Finding the intersection of a pencil of lines with a plane and making a 3D plot of the ensemble

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
2
down vote

favorite












I've computed the intersection of a plane with some lines. It looks OK until I try to make a 3D graph from intersec_lines.



alpha = Pi/5;
r1 = 5;
r2 = 2;
h = 3;
n = 20;
plane = InfinitePlane[0, 0, 0, Cos[alpha], 0, Sin[alpha], 0, 1, 0];
lines = 
 Table[
 InfiniteLine[
 r1*Cos[2*Pi*x/n], r1*Sin[2*Pi*x/n], 0, 
 r2*Cos[2*Pi*x/n], r2*Sin[2*Pi*x/n], h], 
 x, n];
intersec_points = NSolve[x, y, z ∈ plane && x, y, z ∈ #]& /@ lines


Does anyone know how to do it? It seem it should be pretty basic, but I'm just starting to use Mathematica.






plotting graphics3d







share|improve this question









New contributor




Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.















  • 2




    Do not use _ in variable names, since _ has a special meaning in Mathematica.
    – J. M. is somewhat okay.♦
    1 hour ago














up vote
2
down vote

favorite












I've computed the intersection of a plane with some lines. It looks OK until I try to make a 3D graph from intersec_lines.



alpha = Pi/5;
r1 = 5;
r2 = 2;
h = 3;
n = 20;
plane = InfinitePlane[0, 0, 0, Cos[alpha], 0, Sin[alpha], 0, 1, 0];
lines = 
 Table[
 InfiniteLine[
 r1*Cos[2*Pi*x/n], r1*Sin[2*Pi*x/n], 0, 
 r2*Cos[2*Pi*x/n], r2*Sin[2*Pi*x/n], h], 
 x, n];
intersec_points = NSolve[x, y, z ∈ plane && x, y, z ∈ #]& /@ lines


Does anyone know how to do it? It seem it should be pretty basic, but I'm just starting to use Mathematica.






plotting graphics3d







share|improve this question









New contributor




Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.















  • 2




    Do not use _ in variable names, since _ has a special meaning in Mathematica.
    – J. M. is somewhat okay.♦
    1 hour ago












up vote
2
down vote

favorite









up vote
2
down vote

favorite











I've computed the intersection of a plane with some lines. It looks OK until I try to make a 3D graph from intersec_lines.



alpha = Pi/5;
r1 = 5;
r2 = 2;
h = 3;
n = 20;
plane = InfinitePlane[0, 0, 0, Cos[alpha], 0, Sin[alpha], 0, 1, 0];
lines = 
 Table[
 InfiniteLine[
 r1*Cos[2*Pi*x/n], r1*Sin[2*Pi*x/n], 0, 
 r2*Cos[2*Pi*x/n], r2*Sin[2*Pi*x/n], h], 
 x, n];
intersec_points = NSolve[x, y, z ∈ plane && x, y, z ∈ #]& /@ lines


Does anyone know how to do it? It seem it should be pretty basic, but I'm just starting to use Mathematica.






plotting graphics3d







share|improve this question









New contributor




Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I've computed the intersection of a plane with some lines. It looks OK until I try to make a 3D graph from intersec_lines.



alpha = Pi/5;
r1 = 5;
r2 = 2;
h = 3;
n = 20;
plane = InfinitePlane[0, 0, 0, Cos[alpha], 0, Sin[alpha], 0, 1, 0];
lines = 
 Table[
 InfiniteLine[
 r1*Cos[2*Pi*x/n], r1*Sin[2*Pi*x/n], 0, 
 r2*Cos[2*Pi*x/n], r2*Sin[2*Pi*x/n], h], 
 x, n];
intersec_points = NSolve[x, y, z ∈ plane && x, y, z ∈ #]& /@ lines


Does anyone know how to do it? It seem it should be pretty basic, but I'm just starting to use Mathematica.






plotting graphics3d




plotting graphics3d






share|improve this question









New contributor




Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 15 mins ago









m_goldberg

82.3k869190




82.3k869190






New contributor




Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 1 hour ago









Lorenzo F.

