This SOFA plug-in implement the Position-Based Dynamic algorithm and 8 constraints for 1,2 and 3D meshes. Each constraint contains in its header the article which it's coming from.
Some optimisations have been made, some part of the code might not look like the equations, but, it's mathematically equivalent.
Link to SOFA : https://www.sofa-framework.org
Their github : https://github.com/sofa-framework/sofa