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Grassmannian Shape Representations for Aerodynamic Applications



Olga Doronina, Zachary J. Grey, Andrew Glaws


Airfoil shape design is a classical problem in engineering and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach. Traditional analyses of airfoil shapes emphasize a flow-based sensitivity to deformations which can be represented generally by affine transformations (rotation, scaling, shearing, translation). We present a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes.


Shape representation, Grassmannian, Principal Geodesic Analysis, data-driven deformations, blade representation


Doronina, O. , Grey, Z. and Glaws, A. (2022), Grassmannian Shape Representations for Aerodynamic Applications, ADAM AAAI 2022, [online],, (Accessed May 24, 2024)


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Created February 28, 2022, Updated November 29, 2022