added more explanation of algos

.gitignore

@@ -1,3 +1,5 @@
 .jupyter_cache
 *.log
-*.tex
+*.tex
+*.html
+*.pdf

report.qmd

@@ -39,16 +39,26 @@ of space debris are more thoroughly understood, we can begin mitigating the crea
 future space debris by implementing improved satellite construction methods and more advanced debris
 avoidance measures.
 
-### Current Progress
+## Current Progress
 
 This project aims to fix very difficult issues, and although great progress has been made there is
 still plenty of work to be done. Currently, algorithms have been made that are capable of getting
 many key features from solid ^[A mesh with a surface that is fully closed and has no holes in its
-geometry.] models that are in the `stl` format. The algorithm for processing the 3D meshes is
-implemented in the Julia programming language. Syntactically the language is very similar to Python
-and Matlab. Julia was chosen because it is nearly as performant as compiled languages like C, while
-still having tooling geared towards engineers and scientists. The code produces a struct with all
-the calculated properties as follows:
+geometry.] models that are in the `stl` format. Processing the 3D scans produced by the scanner in
+the RPL lab is no easy task and something I chose to avoid for now. I suspect that the best method
+to work with data from the scanner will be to export a point cloud from the scanner software, then
+from there use the points to create a triangulated mesh. The amount of scans needed means that the
+only real way to hit the order of magnitude required is to have the only part of the workflow that
+isn't fully automated by code to be taking the scans. My semester planned to do most of the
+processing of the mesh in CATIA which proved to take far too long and isn't scalable.
+
+## Mesh Properties Algorithm Breakdown
+
+The algorithm for processing the 3D meshes is implemented in the Julia programming language.
+Syntactically the language is very similar to Python and Matlab, but was chosen because it is nearly
+as performant as compiled languages like C, while still having tooling geared towards engineers and
+scientists. The current code is quite robust and well tested and for a given `stl` file produces the
+following data:
 
 ```julia
 struct Properties
@@ -67,6 +77,34 @@ struct Properties
 end
 ```
 
+### Volume, Center of Gravity, Inertia
+
+These properties all come from [@eberlyPolyhedralMassProperties2002] which provides a great
+explanation of the algorithm. The algorithm is quite complicated, but is really robust, accurate and
+vectorized which means it is extremely fast. All the other algorithms are implemented from scratch
+by me and have plenty of room for improvement, but the algorithm for these properties is probably as
+good as it can get.
+
+### Surface Area
+
+Calculating the surface area is currently very simple but does have some shortcomings. The whole
+algorithm is one line of code:
+
+```julia
+surface_area = sum(norm.(eachrow([x0 y0 z0] - [x1 y1 z1]) .× eachrow([x1 y1 z1] - [x2 y2 z2])) / 2)
+```
+
+The algorithm is finding the area of a triangle made up by 3 points in 3D space using some Calculus
+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.
+
+### Characteristic Length
+
+### Solid Body Values
+
+### `find_scale` and `fast_volume` Functions
+
 ```{julia}
 #| echo: false
 #| output: false