Shrinkwrap project from a single point

I want to project my model from a single point onto a plane. It seems like shrinkwrap project mode does just that. But for some reason, results are different if I have normal poligonal model(pic 1), or just edges, with no faces in between (pic 2). Pic 3 - model close up. The second one seems to be correct. Question is: is it the right way to do it? And why does presence of faces affects the result?

If you shrinkwrap a model with faces, you put one face on each other. This causes the weird look.
Specially if the model you project is not plain, so it have faces on itself too.
If you want to cut your model into the plane you should delete all faces and rebuild them in the plane.

Ok, I think I figured what happens, shrinkwrap tries to preserve the size of each face.
Here how it looks if I split the faces:

I guess, I’ll have to rebuild faces on the plane, as @rigoletto suggested.

Shrinkwrap does not try to preserve the facesize, it works like a overhead projector. It cant, cause your 3d model goes to a 2d plane.
Maybe try another method, looks like you want mode “Nearest surface point”.

If you apply your shrinkwrap, extrude your plained model so you got a cookie cutter, you can try to cut out your model in the plane. cookie_cutter.blend (648.5 KB)

I don’t want Nearest surface point, I want single point projection.
I can use cookie cutter technique if I extrude my edges and scale them outward. Thank you for suggestion.
The result seems to be identical to faceless shrink wrap projection, but can handle out of bound points.

Left to right: shrinkwrap faces, shrinkwrap edjes, cookie cutter.

Too bad boolean modifier don’t have knife-cut and I have to do it in edit-mode.

Here is my scene if anyone interested:
sundeal3.blend1 (737.1 KB)