How do I remove artifacts from my ContourPlot3D Valentine?












8












$begingroup$


My version (below) of the "Valentine Formula" that appeared in today's New York Times, has some ugly artifacts that don't appear in the NYT (Java) version:



enter image description here



How do I remove these artifacts?




Manipulate[

    ContourPlot3D[(x^2+((1+b)*y)^2+z^2-1)^3-x^2*z^3-a*y^2*z^3 ==0,

        {x,-scale,scale},{y,-scale,scale},{z,-scale,scale},

        Mesh->None,Axes->None,Boxed->False,

        ContourStyle->Directive[Red,Opacity[0.8],Specularity[White,30]],

        PerformanceGoal->"Quality"

    ],

    {{a,.1},.0001,1},

    {{b,1},.00001,5},

    {{scale,1.25},1,5},

    SynchronousUpdating->False]





graphics performance-tuning graphics3d







share|improve this question











$endgroup$

















    8












    $begingroup$


    My version (below) of the "Valentine Formula" that appeared in today's New York Times, has some ugly artifacts that don't appear in the NYT (Java) version:



    enter image description here



    How do I remove these artifacts?




    Manipulate[
    
    ContourPlot3D[(x^2+((1+b)*y)^2+z^2-1)^3-x^2*z^3-a*y^2*z^3 ==0,
    
        {x,-scale,scale},{y,-scale,scale},{z,-scale,scale},
    
        Mesh->None,Axes->None,Boxed->False,
    
        ContourStyle->Directive[Red,Opacity[0.8],Specularity[White,30]],
    
        PerformanceGoal->"Quality"
    
    ],
    
    {{a,.1},.0001,1},
    
    {{b,1},.00001,5},
    
    {{scale,1.25},1,5},
    
    SynchronousUpdating->False]





    graphics performance-tuning graphics3d







    share|improve this question











    $endgroup$















      8












      8








      8


      3



      $begingroup$


      My version (below) of the "Valentine Formula" that appeared in today's New York Times, has some ugly artifacts that don't appear in the NYT (Java) version:



      enter image description here



      How do I remove these artifacts?




      Manipulate[
      
    ContourPlot3D[(x^2+((1+b)*y)^2+z^2-1)^3-x^2*z^3-a*y^2*z^3 ==0,
      
        {x,-scale,scale},{y,-scale,scale},{z,-scale,scale},
      
        Mesh->None,Axes->None,Boxed->False,
      
        ContourStyle->Directive[Red,Opacity[0.8],Specularity[White,30]],
      
        PerformanceGoal->"Quality"
      
    ],
      
    {{a,.1},.0001,1},
      
    {{b,1},.00001,5},
      
    {{scale,1.25},1,5},
      
    SynchronousUpdating->False]





      graphics performance-tuning graphics3d







      share|improve this question











      $endgroup$




      My version (below) of the "Valentine Formula" that appeared in today's New York Times, has some ugly artifacts that don't appear in the NYT (Java) version:



      enter image description here



      How do I remove these artifacts?




      Manipulate[
      
    ContourPlot3D[(x^2+((1+b)*y)^2+z^2-1)^3-x^2*z^3-a*y^2*z^3 ==0,
      
        {x,-scale,scale},{y,-scale,scale},{z,-scale,scale},
      
        Mesh->None,Axes->None,Boxed->False,
      
        ContourStyle->Directive[Red,Opacity[0.8],Specularity[White,30]],
      
        PerformanceGoal->"Quality"
      
    ],
      
    {{a,.1},.0001,1},
      
    {{b,1},.00001,5},
      
    {{scale,1.25},1,5},
      
    SynchronousUpdating->False]





      graphics performance-tuning graphics3d




      graphics performance-tuning graphics3d






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Feb 14 at 16:45









      xzczd

      27.3k573251




      27.3k573251










      asked Feb 14 at 16:24









      oromeorome

      6,07223883




      6,07223883






















          2 Answers
          2






          active

          oldest

          votes


















          6












          $begingroup$

          RegionPlot3D can sometimes give cleaner results out of the box. I also upped the PlotPoints manually.



          Manipulate[
          
 RegionPlot3D[(x^2 + ((1 + b)*y)^2 + z^2 - 1)^3 - x^2*z^3 - 
          
    a*y^2*z^3 <= 0, {x, -scale, scale}, {y, -scale, 
          
   scale}, {z, -scale, scale}, Mesh -> None, Axes -> None, 
          
  Boxed -> False, 
          
  PlotStyle -> Directive[Red, Opacity[0.8], Specularity[White, 30]], 
          
  PlotPoints -> ControlActive[Automatic, 40]], {{a, .1}, .0001, 
          
  1}, {{b, 1}, .00001, 5}, {{scale, 1.25}, 1, 5}, 
          
 SynchronousUpdating -> False]







          share|improve this answer









          $endgroup$













          • $begingroup$
            That's much nicer!
            $endgroup$
            – orome
            Feb 14 at 16:40





















          2












          $begingroup$

          Adding the ContourPlot3D option PlotPoints -> n where n is some number greater than or equal to 100 improved things considerably for me. There is still a very faint ring around the lower portion of the heart when I do this, but it's a considerable improvement.



