I had a question about making mesh
With Mortar Hopper, this mesh model can be made or Python must be used.
It is not a clear question. For sure you can use python to make a mesh.
it is both a clear and not clear question. So I understand that a method and a tool for “Designing Patterns using Triangle-Quad Hybrid Meshes” have been developed by
Chi-Han Peng, Helmut Pottmann, and Peter Wonka. 2018. Designing Patterns
using Triangle-Quad Hybrid Meshes. ACM Trans. Graph. 37, 4, Article 107
(August 2018), 14 pages. https://doi.org/10.1145/3197517.3201306
If you want the whole functionality it is surely best you ask the authors to give/sell you the tool. Because there are many many options, so at the end it is very complex tool dedicated to this particular meshing.
If you want some functionality as in your first screenshot it could surely be doable using/tweaking quad-remesher and tri-remesher.
By the way nice paper. @DanielPiker have you some thought about this type of tessellation?