Visualizing the Orion Constellation and a question for those who have already done this project


this is my project Orion Constellation.
on this project, I still have a question:
where are from the coordinates x,y,z that mentioned in pdf file “The Orion constellation as an installation”
The celestial coordinates x,y,z from are differ.
or how transform them into the same system
for example: in stellar-database for alpha orionis Celestial (X,Y,Z) coordinates in ly: 8.9, 424, 55
and we have x=-0.41 y = 4.12 z = 2.06
it would be very nice if you could check my solution and answer the question.