phere with the maximum number of triangles but not much than a defined threshold.
I scaled that mesh just to fit Rhino grid, but it is not mandatory. What is useful, is to scale not uniformly the mesh (Scale NU). It could be done after cellular modifier applied or before or before and after. The 3 options are possible in the script. If you don’t need them just put 1 in scale sliders.
Ellipsoid mesh is the populated with points, I put 2 independents populations to randomize a bit further. For each vertices of the mesh the closest distance from the populated points is calculated.
Here is an illustration in color of this distance.
This distance is then used to calculate a bump. If domain for bump is beginning with negatives values to 0, it carves the mesh. Instead it bumps/inflates it.
Some images to illustrate the difference with populating 100 points with one or two populations.
Here some images to illustrate the application of scale before carving or after.
Next phase apply noise. At the moment I don't find it good.…
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
…
rrect, the heat balance of a zone is always 0 = Qcool/heat + Qinf + Qvent + Qtrans + Qinternalgains + Qsol. These parameters also correspond with the readEPresult element. However, if i sum up these values there is a slight deviation.
The deviation is greater during daytimes and in winter, suggesting it has something to do with the heating values.
Attached you'll find an image of the energy plus outputs that I use and the resulting -.CSV file that I constructed. In this you'll see that the balance does not add up.
Am i missing some energy flows?
Thanks for the help.
Hour[H]
Qbal{kWh]
Qint[kWh]
Qsol[kWh]
Qinf[kWh]
Qvent[kWh]
Qtrans[kWh]
Tair[°C]
Tdrybulb[°C]
DIFFERENCE
1
3,039357
0,137702
0
-0,253218
-0,321929
-2,000028
20
5,1
0,601884
2
3,107099
0,125462
0
-0,247457
-0,315484
-1,881276
20
4,6
0,788344
3
3,181073
0,119342
0
-0,261765
-0,334485
-2,473788
20
4,3
0,230377
…
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.
…
ndard length elements without any cutting, and using only simple connections, such as cable ties or scaffold swivel couplers.
To summarize the approach I present here:
Design an initial shape
Remesh this form so that the edges are all roughly the length of the tubes we will use to build the structure
Rotate and extend the edges of this mesh to create the crossings
Apply a relaxation to optimize the positions of the tubes for tangency
demo_reciprocal_structures.gh
Initial form
In this example I show how to apply this system to a simple sphere. You can replace this with any arbitrary shape. It can be open or closed, and have any topology.
Remeshing
The new ReMesher component takes an input mesh, and a target edge length, and iteratively flips/splits/collapses edges in order to achieve a triangulated mesh of roughly equal edge lengths.
Press the Reset button to initialize, then hold down the F5 key on your keyboard to run several iterations until it has stabilized. (F5 just recomputes the solution, and this can be a quick alternative to using a timer)
Once the remeshing is complete, bake the result into Rhino and reference it into the next part of the definition (I recommend doing this rather than connecting it directly, so that you don't accidentally alter the mesh and recompute everything downstream later).
Alternatively you can create your mesh manually, or using other techniques.
Rotate and Extend
We generate the crossings using an approach similar to that described by Tomohiro Tachi for tensegrity structures here:
http://www.tsg.ne.jp/TT/cg/FreeformTensegrityTachiAAG2012.pdf
Using the 'Reciprocal' component found in the Kangaroo mesh tab, each edge is rotated about an axis through its midpoint and normal to the surface, then extended slightly so that they cross over.
By changing the angle you can change whether the fans are triangular or hexagonal, and clockwise or counter-clockwise.
Choose values for the angle and scaling so that the lines extend beyond where they cross, but not so far that they clash with the other edges.
Note that each rod has 4 crossings with its surrounding rods.
There are multiple possibilities for the over/under pattern at each 'fan', and which one is used affects the curvature:
A nice effect of creating the pre-optimization geometry by rotating and extending mesh edges in this way is that the correct over/under pattern for each fan gets generated automatically.
Optimization for tangency
We now have an approximate reciprocal structure, where the lines are the centrelines of our rods, but the distances between them where they cross vary, so we would not actually be able to easily connect the rods in this configuration.
To attach the rods to form a structure, we want them to be tangent to one another. A pair of cylinders is tangent if the shortest line between their centrelines is equal to the sum of their radii:
Achieving tangency between all crossed rods in the structure is a tricky problem - if we move any one pair of rods to be tangent, we usually break the tangency between other pairs, and because there are many closed loops, we cannot simply start with one and solve them in order.
Therefore we use a dynamic relaxation approach, where forces are used to solve all the tangency constraints simultaneously, and over a number of iterations it converges to a solution where they are all met. The latest Kangaroo includes a line-line force, which can be used to pull and push pairs of lines so that they are a certain distance apart. Each rod is treated as a rigid body, so forces applied along its length will cause it to move and rotate.
The reciprocal component uses Plankton to find the indices of which lines in the list cross, which are then fed into the force for Kangaroo. We also use springs to keep each line the same length.
