planar Conic Sections plot - Mathematica Stack Exchange most recent 30 from mathematica.stackexchange.com 2020-01-27T16:32:52Z https://mathematica.stackexchange.com/feeds/question/105060 https://creativecommons.org/licenses/by-sa/4.0/rdf https://mathematica.stackexchange.com/q/105060 1 planar Conic Sections plot Narasimham https://mathematica.stackexchange.com/users/19067 2016-01-28T11:14:07Z 2016-07-27T07:40:31Z <p>Among answers of <a href="https://math.stackexchange.com/questions/1628842/does-a-right-circular-cone-only-consists-of-pair-of-straight-lines-hyperbolas/1628906#1628906">ConicsAssemblyQuery</a>, I posted images that are not pretty. In particular, the parabola is elusive due to large parameter step. Please help. </p> <p>The program attempts to translate and rotate a cutting plane ( by varying $CC, \beta$ respectively ) acting on a cone of given semi-vertical angle $\alpha$. Change of sign in front of sqrt produces cone shell below $xz$ plane that can be Shown together.</p> <pre><code>al = .81; XYZ[x_, bt_, CC_] := {x, Tan[bt] x - CC, Sqrt[x^2 (Tan[al]^2 - Tan[bt]^2) + 2 Tan[bt] x CC - CC^2]}; ParametricPlot3D[ XYZ[x, bt, 0.7], {x, 0, 3}, {bt, 0.85, 3}, Mesh -&gt; {12, 30}] ParametricPlot3D[XYZ[x, 1.14, CC], {x, -1.3, 1.3}, {CC, -1.2, 1.2}, Mesh -&gt; {12, 30}] </code></pre> https://mathematica.stackexchange.com/questions/105060/-/105069#105069 0 Answer by user9660 for planar Conic Sections plot user9660 https://mathematica.stackexchange.com/users/0 2016-01-28T13:50:27Z 2016-01-28T13:50:27Z <p>Have a look at <a href="http://reference.wolfram.com/language/ref/PlotPoints.html" rel="nofollow noreferrer">PlotPoints</a> and <a href="http://reference.wolfram.com/language/ref/MaxRecursion.html" rel="nofollow noreferrer">MaxRecursion</a> the results are quite pleasing</p> <pre><code>ParametricPlot3D[XYZ[x, bt, 0.7], {x, 0, 3}, {bt, 0.85, 3}, Mesh -&gt; {12, 30}, PlotPoints -&gt; 50, MaxRecursion -&gt; 5] </code></pre> <p><a href="https://i.stack.imgur.com/xv55n.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/xv55n.png" alt="enter image description here"></a></p> <pre><code>ParametricPlot3D[XYZ[x, 1.14, CC], {x, -1.3, 1.3}, {CC, -1.2, 1.2}, Mesh -&gt; {12, 30}, PlotPoints -&gt; 50, MaxRecursion -&gt; 5] </code></pre> <p><a href="https://i.stack.imgur.com/SWSRM.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/SWSRM.png" alt="enter image description here"></a></p> https://mathematica.stackexchange.com/questions/105060/-/121581#121581 0 Answer by ubpdqn for planar Conic Sections plot ubpdqn https://mathematica.stackexchange.com/users/1997 2016-07-27T07:40:31Z 2016-07-27T07:40:31Z <p>I post this based on the text of the hyperlink. This was done hurriedly and can be vastly improved (such as plotting conic). Others may wish to do. I am uncertain what the plots shown as graphics aim to do.</p> <pre><code>cone[a_, r_, t_] := {r, r Tan[a] Cos[t], r Tan[a] Sin[t]}; plane[b_, t_, u_, v_] := {0, t, 0} + {u, Tan[b] u, v}; Manipulate[ Module[{p1, p2}, p1 = ParametricPlot3D[{cone[\[Alpha], r, t], cone[\[Alpha], r, t] {-1, 1, 1}}, {t, 0, 2 Pi}, {r, 0, 2}, PlotStyle -&gt; {{Yellow, Opacity[0.5]}}, Mesh -&gt; None]; p2 = ParametricPlot3D[ plane[\[Beta], c, u, v], {u, -2, 2}, {v, -1, 1}, PlotStyle -&gt; {Blue, Opacity[0.5]}, Mesh -&gt; None]; Show[p1, p2, PlotRange -&gt; Table[{-2, 2}, 3], PlotLabel -&gt; Row[{"\[Epsilon]=", Sin[\[Alpha]]/Sin[\[Beta]]}]]], {\[Alpha], Pi/6, Pi/3}, {\[Beta], Pi/6, Pi/3}, {c, -2, 2}] </code></pre> <p><a href="https://i.stack.imgur.com/btfWa.gif" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/btfWa.gif" alt="enter image description here"></a></p>