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MathGroup Archive 2007

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Re: ContourPlot3D Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg75241] Re: ContourPlot3D Problem
  • From: Roger Bagula <rlbagula at sbcglobal.net>
  • Date: Sat, 21 Apr 2007 23:14:53 -0400 (EDT)
  • References: <f079vc$4a0$1@smc.vnet.net>

dennis wrote:

>I am trying to plot a cone with a spherical cap.  The code I am using
>is shown below.
>
>=CE=B8 = 10.*Degree;
>sMax = 10;
>a = {1., 1., 1}/Sqrt[3.];
>{x0, y0, z0} = sMax*(1 + Tan[=CE=B8]^2)*a;
>rCirc = sMax*(Tan[=CE=B8]/Cos[=CE=B8]);
>g1 = ContourPlot3D[
>If[{x, y, z} . a <= sMax, {x, y, z} . a -
>      Sqrt[x^2 + y^2 + z^2]*Cos[=CE=B8], (x - x0)^2 + (y - y0)^2 + (z -
>z0)^2 -
>      rCirc^2], {x, 0, 10}, {y, 0, 10}, {z, 0, 10}, PlotPoints -> {8,
>6},
>    ViewPoint -> {2.651, -2.103, -0.026}, PlotRange ->
>     {{0, 12}, {0, 12}, {0, 10}}];
>
>This produces the cone with a spherical cap, but it also produces a
>plane perpendicular to the cone axis at the junction of the cone and
>sphere.  How can I get the cone-sphere without the plane?
>
>Thanks,
>Dennis
>
>
>  
>
Your code doesn't work here either.
Try plotting it as g1 and g2:
g1-> cone
{x, y, z} . a -
      Sqrt[x^2 + y^2 + z^2]*Cos[ang]
g2->sphere
(x - x0)^2 + (y - y0)^2 + (z - z0)^2 - rCirc^2
Show[{g1,g2}]
Doing this isolates the plane to the cut off cone section.
You have to specify that:
 Sqrt[x^2 + y^2 + z^2]*Cos[ang]<>10
My code works worse than yours but elementates the plane 
((0.5773502691896258` x + 0.5773502691896258` y + 0.5773502691896258` 
z-10==0)

\!\(\*
  StyleBox[\(g1\  = \
    ContourPlot3D[If[0.5773502691896258`\ x + 0.5773502691896258`\
          y + 0.5773502691896258`\ z > 10, \n103.10912041257637`\
\[InvisibleSpace] - 11.906015685221298`\ x +
              x\^2 - 11.906015685221298`\ y + y\^2 - 
11.906015685221298`\ z +
           z\^2, 0], \ {x, \ 0, \ 10}, \ {y, \ 0, \ 10}, \ {z, \ 0, \ 
10}, \ \
PlotPoints\  -> \ {8, \n6}, \n\ \ \ \ ViewPoint\  -> \ {
            2.651, \ \(-2.103\), \ \(-0.026\)}, \ PlotRange\  -> \n\ \ \ 
\ \ \
{{0, \ 12}, \ {0, \ 12}, \ {0, \ 10}}]\),
    FontFamily->"Lucida Grande",
    FontSize->13]\)

\!\(\*
  StyleBox[\(g2\  = \
    ContourPlot3D[If[\((
      0.5773502691896258`\ x + 0.5773502691896258`\
              y + 0.5773502691896258`\ z > 10)\) && 
\((0.984807753012208`\ \@\
\(\(x\^2\)\(+\)\(y\^2\)\(+\)\(z\^2\)\(\ \ \ \ \ \ \ \ \)\))\) <> 10, \n0, \
0.5773502691896258`\ x +
              0.5773502691896258`\ y + 0.5773502691896258`\ z - \
0.984807753012208`\ \@\(x\^2 + y\^2 + z\^2\)], \ {x, \ 0, \ 10}, \ {y, \ 
0, \ \
10}, \ {z, \ 0, \ 10}, \ PlotPoints\  -> \ {8, \n6}, \n\ \ \ \ 
ViewPoint\  -> \
\ {2.651, \ \(-2.103\), \ \(-0.026\)}, \ PlotRange\  -> \n\ \ \ \ \ {{0, \ \
12}, \ {0, \ 12}, \ {0, \ 10}}]\),
    FontFamily->"Lucida Grande",
    FontSize->13]\)

Show[{g1, g2}]

The plane shows up when:
0.984807753012208*Sqrt[x^2+y^2+z^2]==0


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