Laplacian Mesh Smoothing with Bilateral Weight for Characterization of Freeform Surfaces

In additive manufacturing, freeform surfaces are commonly used but difficult to be characterized due to their complex geometrical shapes. Therefore, it is preferable to remove the form in the first step. Freeform surfaces are widely represented by polygon meshes, especially triangular meshes. In cases where general freeform surfaces cannot be fitted with a geometrical form, the form of the surface can be estimated using a smooth version of the surface. The most widely used mesh smoothing method is Laplacian smoothing. Traditional Laplacian mesh smoothing techniques employ uniform, distance, or cotangent weights to discretize the Laplacian-Beltrami operator for each vertex but have limitations in preserving dimensions while effectively dealing with noise. This paper presents an innovative approach to enhance Laplacian mesh smoothing by using a bilateral weight for each vertex, thereby mitigating the limitations.