Import SVG polygon, convert to mesh, force horizontal and vertical mesh lines

I have imported several polygons created in Inkscape and exported as plain SVG files. After importing into Blender I use Convert to Mesh from Curve. The mesh is created by connecting the nodes on the perimeter of the polygon. (There are a lot of nodes on the curves which results in a lot of mesh lines). I would like to force the mesh subdivision lines to all be horizontal and vertical. If that is not possible, then to create a homogeneous field of small triangles inside the polygon. Thanks.

You can kind of do this by converting the vector, as you did, and then using it with knife project to cut its shape out of a finely ( or as finely as you want) subdivided plane that is positioned underneath.