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 >> >> >> >

**References**:**ParametricPlot3D vs Reduce***From:*Andrzej Kozlowski <akozlowski@gmail.com>