       Re: intersecting surfaces

• To: mathgroup at smc.vnet.net
• Subject: [mg107208] Re: [mg107151] intersecting surfaces
• From: "David Park" <djmpark at comcast.net>
• Date: Fri, 5 Feb 2010 03:24:52 -0500 (EST)
• References: <2112561.1265283295770.JavaMail.root@n11>

```Cone equations:

cone1 = ((x - 1)^2 + y^2) Cos[\[Pi]/4]^2 - (z Sin[\[Pi]/4])^2 == 0;
cone2 = (x^2 + y^2) Cos[\[Pi]/6]^2 - (z Sin[\[Pi]/6])^2 == 0;

Solve for x and y:

xysols = Solve[{cone1, cone2}, {x, y}]

Parameterize the intersections:

intersection1[z_] = {x, y, z} /. First[xysols]
intersection2[z_] = {x, y, z} /. Last[xysols]

Plot the cones and the intersections:

Needs["Presentations`Master`"]

Draw3DItems[
{(* The two cones *)
Opacity[.5],
ContourDraw3D[cone1 // Evaluate, {x, -5, 6}, {y, -5, 5}, {z, -5, 5},
ContourStyle -> Orange,
Mesh -> False],
ContourDraw3D[cone2 // Evaluate, {x, -5, 6}, {y, -5, 5}, {z, -5, 5},
ContourStyle -> Green,
Mesh -> False],
(* The intersections *)
Opacity, Black, AbsoluteThickness,
ParametricDraw3D[intersection1[z], {z, -3, 3}],
ParametricDraw3D[intersection2[z], {z, -3, 3}]},
NeutralLighting[0, .5, .1],
NiceRotation,
Boxed -> False]

Each intersection solution is split between the upper and lower cones.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: cire g [mailto:eric.phys at gmail.com]

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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