Reverse engineering of CAD models via clustering and approximate implicitization
This work addresses the need for automated reverse engineering in computer-aided design for applications like redesign and isogeometric analysis, representing an incremental improvement by integrating existing techniques into a more automated framework.
The paper tackles the problem of reverse engineering CAD models to extract underlying primitive shapes by developing a novel method that combines clustering analysis with approximate implicitization, achieving automatic recovery of algebraic hypersurfaces of any degree in any dimension with exact results in exact arithmetic.
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.