x geometry which will be the basis in plan for a building facade. The problem is as follows:
I am generating a series of arcs using 3 different ranges for radii. Each segment of the geometry is assigned one of the radii. The length of each arc segment is controlled by a specific number, also within a range -- the end goal is to divide this geometry into perfectly equal segments.
(Parameter Ranges)
I am building these arcs in such a way that they are tied to the arc drawn before it - meaning that as the length of the previous arc is adjusted, the arc in question will still begin where the previous arc ends, and be tangent from said previous arc.
This approach works well until I get to the final segment of the form. I want to be able to close the form in a way that the final arc both meets the first arc at its tangent point and is a length divisible by the desired segment length.
Through a series of trial and error by means of adjusting the radii, panel size, and arc lengths, I have been able to get the geometry to being very close to closed, but there is always some sort of remainder, or the last arc is not tangent to the first arc.
My thought is that this would be a perfect scenario to use Galapagos, but my attempts to do so have resulted in an almost immediate crash of rhino. I'm not sure if I'm feeding too many inputs into galapagos (the radii ranges and segment length ranges), or that the number I'm telling it to minimize is incorrect (distance between the end of the final segment and the start of the first segment), or if there is a larger issue with the definition I've written, but I haven't been able to figure out the issue.
Are there any thoughts out there on how I might be able to reach a possible solution? Or at the very least is there any precedent for a geometric shape similar to what I am trying to create which follows the same number of parameters I'm using?
I've attached the GH definition as well as a rhino model for your visual reference. To preview the GH form in rhino, simply assign the only curve in the attached rhino model to the crv node in grasshopper:
This simply locates everything that's being generated in grasshopper in space in rhino.
Thanks in advance for any thoughts, and also apologies for a somewhat potentially messy definition.
…
Added by Ray LeChase at 11:12am on August 31, 2016
d simulate the bending process of a flat stell sheet in order to get the same shape. This can be really interesting so we can evaluate the material beheaviour, the deformation on the cross section a
nd explore big deformations in mecanics analysis of materials.
I am not a mecanical engineer nor a civil engineer, I´m an Architect and my interest is the construcction method and extracting the necesary information to consider fabricating the project.
I´m having conceptual challengings on the methodology for this simulation, so I will post a small overview of what I`ve done.
1.- Understanding the Geometry.
This is a sclupture by the Venezuelan/Hungarian/German artist Zoltan Kunckel (KuZo).
The shape is achieved bending a pre water cut square sheet of stainless steel. After bended manually, the different lashes are pulled on the opposite direction. New curvatures are produced after all is deployed.
2.- Reproducing the Shape digitally.
Using Karamba I built a definition to reproduce the produced by physical stress. This model served to find deformations that occur when a set of loads are applied to a mesh. Following this process will allow us to find a coherent and more natural cross section so then we could re-shape simulating the bending process of a piece of ductile material.
3.- Discretizing curve
Reducing the model to its simplest element is a key aspect of finite nonlinear analysis. Once our shape is already defined we can divide its principal characteristic of its principal given curve.
At this point I have already found the desired curve.
I Think the better strategy to simulate bending the steel sheet into this shape, is rationalize the curve and divide it finding the tangents one of the curve that compose this sort of parabola. bur i don`t know how to parametrize that in GH.
Please. If someone have a better Idea about this process I`ll glad to read sugestions.
Tomás Mena
…
to enter the programming world and tinker more complex, interactive solutions. We will also explore advanced programming paradigms. There is no class official programming language, as both C# and Vb.Net are possible on the participant’s side, and all examples will be provided in both C# and Vb.Net. Additionally, we will see how to get started writing full .Net plug-ins. Finally, we will have time to explore user’s own proposals on the third day.
Day 1 Morning: programming introduction in .Net
• The Grasshopper scripting components. Choosing a .Net language. Language developments
• Variables declaration, assignment and utilization. Operators. Methods [functions]. Calls
• Classes: declaration and instancing. Constructors. Importing a namespace. Point3d, Lines
• Arrays declaration and usage. Lists. Adding to arrays and lists, advantages and opportunities.
