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RE: 3D graph with assumptions

The DrawGraphics package at my web site below has the command
IteratorSubstitution that allows one to rewrite a function in terms of
variables that do have a fixed iteration limit.

Here is an example.


f[x_, y_] := Cos[x y]

IteratorSubstitution[{y, f[x, y]}, {y, 0, Sqrt[x]}]
{{w*Sqrt[x], Cos[w*x^(3/2)]}, {w, 0, 1}}

IteratorSubstitution rewrote y and f[x,y] in terms of the new variables x
and w. w has a fixed iterator range {w, 0, 1}. Now we can make a plot and
the easiest method is to use ParametricPlot3D since we have expressions for
x, y and f[x,y].

ParametricPlot3D[{x, w*Sqrt[x], Cos[w*x^(3/2)]}, {x, 0, 1}, {w, 0, 1},
   PlotRange -> {0.5, 1}, ViewPoint -> {1.722, 1.566, 2.456},
   ImageSize -> 450];

David Park
djmp at

From: Mukhtar [mailto:mbekkali at]
To: mathgroup at

Suppose I have f(x,y) that I need to Plot in 3D, however, the range of
x is (0,1) while the range of y is (0,g(x)), where g(x) is some
explicit function of x, say x^1/2.  Is there a way to do it since
specifying it directly the way I outlined above in Plot3D gives me the
error message that "Plot3D :: plln: Limiting value g(x) in {y,0,g(x)}
is not a machine-size real number". Perhaps I can do this indirectly
by plotting two surfaces and then consider the relevant part of
surface f(x,y), however, it would look ugly. Thanks.

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