# A Classification of Topological Discrepancies in Additive Manufacturing

## TL;DR

This paper introduces a method to analyze and correct topological discrepancies in additive manufacturing, helping to improve the fidelity of complex 3D printed structures by identifying and addressing defects related to material deposition.

## Contribution

It presents a generic topological analysis method for AM discrepancies and demonstrates how to modify structures to preserve topology within printer limitations.

## Key findings

- Effective detection of topological defects in 3D printed structures
- Systematic modifications improve structural connectivity
- Validated on complex lattice and foam structures

## Abstract

Additive manufacturing (AM) enables enormous freedom for design of complex structures. However, the process-dependent limitations that result in discrepancies between as-designed and as-manufactured shapes are not fully understood. The tradeoffs between infinitely many different ways to approximate a design by a manufacturable replica are even harder to characterize. To support design for AM (DfAM), one has to quantify local discrepancies introduced by AM processes, identify the detrimental deviations (if any) to the original design intent, and prescribe modifications to the design and/or process parameters to countervail their effects. Our focus in this work will be on topological analysis. There is ample evidence in many applications that preserving local topology (e.g., connectivity of beams in a lattice) is important even when slight geometric deviations can be tolerated. We first present a generic method to characterize local topological discrepancies due to material under- and over-deposition in AM, and show how it captures various types of defects in the as-manufactured structures. We use this information to systematically modify the as-manufactured outcomes within the limitations of available 3D printer resolution(s), which often comes at the expense of introducing more geometric deviations (e.g., thickening a beam to avoid disconnection). We validate the effectiveness of the method on 3D examples with nontrivial topologies such as lattice structures and foams.