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Thanx……
erning how to do that on a sphere.
So I know already all the different approches of how to get a relaxed voronoi pattern on a free-form open surface, but still don't know how to obtain the same elegant effect on a sphere (or an ellipsoid closed surface, whatever), or how to relax the facet dome cells.
Andrew stated on his site that he used kangaroo for this project, so the Spore Lamp consists in my opinion either of a relaxed voronoi 3d diagram (b-rep, b-rep intersection) on a sphere the cells of which have been planarized later on, or more likely it is a sort of relaxed facet dome.
The trick is to:
1. obtain a nicely-balanced voronoish diagram (or facet dome cells) on a sphere
2. keep each cell/polyline planar (or force them with kangaroo to be planar) in order to move scale and loft them later on.
Here is what I have by now.(files: matsys spore lamp attempt)
That's the closest appearance that I got so far (simple move scale and loft of facet dome cells with the amount of transformations being proportional to the power of the initial cell area: bigger cell = bigger opening etc.) - with no relaxation of the diagram. But it's obviously not the same thing as the matsys design.
Here are some of my attempts of facet dome relaxation, but well, it's certainly still not the right approach, and most importantly I don't know how to keep or force the cells to be planar after the relaxation.
1. pulling vertices to a sphere - no anchor points. That obviously doesn't make sense at all, but the relaxation without anchor points gives at the beginning a pattern that is closer to what I am looking for. (files: relaxation 01)
2. pulling vertices to a sphere - two faces of the initial facet dome anchored (files: relaxation 02)
3. pulling vertices to the initial geometry (facet dome) no anchor points (files: relaxation 03)
The cell pattern of the lamp kinda looks like this:
You can find it here: http://www.grasshopper3d.com/forum/topics/kangaroo-0-095-releasedgroupUrl=kangaroo&x=1&groupId=2985220%3AGroup%3A120977&id=2985220%3ATopic%3A972434&page=2#comments
Done with Plankton (of course without the "gradient increase" appearance), but in fact not, I took a look at Daniel Parker's Plankton example files, and it's not quite the same thing. Also the cells aren't planar...
The last problem is that during the relaxation attempts that I did, the biggest initial cells became enormous, and it's not like that in the elegant project by Andrew Kudless, that I'd like to achieve.
So to sum up:
Goal no 1: Obtain an elegant voronoi /facet dome cell pattern on a sphere (or an ellipsoid surface, whatever).
Goal no 2: How to keep the cells planar in order to be able to loft them later, obtain those pyramidal forms, and assemble easily
Have you got any ideas? Or maybe there's a completely different approach to that?
Cheers, and thanks in advance…
mers considering extreme sports reject mainstream retailers and like to check out small stores rather of at chains plus malls. Several smaller retailers discuss trends in sports shoe sales. http://skateszone.com/
Though athletic shoes and sports stores and from doorways retailers have reported somewhat uptick in footwear sales due to the increase in extreme sports, the particular beneficiaries inside the trend are independent surf and skate niche stores.
Some West Coast surf and skate shops stated teenagers and even more youthful Generation Xers are not only rejecting traditional sports, but they're also shunning mainstream retailers and malls meant for smaller niche shops transporting hard-to-come-by brands.
Eddie Miyoshi, district manager at Atomic Garage, a 3-store chain situated in Gardena, Calif., stated the soaring recognition of skateboard footwear has boosted the retailer's total footwear business 20-thirty percent this year, rather of '95.
Skate footwear presently represent 80-90 % of Atomic Garage's shoe sales, while couple of years back, Dr. Martens and Timberland drove the retailer's footwear business.
Like many retailers, Miyoshi pointed to Airwalk since the trend's catalyst.
However, if Airwalk broadened its distribution to larger chains, which are frequently located in malls, only a few skate shoe customers adopted. Rather, many youthful males have switched for your skate shops for additional elusive brands like Etnies, Duffs, and Electricity Footwear by Circus. By refusing to market bigger retailers or sports stores, these brands are increasing their cachet among youthful consumers.
"Kids don't want stuff which have been within the shops,In . Miyoshi added.
Searching ahead, Miyoshi forecasted skate shoe sales will remain strong through spring '97 provided "the [hot] vendors don't auction other [non-particularly shop] retailers."
