This library makes 3D geometry easy so that you can easily build 3D plots using ggplot. The below is a set of plots built using ggplot with the underlying data processed using this library and stitched together into a GIF to emphasise the 3D-ness.
The functions are a little low level so you may need some programming comfort to use it at this point. The code in the README.Rmd file should give you some ideas on how to use it. The source code is disgusting so go into it at your own peril. Some day it will be clean.
Bug reports are welcome! Feature requests are also welcome but this is a side project for me so they will be worked on at a lower priority and at author’s discretion.
The data in this example is just a cube with eight corners specified. We’re going to draw a 3D scatter plot of these 8 points with their projections / shadows on each of the three planes.
| x | y | z |
|---|---|---|
| 2 | 2 | 2 |
| 2 | 2 | 3 |
| 2 | 3 | 2 |
| 2 | 3 | 3 |
| 3 | 2 | 2 |
| 3 | 2 | 3 |
| 3 | 3 | 2 |
| 3 | 3 | 3 |
We calculate the shadow of the data on a plane as if the light source was very large, and very far away from the points, perpendicular to the plane. Think of it as the noon sun casting a shadow on the ground where the ground is the plane. In any other orientation, the shadow will be a little distorted. Play around with the parameters to see the results
We will do this thrice, once for each plane - the XY, the YZ, and the XZ plane.
The projection on the XY plane is:
| 1.998997 | 1.998997 | 0 |
| 1.998494 | 1.998494 | 0 |
| 1.998997 | 3.001003 | 0 |
| 1.998494 | 3.001506 | 0 |
| 3.001003 | 1.998997 | 0 |
| 3.001506 | 1.998494 | 0 |
| 3.001003 | 3.001003 | 0 |
| 3.001506 | 3.001506 | 0 |
You can see the z coordinate being zero, and the x and y coordinates being four points repeated twice each with a minor change in the coordinates. This difference between the almost duplicates is because our light sources is not actually at infinity and the change in the z coordinates causes a really small change in the shadow’s position as well. You can also think of it as you seeing a cube from very far away from the same point as where the light source is. You’d almost see only a square but in actuality there is just a little bit of the rest of the cube that also sticks out from begind the face that you can see. Try reducing the value of the nInfinitySubstitute variable and see the difference.
I’d plot it but it just looks like a square which you can sort of make out from the data so not bothering.
We similarly also calculate shadows on the other two planes
Now that we have the 3D coordinates of the shadows, we can calculate what it would look like when viewed from a particular point.
We don’t need to do the first step for the data, since its coordinates are what they are. So we directly calculate their project on the screen.
Let’s see what this looks like now
Looks sort of correct but it’s a little hard to comprehend it without some visual guides. Let’s add some.
Let us first add some line segments parallel to the X axis
Sort of looks like one of the planes, right?
Let’s repeat it for the other two planes as well
Better. The shadows make sense, the planes make sense, the data makes sense.
I’ve wrapped up this code in a function,f3DScatterPlot and demonstrate
how this same plot comes out if you move the origin coordinate. This
function is available form the library.
The GIF is made from stitching together the outputs of plots from different coordinates. You can get the individual plots from the functionality in this library but stitching them together will need you to have another program, like image magick.
I do a lot of fooball related work so a couple of things I’ve put together using this library in the football context -
Sneak peek into a slow moving side project - 3D views and slices of football pitches.\#TidyTuesday \#ggplot2 \#RStats pic.twitter.com/BSEba2zs9T
— The Come On Man (@thecomeonman) July 28, 2020
This was generated using `geom_pitch` from my other library, [CodaBonito](https://github.com/thecomeonman/CodaBonito) Here’s a simple example to demonstrate usage. Play around with the arguments to get a feel for how it works.
