Shape Correspondences and Example-Based Modelling for Boomerang Design
A Framework for Alignment, Parameterization, Modelling and Analysis of Aerodynamic Boomerang Shapes
N. van Veen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
K Hildebrandt – Mentor (TU Delft - Computer Graphics and Visualisation)
R. Marroquim – Mentor (TU Delft - Computer Graphics and Visualisation)
Xucong Zhang – Graduation committee member (TU Delft - Pattern Recognition and Bioinformatics)
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Abstract
This thesis presents a computational framework aimed at enabling the analysis and modeling of boomerangs from example shapes. The goal is to provide a systematic and data-driven tool for boomerang design based on real-world geometries. A key challenge in this context is establishing accurate shape correspondences between handcrafted, asymmetric, and aerodynamically functional boomerangs.
To address this, the proposed pipeline integrates multiple components: landmark-based pre-alignment, boundary extraction using alpha shapes, curve parameterization, and Least Squares Conformal Mapping (LSCM) to compute surface correspondences. Building on these correspondences, the framework further incorporates principal component analysis (PCA) and Free-Form Deformation (FFD) to enable the generation of new shapes.
Experimental results show that the method achieves low Hausdorff and Chamfer distances and has been evaluated using area- and shear-based distortion metrics. Nonetheless, some localized inaccuracies - particularly near high-curvature regions - highlight areas for improvement in boundary handling and local control. Additional limitations include the reliance on manual landmark selection, the linearity of PCA, and the sensitivity of the pipeline to alpha shape parameters.
By combining elements of computational geometry with principles of aerodynamic design, this research bridges the gap between empirical craftsmanship and formal shape analysis. The resulting methodology not only enables the comparison and modeling of boomerangs but also lays the groundwork for future tools in boomerang shape exploration and design.