# Direct structural analysis of domains defined by point clouds

## TL;DR

This paper introduces a novel numerical analysis method for solids represented by point clouds, utilizing the Finite Cell Method to perform accurate, tessellation-free boundary analysis directly on point cloud data.

## Contribution

It presents a new approach that enables direct structural analysis from point clouds without surface reconstruction, integrating high-order immersed boundary techniques.

## Key findings

- Achieves accuracy comparable to traditional surface-based methods.
- Demonstrates applicability on 3D historical structures.
- Provides controlled error through point cloud density.

## Abstract

This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a high-order immersed boundary technique that computes on a regular background grid of finite elements and requires only inside-outside information from the geometric model. It is shown that oriented point clouds provide sufficient information for these point-membership classifications. Further, we address a tessellation-free formulation of contour integrals that allows to apply Neumann boundary conditions on point clouds without having to recover the underlying surface. Two-dimensional linear elastic benchmark examples demonstrate that the method is able to provide the same accuracy as those computed with conventional, continuous surface descriptions, because the associated error can be controlled by the density of the cloud. Three-dimensional examples computed on point clouds of historical structures show how the method can be employed to establish seamless connections between digital shape measurement techniques and numerical analyses.