Multi-level k -nearest neighbors algorithm for direct point cloud-based engineering analysis

Point cloud representations are increasingly being used for geometric modeling in science and engineering applications, largely due to the widespread adoption of advanced scanning technologies. While point clouds are highly flexible in representing different objects, their unstructured nature presents several challenges for their direct use in engineering analysis. To address this issue, most analysis methods require reconstructing an approximate mesh from the point cloud. However, many mesh reconstruction techniques require manual tuning when faced with complicated geometries and often struggle to correctly reconstruct noisy, low-density, or topologically ambiguous point clouds without manual intervention. While the $k$ -nearest neighbors $\left(k\text{NN}\right)$ algorithm is widely used in mesh reconstruction methods, it requires manual tuning of parameters, including the value of $k$ , for different point clouds based on their density and the topological complexity of the underlying object. To address these issues, we propose a novel multi-level $k$ -nearest neighbors $\left(\text{M-}k\text{NN}\right)$ approach that iteratively expands local neighborhoods to identify the surface connectivity of the underlying object represented by the point cloud. $\text{M-}k\text{NN}$ enables improved point cloud resampling and more accurate geometry processing, particularly for geometries with close, non-intersecting structures, as demonstrated in both synthetic and real-world datasets. The proposed approach also enables the use of raw point clouds in point-cloud-based engineering analysis, rather than requiring the reconstruction of surface meshes.