plotting - How to draw some 2D curves in a 3D plot?

I want to plot several 2D curves (Sin[x] at y=0, Cos[x] at y=1) in a 3D plot, what function should i use?

f[x_, y_] := Piecewise[{{0, y < 0 || y > 0}, {Sin[x], y == 0}}]
g[x_, y_] := Piecewise[{{0, y < 1 || y > 1}, {Cos[x], y == 1}}]
Plot3D[{f[x, y], g[x, y]}, {x, 0, 10}, {y, 0, 10}]

doesn't work. Any ideas?

Answer

ParametricPlot3D[{{Sin[u], 0, u}, {Cos[u], 1, u}}, {u, 0, 20}, 
 BoxRatios -> 1, PlotRange -> {{-2, 2}, {-.5, 2}, {0, 20}}]

enter image description here

=== update - general thoughts ===

I've seen the comments to this question and a few other approaches to the waterfall (or wire) plot are given in this question: Plotting several functions. Also I cannot not mention one of my favorite Mathematica blogs - Archery with this post on the story of discovery of 1st pulsar and an its infamous graphics - code is given in the post:

enter image description here

Comments

functions - Get leading series expansion term?

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mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

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