Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2208.04743

Separable Shape Tensors for Aerodynamic Design

Zachary Grey·Olga Doronina·Andrew Glaws
View original source ↗Read source document ↗Export metadata ↓

Abstract

Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and traditional analyses of 2D and 3D aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable 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) an improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.

Explore related subjects

cs.GR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zachary Grey, Olga Doronina, Andrew Glaws. 2023-01-03. Separable Shape Tensors for Aerodynamic Design. https://doi.org/10.1093/jcde%2Fqwac140

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Opacity Is Not Just Opacity

Web graphics travel with content across pages and themes, where changing backgrounds can require recoloring and maintenance. Opacity already makes a fixed object's appearance depend on its background, yet is usually understood only as how much the object obscures it. In fact, opacity controls the scaling of the object-background color difference; transparency is only one effect of this relationship. Zero places the output at the background and one at the source color, but difference scaling need not stop at either position. We retain the compositing expression and extend the coefficient domain from $[0,1]$ to the real numbers: negative values reverse the difference, whereas values above one expand it in the same direction. We focus on same-direction expansion for reusing Web graphics across backgrounds. Each object carries a fixed source color and coefficient, while the actual background determines the enhancement direction. Background-adaptive contrast enhancement thus becomes part of the object's compositing properties, reducing the design and maintenance of separate color variants. The implementation reuses the original equation without increasing the per-pixel arithmetic operation count within the same pipeline. Enumerating all 8-bit sRGB source colors on 16 predefined light and dark canvases, a fixed $α=1.1$ increases the contrast ratio in 99.8145% of combinations. Without changing source colors, 4.8346% of all combinations newly reach the $3:1$ contrast threshold. Output validation and timing across three browsers demonstrate implementation in the same WebGL pipeline, with no sustained additional runtime observed.

cs.GR↗
arXiv2026

Constrained Program Generation for 3D Reaction Animation with a 0.8B Model

Visualizing a chemical reaction requires making its molecular changes visible while keeping the animation faithful to the stated chemistry. Equations, structural diagrams and molecular viewers provide complementary descriptions, but assembling an interactive three-dimensional explanation still requires specifying the changes and checking their consistency. We present ChemXRG, a domain-specific language (DSL) framework that addresses this gap by representing a reaction animation as an executable program. Persistent atom identifiers and explicit bond, charge and grouping operations connect the symbolic reaction to the displayed transformation. This shared representation lets generation, verification and rendering operate on the same account of what changes. Given known, atom-mapped reactant and product structures, reaction-grounded constraints fix input-determined facts and restrict action choices; execution checks validate the resulting transformation before geometry and frames are constructed. We implement this paradigm with a reaction-program corpus and ChemQwen, a trained 0.8B DSL generator. Paired and component evaluations show improved compiler acceptance and normalized full-program agreement under input-conditioned constraints, while identifying remaining failures that require execution checks. A public browser application demonstrates the connection from symbolic reaction descriptions to inspectable programs and interactive 3D animations.

cs.GR↗
arXiv2026

NaRPA: Navigation and Rendering Pipeline for Astronautics

This paper presents the applications of scientific ray-tracing in modeling and simulating light transport for space-borne image data generation. A ray-tracing engine, the Navigation and Rendering Pipeline for Astronautics (NaRPA), is introduced as a rendering framework to generate virtual datasets and support simulations for robust navigation pipelines. Sensor and environment models that enable the synthesis of space-to-space and ground-to-space virtual observations are presented. The work demonstrates the capabilities of simulating passive and active vision-based sensors using NaRPA to facilitate the design, testing, and verification of aerospace visual navigation algorithms. Additionally, the paper describes a velocimeter LiDAR model and its statistical validation with experimental data.

cs.GR↗