Re: intersecting surfaces

• To: mathgroup at smc.vnet.net
• Subject: [mg107179] Re: intersecting surfaces
• From: dh <dh at metrohm.com>
• Date: Fri, 5 Feb 2010 03:19:37 -0500 (EST)
• References: <hkeaqm\$t14\$1@smc.vnet.net>

```Hi Eric,
we may calculate the intersection curves by:

intersec =  {x, y, z} /.
Solve[{((x - 1)^2 + (y)^2) Cos[Pi/4]^2 - ((z) Sin[Pi/4])^2 == 0,
0 == (x^2 + y^2) Cos[Pi/6]^2 - (z Sin[Pi/6])^2}, {z, y}]

we may then insert these curves into the plot of the two surfaces:

Show[{ContourPlot3D[{((x - 1)^2 + (y)^2) Cos[
Pi/4]^2 - ((z) Sin[Pi/4])^2 == 0,
0 == (x^2 + y^2) Cos[Pi/6]^2 - (z Sin[Pi/6])^2}, {x, -5,
6}, {y, -5, 5}, {z, -5, 5}],
ParametricPlot3D[intersec, {x, -2, 1}, PlotStyle -> Thickness[0.01]]
}]

Daniel
cire g wrote:
> Hello Guys,
> How to set CountourPlot3D to plot the intersection of two surfaces.
> For example I would like to see the curve of the intersection of these
> cones:
> ContourPlot3D[{((x - 1)^2 + (y)^2) Cos[Pi/4]^2 - ((z
>        ) Sin[Pi/4])^2 == 0 ,
>   0 == (x^2 + y^2) Cos[Pi/6]^2 - (z Sin[Pi/6])^2}, {x, -5, 6}, {y, -5,
>    5}, {z, -5, 5}]
> Best regards,
> eric
>

```

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