Visualize manifold specified by equalities [duplicate]












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  • Plotting implicitly-defined space curves

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Suppose I have two nonlinear equalities $x^3 = y^2, y = z^3$. How can I visualize the manifold in $mathbb{R}^3$ that is generated by simultaneously satisfying the two equalities? I think ContourPlot3D is the one to use but I couldn't get it to work show the set of points in $mathbb{R}^3$ that satisfy the two equalities. The best I can do is make it show the intersection of the surfaces:



enter image description here



How can I plot the curve defined by the intersection in 3D?






plotting







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marked as duplicate by J. M. is slightly pensive♦ Feb 27 at 0:29


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.























    5












    $begingroup$



    This question already has an answer here:




    • Plotting implicitly-defined space curves

      4 answers




    Suppose I have two nonlinear equalities $x^3 = y^2, y = z^3$. How can I visualize the manifold in $mathbb{R}^3$ that is generated by simultaneously satisfying the two equalities? I think ContourPlot3D is the one to use but I couldn't get it to work show the set of points in $mathbb{R}^3$ that satisfy the two equalities. The best I can do is make it show the intersection of the surfaces:



    enter image description here



    How can I plot the curve defined by the intersection in 3D?






    plotting







    share|improve this question











    $endgroup$



    marked as duplicate by J. M. is slightly pensive♦ Feb 27 at 0:29


    This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.





















      5












      5








      5


      1



      $begingroup$



      This question already has an answer here:




      • Plotting implicitly-defined space curves

        4 answers




      Suppose I have two nonlinear equalities $x^3 = y^2, y = z^3$. How can I visualize the manifold in $mathbb{R}^3$ that is generated by simultaneously satisfying the two equalities? I think ContourPlot3D is the one to use but I couldn't get it to work show the set of points in $mathbb{R}^3$ that satisfy the two equalities. The best I can do is make it show the intersection of the surfaces:



      enter image description here



      How can I plot the curve defined by the intersection in 3D?






      plotting







      share|improve this question











      $endgroup$





      This question already has an answer here:




      • Plotting implicitly-defined space curves

        4 answers




      Suppose I have two nonlinear equalities $x^3 = y^2, y = z^3$. How can I visualize the manifold in $mathbb{R}^3$ that is generated by simultaneously satisfying the two equalities? I think ContourPlot3D is the one to use but I couldn't get it to work show the set of points in $mathbb{R}^3$ that satisfy the two equalities. The best I can do is make it show the intersection of the surfaces:



      enter image description here



      How can I plot the curve defined by the intersection in 3D?





      This question already has an answer here:




      • Plotting implicitly-defined space curves

        4 answers







      plotting




      plotting






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Mar 1 at 9:34









      J. M. is slightly pensive♦

      98.8k10311467




      98.8k10311467










      asked Feb 26 at 23:25









      ITAITA

      1625




      1625




      marked as duplicate by J. M. is slightly pensive♦ Feb 27 at 0:29


      This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.









      marked as duplicate by J. M. is slightly pensive♦ Feb 27 at 0:29


      This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
























          2 Answers
          2






          active

          oldest

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          6












          $begingroup$

          You can use the option BoundaryStyle to mark the intersection of the two contour surfaces as follows:



          ContourPlot3D[{x^3 == y^2, y == z^3}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
          
 Mesh -> None, ContourStyle -> Opacity[.3], 
          
 BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Directive[Thick, Red]}]


          enter image description here



          Also



          SliceContourPlot3D[y - z^3,  x^3 == y^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
          
 Contours -> {{0}}, BoundaryStyle -> None, ContourShading -> None, 
          
 ContourStyle -> Directive[Red, Thick]]


          enter image description here






          share|improve this answer











          $endgroup$













          • $begingroup$
            That's exactly what I needed. I follow most of it: Since a list was passed as first argument the '{1 -> None, 2-> None ... }' but how Mathematica knew to handle {1,2} -> is just magic!
            $endgroup$
            – ITA
            Feb 26 at 23:44



















          4












          $begingroup$

          r = 1;
          
R = ImplicitRegion[{x^3 == y^2, y == z^3}, {{x, -r, r}, {y, -r, r}, {z, -r, r}}];
          
Region[R]





          share|improve this answer









          $endgroup$




















            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            6












            $begingroup$

            You can use the option BoundaryStyle to mark the intersection of the two contour surfaces as follows:



            ContourPlot3D[{x^3 == y^2, y == z^3}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
            
 Mesh -> None, ContourStyle -> Opacity[.3], 
            
 BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Directive[Thick, Red]}]


            enter image description here



            Also



            SliceContourPlot3D[y - z^3,  x^3 == y^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
            
