Integer Input(0-4) = Sets the display Mode 0:Shaded 1:Wireframe 2:Rendered 3:Ghosted 4:XRay Default:Shaded
I remember I took some code from somewhere but I forgot exactly the source, (if someone could remind me I would love to cite) I rewrite most of them though. But the attribution header in the code still remains there and now it seems a bit interesting to see the family tree:
'////// Marc Hoppermann ///////////tweaked by Damien Almor ///////rewritten for curves by to]///////adapted by u]...www.utos.blogspot.com ///readapted by Victor Leung @ www.dreamationworks.com
Visit my blog if you have time: www.dreamationworks.com…
nition. Using RenderAnimation component from http://www.giuliopiacentino.com/grasshopper-tools/, I could do all of above except for the Toon material part.
I have found a post regarding same matter ( http://www.grasshopper3d.com/forum/topics/how-to-add-materials-to-material-table ), but since I am not very familiar with scripts, this is what I think his definition does. Correct me if I am wrong.
Since Rhino Vray only supports Toon environment per material (unlike Max Vray has global override feature),
1. import toon material from Rhino material editor
2. add colors to the toon material and make new toon materials with color (as many as needed)
3. import that new materials back into grasshopper
4. match them with designated geometries and render. (RenderAnimation component by Giulio does this job) Here is the final work he did : http://vimeo.com/34728433
Grasshopper + Vray from Marc Syp on Vimeo.
I am using rhino 4 with vray 1.5.
I have uploaded my definition, simple definition that transforms box height along with color as frame advances. The definition works but toon effect is not there.…
case for sure (started by Giorgio a couple of days before). Ive got involved because I exploit ways to "relax" shapes on nurbs (say patterns created by Lunchbox or "manually) without using any kind of mesh (more explanations soon).
Here's 5 test cases (SDK appears that doesn't have some "thicken surface" thing ... thus the algo that finds the "whole" shapes is rather naive) VS 2 Kangaroo "methods" and the why bother (he he) option as well.
If the goal is to "fit" these shapes within the nurbs ... does it work so far? No I'm afraid (appears that "springs" used are not the proper ones - or [Kangaroo1 option] the lines that pull should been originated from valance 2 points only)
Tricky points:
1. Internalize appears having a variety of serious issues (see Input inside definition) - Load Rhino file first (but even so ...).
2. Pull to surface is deactivated - this is not the issue here (and it's very slow).
3. Since Starling/WB alter the "curves - points" related order
the issue here (Pull points to curves) is to correspond apples to apples:
and that's what Anemone does:
From chaos :
to order:
this means that prior activating Kangaroo you should double click to the Anemone start component in order to "sort" properly the curves.
But .. fact is that results are pathetic:
more soon
best, Peter…
bsp;
-Vehicle elements (3D objects and a component for custom vehicles; models from Google Warehouse)
-Traffic Velocity Graphs, drawn on every trajectory curve (allow custom graphs drawn)
-Traffic regulation elements (such as Traffic Lights and Stop Signals) and traffic density
-Particle Systems on trajectory curves, just to manage the traffic regulations and avoid collisions based on security distances
-Traffic Vehicle Animation Modes (Dots, Bounding Boxes or complex Meshes with attributes for final rendering (Giulio Piacentino´s Render Animation)
-Vehicle Lights and Vehicle Sights, to make visual studies
Team:
-Sergio del Castillo Tello (Doctor No, lead programmer)
-Everyone that wants to be involved, support.. these tools
The development of Roadrunner is planned to take part within a Research Group Program at ETSAM (University of Architecture in Madrid); This forum group is created just to test the interest of the community, while we keep on developing (it is still being tested), probably we will share the whole thing in the future. Cheers!
Traffic Cluster Scheme
Traffic Elements
Traffic Urban Systems
Vehicle Elements
Roadrunner - overview
Roadrunner 0 Basics
Roadrunner 1 Modes
Roadrunner 2 Elements
Roadrunner 3 Urban Systems…
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.
…
ion of both Ladybug and Honeybee. Notable among the new components are 51 new Honeybee components for setting up and running energy simulations and 15 new Ladybug components for running detailed comfort analyses. We are also happy to announce the start of comprehensive tutorial series on how to use the components and the first one on getting started with Ladybug can be found here:
https://www.youtube.com/playlist?list=PLruLh1AdY-Sj_XGz3kzHUoWmpWDXNep1O
A second one on how to use the new Ladybug comfort components can be found here:
https://www.youtube.com/playlist?list=PLruLh1AdY-Sho45_D4BV1HKcIz7oVmZ8v
Here is a short list highlighting some of the capabilities of this current Honeybee release:
1) Run EnergyPlus and OpenStudio Simulations - A couple of components to export your HBZones into IDF or OSM files and run energy simulations right from the grasshopper window! Also included are several components for adjusting the parameters of the simulations and requesting a wide range of possible outputs.
