I have imported in Cinema 4D, and then under the subdivision menus, I did extrude.
Though the geometry is really not converted in a way I need. I'm a long time Maya user, but too newbie to Cinema 4D (for helping a friend of mine in a project).
I like the new geometry (extruded) be quad-faced. Now it is neither triangular nor quad, and from points (points of curves in AI) of the curve, edges are pulled toward the center of the geometry. My geometry is like curved (rounded) diamond, and the front faces of it are made like this. How should I make a quad-faced conversion of the diamond-curves in C4D?
Go into the Extrude object's Caps tab and check "regular grid". Then set the grid to quadrangles. You can adjust the density with the grid size setting. You'll still get some triangles along the seams but it will be mostly quads.