From 1b9d9e535222163108c93579578ef8ccd227a951 Mon Sep 17 00:00:00 2001 From: Anson Date: Sun, 1 May 2022 01:20:55 -0700 Subject: [PATCH] lotta text added --- .vscode/ltex.dictionary.en-US.txt | 1 + .vscode/ltex.hiddenFalsePositives.en-US.txt | 2 + Figures/solid_body.png | Bin 0 -> 114594 bytes citations.bib | 16 ++++ report.qmd | 89 ++++++++++++++------ 5 files changed, 84 insertions(+), 24 deletions(-) create mode 100644 .vscode/ltex.dictionary.en-US.txt create mode 100644 Figures/solid_body.png diff --git a/.vscode/ltex.dictionary.en-US.txt b/.vscode/ltex.dictionary.en-US.txt new file mode 100644 index 0000000..8879167 --- /dev/null +++ b/.vscode/ltex.dictionary.en-US.txt @@ -0,0 +1 @@ +DebriSat diff --git a/.vscode/ltex.hiddenFalsePositives.en-US.txt b/.vscode/ltex.hiddenFalsePositives.en-US.txt index 8909cac..516ed88 100644 --- a/.vscode/ltex.hiddenFalsePositives.en-US.txt +++ b/.vscode/ltex.hiddenFalsePositives.en-US.txt @@ -1 +1,3 @@ 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a/citations.bib +++ b/citations.bib @@ -24,3 +24,19 @@ url = {https://grabcad.com/library/6u-cubesat-model-1}, urldate = {2022-02-15} } + +@article{hillMeasurementSatelliteImpact, + title = {Measurement of Satellite Impact Test Measurement of Satellite Impact Test Fragments for Modeling Orbital Debris}, + author = {Hill, Nicole M.}, + url = {https://ntrs.nasa.gov/api/citations/20090019123/downloads/20090019123.pdf}, + urldate = {2009} +} + +@misc{plane_line, + title = {determine where a vector will intersect a plane}, + author = {David Mitra (https://math.stackexchange.com/users/18986/david-mitra)}, + howpublished = {Mathematics Stack Exchange}, + note = {URL:https://math.stackexchange.com/q/100447 (version: 2012-01-19)}, + eprint = {https://math.stackexchange.com/q/100447}, + url = {https://math.stackexchange.com/q/100447} +} \ No newline at end of file diff --git a/report.qmd b/report.qmd index f917acd..8007cb0 100644 --- a/report.qmd +++ b/report.qmd @@ -1,8 +1,13 @@ --- title: "Characterization of Space Debris using Machine Learning Methods" subtitle: "Advanced processing of 3D meshes using Julia, and data science in Matlab." -author: Anson Biggs +author: + - name: Anson Biggs + url: https://ansonbiggs.com + date: "4/30/2022" +thanks: Mehran Andalibi + latex-auto-install: true format: html: @@ -19,6 +24,7 @@ execute: filters: - filter.lua +# theme: litera --- ## Introduction @@ -98,17 +104,66 @@ The algorithm is finding the area of a triangle made up by 3 points in 3D space 3 vector math. The area of a triangle is $S=\dfrac{|\mathbf{AB}\times\mathbf{AC}|}2$, then the sum of all the triangles that make up the mesh should produce the surface area. This can be inaccurate if a mesh is missing triangles, has triangles that overlap, or is a mesh that has internal geometry. +None of which should be an issue for 3D scans. ### Characteristic Length +This is a property that is heavily used by the DebriSat^[@DebriSat2019] program, so it is definitely +worth having specifically since DebriSat is a very interesting partner for this project. It is +unclear if the current implementation is the same value that DebriSat uses. Wikipedia gives a +different +definition^[[Wikipedia: Characteristic Length](https://en.wikipedia.org/wiki/Characteristic_length)] +that defines characteristic length as the volume divided by the surface area. DebriSat mentions it +in various papers with slightly different definitions. + +The current implementation is quite complicated and is the most involved algorithm used. The key +fact that makes this algorithm work is that the eigenvectors are orthonormal and oriented so that +they are pointing in the direction of most mass. Assuming the mesh has uniform density, this means +that the eigenvectors