8
votes
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}{\...
- 8,370
7
votes
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
7
votes
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-...
- 4,822
5
votes
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 ...
- 10.1k
5
votes
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 ...
- 2,219
5
votes
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,...
- 2,219
4
votes
Accepted
Is model-view-controller useful pattern useful to build scientific simulation programs?
This answer is my personal opinion. I believe that high performance numerical solvers are not a good place to use MVC pattern. Additional layers and specific data flow will not help to get a better ...
3
votes
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 ...
- 10.1k
3
votes
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 ...
- 2,219
2
votes
Fitting orthogonal planes to a point set
Here I devise a novel strategy, based on only 3D points, that I think, would work.
I will parametrize a 3D plane by a point $\mathbf{p}$ and its normal $\mathbf{n}$.
Imaging you take a pair of ...
- 2,219
2
votes
Is model-view-controller useful pattern useful to build scientific simulation programs?
Whilst the MVC/MMVM patterns can be useful where appropriate, I would avoid trying to shoehorn the numerics into a pattern led by your chosen GUI (or other UI) framework. Unless you multi-thread in ...
- 31
2
votes
Iterative Closest Point Algorithm
Using angles is a very bad idea of storing rotations. They are ambiguous and not always consistently defined.
Store your pose matrix as an augmented matrix of rotation and translation: $P=[R | t]$. ...
- 2,219
2
votes
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 ...
- 337
2
votes
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 ...
- 54.1k
2
votes
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
2
votes
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 ...
- 8,602
2
votes
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 ...
- 1,271
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 ...
- 54.1k
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 ...
- 3,921
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
...
- 8,370
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
1
vote
Fitting orthogonal planes to a point set
I think your problem can be written as an optimization problem.
$\{x_i\}$ is the set of points for plane 1, $\{x_j\}$ for plane 2 respectively. Their orthonormal vectors are $n_1$ and $n_2$ with ...
- 1,275
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