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# Plot the Intersection of Two Surfaces

Posted 10 years ago
 I would like to know how it can be possible,in Wolfram, to plot an explicit graph of intersection of two surfaces. For instance: 13x^2+40y^2+4z^2+28xy-8xz-8yz-x+y+z+1and x-y+zThank you very much!
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Posted 10 years ago
 Building on Michael Rogers version ( also see this tutorial ) we get:h = 13 x^2 + 8 y^2 + 4 z^2 + 2 x y - 8 x z - 8 y z - x + y + z - 1;g = x - y + z;ContourPlot3D[{h == 0, g == 0}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, MeshFunctions -> {Function[{x, y, z, f}, h - g]}, MeshStyle -> {{Thick, Blue}}, Mesh -> {{0}}, ContourStyle -> Directive[Orange, Opacity[0.5], Specularity[White, 30]], PlotPoints -> 60, SphericalRegion -> True] Posted 10 years ago
 Reduce[13 x^2 + 40 y^2 + 4 z^2 + 28 x y - 8 x z - 8 y z - x + y + z +    1 == 0, {x, y, z}, Reals]False
Posted 10 years ago
 If by surfaces you mean where each formula is zero, then it turns out that 13x^2+40y^2+4z^2+28xy-8xz-8yz-x+y+z+1 = 0 has no real solutions.  Substituting another formula, here is a way.ContourPlot3D[{13 x^2 + 8 y^2 + 4 z^2 + 2 x y - 8 x z - 8 y z - x +    y + z - 1, x - y + z}, {x, -4, 4}, {y, -2, 2}, {z, -2, 2}, Contours -> {0}, ContourStyle -> None, Mesh -> None, BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> {{Thick, Blue}}}] 