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J. M.'s missing motivation
J. M.'s missing motivation
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Case of explicit functions:

ParametricPlot3D[Evaluate[Table[{ww, zz, Exp[-(ww - 0.5 zz)^2/zz^2]}, {zz, {0.2, 0.4, 0.6, 0.8, 1.0, 1.2}}]], {ww, -2, 2}, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}, {Yellow, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of Interpolatinginterpolating functions:

mmax = 4; tm = Table[m, {m, 1, mmax}]; tap = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; tfp = Table[(n - 1)^m, {m, 1, mmax}, {n, 1, 10}]; tif = Table[{tap[[n]], tfp[[m, n]]}, {m, 1, Length[tfp]}, {n, 1, Length[tap]}] tg = Table[Interpolation[tif[[m]]], {m, 1, mmax}]; ParametricPlot3D[ Evaluate[Table[{x, zz, tg[[zz]][x]}, {zz, tm}]], {x, 0, 1}, PlotStyle -> {{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of explicit functions:

ParametricPlot3D[Evaluate[Table[{ww, zz, Exp[-(ww - 0.5 zz)^2/zz^2]}, {zz, {0.2, 0.4, 0.6, 0.8, 1.0, 1.2}}]], {ww, -2, 2}, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}, {Yellow, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of Interpolating functions:

mmax = 4; tm = Table[m, {m, 1, mmax}]; tap = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; tfp = Table[(n - 1)^m, {m, 1, mmax}, {n, 1, 10}]; tif = Table[{tap[[n]], tfp[[m, n]]}, {m, 1, Length[tfp]}, {n, 1, Length[tap]}] tg = Table[Interpolation[tif[[m]]], {m, 1, mmax}]; ParametricPlot3D[ Evaluate[Table[{x, zz, tg[[zz]][x]}, {zz, tm}]], {x, 0, 1}, PlotStyle -> {{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of explicit functions:

ParametricPlot3D[Evaluate[Table[{ww, zz, Exp[-(ww - 0.5 zz)^2/zz^2]}, {zz, {0.2, 0.4, 0.6, 0.8, 1.0, 1.2}}]], {ww, -2, 2}, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}, {Yellow, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of interpolating functions:

mmax = 4; tm = Table[m, {m, 1, mmax}]; tap = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; tfp = Table[(n - 1)^m, {m, 1, mmax}, {n, 1, 10}]; tif = Table[{tap[[n]], tfp[[m, n]]}, {m, 1, Length[tfp]}, {n, 1, Length[tap]}] tg = Table[Interpolation[tif[[m]]], {m, 1, mmax}]; ParametricPlot3D[ Evaluate[Table[{x, zz, tg[[zz]][x]}, {zz, tm}]], {x, 0, 1}, PlotStyle -> {{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Magenta, Thick}}]
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Case of explicit functions:

ParametricPlot3D[ Evaluate[Table[{ww, zz, Exp[-(ww - 0.5 zz)^2/zz^2]}, {zz, {0.2, 0.4, 0.6, 0.8, 1.0, 1.2}}]], {ww, -2, 2}, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}, {Yellow, Thick}, {Green, Thick}, {Magenta, Thick}}]

ParametricPlot3D[Evaluate[Table[{ww, zz, Exp[-(ww - 0.5 zz)^2/zz^2]}, {zz, {0.2, 0.4, 0.6, 0.8, 1.0, 1.2}}]], {ww, -2, 2}, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}, {Yellow, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of Interpolating functions:

mmax = 4;

tm = Table[m, {m, 1, mmax}]; tap = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; tfp = Table[(n - 1)^m, {m, 1, mmax}, {n, 1, 10}]; tif = Table[{tap[[n]], tfp[[m, n]]}, {m, 1, Length[tfp]}, {n, 1, Length[tap]}] tg = Table[Interpolation[tif[[m]]], {m, 1, mmax}]; ParametricPlot3D[ Evaluate[Table[{x, zz, tg[[zz]][x]}, {zz, tm}]], {x, 0, 1}, PlotStyle -> {{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Magenta, Thick}}]

mmax = 4; tm = Table[m, {m, 1, mmax}]; tap = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; tfp = Table[(n - 1)^m, {m, 1, mmax}, {n, 1, 10}]; tif = Table[{tap[[n]], tfp[[m, n]]}, {m, 1, Length[tfp]}, {n, 1, Length[tap]}] tg = Table[Interpolation[tif[[m]]], {m, 1, mmax}]; ParametricPlot3D[ Evaluate[Table[{x, zz, tg[[zz]][x]}, {zz, tm}]], {x, 0, 1}, PlotStyle -> {{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of explicit functions:

ParametricPlot3D[ Evaluate[Table[{ww, zz, Exp[-(ww - 0.5 zz)^2/zz^2]}, {zz, {0.2, 0.4, 0.6, 0.8, 1.0, 1.2}}]], {ww, -2, 2}, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}, {Yellow, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of Interpolating functions:

mmax = 4;

tm = Table[m, {m, 1, mmax}]; tap = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; tfp = Table[(n - 1)^m, {m, 1, mmax}, {n, 1, 10}]; tif = Table[{tap[[n]], tfp[[m, n]]}, {m, 1, Length[tfp]}, {n, 1, Length[tap]}] tg = Table[Interpolation[tif[[m]]], {m, 1, mmax}]; ParametricPlot3D[ Evaluate[Table[{x, zz, tg[[zz]][x]}, {zz, tm}]], {x, 0, 1}, PlotStyle -> {{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of explicit functions:

ParametricPlot3D[Evaluate[Table[{ww, zz, Exp[-(ww - 0.5 zz)^2/zz^2]}, {zz, {0.2, 0.4, 0.6, 0.8, 1.0, 1.2}}]], {ww, -2, 2}, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}, {Yellow, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of Interpolating functions:

mmax = 4; tm = Table[m, {m, 1, mmax}]; tap = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; tfp = Table[(n - 1)^m, {m, 1, mmax}, {n, 1, 10}]; tif = Table[{tap[[n]], tfp[[m, n]]}, {m, 1, Length[tfp]}, {n, 1, Length[tap]}] tg = Table[Interpolation[tif[[m]]], {m, 1, mmax}]; ParametricPlot3D[ Evaluate[Table[{x, zz, tg[[zz]][x]}, {zz, tm}]], {x, 0, 1}, PlotStyle -> {{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Magenta, Thick}}]
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Andrey Konovko
Andrey Konovko
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Case of explicit functions:

ParametricPlot3D[ Evaluate[Table[{ww, zz, Exp[-(ww - 0.5 zz)^2/zz^2]}, {zz, {0.2, 0.4, 0.6, 0.8, 1.0, 1.2}}]], {ww, -2, 2}, PlotStyle -> {{Black, Thick}, {Blue, Thick}, {Red, Thick}, {Yellow, Thick}, {Green, Thick}, {Magenta, Thick}}]

Case of Interpolating functions:

mmax = 4;

tm = Table[m, {m, 1, mmax}]; tap = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; tfp = Table[(n - 1)^m, {m, 1, mmax}, {n, 1, 10}]; tif = Table[{tap[[n]], tfp[[m, n]]}, {m, 1, Length[tfp]}, {n, 1, Length[tap]}] tg = Table[Interpolation[tif[[m]]], {m, 1, mmax}]; ParametricPlot3D[ Evaluate[Table[{x, zz, tg[[zz]][x]}, {zz, tm}]], {x, 0, 1}, PlotStyle -> {{Blue, Thick}, {Red, Thick}, {Green, Thick}, {Magenta, Thick}}]