# Tag Info

### What are systematic ways of approximating a non-smooth (non-continuously differentiable) system dynamic to be n-smooth?

Two systematic ways of smoothing a function $h$ would be: 1. Join the piecewise smooth parts of your function using Hermite interpolation so that the derivatives are matched to your satisfaction. 2. ...
• 3,994

### How to "smoothen" (not just refine) a 2D/3D polygonal mesh

To complement the two answers from Daniel Shapero and Nicoguaro: Basically, there are two ways of smoothing a mesh, subdivision (generate new vertices) and smoothing (move the points in such a way ...
• 2,315

### How to "smoothen" (not just refine) a 2D/3D polygonal mesh

As mentioned in the answer by @DanielShapero, you can follow an approach based on local approximations of the curvature for your nodes. In the post he suggest, there is an article by Desbrun. I would ...
• 8,524

### How to "smoothen" (not just refine) a 2D/3D polygonal mesh

For just mesh smoothing, you can start by looking at Laplacian smoothing and some of the references therein. The idea is to update the position of every vertex in the interior of the mesh by replacing ...
• 10.3k
Accepted

### Smoothness regularisation of a 2D field on a triangular mesh?

In microwave imaging, a great chunk of literature is devoted to regularization and its effect on the solution process and inversion results. One of the common methods for microwave imaging is the ...
• 8,692

### How to "smoothen" (not just refine) a 2D/3D polygonal mesh

Surprisingly, Lloyd smoothing hasn't come up here yet. Check out Du, Qiang; Faber, Vance; Gunzburger, Max (1999), "Centroidal Voronoi tessellations: applications and algorithms", SIAM Review, 41 (4):...
• 3,126

### How the number of pre-smoothing and post-smoothing steps affect the asymtotic convergence rate of geometrical Multigrid?

Separately, but it does depend. Not very strongly, however: A very large number of pre- and post-smoothing steps only improves the convergence rate a little bit over a large number of steps. The ...
• 55.8k
Accepted

### Averaging oscillatory data

I usually use digital filters, e.g a high order (e.g. 10) low pass Butterworth filter, with the cutoff frequency such that the high frequencies are removed. You should perform a Forward-Backward ...
• 1,943
Accepted

### What penalty function produces optimization-based Gaussian smoothing?

The least squares optimization problem in your question has a penalty term that only penalizes 1st derivatives. However, for a Gaussian kernel, the corresponding penalty term would have to penalize ...
• 136
1 vote

### Prevent single node spikes in a FEM-simulation (using continuous Galerkin)

I believe these issues arise because you are solving the transient form of the heat equation which, being parabolic, can lead to some instability for continuous galerkin method. There are ways to ...
• 1,157
1 vote

### How to connect two fitted B-spline curve?

Fitting together B-splines with a given continuity is a hard problem. This was actually the motivation behind developing a generalization of NURBS called T-splines. There are many articles on T-...
• 383

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