2) Assign EnergyPlus Constructions - A set of components that allow you to assign constructions from the OpenStudio library to your Honeybee objects. This also includes components for searching through the OpenStudio construction/material library and components to create your own constructions and materials.
3) Assign EnergyPlus Schedules and Loads - A set of components for assigning schedules and Loads from the Openstudio library to your Honeybee zones. This includes the ability to auto-assign these based on your program or to tweak individual values. You can even create your own schedules from a stream of 8760 values with the new “Create CSV Schedule” component. Lastly, there is a component for converting any E+ schedule to 8760 values, which you can then visualize with the standard Ladybug components
4) Assign HVAC Systems - A set of components for assigning some basic ASHRAE HVAC systems that can be run with the Export to OpenStudio component. You can even adjust the parameters of these systems right in Grasshopper.
Note: The ASHRAE systems are only available for OpenStudio and can’t be used with Honeybee’s EnergyPlus component. Also, only ideal air, VAV and PTHP systems are currently available but more will be on their way soon!
5) Import And Visualize EnergyPlus Results - A set of components to import numerical EnergyPlus simulation results back into grasshopper such that they can be visualized with any of the standard Ladybug components (ie. the 3D chart or Psychrometric chart). Importers are made for zone-level results as well as surface results and surfaces results can be easily separated based on surface type. This also means that E+ results can be analyzed with the new Ladybug comfort calculator components and used in shade or natural ventilation studies. Lastly, there are a set of components for coloring zone/surface geometry with EnergyPlus results and for coloring the shades around zones with shade desirability.
6) Increased Radiance and Daysim Capabilities - Several updates have also been made to the existing Radiance and Daysim components including parallel Radiance Image-based analysis.
7) Visualize HBObject Attributes - A few components have been added to assist with setting up honeybee objects and ensuing the the correct properties have been assigned. These include components to separate surfaces based on boundary condition and components to label surfaces and zones with virtually any of their EnergyPlus or Radiance attributes.
8) WIP Grizzly Bear gbxml Exporter - Lastly, the release includes an WIP version of the Grizzly Bear gbXML exporter, which will continue to be developed over the next few months.
And here’s a list of the new Ladybug capabilities:
1) Comfort Models - Three comfort models that have been translated to python for your use in GH: PMV, Adaptive, and Outdoor (UTCI). Each of these models has a “Comfort Calculator” component for which you can input parameters like temperature and wind speed to get out comfort metrics. These can be used in conjunction with EPW data or EnergyPlus results to calculate comfort for every hour of the year.
2) Ladybug Psychrometric Chart - A new interactive psychrometric chart that was made possible thanks to the releasing of the Berkely Center for the Built Environment Comfort Tool Code (https://github.com/CenterForTheBuiltEnvironment/comfort-tool). The new psychrometric chart allows you to move the comfort polygon around based on PMV comfort metrics, plot EPW or EnergyPlus results on the psych chart, and see how many hours are made comfortable in each case. The component also allows you to plot polygons representing passive building strategies (like internal heat gain or evaporative cooling), which will adjust dynamically with the comfort polygon and are based on the strategies included in Climate Consultant.
3) Solar Adjusted MRT and Outdoor Shade Evaluator - A component has been added to allow you to account for shortwave solar radiation in comfort studies by adjusting Mean Radiant Temperature. This adjusted MRT can then be factored into outdoor comfort studies and used with an new Ladybug Comfort Shade Benefit Evaluator to design outdoor shades and awnings.
4) Wind Speed - Two new components for visualizing wind profile curves and calculating wind speed at particular heights. These allow users to translate EPW wind speed from the meteorological station to the terrain type and height above ground for their site. They will also help inform the CFD simulations that will be coming in later releases.
5) Sky Color Visualizer - A component has been added that allows you to visualize a clear sky for any hour of the year in order to get a sense of the sky qualities and understand light conditions in periods before or after sunset.
Ready to Start?
Here is what you will need to do:
Download Honeybee and Ladybug from the same link here. Make sure that you remove any old version of Ladybug and Honeybee if you have one, as mentioned on the Ladybug group page.
