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…
g-in, brief theory of complex systems, introduction to multi-agent systems and non-linear design, flocking, Boid library, basic examples - brownian motion, adhesion, separation, alignment, geometry following.-----------------------TIME: first session10am – GMT, London11am – Paris, Brussels, Rome, Vienna, Budapest, Bratislava, Warsaw9pm - Sidney7pm – Tokyo6pm – Beijing, Shanghai, Shenzhen, Hong Kong, Taipei3:30pm – Mumbai3pm – Karachi2pm - Samara1pm – Baghdad, Moscow, St Petersburg12pm – Istanbul, Athens, Helsinki, Cairo, JohannesburgTIME: second session3pm – GMT, London4pm – Paris, Brussels, Rome, Vienna, Budapest, Bratislava, Warsaw7pm – Dubai, Abu Dhabi, Baku6:30pm – Tehran6pm – Baghdad, Moscow, St Petersburg5pm – Istanbul, Athens, Helsinki, Cairo, Johannesburg1pm – Rio de Janeiro, São Paulo, Montevideo12pm – Buenos Aires, Santiago10am – Toronto, New York City, Bogota, Lima9am – Mexico City7am – Los AngelesWEBINARSThe rese arch Grasshopper® sessions are unique for their thorough explanation of all the features, which creates a sound foundation for your further individual development or direct use in the practice. The webinars are divided into four groups: Essential, Advanced, Iterative and Architectural. If you are a Rhinoceros 3D or Grasshopper® newcomer, you are advised to take all the Essential sessions before proceeding to the next level. If none of the proposed topics suit your needs or if you require special treatment, you can request a custom-tailored 1on1 session. All sessions are held entirely in English.The webinars are series of on-line live courses for people all over the world. The tutor broadcasts the screen of his computer along with his voice to the connected spectators who can ask questions and comment in real time. This makes webinars similar to live workshops and superior to tutorials.…
Added by Jan Pernecky at 3:36pm on February 17, 2015
ally to describe a process of repeating objects in a self-similar way. Simply stated, the definition of a recursive function includes the function itself. Fractals are among the canonical examples of recursion in mathematics and programming. A loop can simply be a way to apply the same operation to a list of elements, but it is an iterative loop if the results from one step are used in the calculation of the next step. In design research controlling recursion becomes a new strategy to define new forms and spaces.
BRIEF
In this workshop we will be exploring iterative strategies through parametric design. Main tool for the course will be grasshopper3d and its add-on Anemone. Anemone is a simple but effective plug-in for Grasshopper that enables for loops in a simple and linear way. We will explore several strategies such iterative growth, L systems, fractals, recursive subdivisions and more. Our course will focus on how those methods can affect three-dimensional geometries, generating unexpected conformations.
TOPICS
intro to rhinointro to grasshopperadvanced grasshopperdata managementintro to loopscellular automatal-systemsagent based modelling
SCHEDULE
Day 1 / friday 16:00Tour Green Fab LabBasics of 3D modeling in RhinocerosBasics of GrasshopperOpen Lecture by Jan Pernecky, founder of rese arch
Day 2 / saturday 10 am- 18 pmRecursive iterative methodsAdvanced Topics of looping
Day 3 / sunday 10 am – 18 pmRecursive iterative methodsFinal presentation session
REQUIREMENTS
The workshop is open to all participants, no previous knowledge of Rhinoceros and Grasshopper is required (although an introductory knowledge is welcome). Participants should bring their own laptop with a pre-installed software. The software package needed has no additional cost for the participant (Rhino can be downloaded as evaluation version, Grasshopper and plugins are free). These softwares are subject to frequent updates, so a download link to the version used in the workshop will be sent to the participants a few days before the workshop.…
Added by Aldo Sollazzo at 11:10am on October 6, 2015
instead of ballooning outwards, just puffing upwards.
THIS WILL WORK! Creating the mesh springs is only three seconds for 200X200 and the Unary Force is still milliseconds. Only Kangaroo takes an initiation time then cycles rapidly (0.5 seconds each) and it only takes a few cycles, maybe a dozen or two.
There is considerable 3D aliasing from the 2D mesh crudeness.
Now, to best Laurent's scheme, let's double down to 400X400. First I disable Kangaroo, and the timer. The preparation takes...FOREVER....and...ever...4.6 minutes to cull the points is all, a trivial step there is likely a better strategy for than finding the ones on the inside then using those to cull duplicates from the whole collection. The springs only took 12 seconds and the forces again milliseconds.
Kangaroo, to initialize takes...after hitting the reset button to start it...over 15 minutes and counting...well 400X400 is 160K vertices and Rhino tends to bog down at 30K points...but it was done in 30 minutes. Then I enable the timer and each cycle takes...uh...it's not in any error mode but nothing is happening past a very faint first automatic cycle that shows in the mesh...yet no CPU power is being used by Rhino...well...it's simply not running...ah, well, there's just a dummy delay of another 5 minutes and then the cycles take 2.7 seconds...what a stupid delay that was not using CPU power.
