  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.
