Revisions to Conic sections: intersection of a plane and a cone. How can I change the equation of the plane to get conic sections automatically?

added 87 characters in body

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edited Mar 28 at 0:49

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For any plane equation {a,b,c}.{x,y,z}=d, we use MeshFunction->Function[{x, y, z}, {a, b, c} . {x, y, z} - d and Hyperplane[{a,b,c},d].

Clear["Global`*"]
myh = 5;
myr = 4;
pA = {0, 0, myh};
pT = {0, 0, 2*myh};
pO = {0, 0, 0};
cone1 = Cone[{pO, pA}, myr];
cone2 = Cone[{pT, pA}, myr];
{a, b, c} = RandomPoint[Sphere[]];
d = RandomReal[];
plot3d = 
  RegionPlot3D[{cone1, cone2}, 
   MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
   Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
plane = Graphics3D[Hyperplane[{a, b, c}, d]];
Show[plot3d, plane]

Manipulate

Manipulate[
 Module[{plot3d, plane}, 
  plot3dmesh = 
   RegionPlot3D[{cone1, cone2}, 
    MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
    Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];, 
  plane  PlotStyle -> Transparent];
  g3d = Graphics3D[Hyperplane[Graphics3D[{cone1, cone2, Hyperplane[{a, b, c}, d]];d]}];
  Show[plot3dShow[g3d, plane]]mesh, 
   PlotRange -> {Automatic, Automatic, {0, 10}}]], {a, -1, 1}, {b, -1,
   1}, {c, -1, 1}, {d, -1, 
  1}]

For any plane equation {a,b,c}.{x,y,z}=d, we use MeshFunction->Function[{x, y, z}, {a, b, c} . {x, y, z} - d and Hyperplane[{a,b,c},d].

Clear["Global`*"]
myh = 5;
myr = 4;
pA = {0, 0, myh};
pT = {0, 0, 2*myh};
pO = {0, 0, 0};
cone1 = Cone[{pO, pA}, myr];
cone2 = Cone[{pT, pA}, myr];
{a, b, c} = RandomPoint[Sphere[]];
d = RandomReal[];
plot3d = 
  RegionPlot3D[{cone1, cone2}, 
   MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
   Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
plane = Graphics3D[Hyperplane[{a, b, c}, d]];
Show[plot3d, plane]

Manipulate

Manipulate[
 Module[{plot3d, plane},
  plot3d = 
   RegionPlot3D[{cone1, cone2}, 
    MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
    Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
  plane = Graphics3D[Hyperplane[{a, b, c}, d]];
  Show[plot3d, plane]], {a, -1, 1}, {b, -1, 1}, {c, -1, 1}, {d, -1, 
  1}]

For any plane equation {a,b,c}.{x,y,z}=d, we use MeshFunction->Function[{x, y, z}, {a, b, c} . {x, y, z} - d and Hyperplane[{a,b,c},d].

Clear["Global`*"]
myh = 5;
myr = 4;
pA = {0, 0, myh};
pT = {0, 0, 2*myh};
pO = {0, 0, 0};
cone1 = Cone[{pO, pA}, myr];
cone2 = Cone[{pT, pA}, myr];
{a, b, c} = RandomPoint[Sphere[]];
d = RandomReal[];
plot3d = 
  RegionPlot3D[{cone1, cone2}, 
   MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
   Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
plane = Graphics3D[Hyperplane[{a, b, c}, d]];
Show[plot3d, plane]

Manipulate

Manipulate[
 Module[{plot3d, plane}, 
  mesh = RegionPlot3D[{cone1, cone2}, 
    MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
    Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}, 
    PlotStyle -> Transparent];
  g3d = Graphics3D[{cone1, cone2, Hyperplane[{a, b, c}, d]}];
  Show[g3d, mesh, 
   PlotRange -> {Automatic, Automatic, {0, 10}}]], {a, -1, 1}, {b, -1,
   1}, {c, -1, 1}, {d, -1, 1}]

edited body

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edited Mar 28 at 0:11

cvgmt

84.1k
6
97
179

For any plane equation {a,b,c}.{x,y,z}=d, we use MeshFunction->Function[{x, y, z}, {a, b, c} . {x, y, z} - d and Hyperplane[{a,b,c},d].

