# 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 ...
• 3,984
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 ...
• 4,634
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 ...
• 2,169

### 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 ...
• 52.4k

### Minimum distance from point to surface

You could try with gradient projection, here is a quick implementation in python: ...
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 ...
• 4,571
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) ...
• 52.4k

### 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 ...
• 3,596
Accepted

• 4,829
Accepted

### Finding smallest cube in $\mathbb R^n$ that contains intersection between two regions

Here is a suggestion. Partition your problem into two parts: (1) Construct the intersection, (2) Find the smallest cube. (1) The intersection is a polytope defined by the union of your inequalities ...

### Distance between points

If $n$ is too large and the side length of your squarer $a$ is fixed then there may not be a solution to your problem. If you are willing to increase the size of the square to fit the points then the ...
• 336

### Minimizing the edge length of a polygon preserving its angles

If you multiply the length of every side by a constant then all the angles will be preserved, this just produces a similar polygon. Multiply by a very small constant and you get a very small length, ...
• 4,571

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

For me, a classic problem in linear algebra that got me climbing down a rabbit hole of complex analysis, conformal mappings, and polynomials, was in trying to prove converge rate bounds and iteration ...
• 2,435

### Generate random smooth 2D closed curves

What I ended up doing is to download thousands of random images, smooth them with a Gaussian filter, and extract contours at different levels. I took 2-3 closed contours from each blurred image and ...
• 173
Accepted

• 3,809

### 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 ...
• 2,169

### 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 ...
• 3,596