A considerable amount of effort has been devoted in organizing the managerial structure of the Project. We have set up a mechanism that efficiently designed, implemented and monitored all activities within the Project and provided the best possible training to our fellows. This was complemented by a strong network, including industrial stakeholders. The main results achieved can be partitioned into 3 scientific domains:
1.High-order methods and alternative representations deal with nonlinear methods for accurately representing complex shapes, while switching between representations offers complementary advantages. We have proposed original algebraic methods, including some prototype software for testing the new algorithms. Our emphasis has been on methods that exploit the structure of the given equations, such as their sparseness.
Extraction of geometric primitives from 3D point clouds is an important problem in reverse engineering. Key ingredients in this approach are geometric routines that produce a given type of shape (plane, sphere, cylinder, cone, torus) from a small number of points.
Splines made of Dupin cyclide patches (cyclidic splines) have nice modeling properties, but were known to be too rigid. Our goal was to make them more flexible by studying and utilizing their deeper geometric properties, including their 3D generalizations. This could have direct applications in architecture for construction-aware free-form modeling.
We explored the reconstruction of 3D shapes from defect-laden, unstructured 3D point clouds and contributed a deep-learning framework designed to segment 3D point clouds, and a shape reconstruction method that generates isotropic surface triangle meshes from 3D point clouds capable to estimate the local curvature, thickness and separation between objects.
2.Algebraic & numeric tools in shape optimisation and analysis have focused on isogeometric analysis (IGA), which allows for combining geometric modeling with computational fluid mechanics. We investigated novel spline constructions over unstructured meshes to be applied for modeling purposes, approximation problems and in the numerical resolution of partial differential equations. We devised a new construction of spline basis functions suitable for IGA simulations in the conversion of CAD models into smooth spline objects and for solving the shallow-water equation.
We worked on identification problems that arise in the context of image processing where spatial information needs to be inferred from planar images. We assume that only a single picture is given, plus some additional information about the type of three-dimensional object.
We developed methods and software tools that combine geometry, continuum mechanics and ML for boosting Maritime Engineering: (i) We introduced the concept of intra-sensitivity to identify parameters whose perturbation has a major impact on the sensitivity index of the remaining parameters. (ii) In shape optimisation, we used higher-level information about the shape in terms of its geometric integral properties. (iii) We developed ShipHullGAN, a generic parametric modeler built using GANs which addresses the current conservatism in the parametric ship design paradigm, where parametric modelers can only handle a particular ship type.
Bézier and B-spline curves are the current de-facto-standard for describing and modeling curved shapes in CAD. We explored an alternative representation based on barycentric rational interpolation which provides more direct control, as it allows to modify the shape by moving points that are on the curve.
We introduced (locally refined) Tchebycheffian splines in IGA which offer better local refinement and outperform Tensor-product B-splines in several benchmark problems. This has a significant impact in computational mechanics and data compression. Our methods meet the requirements of both geometric design and engineering analysis, faithful to IGA.
3.ML for shapes has concentrated on supervised methods (often with limited supervision) for representing shapes and for offering robust methods in similarity search and object segmentation, as well as shape editing. We pioneered specific neural network (NN) architectures for 3D objects as well as the combination of 2D image and 3D information for handling deformable objects. We explored advanced NN techniques to overcome the limitations of implicit neural shapes (lack of interpretability, intuitive control, and shape generation methods when there is little data).
We aimed to improve temporal 3D point cloud understanding, vital for fields like geoscience, and manufacturing. We addressed challenges in analysing noisy and unstructured temporal point clouds, benchmarked segmentation models, analysed deep-learning architectures, and developed a new visualization tool. We proposed methods to enhance rockfall detection using ML and spatiotemporal data, and adapted models for identifying machining tools from 3D point clouds to optimize industrial processes. Our work advances the field by addressing accuracy, efficiency, and robustness in 3D point cloud analysis.
We investigated a novel approach for generalizing the well-known Doo-Sabin surface subdivision algorithm to the volumetric setting and used ML to deal with the large number of different local mesh layouts that can occur
