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Re: visualizing a maximum in the intersection between two surfaces

• To: mathgroup at smc.vnet.net
• Subject: [mg131100] Re: visualizing a maximum in the intersection between two surfaces
• From: Dusko Cakara <dusko.cakara at gmail.com>
• Date: Tue, 11 Jun 2013 02:32:11 -0400 (EDT)
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• References: <20130608063415.570076A22@smc.vnet.net>

What also looks good to me (a small addition to Bob's solution)

Show[ContourPlot3D[
  Tooltip[x + y == 1], {x, 0, 1}, {y, 0, 1}, {z, 0, 1/2},
  ContourStyle -> Opacity[0.7], MeshStyle -> Gray,
  RegionFunction -> Function[{x, y, z}, z < x*y]],
 Plot3D[Tooltip[x*y], {x, 0, 1}, {y, 0, 1}, PlotStyle -> Opacity[.7],
  Exclusions -> {{x == 1/2, y < 1/2}, {y == 1/2, x < 1/2},
    x + y == 1,},
  ExclusionsStyle -> Directive[Opacity[1], Black, Thick],
  MeshStyle -> Gray, PlotPoints -> 100]]

Dusko


On Mon, Jun 10, 2013 at 10:52 AM, Dusko Cakara <dusko.cakara at gmail.com>wrote:

> Dear Bob,
> What you posted as the alternative method is exactly what I was looking
> for (I particularly like you manipulation with Exclusions), but the first
> one is absolutely sleek! Thanks a lot!
> Best regards
> Dusko
>
> ------------------------------------------------------
> Dr. Dusko Cakara
> Dpt. of Biotechnology
> University of Rijeka
> Radmile Matejcic 2, 51000 Rijeka, Croatia
>
> Email: dusko.cakara at uniri.hr
> Tel: +385/51/584555
> Fax: +385/51/584599
> Mobile: +385/91/9570399
> -------------------------------------------------------
>
>
>
>
>
> On Sun, Jun 9, 2013 at 4:42 PM, Bob Hanlon <hanlonr357 at gmail.com> wrote:
>
>> An alternate method
>>
>>
>> Show[
>>  ContourPlot3D[Tooltip[x + y == 1],
>>   {x, 0, 1}, {y, 0, 1}, {z, 0, 1/2},
>>   ContourStyle -> Opacity[.7],
>>   MeshStyle -> Gray],
>>  Plot3D[Tooltip[x*y], {x, 0, 1}, {y, 0, 1},
>>   PlotStyle -> Opacity[.7],
>>   Exclusions -> {x == 1/2, y == 1/2, x + y == 1},
>>   ExclusionsStyle ->
>>    Directive[Opacity[1], Black, Thick],
>>   MeshStyle -> Gray,
>>   PlotPoints -> 100]]
>>
>>
>>
>> Bob Hanlon
>>
>>
>>
>>
>> On Sat, Jun 8, 2013 at 2:34 AM, <dusko.cakara at gmail.com> wrote:
>>
>>> Hello,
>>> can somebody please help:
>>> I want to visualize that for x+y=1, maximum x*y occurs when y=0.5 and
>>> x=0.5.
>>>
>>> Graphically, this can be visualized as the maximum of the projection
>>> curve of the x+y=1 line in the x-y plane, at the x*y surface. Equivalently,
>>> we can look for the maximum in the intersection curve between the surface
>>> x*y and the surface peripendicular to the x-y plane with the base x+y=1.
>>>
>>> Can I plot this in a simple manner?
>>>
>>> Thanks in advance!
>>> Dusko
>>>
>>>
>>
>

• References:
  • visualizing a maximum in the intersection between two surfaces
    • From: dusko.cakara@gmail.com