 Contours -> {{0}}, BoundaryStyle -> None, ContourShading -> None, 
            
 ContourStyle -> Directive[Red, Thick]]


            enter image description here






            share|improve this answer











            $endgroup$













            • $begingroup$
              That's exactly what I needed. I follow most of it: Since a list was passed as first argument the '{1 -> None, 2-> None ... }' but how Mathematica knew to handle {1,2} -> is just magic!
              $endgroup$
              – ITA
              Feb 26 at 23:44
















            6












            $begingroup$

            You can use the option BoundaryStyle to mark the intersection of the two contour surfaces as follows:



            ContourPlot3D[{x^3 == y^2, y == z^3}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
            
 Mesh -> None, ContourStyle -> Opacity[.3], 
            
 BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Directive[Thick, Red]}]


            enter image description here



            Also



            SliceContourPlot3D[y - z^3,  x^3 == y^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
            
 Contours -> {{0}}, BoundaryStyle -> None, ContourShading -> None, 
            
 ContourStyle -> Directive[Red, Thick]]


            enter image description here






            share|improve this answer











            $endgroup$













            • $begingroup$
              That's exactly what I needed. I follow most of it: Since a list was passed as first argument the '{1 -> None, 2-> None ... }' but how Mathematica knew to handle {1,2} -> is just magic!
              $endgroup$
              – ITA
              Feb 26 at 23:44














            6












            6








            6





            $begingroup$

            You can use the option BoundaryStyle to mark the intersection of the two contour surfaces as follows:



            ContourPlot3D[{x^3 == y^2, y == z^3}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
            
 Mesh -> None, ContourStyle -> Opacity[.3], 
            
 BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Directive[Thick, Red]}]


            enter image description here



            Also



            SliceContourPlot3D[y - z^3,  x^3 == y^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
            
 Contours -> {{0}}, BoundaryStyle -> None, ContourShading -> None, 
            
 ContourStyle -> Directive[Red, Thick]]


            enter image description here






            share|improve this answer











            $endgroup$



            You can use the option BoundaryStyle to mark the intersection of the two contour surfaces as follows:



            ContourPlot3D[{x^3 == y^2, y == z^3}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
            
 Mesh -> None, ContourStyle -> Opacity[.3], 
            
 BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Directive[Thick, Red]}]


            enter image description here



            Also



            SliceContourPlot3D[y - z^3,  x^3 == y^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
            
 Contours -> {{0}}, BoundaryStyle -> None, ContourShading -> None, 
            
 ContourStyle -> Directive[Red, Thick]]


            enter image description here







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited Feb 26 at 23:46

























            answered Feb 26 at 23:33









            kglrkglr

            190k10206424




            190k10206424












            • $begingroup$
              That's exactly what I needed. I follow most of it: Since a list was passed as first argument the '{1 -> None, 2-> None ... }' but how Mathematica knew to handle {1,2} -> is just magic!
              $endgroup$
              – ITA
              Feb 26 at 23:44


















            • $begingroup$
              That's exactly what I needed. I follow most of it: Since a list was passed as first argument the '{1 -> None, 2-> None ... }' but how Mathematica knew to handle {1,2} -> is just magic!
              $endgroup$
              – ITA
              Feb 26 at 23:44
















            $begingroup$
            That's exactly what I needed. I follow most of it: Since a list was passed as first argument the '{1 -> None, 2-> None ... }' but how Mathematica knew to handle {1,2} -> is just magic!
            $endgroup$
            – ITA
            Feb 26 at 23:44




            $begingroup$
            That's exactly what I needed. I follow most of it: Since a list was passed as first argument the '{1 -> None, 2-> None ... }' but how Mathematica knew to handle {1,2} -> is just magic!
            $endgroup$
            – ITA
            Feb 26 at 23:44











            4












            $begingroup$

            r = 1;
            
R = ImplicitRegion[{x^3 == y^2, y == z^3}, {{x, -r, r}, {y, -r, r}, {z, -r, r}}];
            
Region[R]





            share|improve this answer









            $endgroup$


















              4












              $begingroup$

              r = 1;
              
R = ImplicitRegion[{x^3 == y^2, y == z^3}, {{x, -r, r}, {y, -r, r}, {z, -r, r}}];
              
Region[R]





              share|improve this answer









              $endgroup$
















                4












                4








                4





                $begingroup$

                r = 1;
                
R = ImplicitRegion[{x^3 == y^2, y == z^3}, {{x, -r, r}, {y, -r, r}, {z, -r, r}}];
                
Region[R]





                share|improve this answer









                $endgroup$



                r = 1;
                
R = ImplicitRegion[{x^3 == y^2, y == z^3}, {{x, -r, r}, {y, -r, r}, {z, -r, r}}];
                
Region[R]






                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered Feb 26 at 23:35









                Henrik SchumacherHenrik Schumacher

                58.7k581162




                58.7k581162















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