111




111




New contributor




Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







  • 2




    Do not use _ in variable names, since _ has a special meaning in Mathematica.
    – J. M. is somewhat okay.♦
    1 hour ago












  • 2




    Do not use _ in variable names, since _ has a special meaning in Mathematica.
    – J. M. is somewhat okay.♦
    1 hour ago







2




2




Do not use _ in variable names, since _ has a special meaning in Mathematica.
– J. M. is somewhat okay.♦
1 hour ago




Do not use _ in variable names, since _ has a special meaning in Mathematica.
– J. M. is somewhat okay.♦
1 hour ago










1 Answer
1






active

oldest

votes

















up vote
3
down vote













Using RegionIntersection is the most straightforward route for finding the intersection points:



With[α = π/5, r1 = 5, r2 = 2, h = 3, n = 20,
 plane = InfinitePlane[0, 0, 0, Cos[α], 0, Sin[α], 0, 1, 0];
 lines = Table[InfiniteLine[r1 Cos[2 π x/n], r1 Sin[2 π x/n], 0,
 r2 Cos[2 π x/n], r2 Sin[2 π x/n], h], x, n];]

pts = RegionIntersection[plane, #] & /@ lines;

Graphics3D[plane, lines, Sphere[#, 1/4] & @@@ pts, Axes -> True, PlotRange -> 10]


intersection points of a cone and a plane






share|improve this answer




















    Your Answer




    StackExchange.ifUsing("editor", function ()
    return StackExchange.using("mathjaxEditing", function ()
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    );
    );
    , "mathjax-editing");

    StackExchange.ready(function()
    var channelOptions =
    tags: "".split(" "),
    id: "387"
    ;
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function()
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled)
    StackExchange.using("snippets", function()
    createEditor();
    );

    else
    createEditor();

    );

    function createEditor()
    StackExchange.prepareEditor(
    heartbeatType: 'answer',
    convertImagesToLinks: false,
    noModals: false,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    );



    );






    Lorenzo F. is a new contributor. Be nice, and check out our Code of Conduct.









     

    draft saved


    draft discarded


















    StackExchange.ready(
    function ()
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f182818%2ffinding-the-intersection-of-a-pencil-of-lines-with-a-plane-and-making-a-3d-plot%23new-answer', 'question_page');

    );

    Post as a guest

















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    3
    down vote













    Using RegionIntersection is the most straightforward route for finding the intersection points:



    With[α = π/5, r1 = 5, r2 = 2, h = 3, n = 20,
     plane = InfinitePlane[0, 0, 0, Cos[α], 0, Sin[α], 0, 1, 0];
     lines = Table[InfiniteLine[r1 Cos[2 π x/n], r1 Sin[2 π x/n], 0,
     r2 Cos[2 π x/n], r2 Sin[2 π x/n], h], x, n];]

    pts = RegionIntersection[plane, #] & /@ lines;

    Graphics3D[plane, lines, Sphere[#, 1/4] & @@@ pts, Axes -> True, PlotRange -> 10]


    intersection points of a cone and a plane






    share|improve this answer
























      up vote
      3
      down vote













      Using RegionIntersection is the most straightforward route for finding the intersection points:



      With[α = π/5, r1 = 5, r2 = 2, h = 3, n = 20,
       plane = InfinitePlane[0, 0, 0, Cos[α], 0, Sin[α], 0, 1, 0];
       lines = Table[InfiniteLine[r1 Cos[2 π x/n], r1 Sin[2 π x/n], 0,
       r2 Cos[2 π x/n], r2 Sin[2 π x/n], h], x, n];]

      pts = RegionIntersection[plane, #] & /@ lines;

      Graphics3D[plane, lines, Sphere[#, 1/4] & @@@ pts, Axes -> True, PlotRange -> 10]


      intersection points of a cone and a plane






      share|improve this answer






















        up vote
        3
        down vote










        up vote
        3
        down vote









        Using RegionIntersection is the most straightforward route for finding the intersection points:



        With[α = π/5, r1 = 5, r2 = 2, h = 3, n = 20,
         plane = InfinitePlane[0, 0, 0, Cos[α], 0, Sin[α], 0, 1, 0];
         lines = Table[InfiniteLine[r1 Cos[2 π x/n], r1 Sin[2 π x/n], 0,
         r2 Cos[2 π x/n], r2 Sin[2 π x/n], h], x, n];]

        pts = RegionIntersection[plane, #] & /@ lines;

