As-exact-as-possible repair of unprintable STL files

TL;DR

This paper introduces a mathematically rigorous, fully automatic repair algorithm for STL files that ensures models are printable with minimal distortion, addressing the gap between printable models and those representable by STL.

Contribution

It provides the first exact repair method based on combinatorial topology that minimally distorts models while guaranteeing printability, improving over approximate previous solutions.

Findings

The algorithm distinguishes between solid-boundary triangles and zero-thickness sheets.

It repairs all configurations without unnecessary distortion.

The method simplifies the modeling-printing process for maker communities.

Abstract

Purpose: The class of models that can be represented by STL files is larger than the class of models that can be printed using additive manufacturing technologies. Stated differently, there exist well-formed STL files that cannot be printed. In this paper such a gap is formalized and a fully automatic procedure is described to turn any such file into a printable model. Approach: Based on well-established concepts from combinatorial topology, we provide an unambiguous description of all the mathematical entities involved in the modeling-printing pipeline. Specifically, we formally define the conditions that an STL file must satisfy to be printable and, based on these, we design an as-exact-as-possible repairing algorithm. Findings: We have found that, in order to cope with all the possible triangle configurations, the algorithm must distinguish between triangles that bound solid parts and triangles that constitute zero-thickness sheets. Only the former set can be fixed without distortion. Originality: Previous methods that are guaranteed to fix all the possible configurations provide only approximate solutions with an unnecessary distortion. Conversely, our procedure is as exact as possible, meaning that no visible distortion is introduced unless it is strictly imposed by limitations of the printing device. Thanks to such an unprecedented flexibility and accuracy, this algorithm is expected to significantly simplify the modeling-printing process, in particular within the continuously emerging non-professional "maker" communities.