# Tag Info

### Linear algebraic research direction that's not to do with differential equations and physics?

Randomized linear algebra might be something you'd like. It has direct applications in data analysis and is related to several branches of Mathematics such as Geometry (see the Johnson-Lindenstrauss ...
• 3,954
Accepted

### Generate random smooth 2D closed curves

Since your figure is a closed loop, its parametric curves $x(t)$ and $y(t)$ must be periodic functions. This suggests one way to generate such figures, by constructing random smooth periodic functions ...
• 4,316
Accepted

### Fitting Implicit Surfaces to Oriented Point Sets

I was surprised for not receiving a satisfactory answer to the question above and my investigations showed me that this, indeed is an unexplored area. Hence, I put some effort in developing solutions ...
• 2,139

### Linear algebraic research direction that's not to do with differential equations and physics?

Here's another interesting connection: There is a research area that looks into the complexity of computing matrix-matrix products from a geometric perspective. It's a totally bizarre connection, but ...
• 51.3k
Accepted

### Commonly-used metrics to quantify the irregularity of a triangular mesh

As @Nicoguaro and @Paul have said in the comments to the question post, there are a great many ways to do this kind of thing, and I'm not sure if there is a single "best" approach. From a review ...
Accepted

### Distance between points

Choose n random points in the unit square. Compute the minimum point-to-point distance, $D$. Re-scale the space by $1/D$. The minimum point-to-point distance is now equal to 1. Edit: The best ...
• 4,521
Accepted

### How to find the nearest point inside a list in a given direction

The question really boils down to how far two points $x,y$ are from each other in direction $u$. This is easily answered: You need to compute the component of $y-x$ onto $u$, i.e., their (signed) ...
• 51.3k

### Approximating the boundary between two sets of points (in 2D): Fitting a region

Theory Clustering is unlikely to work in this case because your red points are separated from each other by the green points. You could use more clusters, but this will require a lot of manual ...
• 3,131
Accepted

• 3,789

### 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 ...
• 2,139

### How can I find a line segment with the most intersections along with the coordinates of the intersection points?

You can use the Bentley–Ottmann algorithm for this. Given a set of $n$ line segments with $k$ intersections, the algorithm can identify all intersections in $O((n+k)\log n)$ time and $O(n)$ space. In ...
• 3,131
Accepted

### Does some form of documentation of GMSH exist?

Currently there is a GMSH API in the works: https://gitlab.onelab.info/gmsh/gmsh/tree/master/api Also, there are rumors that there will be a fully documented API by version 4.0. In short, there is ...
• 489

### Fast comparison of line segments lengths

I want to submit a separate answer to this question, because there is a way to automatically simplify such formulas to remove square roots. I will use sage and QEPCAD (both free). The tutorial is here....
• 11.4k
You can uniformly distribute points and apply transformation, $$N_s(\zeta)=1-\zeta\\ N_e(\zeta)=\zeta\\ \phi(\zeta)=x_sN_s(\zeta)+x_eN_e(\zeta)+ \sum_i \alpha_i L_i(2\zeta-1) N_s(\zeta)N_e(\zeta)$$ ...