If the input is good, when we run the relaxation (by double clicking Kangaroo and pressing play), the rods should move only a little. We can see whether tangency has been achieved by looking at the shortest distance between the centerlines of the crossing rods. When this is twice the rod radius, they are tangent. Wait for it to solve to the desired degree of accuracy (there's no need to wait for 1000ths of a millimeter), and then press pause on the Kangaroo controller and bake the result.
The radius you choose for the pipes, curvature of the form and length of the edges all affect the result, and at this stage you may need to tweak these input values to get a final result you are happy with. If you find the rods are not reaching a stable solution but are sliding completely off each other, you might want to try adding weak AnchorSprings to the endpoints of the lines, to keep them from drifting too far from their original positions.
For previewing the geometry during relaxation I have used the handy Mesh Pipe component from Mateusz Zwierzycki, as it is much faster than using actual surface pipes.
To actually build this, you then need to extract the distances along each rod at which the crossings occur, and whether it crosses over or under, mark the rods accordingly, and assemble (If there is interest I will also clean up and post the definition for extracting this information). While this technique doesn't require much equipment, it does need good coordination and numbering!
There is also a ReciprocalStructure user object component that can be found in the Kangaroo utilities tab, which attempts to apply steps 3 and 4 automatically. However, by using the full definition you have more control and possibility to troubleshoot if any part isn't working.
The approach described here was first tested and refined at the 2013 Salerno Structural Geometry workshop, lead by Gennaro Senatore and myself, where we built a small pavilion using this technique with PVC tubes and cable ties. Big thanks to all the participants!
Finally - this is all very experimental work, and there are still many unanswered questions, and a lot of scope for further development of such structures. I think in particular - which of the relative degrees of freedom between pairs of rods are constrained by the connection (sliding along their length, bending, and twisting) and how this affects the structural behaviour would be interesting to examine further.
Steps 3 and 4 of the approach presented above would also work with quad meshes, which would have different stability characteristics.
There is also the issue of deformation of the rods - as the procedure described here solves only the geometric question of how to make perfectly rigid straight cylinders tangent. The approach could potentially be extended to adjust for, or make use of the flexibility of the rods.
I hope this is useful to somebody. Please let me know if you do have a go at building something using this.
Any further discussion on these topics is welcome!
Further reading on reciprocal structures:
http://vbn.aau.dk/files/65339229/Three_dimensional_Reciprocal_Structures_Morphology_Concepts_Generative_Rules.pdf
http://www3.ntu.edu.sg/home/cwfu/papers/recipframe/
http://albertopugnale.wordpress.com/2013/04/05/form-finding-of-reciprocal-structures-with-grasshopper-and-galapagos/
…
o está dirigido a estudiantes de arquitectura y diseño de interiores, recién titulados y profesionales interesados en el software o que necesiten conocer las herramientas básicas de las que dispone el programa en los diferentes ámbitos y cómo enfocarlas a arquitectura.
Descripción:El contenido del curso enseñará a utilizar el programa de diseño Rhinoceros 3D aplicando su metodología de trabajo en el campo de la arquitectura, básandose además de la creación de pequeños elementos paramétricos para controlar el diseño y acabar renderizando las geometrías 3d con V-Ray para Rhino.
El curso consta de 3 módulos de 12h de duración cada uno (que pueden realizarse juntos o por separado) en los cuales se profundizará en herramientas de Rhino, Grasshopper y V-Ray a medida que se realizan casos prácticos sobre proyectos arquitectónicos.Se pretende establecer un sistema de trabajo eficiente desde el inicio del modelado hasta la posterior creación de imágenes para documentación del proyecto.
Módulo Rhinoceros Arquitectura:• Conceptos básicos e interfaz de usuario Rhino• Introducción al sistema cartesiano en Rhino• Clases de complejidad de geometría• Importación/exportación de archivos compatibles• Topología NURBS• Trabajo con Sólidos• Estrategias básicas de Superficies• Introducción a Superficies Avanzadas
Módulo Grasshopper:• Conceptos básicos e interfaz de usuario Grasshopper• Introducción a parámetros base y componentes• Matemáticas y trigonometría como herramientas de diseño• Matemáticas aplicadas a creación de Geometría• Introducción a listas simples• Análisis de Superficies y Curvas• Dominios de Superficies y Curvas• Panelado de superficies• Manejo de listas y componentes relacionados• Modificación de panelados en función de atractores• Exportación/Importación de información a Grasshopper
Módulo V-Ray para Rhinoceros:• Conceptos básicos e interfaz de usuario V-Ray• Vistas guardadas• Materiales V-Ray• Materiales, creación y edición• Iluminación (Global Illumination, Sunlight, Lights)• Cámara Física vs Cámara default• Canales de Render• Postprocesado básico de canales
Detalles:Instructores: Alba Armengol Gasull y Oriol Carrasco (SMD Arquitectes)Idioma: CastellanoHorario: 22 JULIO al 26 JULIO 2013 // 10.00 – 14.00 / 16.00 – 20.00Organizadores: SMDLugar: SMD lab, c/Lepant 242 Local 11, 08013 Barcelona (map)
Software:Rhinoceros 5Grasshopper 0.9.00.56V-Ray 1.5 for RhinoAdobe Photoshop CS5Links de versiones de evaluación de los Softwares serán facilitadas a todos los asistentes. Se usará unica y exclusivamente la versión de Rhino para PC. Se ruega a los participantes traer su propio ordenador portátil.
