xpt[j_] := pts[[j,1]];
ypt[j_] := pts[[j,2]];
Needs["VectorAnalysis`"]
SetCoordinates[Cartesian];
gradu = {D[u, x], D[u, y],0};
Do[Clear[normal, dirder], j = n;
normal =  Normalize[Cross[{xpt[j + 1] - xpt[j-1],ypt[j + 1] - ypt[1, j-1],0}, {0,0,1}]];
dirder = (normal.gradu) /. {x -> xpt[j], y -> ypt[j]}
PutAppend[dirder, "dirder.dat"], {j, 2, Length[pts]}];
rl = ReadList["dirder.dat"];
dirderu = Mean[rl]