Reverse engineering of CAD models via clustering and approximate implicitization

TL;DR

This paper presents an automatic method combining clustering and approximate implicitization to reverse engineer primitive geometric shapes from CAD models represented as polynomial splines or NURBS, applicable in design and analysis.

Contribution

It introduces a novel, fully automatic approach capable of recovering algebraic hypersurfaces of any degree and dimension with minimal manual parameter tuning.

Findings

Method is effective, efficient, and robust.

Algorithm can recover exact algebraic shapes in exact arithmetic.

Numerical examples demonstrate practical applicability.

Abstract

In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is of interest to extract information about the underlying geometry through reverse engineering. In this work we develop a novel method to determine these primitive shapes by combining clustering analysis with approximate implicitization. The proposed method is automatic and can recover algebraic hypersurfaces of any degree in any dimension. In exact arithmetic, the algorithm returns exact results. All the required parameters, such as the implicit degree of the patches and the number of clusters of the model, are inferred using numerical approaches in order to obtain an algorithm that requires as little manual input as possible. The effectiveness, efficiency and robustness of the method are shown both in a theoretical analysis and in numerical examples implemented in Python.