補間にスプラインを使う
Interpolationでスプラインメソッドを使うと，比較的低い次数で高度に連続的な結果が得られる．
SeedRandom[4];data = RandomReal[5, {15}];
f = Interpolation[data, Method -> "Spline"];
g = Interpolation[data, Method -> "Hermite"];
drawfun[f_, t_] := Plot[f[x], {x, 1, 15}, Mesh -> {Range[15]}, MeshStyle -> Red, AxesOrigin -> {0, 0}, PlotLabel -> t];
SeedRandom[5];data2 = Flatten[Table[{x, y, RandomReal[]}, {x, 7}, {y, 7}], 1];
f2 = Interpolation[data2, Method -> "Spline"];
g2 = Interpolation[data2, Method -> "Hermite"];
drawfun2[f_, t_] := Plot3D[f[x, y], {x, 1, 7}, {y, 1, 7}, Mesh -> None, PlotPoints -> 30, PlotLabel -> t, PlotStyle -> Directive[Orange, Specularity[White, 50]]]
GraphicsGrid[{{drawfun[f, "スプラインメソッド"], drawfun[g, "エルミートメソッド"]}, {drawfun2[f2, "スプラインメソッド"], drawfun2[g2, "エルミートメソッド"]}}, ImageSize -> {500, 500}]