Afternoon: patterns
• About OOP (object oriented programming) as opposed to procedural programming. Discussion
• Example of OOP good code reuse: sorting points by coordinates using the .Net SDK classes
• Lists as input parameters. Trees as input parameters. Usage and limitations
• Finding resources: on the net with website that can help getting started and troubleshoot. And books
Day 2 Morning: extending Grasshopper functionality with our definitions
• Store data between updates. The use of fields [globals, or static locals]
• Examples on how to use stored data between updates: a simple agents simulation
• Baking geometry with scripting directly into the Rhino document. Baking with names
• Passing custom types from a scripted component to another one. Our own code reusability
• Rendering an animation from Grasshopper. How to get started and final results
Afternoon: customizing our tools
• Our Rhino plug-in with Visual Studio C# [Vb.Net] Express Edition & wizard. Parametric mesher
• Writing a custom Grasshopper component: hacking an exporter for our data to Excel
Day 3 All day: personal project
• Rehearsal on any example from the first two days. A project that you want to start on your own, being it a Rhinoceros plug-in, a Grasshopper assembly or a script. Example might be to send data through network with UDP to Processing
MINIMUM REQUIREMENTS
A good foundation of Grasshopper visual programming is mandatory. You will need a level which corresponds to the Grasshopper 101 course outline. Examples of things that will not be covered in this course are: sorting document spheres by diameter, paneling of a surface with grasshopper components. You are expected to already know these from the Grasshopper course.…
So it's not true that Bounds.X is only a getter. However it does behave as though it is. This is because RectangleF is a Value Type instead of a Reference Type. When you assign a variable of one value type to another variable of the same type, you always assign a copy of the first value. So when you request the Bounds from an attributes class, what you get is a copy of the actual bounds. Changing the X on this copy would be a useless operation which is why Visual Studio catches this mistake.
Let's assume that Dog is a class (a reference type) and it has a get/set property for fur type. Then, if I type:
Dog A = new Dog();
A.Coat = Long;
Dog B = A;
B.Coat = Short;
At the end of these lines, both A and B have a short coat, because the act of assigning A to B (line 3) means that both A and B now point to the same instance of Dog in memory. In effect, A and B are the same. If Dog were a struct (a value type), then at the end of this code A and B would have different coats, because assigning A to B means creating a copy of A. Any changes made to B will not affect A.
The one place where this causes annoying situations is exactly where you ran into it. If a property returns a value type then it's typically not useful to call properties and methods on that returned data, as it would only affect the copy of the actual data instead of the original data. That's why, if you want to change the Bounds of an attribute, you need code like this:
RectangleF box = Bounds;
box.X +=10;
Bounds = box;
On to the second problem, which is that doing it this way won't help you one bit. Laying out a component is a difficult job and the size of the Bounds depends on many things:
The display mode of the component (icon or text).
The size of the text (depending on which Font to use).
The maximum number of input and output parameters.
The maximum width of the longest input/output parameter name.
The maximum number of state icons to draw on the input/output parameters.
Changing the Bounds after the layout has occurred will basically just invalidate the parameter layout, resulting in parameter names and grips being drawn in the wrong places.
If you want to affect the size of the Bounds for a GH_Component class, you're going to have to dive in and do the laying out yourself. As mentioned before, this is not trivial.
There are static methods on GH_ComponentAttributes which are helpful when doing this, have a look at:
LayoutComponentBox()
LayoutInputParams()
LayoutOutputParams()
LayoutBounds()
Unfortunately they are undocumented.
--
David Rutten
david@mcneel.com…
Added by David Rutten at 1:39pm on January 31, 2014
s levels of detail by subdividing a 6 sided cube mesh and projecting its vertices according to a referenced height map. This is one of the standard conventions for building full sizes planets. At the lowest level (0) the mesh planet is made of 6 pieces(each 32x32 resolution). The next level down (1) is made of 24 pieces... 6 divided by 4 = 24. Level (2) is 96 quads etc etc. The script will generate each quad at its sub-division level and compare edge vertices to neighboring quads. It will then make sure any shared vertices are in fact at the same projected vector. This ensures a planet quad with edge vertices that match.
The problems comes in texturing each quad.
If I build the quad as a nurb surface from points I can place the texture easily because each surface UV maps squarely to my texture map (which is also square).
If I build the quad as a mesh I cannot just apply the square texture to the mesh UVs. This is because when you unwrap the UVs from a mesh they will not unwrap like a nurb surface's UVs. Therefore to get the correct mapping I would have to manipulate each UV back to an evenly aligned array (which is 1024 points in a 32x32 resolution UV). Maya and blender have 'relax uv' and 'align UV' functions but they don't do the trick and manual corrections are out of the question. So why not skip the mesh method and use the nurb method?
I did this and there is a trade off. The nurb will accept the material texture I want with no other work on my end but when I export the object as an .obj rhino creates its own mesh to describe the nurb(with various unsatisfactory setting options). This works great up to a point because at some level the interpreted mesh will have vertices that do no match at the edges, ie .. creating visible seams in the mesh. The picture below is the nearly seamless planet at LOD(1) made of 24 quads, each with 32x32 vertice resolution and a 512x512 jpg texture running in Unity3d 5. It works but at close level there are seams. This will be resolved simply by having the next LOD(x) instantiate before getting close enough to see the seam but at core nerd level I want the seamless mesh.
