Adaptive spline approximation: data-driven parameterization and CAD model (re-)construction

This thesis combines Computer Aided Geometric Design with Deep Learning to develop geometric reverse engineering methods for data-driven free-form spline geometries. We focus on reconstructing CAD models from point clouds with varying configurations, from uniform to scattered and noisy. Central to this is the parameterization problem: mapping input data to a parametric domain. We propose data-driven parameterization methods based on geometric deep learning for both univariate and multivariate cases, achieving higher accuracy than standard methods. We also introduce adaptive fitting schemes combining moving parameterization with hierarchical B-splines, significantly enhancing model quality, also compared to state of the art reconstruction schemes.