.
For my project I want to make a sphere or spherical-like shape and pack it with circles of varying sizes. The circles all have to touch each other and thus on a point where three circles 'sort of' meet, there can only be three circles. This is shown in the second picture I have attached, a 2D circle packing made by Daniel Piker. So basically what I want to achieve is having the second picture projected on a 3d surface, that I can also edit. Also I would like to be able to change the size and amount of the circles that populate the surface. This means that I would be able to say 'there should be 30 circles with a radius of 2, 40 circles with a radius of 3 and 50 circles with a radius of 4, put them on this particular shape'.
As I've just started the project I haven't done so much research yet. What I have found is for example this Kangaroo definition of circle packing in 2D: http://www.grasshopper3d.com/group/kangaroo/forum/topics/circle-packing-definition?xg_source=activity
It is very beautiful and does exactly what I want to achieve, except that it is in two dimensions. I also have to say that I feel pretty confident working with both Grasshopper and Rhino, but not really with Kangaroo. I have used it a few times but not extensively.
So what I'm wondering is, how could I best approach this project? I looked into the concept of 'circle packing' and I noticed that it can be approached very mathematically. As I am an architecture student I don't know much about the math behind the geometry (although I do think it is very interesting) and thus I'm wondering if I will be able to achieve what I want to achieve. Also, do you think I could best approach the project in Kangaroo and do you think it is realistic for me to think I could finish the project? I'm just trying to see if I'm not going to try to tackle a problem that is very difficult to solve even for skilled mathematicans or something. Sorry for the long and perhaps vague read, but I would be very happy with any sort of input you might have on my problem!
Thanks in advance!
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ectly in grasshopper (drawing a curve on top of a line with different angles), i did the curve shape in rhino and import it into grasshopper.
i'm having a problem where some of the sine curve shape can orient or map onto the triangle surfaces nicely, but some of them do not. whenever i try to orient the shape onto the bottom portion of the icosahedron, the shape becomes 'negative', forcing me to flip the lines before offsetting and patch (i am using loft method) or else it will become a weird loft (image 3).
i have tried several different ways to orient the ones that worked (orient 3d in rhino, rotate 3d etc.) and still could not get them to work.
the reason that i want them to face in the same direction is so that i can use WB thicken and make sure they extrude in the same direction. i have tried to unify the normal faces in grasshopper and still it is not working.
does anyone have any idea why or how can i do this? your help will be greatly appreciated. i am fairly a beginner in GH so if there is any other easier method to do this will also be great :)
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between internal structural frameworks and non-bearing skin elements, this approach promotes heterogeneity and differentiation of material properties. The project demonstrates the notion of a structural skin using a Voronoi pattern, the density of which corresponds to multi-scalar loading conditions. The distribution of shear-stress lines and surface pressure is embodied in the allocation and relative thickness of the vein-like elements built into the skin. Its innovative 3D printing technology provides for the ability to print parts and assemblies made of multiple materials within a single build, as well as to create composite materials that present preset combinations of mechanical properties.
for registration please contact:
bioskinarc@gmail.com
tel: 09197804306
…
and the degree of your periodic curve is 3, then start picking one point to the left. If the degree is 5, start pickin 2 points to the left, etc.
Every curve has a domain. A domain is a numeric range defined by two numbers (a lower and an upper bound). Within the domain, the curve exists and the equations which govern the geometry of the curve yield decent answers. The lower limit represents the start of the curve, the upper limit the end of the curve. Everywhere in between you can evaluate curve properties (position, tangency, curvature and any other derivatives, tension, torsion etc. etc.).
There is no significance attached to the actual numbers in a domain. All that is required is that the lower limit is smaller than the upper limit. When we create curves in Rhino we tend to pick domains that represent the length of a curve, but if you scale a curve afterwards you change the length, but not the domain.
Curve parameters are numbers inside this domain. Basically, think of all curves as finite line segments which can be bend, kinked and stretched in 3D space. Curve parameters are locations on the 1-dimensional space that is defined by the line. The curve equations are all about converting those one-dimensional parameters into three-dimensional points and vectors.
Like I said, the mathematics are pretty involved and periodic curves are more difficult still.
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David Rutten
david@mcneel.com
Tirol, Austria…
Added by David Rutten at 4:23am on September 13, 2013
mber of ways, and how they are represented will dictate the final outcome.
2)If you use rectangles a question for area would be how do you dictate the ratio between the width and length? It may be easier to use circles or rather simple points with a specific charge attached relating to required area, think of the metaball component in 2d or using an isosurface in 3d (I recommend Daniel Piker's Aether plugin). So do you want something orthogonal or more amorphous?