"Skaters and non-skaters are rebelling against mainstream retailers so on to surf and skate shops for many looks," echoed Mark Richards, co-online sources Val Surf, a 3-store chain situated in North Hollywood, Calif. Soaring sales of skate footwear have driven total footwear receipts up 25 percent this year rather of '95.
"The quantity of that increase might be connected while using exposure of maximum games? I am unsure. [Skate footwear] may also be actually the think about the moment,In . Richards acknowledged. And in relation to getting this right look, youthful customers can be very picky.
"Skateboard footwear is a huge category for people, but we're not able to own the brands, Etnies, Duffs, Electricity and Nice, simply because they won't sell us," stated Mark Anderson, buyer at Chick's Sports, a six-store chain in Covina, Calif. "We have people coming every single day requesting them." Consequently, skate footwear have consistently ongoing to obtain about 5 % of Chick's overall footwear business. http://skateszone.com/the-top-8-best-skateboards-for-beginners-reviews-2017/
Nonetheless, some outdoors, niche sports and sports retailers are noting the growing recognition and coverage of maximum sports will receive a modest impact on footwear sales. Trailrunning footwear and approach/outdoors crosstrainers will be the two groups benefiting the very best inside the recognition. Like the skate shoe business, some retailers realize that styling instead of function frequently drives sales of individuals footwear.
"At this time the merchandise is a lot more visual than function," stated Chet James, gm of Super Jock 'N Jill, Dallas, speaking about trailrunning footwear. Still, James noted the current hype over adventure sports helps draw more customer traffic. "The marketing campaigns and media help bring growing figures of people in, nonetheless they frequently occasions day an issue that increases results on their own account,Inch he conceded.
John Wilkinson, executive vp inside the 85-store chain Track 'N Trail, Eldorado Hillsides, Calif., stated the shop has "seen some activity in approach footwear," but he requested the amount of consumers depend in it commercially sport. And, instead of accelerating total footwear business, Wilkinson speculated elevated sales of approach footwear and trailrunners are gnawing away at traditional hiking shoe and boot volume.
But Dan Bazinet, president of Overland Exchanging, a 34-store chain situated in Westford, Mass., believes the company-new looks have breathed existence for the wilting hiking boot category. "[Approach-type footwear] don't represent the lion's participate the hiking market, nonetheless they have elevated the hiking business and provided us extra sales," Bazinet stated.
He designated Timberland's Treeline Series and Rockport's Leadville line as strong performers. Unsurprisingly, he noted the company-new looks are attractive to youthful consumer base than traditional hikers.
For that month of June, sales of men's hikers were up 49 percent at Overland, rather of June '95, while sales of women's hikers were up 17 % for that month. Bazinet also attributed elevated sales that shops walked inside the hiking business, departing that business for that specialists.
Some retailers draw a good example concerning the hiking boom of two yrs ago combined with the current extreme sport phenomenon. "Plenty of bigger chains will get a specific percent in the industry while [extreme] sports remain a fad because they are selling cost-point type gear," described Steven Carre, assistant hard goods buyer at Adventure 16, a six-store chain situated in Hillcrest.
"However individuals [true enthusiasts] will say `we need real gear' and may shown up at us. That will help us after a while. What Size Skateboard good for an 3 4 5 6 7 8 9 10 11 12 13 14 year old
…
ch has a vertex in each of the vertices of the polyline. But, when I try to create the mesh using the Mesh Brep component, I get a simplified mesh, where the extra vertices in the edges of the polyline have disappeared. I think it is easier to understand what I am trying to say with the following screenshots:
Polyline:
Mesh created with the rhino command:
Mesh created using grasshopper:
The last mesh has less faces, as the Mesh Brep component gets rid of the extra vertices that define the polyline.
Any suggestions?
Thanks,
Diego…
t. So here we go!
1. Honeybee is brown and not yellow [stupid!]...
As you probably remember Honeybee logo was initially yellow because of my ignorance about Honeybees. With the help of our Honeybee expert, Michalina, now the color is corrected. I promised her to update everyone about this. Below are photos of her working on the honeybee logo and the results of her study.
If you think I'm exaggerating by calling her a honeybee expert you better watch this video:
Thank you Michalina for the great work! :). I corrected the colors. No yellow anymore. The only yellow arrows represent sun rays and not the honeybee!
