A Point cloud represents a set of data points in space, generally produced by 3D scanners, and used in CAD models, metrology, animation, etc.
Questions tagged [point-cloud]
33 questions
25
votes
1 answer
Is there a way to describe the pattern this process creates for any set of points in a 2d plane? Will all sets necessarily have a pattern?
I apologize if this is put inelegantly as I'm new to this type of mathematics, but I thought of this experiment and can't stop turning it over in my mind.
Take any set of points on a 2d plane and connect every point to every other point using line…
Ananke
- 353
7
votes
3 answers
Why does the Eigen decomposition of the covariance matrix of a point cloud give its orientation?
I am working with point clouds and one of the problems I had to face was to find the orientation of a given cluster. Most algorithms I have found suggest that one must first calculate the centroid of the cloud and, using that, to compute the…
vladek
- 195
5
votes
2 answers
Robust orientation of a point cloud
I have 2D point clouds which are 4-way symmetrical (invariant by 90° rotation). The points are usually arranged on the nodes of a square grid, densely populated, but some cases can be more complicated. I do know the point pattern in advance.
I need…
user65203
2
votes
1 answer
Random uniform points on the surface of (hyper) ellipsoid
How to generate random uniform points on (hyper) ellipsoid?
Note: Rejection methods are very inefficient specially in higher dimension. Check the ratio of volumes (box VS its inscripted ellipsoid) as the dimension grows.
Note 2: Here's an elegant…
Artashes
- 195
2
votes
0 answers
Advanced Linear Algebra resources for a newbie
At work I'm leveraging some linear algebra concepts that I don't feel confident with or plainly don't understand. I'm hoping to find a book which would help me with that.
I'm using stuffs like:
projecting or intersecting lines on a plane
fitting a…
Jonas Berhin
- 21
- 2
2
votes
1 answer
Solving a least squares problem to align two point clouds.
I have two 3D point clouds which are identical but misaligned. I'm trying to align them (or 'register' them). The very first well-known algorithm that achieves this is the iterative closest point (ICP) algorithm from the 90s. Most of the new methods…
John Katsantas
- 840
2
votes
0 answers
calculating first and fundamental form coefficients with surface normal and Gaussian curvature
I have some points (point cloud), I need first and second fundamental form coefficients at each point.
before I used some polynomial surface fitting algorithm then these coefficients were calculated. but results aren't good because you know all…
M R
- 31
- 2
1
vote
0 answers
Maximize the internal distance between 2D points
I am a beginner to optimization and I am trying to create an objective function for a simple 2D problem.
I have a rectangle and a known point $x_c$ at the intersection at its diagonals. I want to find $N$ points (where $N$ is given as input) such…
Ken Adams
- 21
1
vote
0 answers
Intuition on the Levenberg Marquardt Algorithm
I am trying to understand nonlinear least squares to fit spheres in point cloud data. I kind of understand how the linear least squares works but every kind of paper on nonlinear least squares/Levenberge-Marquerdt is just pure magic to me. Well,…
Nope
- 11
1
vote
1 answer
Given a 2D polygon in 3D space identify all points that are not a part of the polygon
I do not have a background in mathematics. I am a developer attempting to process point cloud data, but I believe this to be the correct place to post for this type of problem.
Given points of a planar polygon shape based on point cloud data in 3D…
Phillip
- 13
1
vote
1 answer
Computing 3D Zernike Moments on 3D Point Clouds
I'm trying to understand the formulation for 3D Zernike descriptors used in A Comparative Study of Object Classification Methods Using 3D Zernike Moment on 3D Point Cloud. For context, I'm looking for a translation invariant method for comparing…
Karl
- 111
1
vote
0 answers
Solving an overdetermined system of linear equations with least square roots (not squares)
An overdetermined system of linear equations can be solved by approximation as described in https://en.wikipedia.org/wiki/Overdetermined_system.
I also need to solve such a system $P_{act} = T * P_{nom}$, where the transformation matrix $T$ between…
Tobias Knauss
- 111
1
vote
0 answers
How to define a random infinite point cloud and find Delaunay triangles at any coord?
For a map generator with islands I'm looking for an algorithm that for a given random seed defines am infinite point cloud of 2D points that looks decently random and covers all of infinity (a simple grid is out because it would look horribly…
1
vote
1 answer
Point to Plane distance parallel to Z-axis
I'm currently working with point clouds (that's why the example numbers are so large) and I'm trying to figure out what the z-axis of a point would be if it lay on a plane.
I have:
- the plane's normal: $$\vec E = [-0.506932, -0.539411,…
1
vote
2 answers
Direction vector of tube/cylinder from point cloud
I have a bunch of points that lay on a surface on a cylinder/tube. How can I calculate the properties of this tube (radius and direction)?
The only way I can come up with is to assume find the direction vector using a least square fit, but I cant…
lijas
- 129