Laplacian Mesh Smoothing by Throwing Vertices

Date Sun 09 March 2025 Tags Programming In this blog post, I’ll talk about smoothing and blurring 3D meshes using Laplacian mesh smoothing. A good example of where this is useful is Adobe Substance 3D Modeler’s smooth tool which I implemented using Laplacian mesh smoothing. Laplacian mesh smoothing works by iteratively shifting each vertex towards the average position of that vertex’s neighbors. The math formula for this is: $$v_i = \frac{1}{N} \sum_{j=1}^{N} v_j$$ which we can implement in code as: for ( const Vertex & vertex : mesh . vertices ) { vec3 avrgPosition = vec3 ( 0 ); for ( const Vertex & vertexNeighbor : neighbors ( vertex )) { avrgPosition += vertexNeighbor ; } avrgPosition /= numNeighbors ( vertex ); } Run that a few times, and the mesh smooths out like magic. It’s important to note that this process only changes the vertex data of the mesh; the connectivity (triangle indices) are unchanged. The above is straightforward except that we need the neighbors() and numNe ... Read full article.