2. Yellow or brown, W[here]TH Honeybee is?
I know. It has been a long time after I posted the initial video and it is not fun at all to wait for a long time. Here is the good news. If you are following the Facebook page you probably now that the Daylighting components are almost ready.
Couple of friends from Grasshopper community and RADIANCE community has been helping me with testing/debugging the components. I still think/hope to release the daylighting components at some point in January before Ladybug gets one year old.
There have been multiple changes. I finally feel that the current version of Honeybee is simple enough for non-expert users to start running initial studies and flexible enough for advanced users to run advanced studies. I will post a video soon and walk you through different components.
I think I still need more time to modify the energy simulation components so they are not going to be part of the next release. Unfortunately, there are so many ways to set up and run a wrong energy simulation and I really don’t want to add one new GIGO app to the world of simulation. We already have enough of that. Moreover I’m still not quite happy with the workflow. Please bear with me for few more months and then we can all celebrate!
I recently tested the idea of connecting Grasshopper to OpenStudio by using OpenStudio API successfully. If nothing else, I really want to release the EnergyPlus components so I can concentrate on Grasshopper > OpenStudio development which I personally think is the best approach.
3. What about wind analysis?
I have been asked multiple times that if Ladybug will have a component for wind study. The short answer is YES! I have been working with EFRI-PULSE project during the last year to develop a free and open source web-based CFD simulation platform for outdoor analysis.
We had a very good progress so far and our rockstar Stefan recently presented the results of the work at the American Physical Society’s 66th annual DFD meeting and the results looks pretty convincing in comparison to measured data. Here is an image from the presentation. All the credits go to Stefan Gracik and EFRI-PULSE project.
The project will go live at some point next year and after that I will release the Butterfly which will let you prepare the model for the CFD simulation and send it to EFRI-PULSE project. I haven’t tried to run the simulations locally yet but I’m considering that as a further development. Here is how the component and the logo looks like right now.
4. Teaching resources
It has been almost 11 months from the first public release of Ladybug. I know that I didn't do a good job in providing enough tutorials/teaching materials and I know that I won’t be able to put something comprehensive together soon.
Fortunately, ladybug has been flying in multiple schools during the last year. Several design, engineering and consultant firms are using it and it has been thought in several workshops. As I checked with multiple of you, almost everyone told me that they will be happy to share their teaching materials; hence I started the teaching resources page. Please share your materials on the page. They can be in any format and any language. Thanks in advance!
I hope you enjoyed/are enjoying/will enjoy the longest night of the year. Happy Yalda!
Cheers,
-Mostapha
…
imeBinder.CSharpArgumentInfo.Create'
Is it possible to solve this issue?
using System;
using IronPython.Hosting;
using IronPython.Runtime;
using Microsoft.Scripting;
using Microsoft.Scripting.Hosting;
using Microsoft.CSharp;
namespace Bob.Meshes {
public class pythonFromCShapr {
ScriptEngine engine = Python.CreateEngine();
public pythonFromCShapr() {
}
public void something() {
dynamic scope = engine.CreateScope();
scope.Add = new Func<int, int, int>((x, y) => x + y);
Console.WriteLine( scope.Add(2, 3));
}
}
}…
le and grasshopper timer to simplify simulation control. Double click the main Kangaroo component to open this remote. There are buttons for Stop(reset), Play, Pause, and Step (moves the simulation forward one iteration).
Line-line force - allows interaction between line segments - they are treated as rigid cylinders. As with springs, there are settings for offset and rest distance, so this can be used to simulate colliding rods, and also for keeping cylinders tangent to one another (can be used for reciprocal structures).
Gear simulator - collision between curves in a plane, can be used for various mechanical simulations - cams, gears, rack and pinions etc.
Developablize force - adjusts vertices of a mesh locally, to make angles around each interior vertex sum to 2*Pi, so the mesh can be unfolded to a flat sheet without stretching.
Volume dependent pressure force - allows you to set a rest volume for a mesh instead of just a fixed pressure. When combined with Laplacian smoothing for area minimization, this can be used to optimize for CMC (constant-mean-curvature) surfaces. It will also work on open meshes.
Translation lock - maintains a fixed relationship between a pair of points. This can be used to enforce periodic boundary conditions for TPMS.
Equalize angles force - given a set of angles (defined by 3 points each), this tries to adjust them all to become equal.
