How Can convert Birth Intersection to Tysplines?

[MajidAdab]

The tySlice modifier has a cross-section mode you can use to slice up an object similar to your images, but it doesn't rely on intersections.

The Birth Intersections operator just finds intersections and randomly scatters particles on them...you can't really use it to analytically extract intersection splines.

There's not really a straight-forward way to extract intersection splines that I can think of...closest thing would be performing a boolean surface subtract operation between your pieces of geometry using the tyBoolean modifier, then using a tyMeshToSplines modifier to convert the remaining open edges to splines. But that wouldn't only work as intended if the source geometry being sliced is a closed surface.

yes.

- exactly there are nonplanar surfaces and ty-slice modifier does not work here.
I do not know if there is any way to use a ty-slice modifier with non-planar planes or not.

- I used tyBoolean with tyMeshToSplines modifier and it worked. thank you so much.
the only problem with this technique is the slow process. because when I increase the number of planes, tyBoolean would take very long to process.

- but after trying various ways and techniques, I finally succeed to do it via Birth Intersections + Fuse + particle physics. 
with the combination of these 3 op I can uniform the distance of the particle from the birth intersection and then I used tyspline in the neighbor's mode with only 2 neighbors limit.
it is more faster than tyBoolean techniques.

I put a screenshot here for those who are interested in this topic.