2 improve readability by breaking the line
source | link

It seems that interpolation in two dimensions is desired. To do so, interpolate the x- and y-coordinates separately and plot the curve parametrically:

Manipulate[
 Module[{f = Interpolation[#, InterpolationOrder -> iorder] & /@ 
             Transpose[Prepend[pts, {0, 0}]]},
  ParametricPlot[Through[f[x]], {x, 1, Length[pts]+1}, PlotRange -> {Full, Full}]],
 {{pts, {{.2, .1}, {.4, .2}, {.6, .3}, {.8, .25}, {1, 0}}}, Locator},
 {{iorder, 3, "InterpolationOrder"}, Range[3]}]

Plot

Now it does not matter that some of the x-coordinates may have been duplicated.

It seems that interpolation in two dimensions is desired. To do so, interpolate the x- and y-coordinates separately and plot the curve parametrically:

Manipulate[
 Module[{f = Interpolation[#, InterpolationOrder -> iorder] & /@ Transpose[Prepend[pts, {0, 0}]]},
  ParametricPlot[Through[f[x]], {x, 1, Length[pts]+1}, PlotRange -> {Full, Full}]],
 {{pts, {{.2, .1}, {.4, .2}, {.6, .3}, {.8, .25}, {1, 0}}}, Locator},
 {{iorder, 3, "InterpolationOrder"}, Range[3]}]

Plot

Now it does not matter that some of the x-coordinates may have been duplicated.

It seems that interpolation in two dimensions is desired. To do so, interpolate the x- and y-coordinates separately and plot the curve parametrically:

Manipulate[
 Module[{f = Interpolation[#, InterpolationOrder -> iorder] & /@ 
             Transpose[Prepend[pts, {0, 0}]]},
  ParametricPlot[Through[f[x]], {x, 1, Length[pts]+1}, PlotRange -> {Full, Full}]],
 {{pts, {{.2, .1}, {.4, .2}, {.6, .3}, {.8, .25}, {1, 0}}}, Locator},
 {{iorder, 3, "InterpolationOrder"}, Range[3]}]

Plot

Now it does not matter that some of the x-coordinates may have been duplicated.

1
source | link

It seems that interpolation in two dimensions is desired. To do so, interpolate the x- and y-coordinates separately and plot the curve parametrically:

Manipulate[
 Module[{f = Interpolation[#, InterpolationOrder -> iorder] & /@ Transpose[Prepend[pts, {0, 0}]]},
  ParametricPlot[Through[f[x]], {x, 1, Length[pts]+1}, PlotRange -> {Full, Full}]],
 {{pts, {{.2, .1}, {.4, .2}, {.6, .3}, {.8, .25}, {1, 0}}}, Locator},
 {{iorder, 3, "InterpolationOrder"}, Range[3]}]

Plot

Now it does not matter that some of the x-coordinates may have been duplicated.