2022/01/12 by Olga A. Doronina, Doronina, Olga A., Zachary Grey +3 · 1 citation
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Vision and Imaging #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #Optical measurement and interference techniques
paper · pdf · doi:10.48550/arxiv.2201.04649
openalex publication_date 2022/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.