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# Tag Info

Accepted

### 3D laplacian operator

Yes, that finite difference is correct. You can obtain it using a finite difference in each direction for the Laplace operator in each coordinate. \begin{align} \nabla^2 u =& \frac{\partial^2 u}{\...
• 8,525
Accepted

### Why the magnetisation shows abrupt behaviour for this 3D ising spin system

Your lattice consists of 5 x 5 x 5 = 125 spins, so your number of Montecarlo steps to reach equilibrium should be >> 125, because you randomly picking a site and flipping it, so random numbers should ...
• 276
Accepted

### 3D contour mesh computation

I think you could use the "marching cubes" algorithm. If memory serves, it requires a grid of samples as input, so at the very least you should be able to sample your function and run the algorithm as-...
• 4,906

### 3D contour mesh computation

In addition to the voxel-based approach that rchilton suggests, you could also look at Delaunay-type algorithms. For example, the Computational Geometry Algorithms Library (CGAL) has some built-in ...
• 10.3k
Accepted

### Algorithms to extract trajectory lines out of 3D point clouds

I will summarize a couple of possibilities: As a baseline, I would begin with a Hough transform kind of approach: Iterative Hough Transform for Line Detection in 3D Point Clouds Christoph Dalitz,...
• 2,229
Accepted

### Iterative camera calibration - No convergence

I have to tell you. I implemented this algorithm (even double checked with other experienced people), however no luck. I guess, this worked for the authors, but with our data there was really no ...
• 2,229

### Going From Blender Structure defined by triangles to full 3D mesh (Using GMSH?)

Tools like gmsh often require more information than STL provides -- the connectivity between triangles of the input surface mesh. You might be interested in trying TetWild, which can apparently ...
• 10.3k

### Linear Least-Squares Point-to-Plane ICP degenerative case

This approach is the result of a Taylor approximation, which assumes that we are not very far from the solution (solution is the case when $R\approx I$ - no more updates can be made). Under large ...
• 2,229
Accepted

### How to handle 2D and 3D models efficiently

I use C++ template to parameterize dimension in a fluid simulation project. It is not directly related to your application, but I think some general ideas would be the same. Vectorize operations for ...

### On which software can I simulate landmass collisions?

There are a number of software packages out there that you can use -- most are curated by the Computational Infrastructure in Geodynamics initiative (see http://www.geodynamics.org). The fundamental ...
• 55.7k
Accepted

### Find shortest path around a cylinder represented by 3d triangular mesh

OK, after thinking about it for a while, I came up with an answer. Step 1: Find the caps of the cylinder, in other words two closed disjoint paths along the graph's borders. Step 2: Find a path ...
• 253

### Algorithm to determine flat surfaces and camera orientation without specialized hardware

You are quite right, Augmented Reality benefits a lot from a combination of video/image analysis together with the data from motion sensors. Quote from Apple ARKit: Understanding World Tracking: To ...
• 8,672

### What is the name of the theory that combines 3d discretized surfaces and distributed numerical algebra

It's not specifically about parallel computation, but you might encounter some relevant research in the field of isogeometric analysis, i.e., the numerical solution of differential equations via ...
• 11.5k

### How to plot random points in 3 dimensions in order to calculate volume of a torus through Monte Carlo integration

You don't need to plot a torus to calculate its volume. Moreover you can analytically compute the volume integral and it's even on wikipedia. With Monte Carlo you can use rejection sampling to figure ...
• 2,172
1 vote

### Point cloud to height map in C++

Think of this as a point cloud over a chess board. Then, for each of the squares of the board, find all the points that lie over that square (i.e., whose $x,y$ values are within that square) and take ...
• 55.7k
1 vote

### Find shortest path around a cylinder represented by 3d triangular mesh

Find a longitudinal axis of the cylinder (a least-squares linear fit to all your points will yield this). Construct a plane passing through this axis. Any orientation should be fine, but let's say it ...
• 3,971
1 vote

### Algorithms to extract trajectory lines out of 3D point clouds

When the points belong to more than one curve, it will first be necessary to cluster them into curves. A possible approach is described together with a reference implementation in Dalitz, Wilberg, ...
• 481
1 vote

### Data cloning into 3D matrix

This is probably not the most efficient way to do this in MATLAB, but the following works for me in Octave: A=rand(200,200); for i=1:15 B(:,:,i)=A; end And, I ...
• 10.9k
1 vote

### 3-dimensional plotting with nonuniform grids

Your data is already in the right shape, then you don't need to create a meshgrid. See the code below ...
• 8,525
1 vote

### Lid-driven Cavity benchmark in 3D. Classical paper to compare

On a side note perhaps, I think it's funny how the Ghia paper is still used as the benchmark 35 years later on. It had indeed produced great results for its time, but this being a computational ...
• 111
1 vote
Accepted

### Lid-driven Cavity benchmark in 3D. Classical paper to compare

I consider this to be the "classic" 3D-Lid-Driven Cavity (LDC) incompressible flow benchmark paper: Guj, G. & Stella, F. A vorticity-velocity method for the numerical of 3D incompressible flows. ...
• 619

Only top scored, non community-wiki answers of a minimum length are eligible