Now that it's cycling, can I change the stiffness in real time, usually I can...well, no, I seem to be back in the 5 minute delay, but not the 30 minutes interface-locking one...still waiting. Here is a 1/4 scale height model of the above output:
Time's up, life goes on. The aliasing and slow speed make it unworkable except for little logos or something. Some math and parallel processing are needed?
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Added by Nik Willmore at 5:51pm on February 21, 2016
this was about some boring building I wouldn't respond ... but here we are talking sardines.
Here's my take on that matter:
1. The 4 C# first create/use a nurbs, then define some random planes (and transformations) and then (a) either they place some humble stripes or ... er ... (b) sardines as instance definitions (NOTE: Load Rhino file first).
2. All important decisions are the ones in yellow groups.
3. You control what you get via this (priority on stripes or sardines? that's the 1M Q):
4. If you decide for sardines (the right thing to do) then you must ENABLE the Sardiniser(C)(tm)(US patent pending) as follows:
5. The vodkaFactor on that Sardiniser C# adds some spice in the sardine placement (it does that by altering the priority on the "composite" transformation in use: first randomly rotate then planeToPlane .... or the other thing?).
6. Only the finest Da Morgada sardines are used in this definition:
7. Spot the WARNING in the filter related with what sardine to choose > do it wrong and no hard disk on your workstation > no risk no fun > sorry Amigos, he he.
8. 1M question for you all: why placing sardines (it's real-time you know) is WAY faster than creating these humble stripes?
9. Although the sardines are placed in real time as regards your CPU ... the critical factor is your GPU (display mode: rendered).
10.Still WIP (dancing sardines in the next update).
have some sardine fun, best, Lord of SardineLand…
r ideal surface so they add up where lots of points or lines cluster and create rather unintuitive bulges form a 3D modeler's perspective, here done with Millipede's Geometry Wrapper:
I've learned to do marching tetrahedra or cubes in Python to create the surface as needed from a implicit ( f(x,y,z) = 0 ) mathematical equation based on raw trigonometry but am not yet sure how to define an equation for Rhino user created input items like this or find a way to make marching cubes accept such input let alone one that doesn't treat each geometry item as an electric charge with so little decay.
This would afford an old school "organic" modeling paradigm that T-Splines replaced, but the T-Spines pipe command can't do nearby lines right either, which just makes overlapping junk. Metaballs and lines are not as elegant in that there is a real "dumb clay" aspect to the result that affords little natural structure beyond just smoothing, but still, if it works at all that beats T-Splines, and then I can feed the crude mesh result into Kangaroo MeshMachine to afford surface tension relaxation that will add elegant form to it.
I need both quick hacks and some help on how to deeply approach the mathematics of the required isosurface, now that I can think in Python better than ever.
I got a hint the other day here, about using a different power of fall-off but am not sure how to do the overall task mathematically:
"and just as with point based potentials, one can use different power laws for the distance, function, resulting it different amounts of rounding at the junctions. Below is with a 1/d^3 law for comparision with the above 1/d" - Daniel Piker
http://www.grasshopper3d.com/forum/topics/meshes?commentId=2985220%3AComment%3A1324050
He also included this link about bulging:
http://paulbourke.net/geometry/implicitsurf/
Am I supposed to create an actual implicit equation for my assigned points and lines and use that with marching cubes to surface it? If so, how do I define that equation, at all, and then how to control bulging too?
…
cremental release is available for download. It fixes several bugs reported in the 0.9.0005 & 0.9.0006 versions. To wit:
Computer mice with smooth scrolling would not zoom well, this is fixed.
Previewable parameters with a lot of consecutive null items would crash, this is fixed.
Identical GHA files would collide during the loading process, this is handled.
GHA files with identical names would collide during the loading process, this is handled.
Solver Undo setting was not persistent, this is fixed.
Widget ZUI Zoom setting was not persistent, this is fixed.
Markov Widget Corner setting was not persistent, this is fixed.
Markov Widget Suggestion Count setting was not persistent, this is fixed.
Drag and Drop on Document and Template preview materials wasn't recorded, this is fixed.
AssignDataToParameter() COM-Access method was broken, this is fixed.
Geometry and Generic parameters with persistent data would not deserialize correctly, this is fixed.
Operator shortcuts via the Canvas popup instantiation menu no longer assigned data to the second parameter, this is fixed.
Cull Duplicates component did not always show the correct label upon deserialization, this is fixed.
Legacy VB/C# components would not correctly deserialize List access on input parameters, this is fixed.
Cloud Display component would still display old sprites on disconnect, this is fixed.