So, I can make the seamless mesh but I can not realistically texture map it. I can also make the nurb surface from points and texture it at the expense of the edge vertices matching. I am at the split in the road but I want to have my cake and eat it too. Thoughts, comments, trolls...?
Thanks for reading =)
Footnote: For you pros I am not using seamless noise across the map I am using grasshopper to sew up my otherwise non perfect edges.
Other programs in the pipeline:
-WorldMachine 2
-Wilbur
-Photoshop
-Unity3d…
option, after downloading check if .ghuser files are blocked (right click -> "Properties" and select "Unblock"). Then paste them in File->Special Folders->User Object Folder. You can download the example files from here. They act in similar way, Ladybug Photovoltaics components do: we pick a surface, and get an answer to a question: "How much thermal energy, for a certain number of persons can my roof, building facade... generate if I would populate them with Solar Water Heating collectors"? This information can then be used to cover domestic hot water, space heating or space cooling loads:
Components enable setting specific details of the system, or using simplified ones. They cover analysis of domestic hot water load, final performance of the SWH system, its embodied energy, energy value, consumption, emissions... And finding optimal system and storage size. By Dr. Chengchu Yan and Djordje Spasic, with invaluable support of Dr. Willian Beckman, Dr. Jason M. Keith, Jeff Maguire, Nicolas DiOrio, Niraj Palsule, Sargon George Ishaya and Craig Christensen. Hope you will enjoy using the components! References: 1) Calculation of delivered energy: Solar Engineering of Thermal Processes, John Wiley and Sons, J. Duffie, W. Beckman, 4th ed., 2013. Technical Manual for the SAM Solar Water Heating Model, NREL, N. DiOrio, C. Christensen, J. Burch, A. Dobos, 2014. A simplified method for optimal design of solar water heating systems based on life-cycle energy analysis, Renewable Energy journal, Yan, Wang, Ma, Shi, Vol 74, Feb 2015
2) Domestic hot water load: Modeling patterns of hot water use in households, Ernest Orlando Lawrence Berkeley National Laboratory; Lutz, Liu, McMahon, Dunham, Shown, McGrue; Nov 1996. ASHRAE 2003 Applications Handbook (SI), Chapter 49, Service water heating
3) Mains water temperature Residential alternative calculation method reference manual, California energy commission, June 2013. Development of an Energy Savings Benchmark for All Residential End-Uses, NREL, August 2004. Solar water heating project analysis chapter, Minister of Natural Resources Canada, 2004.
4) Pipe diameters and pump power: Planning & Installing Solar Thermal Systems, Earthscan, 2nd edition
5) Sun postion and POA irradiance, the same as for Ladybug Photovoltaics (Michalsky (1988), diffuse irradiance by Perez (1990), ground reflected irradiance by Liu, Jordan (1963))
6) Optimal system and storage tank size: A simplified method for optimal design of solar water heating systems based on life-cycle energy analysis, Renewable Energy journal, Yan, Wang, Ma, Shi, Vol 74, Feb 2015.…
h tubes are redundant so surfaces overlap instead of interpenetrate, so it is not a good system.
Cocoon is the best answer these days unless you can get Exowire/Exoskelton to work. If you want more control over shape, feed your uncapped tubes into Cocoon as meta-surfaces and delete any and all of the inner meshes to just keep the outer single closed one, but this is just duplicate-culled lines used as meta-lines:
Turn down the CS input to 0.005 for this result, from 0.02 used for faster preview. In fact bake the lines and only test Cocoon on a few of them in order to get the result you want before doing the whole thing.
Whole thing at 0.005 cell size takes 5 minutes for Cocoon and 2 minutes for refinement to a smooth and even mesh.
Actually, seems like 0.005 is way too fine, giving a 600MB STL file.
So, 0.01 cell size at less than a minute total:
159MB STL which is still a bit too big for places like Shapeways. Wow. OK then 0.02 cell size, but I have to increase diameter or my two smoothing steps in refine collapse things too much, an in fact I set it to no smoothing, getting more volume and a reasonable 46MB STL file:
Alas, now it's more frail and overly organic rather than mechanical. Increasing diameter just merges it into perforated plates too much. File size is simply an issue with this complexity level, so different 3D printing services will have different file size limits.
Exowire/Exoskeleton would work but your original mesh hasn't been MeshMachine remeshed to be regular, so short segments ruin it. Here is just a corner:
I think that's why more wires fails, at least. Pretty temperamental component.
