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}{\...
- 8,510
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-...
- 4,862
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,...
- 2,229
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 ...
- 2,229
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 ...
- 10.3k
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 ...
- 10.3k
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 ...
- 2,229
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 ...
- 55.5k
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 ...
- 8,672
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: $P=[R | t]$. ...
- 2,229
2
votes
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 ...
- 11.3k
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 ...
- 2,122
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 ...
- 55.5k
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 ...
- 3,961
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
...
- 8,510
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 ...
- 1,285
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