Algorithm for smoothing edges of an open 3D mesh

Question

I have a 3D mesh which represents a surface with some rough boundaries which I would like to smooth: I am using a half edge data structure for storing the geometry so I can easily iterate over the boundary edges, vertices and faces. I can also quite easily determine whether a given pair of edges is a convex/concave using a dot and cross product. What would be the best approach for smoothing the edges out, so they form a continuous, curvy line, rather then the sharp pattern seen in the pictures?

Accepted Answer

compute angle between two neighboring faces

I call it `ada` as abs delta angle. If it is bigger then threshold it means this point is edge. You can compute it as `max` of all angles between all edge lines. In 2D it looks like this:

in 3D mesh there is more then 2 lines per point so you have to check all combinations and select the biggest one

```
ada=max(abs(acos(n(i).n(j)))
```

where `n(i),n(j)` are normal vectors of neighboring faces where `i != j`

identify problematic zones

so find points where `ada > threshold` and create a list of these points

filter this list

if this point is too far from any other (`distance>threshold`) then remove it from list to preserve geometric shape

smooth points

you have to tweak this step to match your needs I would do this:

find a group of points in the list which are close together and apply some averaging geometric or numeric on them for example:

```
pnt(i)=0.5*pnt(i)+0.25*pnt(i-1)+0.25*pnt(i+1)
```

this can be applied repetitive

blue and red dots are original points, green dots are smoothed points

Algorithm for smoothing edges of an open 3D mesh

Solution

Problem