Monograph

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

  • Sofia Imperatore,

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.

  • Keywords:
  • Fitting,
  • Parameterization,
  • Geometric Deep Learning,
  • Graph Neural Networks,
  • Adaptive splines,
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Sofia Imperatore

Eindhoven University of Technology, Netherlands - ORCID: 0009-0003-9116-9978

Sofia Imperatore holds a PhD in Mathematics from the University of Florence (2024), specializing in geometric deep learning. After working at CNR Pavia (2025) on uncertainty quantification, she is now a post-doc at TU Eindhoven, developing geometric deep protein representations for drug discovery.

Sofia Imperatore

Introduction
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pp.3-11


Part I

Sofia Imperatore

Preliminaries
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pp.15-37


Sofia Imperatore

Data fitting schemes with hierarchical splines
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pp.39-68


Part II

Sofia Imperatore

Parameterization for point cloud spline fitting
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pp.71-126


Part II

Sofia Imperatore

Moving parameterization
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pp.129-164


Sofia Imperatore

Conclusion and future development
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pp.165-166


Sofia Imperatore

References
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pp.167-179


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Bibliographic Information

Book Title

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

Authors

Sofia Imperatore

Peer Reviewed

Number of Pages

196

Publication Year

2026

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© 2026 Author(s)

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CC BY 4.0

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Firenze University Press

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Premio Tesi di Dottorato Città di Firenze

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