Reverse engineering (digital shape reconstruction) is an expanding and challenging area of Computer Aided Geometric Design. This technology is utilized in various applications where a given physical object is scanned in 3D, and a computer representation is needed in order to perform various computations. A wide range of applications emerges in engineering, medical sciences, and preserving the cultural heritage of mankind.

In the majority of engineering applications, it is crucial that the reconstructed models satisfy various geometric constraints. The primary surfaces must obey various rules, such as being orthogonal, parallel, tangential, symmetric, concentric, and so on. If we approximate the segmented regions individually, one by one, we may obtain inaccurate surfaces and poor CAD models. The goal of this research is to perfect CAD models created from measured data. We introduced techniques to automatically detect likely engineering constraints, and enforce these by performing constrained fitting.

I. Kovács, T. Várady, Perfecting 3D computer models reconstructed from measured data. Proceedings of the Seventh Hungarian Conference on Computer Graphics and Geometry, pp. 109-115, 2014. Full paper • BibTeX

I. Kovács, T. Várady, Applying engineering constraints in digital shape reconstruction. Proceedings of the 18th Central European Seminar on Computer Graphics (CESCG), pp. 137-144, 2014. Full paper • BibTeX

I. Kovács, T. Várady, P. Salvi, Applying geometric constraints for perfecting CAD models in reverse engineering. Graphical Models, Vol. 82, pp. 44-57, 2015. DOI • BibTeX

Regular surfaces can be defined unambiguously by a few surface parameters; and related trimmed surface regions can be approximated in a numerically stable manner. Fitting free-form surfaces is a much harder task, as there are infinitely many surfaces that can approximate a given data set. The former constrained fitting techniques were capable to handle only regular geometries. We have extended the technology proposed by Benkő et al. to free-form curves and surfaces.

I. Kovács, T. Várady, Constrained fitting with free-form curves and surfaces, Computer-Aided Design, Vol. 122, #102816, 2020. DOI • BibTeX