Switching to MeshMachine is needed, I guess, instead of Cocoon refine, to remesh away so many small triangles along the boring tubes. Crucial for good remeshing was to set Flip to 0 or I failed to get a rough enough mesh.
It's an adaptive mesh so I can retain good detail while roughing out the tubes.
MeshMachine is terribly slow for this whole thing, like 6 minutes, and blows up for this overly rough setting, 20 steps, so less rough, ugh, I'm out of time. I think free Autocad Meshmixer is the way to make a better smaller mesh, after a refined output from Cocoon. MeshMachine is just too slow to tweak and when it blows up, creating massive triangles jutting out, it hangs too when you change settings.
Starting with a Cocoon refined mesh certainly helped Meshmixer. Using triangle budget lets me have full control. Here is 150K triangles instead of 200K:
STL file size down to 40MB. I think Shapeways is 70 or 100MB limit? So it can be even finer. Here is the Cocoon output versus the Meshmixer reduction:
To use Meshmixer, turn on View > Show Wireframe, Command-S to select all and use Edit > Reduce from the palette that appears.
Cocoon can end up making a few inner meshes where things get weird in your uneven original mesh with small holes so fish out the main mesh by adding a List Item node.
The best strategy for Cocoon is indeed to make an overly fine STL so you avoid any need to tweak forever in Grasshopper, but then you can achieve a smaller mesh file size while preserving shape instead of things turning all smearly organic in Grasshopper.…
but rather than keep everyone waiting, I've decided to share some as they become ready.
This also has the advantage that questions about components can be more easily grouped under the relevant post - so please do add any questions / comments / bugs / suggestions about these examples below.
So today I am posting some examples of the mesh utilities that come with the new release.
While these are not directly physics based, many of the forces and types of relaxation in Kangaroo are designed to work with meshes, and in the process of development I've ended up adding a number of simple utilities to make working with them a little easier.
I recommend also installing Weaverbird which has many more subdivision functions and other useful tools for working with meshes in Grasshopper. Also Plankton, Turtle, MeshEdit and Starling extend these possibilities still further.
Diagonalize
This component replaces every edge of a mesh with a new face. The new faces will always be quads, except for along the boundaries, where they will be triangles. It can be used to easily create diagrids. The input mesh can contain any mix of triangles and quads.
When treating the edges of a quad mesh as springs, diagonalizing it will often significantly change its physical behaviour. If you are trying to planarize a quad mesh, diagonalizing may sometimes allow you to stay closer to a target shape if it matches the curvature directions better.
diagonalize.gh
Checkerboard
This component assigns the faces of a mesh into a checkerboard pattern. The output is a list of 1s and 0s (which could represent black/white or true/false) which can be used to dispatch the faces into 2 lists, where no pair of adjacent faces have the same colour.
One nice application I found for this is applying alternating clockwise and counter-clockwise rotations as shown below. Also, on occasion you may want to planarize a quad mesh, but have some constraints on the shape and grid that prevent this, and triangulating only alternating quads to give a hybrid quad/tri mesh can sometimes be a good compromise, allowing a bit more freedom.
Note - Not all meshes can be assigned a checkerboard pattern!
As a simple example, take a mesh with 3 quads around one vertex - If we assign one black face, then both the neighbouring faces should be white, but then we have 2 white faces adjacent to one another, which violates the checkerboard condition.
Generally, we can say that if a mesh has any internal vertex with an odd number of faces around it, then we cannot apply a consistent checkerboard pattern to it (although not having any odd valence vertices is not in itself an absolute guarantee that a mesh is 'checkerboardable').
checkerboard.gh
WarpWeft
This sorts the edges of a quad mesh into 2 lists of line segments, which are like the warp and weft directions of a fabric. They can also be seen as a sort of mesh equivalent to the u and v isocurves on a NURBS surface.
This can be useful if you want to control the shape of a tension structure, because it allows you to assign different stiffnesses in the 2 directions.
As with the checkerboard component, not all meshes can be consistently assigned warp/weft directions. It follows a similar rule - all internal vertices should have an even number of adjacent faces. With a bit of care, it is usually possible to model the initial mesh in such a way as to allow this.
This component also has an output telling us whether or not each line is on a boundary of the mesh, as we will often want to treat these differently.
Same mesh relaxed with different warp/weft stiffness:
warpweft.gh
MeshCorners
This one is hopefully fairly self explanatory. In many simulations we want to anchor the corner points of a mesh. This saves us having to pick them manually in Rhino.
It works on quad meshes, and looks around the boundary vertices for any which do not have exactly 3 connected edges.
corners.gh
That's all for now. Coming soon - a "mesh tools 2" post explaining more of the components.…
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