3)Means of creating adjacency: I think for the best results you will want something that operates recursively. Hoopsnake, Octopus, Loop all allow you to create your own recursive loops, however, you might find that using something like circle/sphere packing within kangaroo will give you the desired results. In the case of Kangaroo, the spheres can be given different volumes and the connective network treated as springs to push and pull things together.
4)At this point you will have your basic geometric relationships, start simple and build up. You will want to go back and embed more intelligence into the script pulling in new parameters and inputs to relate to the given context (orientation, sun angles, topo of site, vertical arrangement, circulation). Here you may add new forces to the kangaroo to create a repelling force or attraction to certain areas.
5)Once you have this all in place it is time to flesh out the model, floor plates, partition, aperture, etc. This can be done strictly in GH native. Your primary challenge is establish believable connection between the recursive solver and the forces and output, not an easy task, but very doable.
Good luck, …
ive input but I have no clue how to begin doing this. I've read about using Processing and have even tried something with Processing but it didn't work for me.
I haven't had any luck finding step by step tutorials on inputing data with the 'read file' tool either. I have a feeling that just knowing how to import data would help a lot but the only examples I've found didn't work for me.
I'll be honest though, when it comes to programming and code, I'm an idiot and at a very beginner level. However, once I have working code to study and play around with, I pick up pretty quickly. I've done this with some of the GH definitions I've found and had some good results.
Basically, it's been very difficult and frustrating since I've spend literally 4 weeks trying to figure this out. Like I said, I'm not good with code! Fortunately I've had a little bit of help from the GH community and am very thankful. With any luck, maybe some other people on here would be willing to help out a couple students working on a thesis project? We don't have money but could exchange fabrication services for your help with code or definitions. We have access to a 3 axis CNC mill, Laser Cutter and FDM printer.
Thanks for your time (and hopefully your help),
Matt.
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to problems. If anyone wants to take a look at the attached file "605b-3" and try to help me, that would be awesome.
The way I'm thinking about creating the louvers:
1. Contour the shape (could be any shape, but I attached the one I'm trying to do it to)
2. Divide those contour curves
3. Find the 4 points on those curves that are furthest away from the center of each curve
4. Move those points slightly away from the center of each curve
5. Replace the unmoved points with the moved points
6. Interpolate/NURBS curve through the new list of points
7. Loft the new curves with the original contour curves
I think I'm close, but I'm getting stuck at the end- I thought shifting lists would be the best way to solve my problem, but I'm a little confused as to how grasshopper is organizing the list of new curves and how to match that organization to the original curves.
Attached is an image of where I am stuck. I can only create a surface in the gap that I'm trying to create by the louvers. Either that, or one or two of the curves tends to create a "tornado" looking thing and i can't figure out how to fix it without individually breaking up the list. Is there a way to set all the curve seams to be at the same location in a list?…
ry branches would be an added bonus.)
I had an idea of using contours to find the center point, then connecting these found center points to create my centerline. However, I am facing a few challenges... specifically, I do not know how deal with splits in the tree branch.
I think I have an idea for how to deal with this, but I am not skilled enough (yet) to execute. The whole idea would look like this:
1) create a list of contours through the tree branch
2) connect the center points of the contour lines
3) when a single contour produces two separate polylines (when the tree splits), AND the previous contour produces only a single polyline, divide the list into two new lists starting at that contour.
4)when a single contour produces two separate polylines, AND the previous contour also produces two separate polylines, draw a polyline between the closest pair of centroids.
Has anyone run into this (or something similar) before? And, is this a good way of going about it?
The attached script is incomplete, but has the oak tree branch internalized.
I have been struggling hard with this....Any help would be greatly appreciated!!
Thanks,
Ethan
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Added by Ethan Davis at 8:55pm on September 4, 2017
ive collaborative environment.
TYPE : Course module and Workshop
The event is open for anybody interested from all the fields of design, including: architecture, interior design, furniture design, product design, fashion design, scenography, and engineering.
1. COURSE MODULE (20-23 April 2014) - optional
+ type: 3 days intensive course regarding basic knowledge in parametric design (LEVEL 1)
+ software: Rhinoceros & Grasshopper
+ plugins: Kangaroo, Weaver Bird, Lunch box, Ghowl, Geco
+ achievements:
- acquainting to the components & the concept of Generative Design
- understanding the strategies in Algorithmic Design
- how to easily insert simple mathematical equation into the project to gain more control
- how to utilize proper plugins with respect to their nature of the project
- interacting with different analysis platforms such as Ecotect & remote controller
- solving several exercises with different scales( 2D- 3D ) during each phase of the workshop
2. WORKSHOP (23-27 April 2014)
A 5 day Design-Based Research Workshop exploring new techniques in Digital Architecture/Fabrication, with a specific focus on the use of generative systems and parametric modeling as tools for creative expression.
