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Re: Intersection of line and a surface of revolution - a problem with

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102605] Re: Intersection of line and a surface of revolution - a problem with
  • From: Harutyun <amirjanyan at gmail.com>
  • Date: Sun, 16 Aug 2009 06:42:26 -0400 (EDT)
  • References: <h65vcp$emh$1@smc.vnet.net>

RevolutionPlot3D[f[r], {r, 0.05, 2.4}] is a plot of z == f[Sqrt[x^2 +
y^2]] surface not z == f[x]

Clear[sr3, l, nsol3, sol3, ip3, ip4, nip3, nip4, x, y, z, t];
f[x_] = 1/2 - x^2 + x^4/2;
sr3 = RevolutionPlot3D[f[x], {x, 0.05, 2.4},
   PlotStyle -> Opacity[0.4], Axes -> True,
   AxesLabel -> {"x", "y", "z"}, Mesh -> False,
   BoxRatios -> {1, 1, 1},
   PlotRange -> {{-4., 4.}, {-4., 4.}, {0., 8.0}}, AspectRatio -> 1];
l = ParametricPlot3D[{t, -t, 4 t - 1}, {t, -3, 3},
   PlotStyle -> {Thickness[0.01], Red}];
nsol3 = NSolve[{z == f[Sqrt[x^2 + y^2]], x == t, y == -t,
    z == 4 t - 1}, {x, y, z, t}];
sol3 = Solve[{z == f[Sqrt[x^2 + y^2]], x == t, y == -t,
    z == 4 t - 1}, {x, y, z, t}];
ip3 = Show[
   Graphics3D[{{AbsolutePointSize[10],
      Point[{x, y, z} /. sol3[[3]]]}}]];
nip3 = Show[
   Graphics3D[{{AbsolutePointSize[10],
      Point[{x, y, z} /. nsol3[[3]]]}}]];
ip4 = Show[
   Graphics3D[{{AbsolutePointSize[10],
      Point[{x, y, z} /. sol3[[4]]]}}]];
nip4 = Show[
   Graphics3D[{{AbsolutePointSize[10],
      Point[{x, y, z} /. nsol3[[4]]]}}]];
Show[sr3, l, ip3, ip4, ViewPoint -> {1.333, 1.765, 0.3479}]
Show[sr3, l, nip3, nip4, ViewPoint -> {1.333, 1.765, 0.3479}]


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