You will also need to install RADIANCE, DAYSIM and ENERGYPLUS on your system. We already sent a video about how to get RADIANCE and Daysim installed (link). You can download EnergyPlus 8.1 for Windows from the DOE website (http://apps1.eere.energy.gov/buildings/energyplus/?utm_source=EnergyPlus&utm_medium=redirect&utm_campaign=EnergyPlus%2Bredirect%2B1).
“EnergyPlus is a whole building energy simulation program that engineers, architects, and researchers use to model energy and water use in buildings.”
“OpenStudio is a cross-platform (Windows, Mac, and Linux) collection of software tools to support whole building energy modeling using EnergyPlus and advanced daylight analysis using Radiance.”
Make sure that you install ENERGYPLUS in a folder with no spaces in the file path (e.g. “C:\Program Files” has a space between “Program” and “Files”). A good option for each is C:\EnergyPlusV8-1-0, which is usually the default locations when you run the downloaded installer.
New Example Files!
We have put together a large number of new updated example files and you should use these to get yourself started. You can download them from the link on the group page.
New Developers:
Since the last release, we have had several new members join the Ladybug + Honeybee developer team:
Chien Si Harriman - Chien Si has contributed a large amount of code and new components in the OpenStudio workflow including components to add ASHRAE HVAC systems into your energy models and adjust their parameters. He is also the author of the Grizzly Bear gbxml exporter and will be continuing work on this in the following months.
Trygve Wastvedt - Trygve has contributed a core set of functions that were used to make the new Ladybug Colored Sky Visualizer and have also helped sync the Ladybug Sunpath to give sun positions for the current year of 2014
Abraham Yezioro - Abraham has contributed an awesome new bioclimatic chart for comfort analyses, which, despite its presence in the WIP tab, is nearly complete!
Djordje Spasic - Djordje has contributed a number of core functions that were used to make the new Ladybug Wind Speed Calculator and Wind Profile Visualizer components and will be assisting with workflows to process CFD results in the future. He also has some more outdoor comfort metrics in the works.
Andrew Heumann - Andrew contributed an endlessly useful list item selector, which can adjust based on the input list, and has multiple applications throughout Ladybug and Honeybee. One of the best is for selecting zone-level programs after selecting an overall building program.
Alex Jacobson - Alex also assisted with the coding of the wind speed components.
And, as always, a special thanks goes to all of our awesome users who tested the new components through their several iterations. Special thanks goes to Daniel, Michal, Francisco, and Agus for their continuous support. Thanks again for all the support, great suggestions and comments. We really cannot thank you enough.
Enjoy!,
Ladybug + Honeybee Development Team
PS: If you want to be updated about the news about Ladybug and Honeybee like Ladybug’s Facebook page (https://www.facebook.com/LadyBugforGrasshopper) or follow ladybug’s twitter account (@ladybug_tool).
…
rmation?" I know that this can already be accomplished using the brilliant Kangaroo plugin, but I wanted a simpler and faster (yet still accurate) single component that could replicate this unique curve using a variety of inputs: the length of the rod/wire, the width/distance between the endpoints, the height of the bend, and the tangent angle at the start. I also wanted make the unknowns (such as height if only length and width are known) easily accessible for plugging into additional components.
The resulting script, being an all-in-one solution, is somewhat unwieldy, but it could easily be broken down into smaller components (custom .gha's which I don't have the ability to code). If someone wants to tackle this, please do! I'm not an expert coder by any means, and as this was only my second time diving into Grasshopper scripting, if the script seems somewhat strange, that's probably why. I did try to comment the code pretty well though. Here's the full description:
--------------------------------------------------
DESCRIPTION: This beast creates the so-called 'elastica curve', the shape a long, thin rod or wire makes when it is bent elastically (i.e. not permanently). In this case, force is assumed to only be applied horizontally (which would be in line with the rod at rest) and both ends are assumed to be pinned or hinged meaning they are free to rotate (as opposed to clamped, when the end tangent angle is fixed, usually horizontally). An interesting finding is that it doesn't matter what the material or cross-sectional area is, as long as they're uniform along the entire length. Everything makes the same shape when bent as long as it doesn't cross the threshold from elastic to plastic (permanent) deformation (I don't bother to find that limit here, but can be found if the yield stress for a material is known).
Key to the formulas used in this script are elliptic integrals, specifically K(m), the complete elliptic integral of the first kind, and E(m), the complete elliptic integral of the second kind. There was a lot of confusion over the 'm' and 'k' parameters for these functions, as some people use them interchangeably, but they are not the same. m = k^2 (thus k = Sqrt(m)). I try to use the 'm' parameter exclusively to avoid this confusion. Note that there is a unique 'm' parameter for every configuration/shape of the elastica curve.
