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Suppose I need to plot a function $z = x^2 - y^2$ using a 3 dimensional surface plot (Plot3D feature). Assume the $x$ limit for this plot is [x_min, x_max] and y limit is [y_min, y_max]. In my case, x_max is a function of co-ordinate y. How do I incorporate this in the Plot3D command ?

Eg. Plot3D[x^2-y^2, {xlim, x_min, x_max(y)}, {ylim, y_min, y_max}] does not work.

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There can be dependency in the limits, the trick is to order the independent variables first:

Plot3D[x^2 - y^2, {y, 0, 1}, {x, 0, y^3}]

enter image description here

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Plot3D[x^2 - y^2, 
      {x, 0, 2}, {y, 0, 2},
 RegionFunction -> Function[{x, y}, 0 < x < y^3 + 4 && 0 < y < 2]]

Here, the upper limit of the region is explicit in 0 < x < y^3 + 4.

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  • $\begingroup$ I am sorry but I didn't understand how we are using the upper limit of x here as a function of y. Say x_max = y^3 + 4. How do we incorporate that using your method. $\endgroup$
    – Astronomer
    Commented Mar 28, 2017 at 20:33
  • $\begingroup$ Equivalently, you can give a region as a plotting domain: Plot3D[x^2 - y^2, {x, y} ∈ ImplicitRegion[0 < x < y^3 + 4 && 0 < y < 2, {x, y}]] $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Mar 29, 2017 at 1:40

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