# Smooth triangular mesh interpolation

I am looking for an algorithm which would smoothly interpolate triangles of a mesh (computed by Delaunay triangulation) where each vertex has some value (elevation in my case). I need it for PDAL where I want to try to implement it. Its current implementation uses linear interpolation which makes the result not so pleasant:

Is there some public algorithm which would interpolate it smoothly, without sharp edges? Result should be a raster (rectangular grid of points).

• en.m.wikipedia.org/wiki/Phong_shading Apr 11, 2022 at 18:55
• @lightxbulb I actually need just to interpolate elevations, not to directly produce visual shading and playing with light direction Apr 12, 2022 at 5:57
• You can try this: en.m.wikipedia.org/wiki/Point-normal_triangle Also if the result is supposed to be on a raster grid and you have sparse data, is there a reason you compute the Delaunay triangulation instead of applying interpolation directly on the sparse data? Apr 12, 2022 at 8:36
• @lightxbulb thanks! I will take a look on PN triangle. And actually you are right - I have sparse points and want them to produce a smooth surface. Can you recommend me a method which could do it? Apr 12, 2022 at 8:58
• I am assuming those are irregularly distributed? If that is the case you can solve the harmonic or biharmonic equation with Dirichlet boundary conditions defined by the point values. I admit that this may be harder though if you lack the mathematical background. You can also look into literature on radial basis functions for interpolation. Apr 12, 2022 at 9:03