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        <title type="main">Adaptive spline approximation: data-driven parameterization and CAD model (re-)construction</title>
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            <forename>Sofia</forename>
            <surname>Imperatore</surname>
            <placeName type="affiliation">Eindhoven University of Technology, Netherlands</placeName>
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        <publisher>Firenze University Press</publisher>
        <pubPlace>Florence</pubPlace>
        <date when="2026">2026</date>
        <idno type="DOI">https://doi.org/10.36253/979-12-215-1002-7</idno>
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          <p>Available for academic research purposes</p>
          <p>Open Access</p>
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        <title>Premio Tesi di Dottorato Città di Firenze</title>
        <idno type="ISSN" subtype="print">3103-3881</idno>
        <idno type="ISSN" subtype="electronic">3103-3989</idno>
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        <tag>peer-reviewed</tag>
        <rs type="FUP_policy" source="https://doi.org/10.36253/fup_best_practice">Firenze University Press Best Practice in Scholarly Publishing</rs>
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      <abstract xml:lang="en">
        <p>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.</p>
      </abstract>
      <abstract xml:lang="it">
        <p>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.</p>
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      <textClass>
        <keywords>
          <list>
            <item>Fitting</item>
            <item>Parameterization</item>
            <item>Geometric Deep Learning</item>
            <item>Graph Neural Networks</item>
            <item>Adaptive splines</item>
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  <text>
    <front>
      <div type="toc">
        <list>
          <item>Table of content</item>
          <item>Introduction</item>
          <item>Part I<list><item>Preliminaries</item><item>Data fitting schemes with hierarchical splines</item></list></item>
          <item>Part II<list><item>Parameterization for point cloud spline fitting</item></list></item>
          <item>Part II<list><item>Moving parameterization</item><item>Conclusion and future development</item></list></item>
          <item>References</item>
          <item>List of Acronyms</item>
          <item>Analytical Index</item>
        </list>
      </div>
    </front>
    <body>
      <p>It is available online at https://doi.org/10.36253/979-12-215-1002-7<ref target="https://doi.org/10.36253/979-12-215-1002-7" /></p>
      <div>
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