Mirror symmetry force - can be used to minimize curvature variation, and optimize for higher order curve continuity. It can also be used for simulating torsional resistance in curved rods.
True minimal surface relaxation - Laplacian smoothing force now includes an option for cotangent weighting, which optimizes for zero mean curvature, unlike spring based methods, or uniform weighted Laplacian smoothing which only roughly approximate this.
Fast sphere collide - allows much faster collision detection between large numbers of spheres. By placing these spheres at the vertices, this can also be used for collision between meshes.
Force-density element - an experimental one, more on this later
Projected-force - adjusts its strength so the component of the force in a given direction stays constant.
New mesh tools:
WarpWeft - sorts the edges of a quad mesh into warp and weft directions. This can be used to assign them different stiffness in fabric form-finding.
Checkerboard - sort the faces of a mesh into 2 lists so that 2 faces of the same colour are never adjacent.
MeshDirection - sorts the vertices of a quad mesh to give it a sort of u-v directionality
Refine Strips - subdivision in one direction only - can be used to generate developable strips
Stripper - separates out the strips of quads from a larger mesh
Unroller - unfolds a quad strip to flat without stretching
MeshMap - maps points from one mesh to another (can be used together with circle-packing to generate conformal mappings)
Reciprocal structure - generates starting geometry for a reciprocal structure from any input mesh (using the Plankton mesh library *Note* If you already have the Plankton components installed, you will need to update to version 0.3.0, which is available from here)
ReMesher - adjusts the connectivity of a mesh by flipping, splitting and collapsing edges to make all edge lengths closer to a target value
Diagonalize - creates a new face for every edge of the original mesh. Can be used on quad meshes to easily convert to a diagrid.
Refine - simple non-smoothing subdivision, splitting quads into 4 quads, and triangles into 4 triangles
QuadDivide - subdivide quads by any number squared, not just powers of 4
Corners - finds the corner vertices of a quad mesh
ByParent - simple quad subdivision, keeping the output grouped by parent face.
User objects:
The download comes with an increased collection of user objects to simplify setting up common simulation types - Including a simple to use origami simulator, a reciprocal structure generator, and a tool to generate compact circle packings from a CP mesh.
General:
Geometry input now accepts polylines and straight curves.
Hinges can now be fold completely flat in both directions.
Various other minor bug fixes and speed improvements (including much faster removeDuplicatePoints/Lines components)
*****
I've not yet updated all the documentation and example files to reflect this new version, but over time I will keep posting here with new demos and explanation of all these new features. I'll try and add a few new examples each week. Vote in the comments below if there is a feature mentioned above that you're particularly keen to hear more about soon.
No doubt there are still some bugs to be discovered. If something isn't working the way you expect or want it to, please post in this forum (ideally with a description or sketch of what you think should be happening, and a clear description of what happens instead and any error messages).
There are also some more new features that weren't quite ready to make it into this release, but are on the way shortly...
Kangaroo remains completely free, for personal, academic, and commercial use. I'm always interested to hear about projects done using it, and suggestions for improvements or additions.
Daniel
…
ger work.
Be aware, this release breaks file-forwards compatibility. You will not be able to open gh and ghx files saved with 0.8.0050 on previous versions, though of course you should be able to open old files without problems. If this is not the case, please yell loudly.
If you're having trouble loading Grasshopper, note that you must have the latest Microsoft C++ Runtimes installed on your machine. They can be downloaded from the microsoft website.
The new release can be downloaded from the usual location.
Here's a list of changes, additions and fixes since 0.8.0013:
File format forwards compatibility has been broken. You will not be able to open files saved with 0.8.0050 on earlier versions.
This release contains many breaking changes and GHA libraries compiled for older version may not work anymore.
Grasshopper Binary files (*.gh) are now saved as compressed data.
Grasshopper Binary files (*.gh) are now the default format.
Support for ancient versions of the Text Panel (still called Post-It from back then) has been removed.
Support for ancient versions of the Path Mapper (still called Path Lexer from back then) has been removed.
Placeholders for ancient versions of the Graph Mapper have been removed.
Gradient input parameters now show state tag icons (Reversed, Flatten etc.).
Geometry Cache name changes are now updated on every key press.
Geometry Cache name changes can now be cancelled with Escape.
Geometry Cache name changes can now be undone.
