# Epsilon-shapes: characterizing, detecting and thickening thin features in geometric models

## TL;DR

This paper introduces epsilon-shapes, a new mathematical model for analyzing thin features in geometric models, enabling effective detection and thickening of these features without complex parameter tuning.

## Contribution

The paper presents a novel epsilon-shape model for characterizing thin features, along with an efficient algorithm for detection and a method for thickening, improving upon existing solutions.

## Key findings

- Effective detection of thin features in shapes and their complements
- Thickening of thin features without altering other shape parts
- Method outperforms state-of-the-art in flexibility, efficiency, and stability

## Abstract

We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and efficiently detected by an algorithm, and propose a novel approach to thicken these features while leaving all the other parts of the shape unchanged. When compared with state-of-the-art solutions, our proposal proves to be particularly flexible, efficient and stable, and does not require any unintuitive parameter to fine-tune the process. Furthermore, our method is able to detect thin features both in the object and in its complement, thus providing a useful tool to detect thin cavities and narrow channels. We discuss the importance of this kind of analysis in the design of robust structures and in the creation of geometry to be fabricated with modern additive manufacturing technology.