Registro:Modalidad de precio reducido por tres módulos 275€Posibilidad de realizar módulos por separado 99€…
to incorporating math and geometry in computational design education, Paneling Tools
Marlo Ransdell, PhD Creative Director, at FSU , Digital Fabrication in Design Research and Education
Andy Payne, LIFT architects | Harvard GSD | FireFly
Jay H Song, Chair, Jewelry School of Design, Jewelry as Personal Expression, Extra+Ordinary@Jewelry.com
Pei- Jung (P.J.) Chen, Professor of Jewelry, SCAD
Gustavo Fontana, designer/co-founder nimbistand, Diseñar, desarrollar y comercializar productos por tu cuenta.
Joe Anand, CEO MecSoft Corporation, RhinoCAM
Julian Ossa, Chair, Industrial Design Director, Diseño – Una opción de vida a todo vapor!, UPB
Minche Mena, SHINE Architecture, Principal
J. Alstan Jakubiec, Daylighting and Environmental Performance in Architectural Design Solemma, LLC
Carlos Garnier R&D Director / Jaime Cadena – General Director, Plug Design, www.plugdesign.com.mx
Mario Nakov, www.chaosgroup.com [ V-Ray ]
Andres Gonzalez, RhinoFabStudio
Workshops:
o) Paneling Tools
o) RhinoCAM
o) Rhinology in Design, for Jewelry
o) Footwear
o) V-Ray: Jewelry Design
o) V-Ray: Architects and Industrial Designers
o) FireFly
o) J. Alstan Jakubiec, DIVA
The cost for each workshop or the Lectures is 95.0 US$
To register:
WORK-SHOPS April 2 - RHINO DAY
WORK-SHOPS April 3 - RHINO DAY
REGISTRATION RHINO DAY
NOTE: All students and faculty members that register to this event, will receive a Rhino 5 Educational License at the event.
…
you will need to deal with all of the curves that intersect the boundry curve, but you will also need to sort through all of the circles inside because the planar surface algorithm won't sort those out for you. The good news is that because you are using circles and linear segments, you can use "pure" geometry equations for some of these intersections instead of relying on NURBS curve "physical" intersections. In the end this means faster and also "more" reliable intersections (especially with the circles).
Method 1: Dealing with everything as a phyisical curve...
First things first, i guess the "easiest" way to do this would be to translate everything into an OnCurve derived class, and then use the IntersectCurve method to find the intersections. You will need to sort through the resulting ArrayON_XEVENT to find the parameter of each intersection. There should always be 2 intersections, and you're always going to be interested in the intersections of the circle not the boundry curve.
To trim the curves, you'll want to use the Split method along with one of the parameters on the curve that you retrieved from the intersection. The only issue is that the split method gets a bit complicated when using it on closed curves. You could either split at both parameters that you retrieved from the intersection results, then sort through the 3 resulting curves to join the two that you need. Or move the start point of the circle to where one of the intersection points happened, translate the other intersection point to the new curve parameter (ie the parameter will be a different number, but it will be physically in the same place), then split with that new curve parameter.
Method 2: Try and work with the circles as circles
Because you can tell if a circle intersects something by seing if the distance to its center point is less than the radius of the circle, this might be a quicker way to go. If you have the boundry curve as an OnCurve derived class, then you can use the GetClosestPoint method and use all of the center points for each of the circles. The nice thing is that after the 3Dpoint in, and the parameter on the curve that you'll get out, you have the option of supplying a maximum distance. If you do supply that value (use the radius of the circles), then you'll only get a result when the distance is less than or equal to that value. In which case there will be an intersection.
To go even further, you can treat the segments of the boundry curve each as a line, and find the closest point/distance to that. That's maybe more complex than your looking to go, but speed wise, it might just be worth it. Take a look at the following link for more code/discussion on the subject.
http://www.codeguru.com/forum/showthread.php?t=194400
Part 2: Circle-Circle intersections
If you're going to want to make a planar surface out of those circes and the boundry curve, then you'll need to resolve all of the intersections that you have there. Again this is probably something that would be best taken care of by doing some distance tests between the center points of all the circles and seeing if that distance is less than the radius your using. After you've found circles that intersect, you can be try intersecting the curves using the same method mentioned above, or even manually generating the intersection with some trig, but ultimately creating a final result might take a bit of work, especially where you have more than two circles intersecting. The "lazy" way out of this is what's used by the curve boolean command, which is to take each individual curve, make a planar surface from that individual curve, and use standard Rhino booleans to get the result. Luckily you're looking for the union of all those areas, which will be the easiest to create and deal with. After you create the planar surface of each one (RhUtil.RhinoMakePlanarBreps), you can use either RhUtil.RhinoBooleanUnion or the more specialized version, RhUtil.RhPlanarRegionUnion. Note that RhPlanarRegionUnion only takes 2 breps at a time and needs the plane of the intersection.…