Random uniform distributions of 2D circles and 3D spheres
Description
This dataset contains random uniform distributions for a large number of 2D and 3D balls, along with the description files and examples of usage. It provides the possibility for fast pick up of the random sets of smaller subsamples, with the guaranteed statistical properties such as random uniform distribution of balls, the predefined expected volume ratio of balls, and also the minimum distance between them. The main data is contained in two files 'kernels2D.npy' and 'kernels3D.npy' which are the arrays of centers of the balls with unitary radius (r=1). Data is stored in NumPy format (https://numpy.org). The shape of these arrays is (nc, nd, N, D), where 'nc' is the number of considered void ratios, 'nd' - number of considered distances, 'N - maximum number of generated centers, and 'D' - space dimension. The 'kernels2D.json' and 'kernels3D.json' files are the description files stored in JavaScript Object Notation format. They can be previewed in the Firefox web browser and edited in any text editor. The most important entries in the description files are: * 'c' - list of considered expected volume ratios of balls (of length 'nc'); * 'd' - list of considered additional distances between balls (of length 'nd'); the final distance is guaranteed to be not less than 2*r + d; * 'Ncd' - numbers of ball centers generated for all (c, d) pairs; * 'nsamples' - a dictionary containing numbers of subsets of different sizes (given by radius 'R' or equivalently by the expected number of balls) required to obtain a mean value of the ball volume ratios at the required accuracy ('rmargin') with assumed 'confidence'; this dictionary contains also the precomputed estimates of the standard errors for the ball volume ratio values ('sigma'). In order to use this data first decide which volume ratio you are interested in and what are the minimum distances between balls required. Then establish the indices 'i', 'j' of your values in 'c' and 'd' lists, respectively. Next, get the number of centers generated for chosen geometric configuration from 'Ncd' array and finally retrieve centers from .npy file. Consider this python code snippet as an example: """ import numpy as np import json description = json.load(open('kernels3D.json', 'r')) kernel = np.load('kernels3D.npy') c = 0.065; i = 11 d = 0.025; j = 5 N = description['Ncd'][i][j] centers = kernel[i, j, :N]` """ The directories 'example2D' and 'example3D' contain the sets of subsamples of different sizes picked up from kernels for specific volume ratio and ball distances. Names of subdirectories are just the expected numbers of balls in the subsamples. Subdirectories contain the self-explanatory description files (.json), the array of centers retrieved form from kernels (.npy file), and the geometry and finite element files for all subsamples (.brep and .msh files) to be used in computations. Description files contain also the results of computations performed in the research paper [to be published].
Files
Steps to reproduce
For reproducing steps please refer to the data paper [to be published].