are pointing in the direction of the points furthest from the center of +gravity. + +The algorithm begins by taking the eigenvectors $\lambda$, and making vectors from the center of +gravity to every point that makes up the mesh, $\bar{P_i}$. Then the angle, $\theta$, between the +eigenvectors and all the point vectors needs to be calculated as follows: + +$$\theta_i = arccos\left(\frac{\lambda \cdot P_i}{\| \lambda \| \| P_i \| }\right)$$ + +For almost every mesh there won't be a point that has a direct intersection with the eigenvector, +i.e. $\theta \approx 0$. To deal with this the 3 points with the smallest angle can be turned into a +plane, then the intersection of the eigenvector and the plane can be calculated^[I won't go into +depth of this math, but you can find a great explanation here [@plane_line]]. This process then +needs to be repeated for the largest 3 angles to be able to get two points that a distance can be +calculated between to be used in the characteristic length. The characteristic length, $L_C$, can +then be calculated simply by taking the average of the distances found for each eigenvector. + +$$L_c = \frac{\mathbf{A} + \mathbf{B} + \mathbf{C}}{3}$$ + ### Solid Body Values +The current algorithm just takes all the points that make up the mesh, then finds the `minmax` for +each axis then averages them like the figure above. No consideration is taken for the orientation of +the model, but I believe that shouldn't matter. Definitely an algorithm that deserves a revisit +especially if DebriSat could be contacted for a rigorous definition of the quantity. + +![Calculation of Solid Body Values, @hillMeasurementSatelliteImpact [slide 9]](Figures/solid_body.png) + ### `find_scale` and `fast_volume` Functions -```{julia} -#| echo: false -#| output: false +These functions are used together to scale the models for machine learning. When performing machine +learning on a dataset with properties of varing magnitudes it is important to do some sort of +scaling. It was determined that scaling by volume was optimal for many reasons, but mainly because +the algorithm to calculate the volume is one of the fastest. The `fast_volume` function is just a +modified version of the main volume function that has all the extra calculations required for center +of gravity and inertia removed. The `find_scale` function uses the `fast_volume` function and a +derivative root finding algorithm to find a scaling factor that can be used to get a volume of 1 +from a model. This process while iterative works incredibly fast and with the current dataset only +adds about 20% to the computation time to calculate all the properties for a mesh. +## stl-process Workflow + +### Imports + +```{julia} using FileIO using MeshIO @@ -116,15 +171,14 @@ using stlProcess using CSV using DataFrames -using Plots -theme(:ggplot2) using LinearAlgebra using Statistics ``` +### `loop` Setup + ```{julia} -#| code-fold: true #| output: false # local path to https://gitlab.com/orbital-debris-research/fake-satellite-dataset @@ -145,6 +199,8 @@ df = DataFrame(; ) ``` +### The `loop` + ```{julia} #| output: false @@ -167,6 +223,8 @@ for path in dataset_path * "\\" .* folders end ``` +### Output + :::{.column-body-outset} ```{julia} @@ -177,23 +235,6 @@ describe(df) ::: -```{julia} -S = cov(Matrix(df)) - -eig_vals = eigvals(S); - -# sorting eigenvalues from largest to smallest -sort_index = sortperm(eig_vals; rev=true) - -lambda = eig_vals[sort_index] -names_sorted = names(df)[sort_index] - -lambda_ratio = cumsum(lambda) ./ sum(lambda) - -plot(lambda_ratio, marker=:x) -xticks!(sort_index,names(df), xrotation = 15) -``` - ## Gathering Data To get started on the project before any scans of the actual debris are made available, I opted to