Minor changes to a document would trigger lengthy preview cache updates, slowing Grasshopper down. This is fixed.
Sphere 4Pt did not work correctly, this it fixed.
Failed data conversions in parameters would result in missing entries, this is fixed.
Text Tag components (2D & 3D) would not bake via the component menu, this is fixed.
There are also some new features:
Added Jump object for quickly navigating across a Canvas (Params.Util dropdown).
Added Relative Differences component which is basically the inverse of Mass Addition (Math.Operators dropdown).
Added tooltip wiggle controls to the Preferences window, Interface section.
'Draw Full Names' now also attempts to change the display of existing components, but only in the active document.
Drag+Dropping GHA, GHPY and GHUSER files onto the canvas now puts the original file into the bin.
Replaced Set Union component with a new one that has variable input parameters.
Replaced Set Intersection component with a new one that has variable input parameters.
Replaced And and Ternary And components with a single new one that has variable input parameters.
Replaced Or and Ternary Or components with a single new one that has variable input parameters.
Replaced Concatenate component with a new one that has variable input parameters.
Concatenate component now has a segment join option available via the component menu.
Added Digit options to the Transform Matrix Display object.
Integer parameters which represent options now have more informative context menus.
--
David Rutten
david@mcneel.com
Poprad, Slovakia
…
Added by David Rutten at 11:06am on September 14, 2012
sinergetici associati alla compresenza simultanea di differenti strumenti di analisi e digital design all'interno di un processo di progettazione in svolgimento. I partecipanti utilizzeranno Grasshopper (modellatore parametrico per Rhino): l'uso di questo editor grafico di algoritmi si integra alla perfezione con gli strumenti di modellazione di Rhinoceros 3D espandendo le possibilità di corstruire modelli parametrici altamente complessi. Per generare una complessità simile saranno utilizzati collegamenti live ai diversi programmi elencati di seguito: . Autodesk Ecotect Analysis via GECO . FEA software GSA via SSI Durante questi intensi 3 giorni, i partecipanti impareranno il workflow dei plug-ins con l'aiuto di esempi esplorando una panoramica dei differenti software, le possibilità di testare le performances di un progetto o l'uso di strumenti addizionali non legati ad un singolo sistema (es. accentuazione, formazione, reazione parametrica) [english text] The focus of the workshop is to integrate and correlate the synergistic effect associated with simultaneous presence of different digital design- and analysis tools in an ongoing design process. The main attention is set on easy to handle interface , which should be used at a early stage of conceptual design to respond to external and internal influences in a intelligent and sustainable way. Participants will use the software Grasshopper as a parametric modeling plug-in for Rhino. The usage of this graphical algorithm editor tightly integrated with Rhino's 3-D modeling tools open up the possibility to construct highly parametrical complex models. To generate this complexity we will use live linkages to several programs listed below: . Autodesk Ecotect Analysis via GECO . FEA software GSA via SSI In this 3 intense days, the participants should learn the workflow of the plug-ins with the help of examples and get an overview of the different software's, there possibilities for evaluating the performance of a design or the usage of additional tools to be not chained to a single system . (e.g. parametrical accentuation, parametrical formation, parametrical reaction) [.] Dettagli : Istruttori: Thomas Grabner & Ursula Frick from [uto]. lingua del corso: inglese (saranno disponibili tutor di supporto ma è richiesta una conoscenza di base della lingua unglese).
Quote d'iscrizione (min 12 max 20 posti): educational* : € 280.00 + iva professional: € 450.00 + iva * studenti, docenti, ricercatori, dottorandi e laureati fino a un anno dalla data di laurea OFFERTA EARLY BIRD SPECIAL: le prime 5 domande di iscrizione pervenute entro il 31 Dicembre 2011 avranno diritto ad una quota di iscrizione scontata del 20% Quote d'iscrizione E.B. SPECIAL: E.B. SPECIAL educational* : € 224.00+ iva E.B. SPECIAL professional: € 360.00+ iva. ulteriori info, dettagli e iscrizioni: http://www.co-de-it.com/wordpress/nexus-advanced-grasshopper-workshop-with-uto.html…
d the workshop PDF from this link: http://goo.gl/bcvRNH Download event poster from this link: http://goo.gl/Q0KWCM Brief: Cairo is filled with barriers controlling people movements, suppressing them as well as detaining green and public spaces to the extent that most people have been taking these spaces for granted. Public spaces have been for a while the periphery of our daily life. We will explore in this workshop how we can manipulate and alter people’s perception and direct their attention to how these spaces are integral for city life. This exploration will be backed up by intensive technical tutorials introducing computational design and fabrication techniques and tools mainly Rhino, Grasshopper, Geco and Ecotect. Not only will this be the typical technical workshop, but rather you will also have the chance to be guided step by step on how these tools are used through out different design stages in a real world scenario. Design prototypes will be produced through 3D printing, the main workshop output will be a fabricated one to one functional model for one of the designs using our new in-house CNC machine. Tutors (check the PDF for bio): Olga Kovrikova, MArch DIA Alexandr Kalachev, MArch DIA Karim Soliman, MArch DIA Islam Ibrahim, MArch DIA Sherif Tarabishy, B.Sc. AAST Application: Application deadline 1 September 2013 ** For students (undergrad / Master), teachers and PhD proof of status is required (university ID with a date or a certificate of enrollment) to apply for the students package. Packages (choose one of the following in the application form): 1. Standard registration Course fee is 4250 EGP For Students 3500 EGP 2. Early bird registration discounted fee For Professionals 3750 EGP For Students 3000 EGP ** Early bird offer ends on 14 August 2013 3. Group registrations discounted fee (5 or more) For Students 20% off - You will have to fill out an application form here: http://goo.gl/0QxAga - You will need to submit your CV and Short Portfolio (max. 10 MB) to info@morph-d.com, email subject: “Morphing Norms Application” (we will decide if you are eligible for an early bird discount or not based on the date of your email submission) - We will confirm receiving emails from all applicants. Successful applicants will be contacted 5 days after each deadline (early bird/final) and will have to confirm participation within 3 days, if they fail to do so, places will be given to others on the waiting list. - A maximum of 30 applicants will be selected.
