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Re: ParametricPlot3D vs Reduce
*To*: mathgroup at smc.vnet.net
*Subject*: [mg124069] Re: ParametricPlot3D vs Reduce
*From*: Heike Gramberg <heike.gramberg at gmail.com>
*Date*: Sun, 8 Jan 2012 04:20:42 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201201071020.FAA19453@smc.vnet.net>
You function is discontinuous at b=0 or d=0 where the
denominator becomes zero. The polygons you see are the result of
Mathematica connecting the points across this discontinuity (similar to
for example the vertical lines in Plot[Tan[x], {x, 0, Pi}]). To get rid
of these you need to specify Exclusions. In this example you could do
ParametricPlot3D[rats, {b, -10, 10}, {d, -10, 10},
AxesLabel -> {"a", "b", "c"},
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}}, Exclusions -> {b d = 0}]
which will produce an empty box.
Heike
On 7 Jan 2012, at 11:20, Andrzej Kozlowski wrote:
> I just came across something somewhat baffling, though it could be the
> result of an imperfect understanding of how 3D graphic functions work.
> Consider the following three rational functions of two variables, which
> we will think of as parameters of a point on a surface in 3D.
>
> rats = {(-b - 2*d - b^3*d^2)/(b*d), (2*b + d + b^4*d +
> 2*b^3*d^2)/(b^2*d), (-1 - 2*b^3*d - b^2*d^2)/(b^2*d)};
>
> Now, note that:
>
> Reduce[Thread[-1 <= rats <= 1], {b, d}]
>
> False
>
> in other words, there are no values of the parameters b and d for which
> the point lies in the unit cube. However:
>
> ParametricPlot3D[rats, {b, -10, 10}, {d, -10, 10},
> PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
> AxesLabel -> {"a", "b", "c"}]
>
> There appear to be several polygons inside the unit cube that should not
> be there?
>
> Andrzej Kozlowski
>
>
>
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