ParametricPlot3D with Table data

Question

t[x_, y_] := x + y;
T = Table[t[x, y], {y, -1, 1, 1}, {x, -1, 1, 1}]
(*{{-2, -1, 0}, {-1, 0, 1}, {0, 1, 2}}*)
x[i_, j_] := T[[i]][[j]];
y[i_, j_] := T[[i]][[j]] + 1;
z[i_, j_] := T[[i]][[j]] + 2;
x[1, 1] (* -2 *)
y[1, 1] (* -1 *)
z[1, 1] (* 0 *)
ParametricPlot3D[{x[i, j], y[i, j], z[i, j]}, {i, 1, 3}, {j, 1, 3}]

Part::pkspec1: The expression 1.0000013571428572' cannot be used as a part specification. Part::pkspec1: The expression 1.0000013571428572' cannot be used as a part specification. Part::pkspec1: The expression 1.0013585` cannot be used as a part specification. General::stop: "Further output of Part::pkspec1 will be suppressed during this calculation. "

I define a table T, then want to ParametricPlot3D (x,y,z). But there are these error information. How to solve this?

Answer 1

Your i and j can only take on 3 discrete values since they are part specifications. So you can build up an array of values and make a ListPointPlot3D from them,

Flatten[Array[{x[#1, #2], y[#1, #2], z[#1, #2]} &, {3, 3}], 
  1] // ListPointPlot3D

Or, since they are all in a line, make a Line

Flatten[Array[{x[#1, #2], y[#1, #2], z[#1, #2]} &, {3, 3}], 1] // 
  Line // Graphics3D

Answer 2

Use the function t directly in ParametricPlot3D:

t[x_, y_] := x + y;
ParametricPlot3D[{t[x, y], t[x, y] + 1, t[x, y] + 2}, {y, -1, 1}, {x, -1, 1}]

or

u[x_, y_] := {t[x, y], 1 + t[x, y], 2 + t[x, y]}; 
ParametricPlot3D[u[x, y], {y, -1, 1}, {x, -1, 1}]

to get