        Graphics3D[plane, lines, Sphere[#, 1/4] & @@@ pts, Axes -> True, PlotRange -> 10]


        intersection points of a cone and a plane






        share|improve this answer












        Using RegionIntersection is the most straightforward route for finding the intersection points:



        With[α = π/5, r1 = 5, r2 = 2, h = 3, n = 20,
         plane = InfinitePlane[0, 0, 0, Cos[α], 0, Sin[α], 0, 1, 0];
         lines = Table[InfiniteLine[r1 Cos[2 π x/n], r1 Sin[2 π x/n], 0,
         r2 Cos[2 π x/n], r2 Sin[2 π x/n], h], x, n];]

        pts = RegionIntersection[plane, #] & /@ lines;

        Graphics3D[plane, lines, Sphere[#, 1/4] & @@@ pts, Axes -> True, PlotRange -> 10]


        intersection points of a cone and a plane







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 1 hour ago









        J. M. is somewhat okay.♦

        93.4k10289445




        93.4k10289445




















            Lorenzo F. is a new contributor. Be nice, and check out our Code of Conduct.









             

            draft saved


            draft discarded


















            Lorenzo F. is a new contributor. Be nice, and check out our Code of Conduct.












            Lorenzo F. is a new contributor. Be nice, and check out our Code of Conduct.











            Lorenzo F. is a new contributor. Be nice, and check out our Code of Conduct.













             


            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f182818%2ffinding-the-intersection-of-a-pencil-of-lines-with-a-plane-and-making-a-3d-plot%23new-answer', 'question_page');

            );

            Post as a guest
































































            Comments

            Post a Comment

            Popular posts from this blog

            What does second last employer means? [closed]

            Image
            Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote -3 down vote favorite Say, for example I have worked in the following companies, Company A => 2010 - 2011 Company B => 2011 - 2012 Company C => 2012 - Till Date Company D => Have offer Now assume Company D is asking to submit documents from my second last employer. So from the list of companies given, which company would be qualified as second last employer? software-industry employer share | improve this question asked Aug 10 '14 at 5:16 Rajaprabhu Aravindasamy 559 1 6 13 closed as off-topic by Jim G., jmort253 ♦ Aug 11 '14 at 1:58 This question appears to be off-topic. The users who voted to close gave this specific reason: "Questions seeking advice on company-specific regulations, agreements, or policies should be directed to your manager or HR department. Questions that address...
            Read more

            Installing NextGIS Connect into QGIS 3?

            Image
            Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote 1 down vote favorite Just acquired free version of NEXTGIS and trying to install the plugin for QGIS. It tells me it was not designed for version 3 of QGIS. How do I set up the QGIS-NEXTGIS interface then? qgis qgis-plugins nextgis share | improve this question edited 3 hours ago PolyGeo ♦ 51.9k 17 77 233 asked 4 hours ago IanGS 16 4 New contributor IanGS is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct. add a comment  |  up vote 1 down vote favorite Just acquired free version of NEXTGIS and trying to install the plugin for QGIS. It tells me it was not designed for version 3 of QGIS. How do I set up the QGIS-NEXTGIS interface then? qgis qgis-plugin...
            Read more

            One-line joke

            A one-liner is a joke that is delivered in a single line. A good one-liner is said to be pithy - concise and meaningful. [1] Comedians and actors use this comedic method as part of their act, e.g. Jimmy Carr, Tommy Cooper, Rodney Dangerfield, Norm Macdonald, Ken Dodd, Stewart Francis, Zach Galifianakis, Mitch Hedberg, Anthony Jeselnik, Milton Jones, Shappi Khorsandi, Jay London, Mark Linn-Baker, Demetri Martin, Groucho Marx, Dan Mintz, Emo Philips, Tim Vine, Steven Wright and Henny Youngman and Arnold Schwarzenegger. [ citation needed ] Many fictional characters are also known to deliver one-liners, including James Bond, who usually includes pithy and laconic quips after disposing of a villain. [ citation needed ] Examples "A baby seal walks into a club." "A dyslexic man walks into a bra." (Anonymous) "There are three types of people, those who can count and those who can't." "Venison's dear, isn't it?" (Jimmy Carr) "An escala...
            Read more