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wrong result in solving equation and parametric ploting

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111900] wrong result in solving equation and parametric ploting
  • From: kamal <azimikamal at gmail.com>
  • Date: Wed, 18 Aug 2010 07:05:03 -0400 (EDT)

hi to every one, i use mathemtica for finding intersection between one
cylindrical shape by a plane but i see that answer in some piece is
wrong. i sent this before but i didn't receive answer. i hope that
someone could help me


if you run following command you can see that plot diverge in some
section
how can i solve this problem?

range = 300000000;
intersec = {x, y, z} /.
  Solve[{1*((x - y)^2 + (y - z)^2 + (z - x)^2)^2 +
      1000*((x - y)^3 + (y - z)^3 + (z - x)^3)^1 == 2*(250*10^6)^4,
    0 == x + y + z}, {z, y}];
p = Show[{ContourPlot3D[{1*((x - y)^2 + (y - z)^2 + (z - x)^2)^2 +
      1000*((x - y)^3 + (y - z)^3 + (z - x)^3)^1 == 2*(250*10^6)^4,
    0 == x + y + z}, {x, -range, range}, {y, -range,
    range}, {z, -range, range}, BoundaryStyle -> None, Mesh -> None,
   BoxRatios -> Automatic, PlotRange -> Automatic,
   AxesLabel -> {Style[x, Large, Bold, Orange],
     Style[y, Large, Bold, Orange], Style[z, Large, Bold, Orange]},
   LabelStyle -> Directive[Purple, Bold], Axes -> True,
   AxesStyle -> {Green, Green, Blue},
   BoxStyle -> Directive[Dashed, Orange],
   ContourStyle -> {{Red, Opacity[0]}, {Yellow, Opacity[0]}},
   Lighting -> "Neutral", ViewPoint -> {1, 1, 1}],
  ParametricPlot3D[intersec, {x, -range, range},
   PlotStyle -> {Black, Black}]}]

intersec1 = {x, y, z} /.
  Solve[{200*((x - y)^2 + (y - z)^2 + (z - x)^2)^4 +
      4*(x - y)^2*(y - z)^2*(z -
          x)^2*((x - y)^2 + (y - z)^2 + (z - x)^2) == 2*(250*10^6)^8,
     0 == x + y + z}, {z, y}];
p1 = Show[{ContourPlot3D[{200*((x - y)^2 + (y - z)^2 + (z - x)^2)^4 +
      4*(x - y)^2*(y - z)^2*(z -
          x)^2*((x - y)^2 + (y - z)^2 + (z - x)^2) == 2*(250*10^6)^8,
     0 == x + y + z}, {x, -range, range}, {y, -range,
    range}, {z, -range, range}, BoundaryStyle -> None, Mesh -> None,
   BoxRatios -> Automatic, PlotRange -> Automatic,
   AxesLabel -> {Style[x, Large, Bold, Orange],
     Style[y, Large, Bold, Orange], Style[z, Large, Bold, Orange]},
   LabelStyle -> Directive[Purple, Bold], Axes -> True,
   AxesStyle -> {Green, Green, Blue},
   BoxStyle -> Directive[Dashed, Orange],
   ContourStyle -> {{Green, Opacity[0]}, {Yellow, Opacity[0]}},
   Lighting -> "Neutral", ViewPoint -> {1, 1, 1}],
  ParametricPlot3D[intersec1, {x, -range, range},
   PlotStyle -> {Black, Black}]}]

intersec2 = {x, y, z} /.
  Solve[{2*((x - y)^2 + (y - z)^2 + (z - x)^2)^4 +
      4*(x - y)^2*(y - z)^2*(z -
          x)^2*((x - y)^2 + (y - z)^2 + (z - x)^2) == 2*(250*10^6)^8,
     0 == x + y + z}, {z, y}];
p2 = Show[{ContourPlot3D[{2*((x - y)^2 + (y - z)^2 + (z - x)^2)^4 +
      4*(x - y)^2*(y - z)^2*(z -
          x)^2*((x - y)^2 + (y - z)^2 + (z - x)^2) == 2*(250*10^6)^8,
     0 == x + y + z}, {x, -range, range}, {y, -range,
    range}, {z, -range, range}, BoundaryStyle -> None, Mesh -> None,
   BoxRatios -> Automatic, PlotRange -> Automatic,
   AxesLabel -> {Style[x, Large, Bold, Orange],
     Style[y, Large, Bold, Orange], Style[z, Large, Bold, Orange]},
   LabelStyle -> Directive[Purple, Bold], Axes -> True,
   AxesStyle -> {Green, Green, Blue},
   BoxStyle -> Directive[Dashed, Orange],
   ContourStyle -> {{Red, Opacity[0]}, {Yellow, Opacity[0]}},
   Lighting -> "Neutral", ViewPoint -> {1, 1, 1}],
  ParametricPlot3D[intersec2, {x, -range, range},
   PlotStyle -> {Black, Black}]}]




thank you for helping


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