How to get mesh-information from `Plot3D`

Question

In a simple example Plot3D shows a triangular mesh:

pic = Plot3D[Sin[x] Sin[y], {x, 0, 1}, {y, 0, 1}, Mesh -> All]

I know how to get the point-coordinates and the vertexnormals of this plot:

p = pic[[1, 1]][[1]]; (* points*)
n = VertexNormals /. pic[[1, 1]][[3]]; (* vertex normals*)

But I didn't get the 2D-elements of the surfaces

poly=Cases[Normal[pic], Polygon[pp_ ]  :> pp, All] (*returns  {} *)

My questions:

How can I get the element infomation?

Is there a more elegant way to get the informations p,n,poly from the plot?

Thanks!

Answer 1

What's wrong with DiscretizeGraphics?

pic = Plot3D[Sin[x] Sin[y], {x, 0, 1}, {y, 0, 1}, Mesh -> All];
DiscretizeGraphics[pic]