For any plane equation {a,b,c}.{x,y,z}=d, we use MeshFunction->Function[{x, y, z}, {a, b, c} . {x, y, z} - d and Hyperplane[{a,b,c},d].

Clear["Global`*"]
myh = 5;
myr = 4;
pA = {0, 0, myh};
pT = {0, 0, 2*myh};
pO = {0, 0, 0};
cone1 = Cone[{pO, pA}, myr];
cone2 = Cone[{pT, pA}, myr];
{a, b, c} = RandomPoint[Sphere[]];
d = RandomReal[];
plot3d = 
  RegionPlot3D[{cone1, cone2}, 
   MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
   Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
plan3plane = Graphics3D[Hyperplane[{a, b, c}, d]];
Show[plot3d, plan3]plane]

Manipulate

Manipulate[
 Module[{plot3d, plane},
  plot3d = 
   RegionPlot3D[{cone1, cone2}, 
    MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
    Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
  plane = Graphics3D[Hyperplane[{a, b, c}, d]];
  Show[plot3d, plane]], {a, -1, 1}, {b, -1, 1}, {c, -1, 1}, {d, -1, 
  1}]

For any plane equation {a,b,c}.{x,y,z}=d, we use MeshFunction->Function[{x, y, z}, {a, b, c} . {x, y, z} - d and Hyperplane[{a,b,c},d].

Clear["Global`*"]
myh = 5;
myr = 4;
pA = {0, 0, myh};
pT = {0, 0, 2*myh};
pO = {0, 0, 0};
cone1 = Cone[{pO, pA}, myr];
cone2 = Cone[{pT, pA}, myr];
{a, b, c} = RandomPoint[Sphere[]];
d = RandomReal[];
plot3d = 
  RegionPlot3D[{cone1, cone2}, 
   MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
   Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
plan3 = Graphics3D[Hyperplane[{a, b, c}, d]];
Show[plot3d, plan3]

For any plane equation {a,b,c}.{x,y,z}=d, we use MeshFunction->Function[{x, y, z}, {a, b, c} . {x, y, z} - d and Hyperplane[{a,b,c},d].

Clear["Global`*"]
myh = 5;
myr = 4;
pA = {0, 0, myh};
pT = {0, 0, 2*myh};
pO = {0, 0, 0};
cone1 = Cone[{pO, pA}, myr];
cone2 = Cone[{pT, pA}, myr];
{a, b, c} = RandomPoint[Sphere[]];
d = RandomReal[];
plot3d = 
  RegionPlot3D[{cone1, cone2}, 
   MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
   Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
plane = Graphics3D[Hyperplane[{a, b, c}, d]];
Show[plot3d, plane]

Manipulate

Manipulate[
 Module[{plot3d, plane},
  plot3d = 
   RegionPlot3D[{cone1, cone2}, 
    MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
    Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
  plane = Graphics3D[Hyperplane[{a, b, c}, d]];
  Show[plot3d, plane]], {a, -1, 1}, {b, -1, 1}, {c, -1, 1}, {d, -1, 
  1}]

Source Link

created Mar 28 at 0:04

cvgmt

84.1k
6
97
179

For any plane equation {a,b,c}.{x,y,z}=d, we use MeshFunction->Function[{x, y, z}, {a, b, c} . {x, y, z} - d and Hyperplane[{a,b,c},d].

Clear["Global`*"]
myh = 5;
myr = 4;
pA = {0, 0, myh};
pT = {0, 0, 2*myh};
pO = {0, 0, 0};
cone1 = Cone[{pO, pA}, myr];
cone2 = Cone[{pT, pA}, myr];
{a, b, c} = RandomPoint[Sphere[]];
d = RandomReal[];
plot3d = 
  RegionPlot3D[{cone1, cone2}, 
   MeshFunctions -> Function[{x, y, z}, {a, b, c} . {x, y, z}], 
   Mesh -> {{d}}, MeshStyle -> Directive@{Thick, Red}];
plan3 = Graphics3D[Hyperplane[{a, b, c}, d]];
Show[plot3d, plan3]

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