This script tries to find that unique 'm' parameter based on the inputs. The algorithm starts with a test version of m, evaluates an expression, say 2*E(m)/K(m)-1, then compares the result to what it should be (in this case, a known width/length ratio). Iterate until the correct m is found. Once we have m, we can then calculate all of the other unknowns, then find points that lie on that curve, then interpolate those points for the actual curve. You can also use Wolfram|Alpha as I did to find the m parameter based on the equations in this script (example here: http://tiny.cc/t4tpbx for when say width=45.2 and length=67.1).
Other notes:
* This script works with negative values for width, which will creat a self-intersecting curve (as it should). The curvature of the elastica starts to break down around m=0.95 (~154°), but this script will continue to work until M_MAX, m=0.993 (~169°). If you wish to ignore self-intersecting curves, set ignoreSelfIntersecting to True
* When the only known values are length and height, it is actually possible for certain ratios of height to length to have two valid m values (thus 2 possible widths and angles). This script will return them both.
* Only the first two valid parameters (of the required ones) will be used, meaning if all four are connected (length, width or a PtB, height, and angle), this script will only use length and width (or a PtB).
* Depending on the magnitude of your inputs (say if they're really small, like if length < 10), you might have to increase the constant ROUNDTO at the bottom
REFERENCES: {1} "The elastic rod" by M.E. Pacheco Q. & E. Pina, http://www.scielo.org.mx/pdf/rmfe/v53n2/v53n2a8.pdf {2} "An experiment in nonlinear beam theory" by A. Valiente, http://www.deepdyve.com/lp/doc/I3lwnxdfGz {3} "Snap buckling, writhing and Loop formation In twisted rods" by V.G.A. GOSS, http://myweb.lsbu.ac.uk/~gossga/thesisFinal.pdf {4} "Theory of Elastic Stability" by Stephen Timoshenko, http://www.scribd.com/doc/50402462/Timoshenko-Theory-of-Elastic-Stability (start on p. 76)
INPUT: PtA - First anchor point (required) PtB - Second anchor point (optional, though 2 out of the 4--length, width, height, angle--need to be specified) [note that PtB can be the same as PtA (meaning width would be zero)] [also note that if a different width is additionally specified that's not equal to the distance between PtA and PtB, then the end point will not equal PtB anymore] Pln - Plane of the bent rod/wire, which bends up in the +y direction. The line between PtA and PtB (if specified) must be parallel to the x-axis of this plane
** 2 of the following 4 need to be specified ** Len - Length of the rod/wire, which needs to be > 0 Wid - Width between the endpoints of the curve [note: if PtB is specified in addition, and distance between PtA and PtB <> width, the end point will be relocated Ht - Height of the bent rod/wire (when negative, curve will bend downward, relative to the input plane, instead) Ang - Inner departure angle or tangent angle (in radians) at the ends of the bent rod/wire. Set up so as width approaches length (thus height approaches zero), angle approaches zero
* Following variables only needed for optional calculating of bending force, not for shape of curve. E - Young's modulus (modulus of elasticity) in GPa (=N/m^2) (material-specific. for example, 7075 aluminum is roughly 71.7 GPa) I - Second moment of area (or area moment of inertia) in m^4 (cross-section-specific. for example, a hollow rod would have I = pi * (outer_diameter^4 - inner_diameter^4) / 32 Note: E*I is also known as flexural rigidity or bending stiffness
OUTPUT: out - only for debugging messages Pts - the list of points that approximate the shape of the elastica Crv - the 3rd-degree curve interpolated from those points (with accurate start & end tangents) L - the length of the rod/wire W - the distance (width) between the endpoints of the rod/wire H - the height of the bent rod/wire A - the tangent angle at the (start) end of the rod/wire F - the force needed to hold the rod/wire in a specific shape (based on the material properties & cross-section) **be sure your units for 'I' match your units for the rest of your inputs (length, width, etc.). Also note that the critical buckling load (force) that makes the rod/wire start to bend can be found at height=0
THANKS TO: Mårten Nettelbladt (thegeometryofbending.blogspot.com) Daniel Piker (Kangaroo plugin) David Rutten (Grasshopper guru) Euler & Bernoulli (the O.G.'s)
--------------------------------------------------
Edit: More on the math behind this here.
Cheers,
Will
…
Added by Will McElwain at 4:08pm on February 26, 2014