Hello sidefx guys, I have a simple problem here. There is a deformed grid is cut by a extruded shape, and I want to keep the inside of the grid. The Boolean operation works, but it turn the original quads into triangles, is there any method for me to keep the quads of the booleaned shape? A file is attached. Thanks in advance!
Best
Sun

Turn off Pre-Convex Geometry on the Cookie SOP. That will not triangulate the incoming geometry.
In your case, the default result left some bad results on the edges. Increase the 3D Tolerance slightly until the artefacts disappear.

Make sure all primitive normals face outward.
The second input geometry, the extruded tube had inward facing primitive normals. This is common. Just insert a Reverse SOP and reverse the U to flip the primitive normals.
The Cookie SOP really likes it when all incoming primitive have outward facing primitive normals.

Make sure that all polygons on the input geometry have approximately the same size edges.
The second input extruded tube had very long and narrow polygons. Not ideal for the Cookie SOP but in your case, wasn't that bad. But still you should ensure that the edges on each polygon face are a bit more square.
This is easily done in your example as the Poly Extrude SOP has a slider for Divisions.

Having done all this, there are still a couple tiny artefacts in the result. When you get multiple non-planar quads with edges that meet on top of each other from both inputs, Cookie can generate these artefacts. This is where triangulating the geometry helps tremendously.
There is just such an artefact in your geometry. I slightly shifted the first input to remove one critical intersection to remove an artefact.

See attached file.

thanks jeff! It is really helps!