…
ow..
It's basically using a 3d framework to define points on the framework and then interpolate curves through them.
Right now Im assuming that I merely translated something incorrectly early in the script that lead to most of the definition issues later on...?? It also seems I am not using the append function correctly... :(
If anybody well versed could take a look it would be awesome... :)
The code I've used is below and the erros I get are attached here:
Private Sub RunScript(ByVal ptSetA As List(Of Point3d), ByVal ptSetB As List(Of Point3d), ByVal divU As Integer, ByVal divV As Integer, ByRef A As Object, ByRef B As Object) Dim n As Integer = 0 Dim ptListA As New List(Of list(Of Point3d)) Dim ptListB As New List(Of list(Of Point3d)) For i As Integer = 0 To divU Dim ptRowA As New List(Of Point3d) Dim ptRowB As New list(Of point3d) For j As Integer = 0 To divV Dim ptA As New Point3d(ptSetA(n)) Dim ptB As New point3d(ptSetB(n)) ptRowA.Add(ptA) ptRowB.Add(ptB) n = n + 1 Next ptListA.Add(ptRowA) ptListB.Add(ptRowB) Next Dim intcvListA As New List(Of NurbsCurve) For i As Integer = 0 To divU - 1 Step 2 For j As Integer = 0 To divV - 1 Step 1 Dim pt01A As New point3d((ptListA(i)(j) + ptListA(i)(j + 1)) / 2) Dim pt01A As New point3d((ptListA(i + 1)(j) + ptListB(i + 1)(j)) / 2) Dim pt01A As New point3d((ptListA(i + 2)(j) + ptListA(i + 2)(j + 1)) / 2) Dim pt01A As New point3d((ptListA(i + 1)(j) + ptListA(i + 1)(j + 1)) / 2) Dim dis01A As Double = pt01A.DistanceTo(pt04A) Dim dis02A As Double = pt03A.DistanceTo(pt04A) Dim vt01A As New Vector3d((pt04A - pt01A) / dis01A) Dim vt02A As New Vector3d((pt03A - pt04A) / dis02A) Dim pt01B As New point3d((ptListB(i)(j) + ptListB(i)(j + 1)) / 2) Dim pt01B As New point3d((ptListA(i + 1)(j) + ptListB(i + 1)(j)) / 2) Dim pt01B As New point3d((ptListB(i + 2)(j) + ptListB(i + 2)(j + 1)) / 2) Dim pt01B As New point3d((ptListB(i + 1)(j) + ptListB(i + 1)(j + 1)) / 2) Dim dis01B As Double = pt01B.DistanceTo(pt04B) Dim dis02B As Double = pt03B.DistanceTo(pt04B) Dim vt01B As New Vector3d((pt04B - pt01B) / dis01B) Dim vt02B As New Vector3d((pt03B - pt04B) / dis02B) Dim ptArrA As New List(Of Point3d) ptArrA.Append(pt01A) ptArrA.Append(pt02A) ptArrA.Append(pt03A) Dim intcvA As New NurbsCurve() intcvA = CreateInterpolatedCurve(ptArrA, 3) intcvListA.Add(intcvA) Dim ptArrB As New List(Of Point3d) ptArrB.Append(pt01B) ptArrB.Append(pt02B) ptArrB.Append(pt03B) Dim intcvB As New NurbsCurve() intcvB = CreateInterpolatedCurve(ptArrB, 3) intcvListB.Add(intcvB) Next Next A = intcvListA…