       Re: ParametricPlot3D vs Reduce

• To: mathgroup at smc.vnet.net
• Subject: [mg124070] Re: ParametricPlot3D vs Reduce
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 8 Jan 2012 04:21:03 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201201071020.FAA19453@smc.vnet.net> <3309337D-A5C2-472E-ACE1-9ECD5161E3B0@gmail.com>

```Thanks. Now it's perfectly obvious and I think I should have seen it
myself (but didn't ;-) )

Andrzej

On 7 Jan 2012, at 12:37, Heike Gramberg wrote:

> 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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