Our ultimate goal is to increasing the efficiency of utilizing digital tools in parallel with geometric performance of the primitive design agent.
+ + CONCEPT
Fashion and Architecture are both based on basic life necessities – clothing and shelter.
However, they are also forms of self-expression – for both creators and consumers.
Both fashion and architecture affect our emotional being in many ways.
The agenda of this workshop is to investigate on the overlap between these two areas of design, art & fashion.
Fashion and architecture express ideas of personal, social and cultural identity, reflecting the concerns of the user and the ambition of the age. Their relationship is a symbiotic one and throughout history, clothing and buildings have echoed each other in form and appearance. This only seems natural as they not only share the primary function of providing shelter and protection for the body, but also because they both create space and volume out of flat, two-dimensional materials.
While they have much in common, they are also intrinsically different – address the human scale, but the proportions, sizes and shapes differ enormously.
+ + + OBJECTIVES
So far, Architects have been using techniques such as folding, bending etc. to create space, structural roofs or different other structural shapes.
The agenda of this workshop goes further with the investigation of algorithmic thinking through generative tools Integrated in design.
The challenge is creating a bridge that connects these two areas of design, architecture and fashion that perform at two opposite scales.
+ + + + TECHNICAL BRIEF
In the early stages physical models and low-tech strategies will be used, allowing the participants to gain a greater understanding of materials, fabrication and assembly methods as well as simple, yet pragmatic structural solutions.
Later in the workshop these strategies will be digitalized and elaborated using software visualizing tools such as Rhinoceros and the algorithmic plug-in Grasshopper.…
t file** - ply file with just x,y,z locations. I got it from a 3d scanner. Here is how first few lines of file looks like - ply format ascii 1.0 comment VCGLIB generated element vertex 6183 property float x property float y property float z end_header -32.3271 -43.9859 11.5124 -32.0631 -43.983 11.4945 12.9266 -44.4913 28.2031 13.1701 -44.4918 28.2568 13.4138 -44.4892 28.2531 13.6581 -44.4834 28.1941 13.9012 -44.4851 28.2684 ... ... ... In case you need the data - please email me on **nisha.m234@gmail.com**. **Algorithm:** I am trying to find principal curvatures for extracting the ridges and valleys. The steps I am following is: 1. Take a point x 2. Find its k nearest neighbors. I used k from 3 to 20. 3. average the k nearest neighbors => gives (_x, _y, _z) 4. compute covariance matrix 5. Now I take eigen values and eigen vectors of this covariance matrix 6. I get u, v and n here from eigen vectors. u is a vector corresponding to largest eigen value v corresponding to 2nd largest n is 3rd smallest vector corresponding to smallest eigen value 7. Then for transforming the point(x,y,z) I compute matrix T T = [ui ] [u ] [x - _x] [vi ] = [v ] x [y - _y] [ni ] [n ] [z - _z] 8. for each i of the k nearest neighbors:<br> [ n1 ] [u1*u1 u1*v1 v1*v1] [ a ]<br> [ n2 ] = [u2*u2 u2*v2 v2*v2] [ b ] <br> [... ] [ ... ... ... ] [ c ] <br> [ nk ] [uk*uk uk*vk vk*vk]<br> Solve this for a, b and c with least squares 9. this equations will give me a,b,c 10. now I compute eigen values of matrix [a b b a ] 11. This will give me 2 eigen values. one is Kmin and another Kmax. **My Problem:** The output is no where close to finding the correct Ridges and Valleys. I am totally Stuck and frustrated. I am not sure where exactly I am getting it wrong. I think the normal's are not computed correctly. But I am not sure. I am very new to graphics programming and so this maths, normals, shaders go way above my head. Any help will be appreciated. **PLEASE PLEASE HELP!!** **Resources:** I am using Visual Studio 2010 + Eigen Library + ANN Library. **Other Options used** I tried using MeshLab. I used ball pivoting triangles remeshing in MeshLab and then applied the polkadot3d shader. If correctly identifies the ridges and valleys. But I am not able to code it. **My Function:** //the function outputs to ply file void getEigen() { int nPts; // actual number of data points ANNpointArray dataPts; // data points ANNpoint queryPt; // query point ANNidxArray nnIdx;// near neighbor indices ANNdistArray dists; // near neighbor distances ANNkd_tree* kdTree; // search structure //for k = 25 and esp = 2, seems to got few ridges queryPt = annAllocPt(dim); // allocate query point dataPts = annAllocPts(maxPts, dim); // allocate data points nnIdx = new ANNidx[k]; // allocate near neigh indices dists = new ANNdist[k]; // allocate near neighbor dists nPts = 0; // read data points ifstream dataStream; dataStream.open(inputFile, ios::in);// open data file dataIn = &dataStream; ifstream queryStream; queryStream.open("input/query.
