ff[{x_, y_}] := Floor[x + y]; 
    pts = Tuples[Range[0, 3, (1/10)], 2];
 Show[
Graphics3D[{
 {PointSize[
                0.02], Blue, Point[{#[[1]], #[[2]], 
                      ff[#]}] & /@ 
                pts}
}], 
BoxRatios -> {1, 1, 1}, Axes -> True
];

Plot3D[ff[{x, y}], {x, 0, 4}, {y, 0, 4}, PlotPoints -> {40, 40}, 
        BoxRatios -> {1, 1, 2}, Axes -> True];

ff[{x_, y_}] := Floor[x ] + Floor[y];
pts = Tuples[Range[0, 3, (1/15)], 2];
 Show[
Graphics3D[{
 {PointSize[
                0.009], 
              Blue, Point[{#[[1]], #[[2]], ff[#]}] & /@ 
                pts}
}], 
BoxRatios -> {1, 1, 1}, Axes -> True, 
        ViewPoint -> {1.484,  -2.340,  
            1.545}
];

Plot3D[ff[{x, y}], {x, 0, 4}, {y, 0, 4}, PlotPoints -> {50, 50}, 
      BoxRatios -> {1, 1, 2}, Axes -> True]

ff[{x_, y_}] := 
        Floor[x ] + Floor[2  y];
pts = Tuples[Range[0, 3, (1/15)], 2];
 Show[
Graphics3D[{
 {PointSize[
                0.009], 
              Blue, Point[{#[[1]], #[[2]], ff[#]}] & /@ 
                pts}
}], 
BoxRatios -> {1, 1, 1}, Axes -> True, 
        ViewPoint -> {1.484,  -2.340,  
            1.545}
];

Plot3D[ff[{x, y}], {x, 0, 4}, {y, 0, 4}, PlotPoints -> {50, 50}, 
      BoxRatios -> {1, 1, 2}, Axes -> True]

ff[{x_, y_}] := 
        Floor[(Sqrt[(x^2) + (y^2)])];
pts = Tuples[Range[0, 3, (1/15)], 2];
 Show[
Graphics3D[{
 {PointSize[
                0.009], 
              Blue, Point[{#[[1]], #[[2]], ff[#]}] & /@ 
                pts}
}], 
BoxRatios -> {1, 1, 1}, Axes -> True, 
        ViewPoint -> {1.484,  -2.340,  
            1.545}
];

Plot3D[ff[{x, y}], {x, 0, 4}, {y, 0, 4}, PlotPoints -> {50, 50}, 
      BoxRatios -> {1, 1, 2}, Axes -> True]