Mesh|Mesh intersection component now uses a different algorithm. The old behaviour is still available from the component menu.
Warning and Error balloons are now drawn as part of a Canvas Widget and will no longer show up in the Hi-Res image export.
Galapagos now accepts multiple fitness values. The true fitness will be the average of the collection.
Galapagos wires are drawn much fainter when the Galapagos object is unselected.
Medium fast redraw mode in Galapagos now immediately redraws instead of at the end of each generation.
Redesigned all Grasshopper file format icons and added larger size icons for high-dpi explorer views.
Redesigned the Most Recently Used files menu, it should now display much quicker.
Compass widget has been rewritten in an attempt to increase display performance.
Added preferences section for Compass widget.
Added preferences section for Align widget.
Added preferences section for Default Preview colours.
Added preferences section for Document Preview colours.
Added preferences section for the Most Recently Used files menu.
The Area component now accepts Breps, Meshes and Planar Closed Curves.
The Area Centroid component now accepts Breps, Meshes and Planar Closed Curves.
The Volume component now accepts Breps and Meshes.
The Volume Centroid component now accepts Breps and Meshes.
Added Merge Faces component (Surface.Util panel).
Added a Mesh Smooth component (Mesh.Util panel).
Added a Curve Seam component (Curve.Util panel).
Added Interpolate Curve With Tangents component (Curve.Spline dropdown).
Added GrasshopperFolders command to open Settings, Components and UserObject folders without loading the core plugin.
The window that reports on certain Loading Errors now has a Copy button.
Added Simplify post-process filter to parameters (in addition to Reverse, Flatten and Graft).
Parameter post processes (Reverse, Flatten, Graft & Simplify) can now also be assigned to output parameters.
Version History window now has formatting (not happy with this, I'm working on something better).
The Process Info window is gone.
Main menu has been redesigned.
Canvas toolbar has been redesigned.
Canvas context menu has been replaced by a Radial Menu.
Canvas now has a radial menu which will pop up on Middle Mouse Button clicks.
It's possible to switch between Radial and Legacy menus in the Preferences (Interface.Canvas section).
'Save As Copy' feature has been replaced by 'Save Backup' which is a GUI-less save including date+time stamp.
Added a 'Show in Folder' item to the File menu.
AutoSave settings are no longer available from the File menu, you now need to use the Preferences.
Selection shifts now also modify the view so you can use Ctrl+Left and Ctrl+Right to navigate up and downstream.
Mesh Edge display can now be toggled with Ctrl+M.
Preview modes now have shortcuts (Ctrl+1 = no preview, Ctrl+2 = wireframe, Ctrl+3 = shaded).
Solution States now have a default name.
Data Viewer window now responds to all required events.
Data Viewer window can now handle input and output parameters as well.
Canvas Navigation pane can now be dragged using the icon in the upper left corner.
The Persistent Data Editor has been redesigned.
It's now possible to select multiple items in the Persistent Data Editor list and edit their properties.
It's now possible to drag multiple items at the same time in the Persistent Data Editor list.
Item addition to the Persistent Data Editor is much improved.
The Persistent Data Editor is now non-modal.
The Canvas would remain black upon maximizing the Rhino window, this is fixed.
Sliders would cause multiple updates under certain conditions, this is fixed.
Digit Scrollers would cause multiple updates under certain conditions, this is fixed.
Pipes were inside out. This is fixed.
The curve component would not adjust invalid nurbs degrees, this is fixed.
Curves referencing Brep edges failed to load, this is fixed.
Points referencing Brep edges failed to load, this is fixed.
Referenced dlls in the VB/C# components sometimes resulted in invalid imports statements, this is fixed.
Pasting geometry in Rhino would cause a recompute of the Grasshopper solution, this is fixed.
Importing a file into the Rhino document would cause a recompute of the Grasshopper solution, this is fixed.
Galapagos would trigger superfluous solutions, this is fixed.
Mesh Solid Difference had a wrong name and description, this is fixed.
Several menu items were not greyed out despite not being usable, this is fixed.
The position and size of the Grasshopper window failed to get stored on Rhino shutdown, this is fixed.
The Persistent Data Editor would crash on parameters that did not support data proxies, this is fixed.
I'll add some additional information regarding some of the new UI features in subsequent posts.
--
David Rutten
david@mcneel.com
Poprad, Slovakia…
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