Is there a powerful interactive tool for visualizing Lorentz transformations of worldlines? This Geogebra demonstration is pretty amazing for obtaining a more intuitive understanding of Lorentz transformations. However, it has its limitations. If it would allow the user to add worldines and see how they transform, use the other sectors of the graph and return coordinates with more significant figures it would be a seriously powerful tool for the beginner wanting to get a better grasp of problems in special relativity. Are there similar resources that allow one to do these things? If not, how would you suggest I go about creating one?
 A: If you can't find a satisfactory interactive tool, you can make your own: either from scratch or to build off the work of others (of course, giving appropriate credit).

GeoGebra comment: When viewing GeoGebra on the web, one can get to the GeoGebra source by clicking the "three vertical dots" in the upper right corner 

to view on the web: Open in App, the upper-right-corner button with the circle and triangle, then three vertical dots, and finally Algebra to show the Algebra window
to view in the GeoGebra application (which is free): Details, then Download the .ggb file

So, you can study what you linked above: GeoGebra visualization Lorentz Transform by Abdul Latiff.

The key idea is to matrix multiply your point-events or vectors by a Lorentz Transformation boost matrix
$$\left(\begin{array}{cc}
C && S \\
S && C \\
\end{array}\right)$$
where $C=\gamma=\displaystyle\frac{1}{\sqrt{1-(v/c)^2}}=\cosh\theta \geq 1$
and $S=\gamma (v/c)=\displaystyle\frac{v/c}{\sqrt{1-(v/c)^2}}=\sinh\theta$
with $(v/c)=\tanh\theta$ (where $-1<(v/c)<1$).
As a check, the determinant must be $C^2-S^2=1$.
As a start, see, for example,
GeoGebra visualization Visualizing Linear Transformations by je1324
with $C=5/4$ and $S=3/4$, which corresponds to $(v/c)=(S/C)=(3/5)$.
You can display the transformed grid and see the effect of transforming a vector.
There are ways to make sliders or have draggable points to systematically vary the parameters.

For more ideas,
refer to this discussion: https://www.physicsforums.com/threads/what-software-can-i-use-to-make-space-time-diagrams.997158/
Here are some possibly interesting ones that I found (but am not familiar with).

*

*http://ibises.org.uk/Minkowski.html - "You can perform a Lorentz boost in two ways. One way is to enter a velocity (positive or negative) as a fraction of the speed of light in the Boost to velocity control and click the Boost button. The other is to select a time-like world-line and click on the Boost to selected line rest frame button. This button is only active when a time-like world-line is selected."


*http://www.trell.org/div/minkowski.html - "The diagram is representing a model of two spacetime events, event A and event B. Two observers in two inertial reference frames pass each other in the origin. At that point is event A - the green ball. The user inputs the time and distance for event B - the red ball - and the relative velocity. The diagram will show time dilation, the relativity of simultaneity and other effects of special relativity."


*https://bytemeta.vip/repo/freixas/gamma - "Gamma is a tool you can use to draw a wide variety of 2D Minkwoski spacetime diagrams. In addition to the usual static diagrams, you can also create animated diagrams and you can add toggles, choices, and sliders to manipulate the diagram." (See also https://www.physicsforums.com/threads/request-for-input-2d-minkowski-spacetime-diagram-generator.1007628/ )


*

*Here is my own visualization in Desmos (which has the equations in the left panel, possibly in folders). So you can play around and develop your own version. See my answer at the physicsforums link for earlier and simpler versions.

robphy's spacetime diagrammer for relativity v.8e-2021 (time upward)
https://www.desmos.com/calculator/emqe6uyzha

Open the BOOST folder and vary the $v_{LAB}$ slider.
The lab-velocities of the inertial worldlines can be tuned.
You can also position events P and Q and see their boosted version.

Scroll down to the "formulae" folder to see my boost formulas.


*Here are some of my GeoGebra ones:

GeoGebra: Relativity-LightClock-MichelsonMorley-2018

GeoGebra: RRGP-CoordinateSystems which uses my Relativity on Rotated Graph Paper visualizations of "light-clock diamonds".
In situations with nice numbers (e.g. $(v/c)=3/5$ or $(v/c)=4/5$ where the Doppler factor is rational, leading to triangles with Pythagrorean triples), you could graphically construct the coordinate grids on graph paper. Thus, you could learn to read off values and relationships from the diagram without having to redraw it manually or with software. (I may update this post later to give more details.)
A: To better understand the resolutions to common paradoxes associated with special relativity, I made this interactive graph in Desmos: Lorentz Transformation (boost)
On this graph, you can specify coordinates of events and change the parameters that define the worldlines of particles moving with constant proper acceleration.
