# Introduction

`pyGeo` is a package for generating and manipulating geometry, particularly for applications involving shape optimization.

## Background

Shape optimization is a field of engineering that uses applied mathematics and computer simulation to find the best possible shape for an object, such as an aircraft or a ship. To do this, optimization software needs to perturb a baseline geometry into a new shape at each iteration. Users define design variables which map numeric inputs from the optimizer to changes in the geometry.

Examples of geometric design variables include:

• Span, aspect ratio, and sweep in a wing design problem

• Freeboard, deadrise, and beam for a ship design problem

• Blade length, twist distribution, and airfoil shape modes for a wind turbine problem

The set of all geometric design variables and their effects on the baseline geometry is called a parameterization. Parameterizations are not unique, and choosing a good one is both an art and a science.

There are two primary approaches to geometry parameterization: generative and deformative. In pyGeo, we primarily use a free form deformation (FFD) approach, which belongs to the latter category. This approach does not require the parameterization of the baseline geometry (as is the case for a generative approach such as CAD) because we only parameterized the changes with respect to the unperturbed geometry

Some geometries that can be generated by a parameterization are not allowable for physical or other engineering reasons. For this reason, geometric constraints must often also be imposed (such as a minimum volume inside a car’s cabin, or a wing thickness).

`pyGeo` enables users to set up a variety of geometric parameterizations and geometric constraints. It is particularly useful for gradient-based optimization because it provides accurate derivatives of geometry with respect to the design variables.

## Package Description

The package consists of the following high-level modules:

• DVGeometry (short for “Design Variable Geometry”) parameterizes and modifies geometry (pointsets) in shape optimization problems, using the free-form deformation (FFD) method

• DVGeometryMulti parameterizes multiple geometric components using multiple FFDs and handles design changes near component intersections

• DVGeometryESP enables CAD-based geometry parameterization using Engineering Sketch Pad (ESP) software

• DVGeometryVSP enables conceptual geometry parameterization using the Vehicle Sketch Pad (OpenVSP) software

• DVConstraints allows users to constrain important geometric parameters during optimization (such as thicknesses and volumes)

• pyGeo generates spline surfaces, either from geometry files or user-defined wing surfaces