File:Quadrics.gif
Summary
| Description |
English: Quadric surfaces are the 3D generalization of conic sections.
(Not plotting the elliptical version of the quadrics, which are obtained by stretching one or more axes) |
| Date | |
| Source | {https://twitter.com/j_bertolotti/status/1232302333717106689 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
cylinder = Table[Show[ContourPlot3D[Evaluate[(x^2/1^2 + y^2/1^2 == 3^2)], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (x/y < Tan[\[Alpha]])]], PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Cylinder", LabelStyle -> {Black, Bold}], {\[Alpha], -\[Pi]/2.01, \[Pi]/ 2.01, \[Pi]/50}];
cone = Table[Show[ContourPlot3D[Evaluate[(x^2/1^2 + y^2/1^2 - z^2/2^2 == 0)], {x, -5, 5}, {y, -5,5}, {z, -5, 5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (x/y < Tan[\[Alpha]])]]
, PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Cone", LabelStyle -> {Black, Bold}], {\[Alpha], -\[Pi]/2.01, \[Pi]/ 2.01, \[Pi]/50}];
sphere = Table[Show[ParametricPlot3D[{x Sin[\[Alpha]], x Cos[\[Alpha]], Sqrt[4^2 - x^2]}, {x, -3, 3}, PlotStyle -> {Thick, Black}], ParametricPlot3D[{x Sin[\[Alpha]], x Cos[\[Alpha]], -Sqrt[4^2 - x^2]}, {x, -3, 3}, PlotStyle -> {Thick, Black}], ContourPlot3D[Evaluate[(x^2/1^2 + y^2/1^2 + z^2/1^2 == 4^2)], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (x/y < Tan[\[Alpha]])]], PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Sphere", LabelStyle -> {Black, Bold}], {\[Alpha], -\[Pi]/2.01, \[Pi]/ 2.01, \[Pi]/50}];
paraboloid = Table[Show[ParametricPlot3D[{x Sin[\[Alpha]], x Cos[\[Alpha]], x^2}, {x, -3, 3}, PlotStyle -> {Thick, Black}],ContourPlot3D[Evaluate[(x^2/1^2 + y^2/1^2 - z^1/1^2 == 0)], {x, -5, 5}, {y, -5,5}, {z, -5, 5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (x/y < Tan[\[Alpha]])]], PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Paraboloid",
LabelStyle -> {Black, Bold}], {\[Alpha], -\[Pi]/2.01, \[Pi]/ 2.01, \[Pi]/50}];
hyperboloid1 = Table[Show[ParametricPlot3D[{x Sin[\[Alpha]], x Cos[\[Alpha]], 2 Sqrt[x^2 - 1]}, {x, -3, 3}, PlotStyle -> {Thick, Black}],ParametricPlot3D[{x Sin[\[Alpha]], x Cos[\[Alpha]], -2 Sqrt[x^2 - 1]}, {x, -3, 3}, PlotStyle -> {Thick, Black}], ContourPlot3D[Evaluate[(x^2/1^2 + y^2/1^2 - z^2/2^2 == 1)], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (x/y < Tan[\[Alpha]])]], PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Hyperboloid of one sheet", LabelStyle -> {Black, Bold}], {\[Alpha], -\[Pi]/2.01, \[Pi]/ 2.01, \[Pi]/50}];
hyperboloid2 = Table[Show[ParametricPlot3D[{x Sin[\[Alpha]], x Cos[\[Alpha]], 2 Sqrt[1 + x^2]}, {x, -3, 3}, PlotStyle -> {Thick, Black}],ParametricPlot3D[{x Sin[\[Alpha]], x Cos[\[Alpha]], -2 Sqrt[1 + x^2]}, {x, -3, 3}, PlotStyle -> {Thick, Black}], ContourPlot3D[Evaluate[(x^2/1^2 + y^2/1^2 - z^2/2^2 == -1)], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (x/y < Tan[\[Alpha]])]], PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Hyperboloid of two sheets", LabelStyle -> {Black, Bold}], {\[Alpha], -\[Pi]/2.01, \[Pi]/ 2.01, \[Pi]/50}];
hyperboliccylinder = Table[Show[ContourPlot3D[Evaluate[(x^2/1^2 - y^2/1^2 == 1)], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (z < \[Alpha])]], PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Hyperbolic Cylinder", LabelStyle -> {Black, Bold}], {\[Alpha], -5.01, 5 - 0.1, 10/50}];
paraboliccylinder = Table[Show[ContourPlot3D[Evaluate[(x^2 + 2 y == 0)], {x, -5, 5}, {y, -5, 5}, {z, -5, 5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (z < \[Alpha])]], PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Parabolic Cylinder", LabelStyle -> {Black, Bold}], {\[Alpha], -5.01, 5 - 0.1, 10/50}];
hyperbolicparaboloid = Table[Show[ContourPlot3D[Evaluate[(x^2 - y^2 - 5 z == 0)], {x, -5, 5}, {y, -5, 5}, {z, -5,5}, Mesh -> None, PlotPoints -> 60, RegionFunction -> Function[{x, y, z}, (x < \[Alpha])]], PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, Axes -> False, PlotLabel -> "Hyperbolic Paraboloid", LabelStyle -> {Black, Bold}], {\[Alpha], -5.01, 5 - 0.1, 10/50}];
p0 = Table[Grid[{{sphere[[j]], cylinder[[j]], cone[[j]]}, {paraboloid[[j]], hyperboloid1[[j]], hyperboloid2[[j]]}, {hyperbolicparaboloid[[j]], paraboliccylinder[[j]], hyperboliccylinder[[j]]}}], {j, 1, 50}];
ListAnimate[p0]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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