import bpy
import bmesh
from mathutils.geometry import barycentric_transform, intersect_point_tri_2d

# this will use the 2D cursor of the first UV editor found
for area in bpy.context.screen.areas:
    if area.type == 'IMAGE_EDITOR':
        space_data = area.spaces.active
        loc = space_data.cursor_location
        norm_coords = space_data.uv_editor.show_normalized_coords
        break
else:
    raise Exception("No UV editor found")

# mesh UVs are always normalized, but not the 2D cursor!
def uv_normalize(tex, uv):
    if tex.image is None:
        x, y = 256, 256
    else:
        x, y = tex.image.size
    return (uv[0] / x, uv[1] / y, 0) # to_3d()

ob = bpy.context.object
assert ob.type == "MESH", "Selected object not a mesh"
me = ob.data
bm = bmesh.new()
bm.from_mesh(me)


# tag selected faces, because triangulate may clear selection state
for f in bm.faces:
    if f.select:
        f.tag = True


# viewport seems to use fixed / clipping instead of beauty
bmesh.ops.triangulate(bm, faces=bm.faces, quad_method=1, ngon_method=1)


# re-select faces
for f in bm.faces:
    if f.tag:
        f.select_set(True)


uv_layer = bm.loops.layers.uv.active
tex = bm.faces.layers.tex.active


def find_coord(loc, face, uvs):
    uv1, uv2, uv3 = uvs
    x, y, z = [v.co for v in face.verts]
    co = barycentric_transform(loc, uv1, uv2, uv3, x, y, z)
    bpy.context.scene.cursor_location = ob.matrix_world * co


random_face = None
sel_faces = [f for f in bm.faces if f.select]
for face in sel_faces:
    uv1, uv2, uv3 = [l[uv_layer].uv.to_3d() for l in face.loops]
    if norm_coords:
        loc_normalized = loc.to_3d()
    else:
        loc_normalized = uv_normalize(face[tex], loc)

    # remember the first face for possible fallback
    if random_face is None:
        random_face = loc_normalized, face, (uv1, uv2, uv3)

    #print("trying", loc_normalized, "vs", uv1, uv2, uv3)
    if intersect_point_tri_2d(loc_normalized, uv1, uv2, uv3):
        print("found intersecting triangle")
        find_coord(loc_normalized, face, (uv1, uv2, uv3))
        break
else:
    print("trying random selected face for extrapolation")
    find_coord(*random_face)