shapes

This repository contains tools to generate random shapes using Bezier curves (images and meshes), controlling the number of points and the local curvature and sharpness. It is also possible to generate shapes by joining specified points using an in-house csv format, and to generate full sets of random shapes with variable parameters. It was elaborated on the basis of this StackOverflow answer: https://stackoverflow.com/a/50751932/3237302, although there are now significant differences in behavior and features. It was used, directly or indirectly, in the following references:

A supervised neural network for drag prediction of arbitrary 2D shapes in laminar flows at low Reynolds number
J. Viquerat, E. Hachem
Computers & Fluids, vol. 210, num. 104645, 2020

A twin-decoder structure for incompressible laminar flow reconstruction with uncertainty estimation around 2D obstacles
J. Chen, J. Viquerat, F. Heymes, E. Hachem
Neural Computing and Applications, vol. 34, iss. 8, 2022

Direct shape optimization through deep reinforcement learning
J. Viquerat, J. Rabault, A. Kuhnle, H. Ghraieb, A. Larcher, E. Hachem
Journal of Computational Physics, vol. 34, iss. 8, 2022

Graph neural networks for laminar flow prediction around random two-dimensional shapes
J. Chen, E. Hachem, J. Viquerat
Physics of Fluids, vol. 33, iss. 12, 2021

If you make use of this repo for your research, please consider citing one of these.

CSV format

n_pts n_splg_pts
x1 y1 r1 e1
x2 y2 r2 e2
...
xn yn rn en

• n_ctrl_pts is the actual number of points you control on the shape. Each such point is joined with the next one using a cubic Bezier curve
• n_splg_pts is the number of sampling points per unit of distance between two control points
• xi yi are the coordinates of the control points
• ri is the local radius around control point i. It measures how far the local control points are from the point you provided
• ei is a local measure of sharpness

Give a look at the examples below for a better understanding of the effects of radius and sharpness parameters. Maximum smoothness is usually obtained for r = 0.5 and e = 0.0 on all points.

Shape examples

csv	shape
4 30 1.0 1.0 0.707 0.0 -1.0 1.0 0.707 0.0 -1.0 -1.0 0.707 0.0 1.0 -1.0 0.707 0.0
4 30 1.0 1.0 0.707 0.0 -1.0 1.0 1.0 0.0 -1.0 -1.0 0.707 0.0 1.0 -1.0 0.0 0.0
4 30 1.0 1.0 0.707 0.0 -1.0 1.0 0.707 0.0 -1.0 -1.0 0.707 0.0 1.0 -1.0 0.707 1.0
4 30 -1.0 0.0 0.5 0.0 0.0 0.1 0.7 0.0 1.0 0.0 0.5 0.0 -0.5 0.4 0.7 0.0
10 30 -0.22344386973718572 -0.11579347020968898 0.5 0.0 -1.086703349116176 0.056471511909076864 0.5 0.0 0.33918645130375696 -0.6285322803621614 0.5 0.0 0.09673486000147186 0.020665843303720587 0.5 0.0 0.7184144807034846 0.07933772977561572 0.5 0.0 0.658776975915066 -0.5602669680651731 0.5 0.0 -0.5629917814532847 0.37355108023884465 0.5 0.0 -0.5526944074292542 0.6349363861837116 0.5 0.0 0.44487187686581814 -0.19528679943835178 0.5 0.0 0.16784876294630274 0.3349169666644063 0.5 0.0

Generating datasets

Generate a dataset of random shapes using python3 dataset.py (parameters of the dataset can be modified inside the python file). It will generate images and meshes in separated folders.