pts", ios::in);// open data file queryIn = &queryStream; while (nPts < maxPts && readPt(*dataIn, dataPts[nPts])) nPts++; kdTree = new ANNkd_tree( // build search structure dataPts, // the data points nPts, // number of points dim); // dimension of space while (readPt(*queryIn, queryPt)) // read query points { kdTree->annkSearch( // search queryPt, // query point k, // number of near neighbors nnIdx, // nearest neighbors (returned) dists, // distance (returned) eps); // error bound double x = queryPt[0]; double y = queryPt[1]; double z = queryPt[2]; double _x = 0.0; double _y = 0.0; double _z = 0.0; #pragma region Compute covariance matrix for (int i = 0; i < k; i++) { _x += dataPts[nnIdx[i]][0]; _y += dataPts[nnIdx[i]][1]; _z += dataPts[nnIdx[i]][2]; } _x = _x/k; _y = _y/k; _z = _z/k; double A[3][3] = {0,0,0,0,0,0,0,0,0}; for (int i = 0; i < k; i++) { double X = dataPts[nnIdx[i]][0]; double Y = dataPts[nnIdx[i]][1]; double Z = dataPts[nnIdx[i]][2]; A[0][0] += (X-_x) * (X-_x); A[0][1] += (X-_x) * (Y-_y); A[0][2] += (X-_x) * (Z-_z); A[1][0] += (Y-_y) * (X-_x); A[1][1] += (Y-_y) * (Y-_y); A[1][2] += (Y-_y) * (Z-_z); A[2][0] += (Z-_z) * (X-_x); A[2][1] += (Z-_z) * (Y-_y); A[2][2] += (Z-_z) * (Z-_z); } MatrixXd C(3,3); C <<A[0][0]/k, A[0][1]/k, A[0][2]/k, A[1][0]/k, A[1][1]/k, A[1][2]/k, A[2][0]/k, A[2][1]/k, A[2][2]/k; #pragma endregion EigenSolver<MatrixXd> es(C); MatrixXd Eval = es.eigenvalues().real().asDiagonal(); MatrixXd Evec = es.eigenvectors().real(); MatrixXd u,v,n; double a = Eval.row(0).col(0).value(); double b = Eval.row(1).col(1).value(); double c = Eval.row(2).col(2).value(); #pragma region SET U V N if(a>b && a>c) { u = Evec.row(0); if(b>c) { v = Eval.row(1); n = Eval.row(2);} else { v = Eval.row(2); n = Eval.row(1);} } else if(b>a && b>c) { u = Evec.row(1); if(a>c) { v = Eval.row(0); n = Eval.row(2);} else { v = Eval.row(2); n = Eval.row(0);} } else { u = Eval.row(2); if(a>b) { v = Eval.row(0); n = Eval.row(1);} else { v = Eval.row(1); n = Eval.row(0);} } #pragma endregion MatrixXd O(3,3); O <<u, v, n; MatrixXd UV(k,3); VectorXd N(k,1); for( int i=0; i<k; i++) { double x = dataPts[nnIdx[i]][0];; double y = dataPts[nnIdx[i]][1];; double z = dataPts[nnIdx[i]][2];; MatrixXd X(3,1); X << x-_x, y-_y, z-_z; MatrixXd T = O * X; double ui = T.row(0).col(0).value(); double vi = T.row(1).col(0).value(); double ni = T.row(2).col(0).value(); UV.row(i) << ui * ui, ui * vi, vi * vi; N.row(i) << ni; } Vector3d S = UV.colPivHouseholderQr().solve(N); MatrixXd II(2,2); II << S.row(0).value(), S.row(1).value(), S.row(1).value(), S.row(2).value(); EigenSolver<MatrixXd> es2(II); MatrixXd Eval2 = es2.eigenvalues().real().asDiagonal(); MatrixXd Evec2 = es2.eigenvectors().real(); double kmin, kmax; if(Eval2.row(0).col(0).value() < Eval2.row(1).col(1).value()) { kmin = Eval2.row(0).col(0).value(); kmax = Eval2.row(1).col(1).value(); } else { kmax = Eval2.row(0).col(0).value(); kmin = Eval2.row(1).col(1).value(); } double thresh = 0.0020078; if (kmin < thresh && kmax > thresh ) cout << x << " " << y << " " << z << " " << 255 << " " << 0 << " " << 0 << endl; else cout << x << " " << y << " " << z << " " << 255 << " " << 255 << " " << 255 << endl; } delete [] nnIdx; delete [] dists; delete kdTree; annClose(); } Thanks, NISHA…