In shape optimisation problems, subspaces generated with conventional dimension reduction approaches often fail to extract the intrinsic geometric features of the shape that would allow the exploration of diverse but valid candidate solutions. More importantly, they also lack incorporation of any notion of physics against which shape is optimised. This work proposes a shape-supervised dimension reduction approach. To simultaneously tackle these deficiencies, it uses higher-level information about the shape in terms of its geometric integral properties, such as geometric moments and their invariants. Their usage is based on the fact that moments of a shape are intrinsic features of its geometry, and they provide a unifying medium between geometry and physics. To enrich the subspace with latent features associated with shape’s geometrical features and physics, we also evaluate a set of composite geometric moments, using the divergence theorem, for appropriate shape decomposition. These moments are combined with the shape modification function to form a Shape Signature Vector (SSV) uniquely representing a shape. Afterwards, the generalised Karhunen–Loève expansion is applied to SSV, embedded in a generalised (disjoint) Hilbert space, which results in a basis of the shape-supervised subspace retaining the highest geometric and physical variance. Validation experiments are performed for a three-dimensional wing and a ship hull model. Our results demonstrate a significant reduction of the original design space’s dimensionality for both test cases while maintaining a high representation capacity and a large percentage of valid geometries that facilitate fast convergence to the optimal solution. The code developed to implement this approach is available at https://github.com/shahrozkhan66/SSDR.git.

Transformation of hardcopy ship drawings to electronic ones is usually accomplished through scanning and raster-to-vector conversions. Such conversions are, however, limited to produce low-degree vector entities, such as line segments, poly-lines and circular arcs. As a consequence, free-form curves, appearing in the original hardcopy, are usually disintegrated to a significant number of overlapping line and/or arc segments. The algorithm presented in this paper, consists of a scan-line processing of line segments that are grouped (clustered) with the aid of a moving scan-line and an appropriately defined distance to previously grouped entities. The performance of the algorithm is illustrated for the body-plan of a bulk carrier.