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

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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







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  • 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




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edited 15 mins ago









m_goldberg

82.3k869190




82.3k869190






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Lorenzo F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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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
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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






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    1 Answer
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    active

    oldest

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    1 Answer
    1






    active

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    active

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    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




















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