          The PlotPoints argument tells Mathematica how many points to use when initially sampling the plot. Many functions (including 2D functions like DensityPlot) accept this argument. For whatever reason, the default is often quite low for functions/plots with rapid changes or singularities.



          Demo:



          First, without any additional argument:
          enter image description here



          Then with PlotPoints -> 200.
          with argument






          share|improve this answer











          $endgroup$













          • $begingroup$
            That doesn't do anything for me.
            $endgroup$
            – orome
            Feb 14 at 16:38










          • $begingroup$
            @orome I bet you place the option in the Directive again.
            $endgroup$
            – xzczd
            Feb 14 at 16:39










          • $begingroup$
            @xzczd: Yep! (God I hate Mathematica's inadequate syntax checking!)
            $endgroup$
            – orome
            Feb 14 at 16:42










          • $begingroup$
            @orome I'm also surprised that Mathematica doesn't give any warning in this case :D
            $endgroup$
            – xzczd
            Feb 14 at 16:43












          • $begingroup$
            It shows improvement now, but still shows (as you point out) artifacts that ruin it.
            $endgroup$
            – orome
            Feb 14 at 16:46











          Your Answer





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          2 Answers
          2






          active

          oldest

          votes








          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          6












          $begingroup$

          RegionPlot3D can sometimes give cleaner results out of the box. I also upped the PlotPoints manually.



          Manipulate[
          
 RegionPlot3D[(x^2 + ((1 + b)*y)^2 + z^2 - 1)^3 - x^2*z^3 - 
          
    a*y^2*z^3 <= 0, {x, -scale, scale}, {y, -scale, 
          
   scale}, {z, -scale, scale}, Mesh -> None, Axes -> None, 
          
  Boxed -> False, 
          
  PlotStyle -> Directive[Red, Opacity[0.8], Specularity[White, 30]], 
          
  PlotPoints -> ControlActive[Automatic, 40]], {{a, .1}, .0001, 
          
  1}, {{b, 1}, .00001, 5}, {{scale, 1.25}, 1, 5}, 
          
 SynchronousUpdating -> False]







          share|improve this answer









          $endgroup$













          • $begingroup$
            That's much nicer!
            $endgroup$
            – orome
            Feb 14 at 16:40


















          6












          $begingroup$

          RegionPlot3D can sometimes give cleaner results out of the box. I also upped the PlotPoints manually.



          Manipulate[
          
 RegionPlot3D[(x^2 + ((1 + b)*y)^2 + z^2 - 1)^3 - x^2*z^3 - 
          
    a*y^2*z^3 <= 0, {x, -scale, scale}, {y, -scale, 
          
   scale}, {z, -scale, scale}, Mesh -> None, Axes -> None, 
          
  Boxed -> False, 
          
  PlotStyle -> Directive[Red, Opacity[0.8], Specularity[White, 30]], 
          
  PlotPoints -> ControlActive[Automatic, 40]], {{a, .1}, .0001, 
          
  1}, {{b, 1}, .00001, 5}, {{scale, 1.25}, 1, 5}, 
          
 SynchronousUpdating -> False]







          share|improve this answer









          $endgroup$













          • $begingroup$
            That's much nicer!
            $endgroup$
            – orome
            Feb 14 at 16:40
















          6












          6








          6





          $begingroup$

          RegionPlot3D can sometimes give cleaner results out of the box. I also upped the PlotPoints manually.



          Manipulate[
          
 RegionPlot3D[(x^2 + ((1 + b)*y)^2 + z^2 - 1)^3 - x^2*z^3 - 
          
    a*y^2*z^3 <= 0, {x, -scale, scale}, {y, -scale, 
          
   scale}, {z, -scale, scale}, Mesh -> None, Axes -> None, 
          
  Boxed -> False, 
          
  PlotStyle -> Directive[Red, Opacity[0.8], Specularity[White, 30]], 
          
  PlotPoints -> ControlActive[Automatic, 40]], {{a, .1}, .0001, 
          
  1}, {{b, 1}, .00001, 5}, {{scale, 1.25}, 1, 5}, 
          
 SynchronousUpdating -> False]







          share|improve this answer









          $endgroup$



          RegionPlot3D can sometimes give cleaner results out of the box. I also upped the PlotPoints manually.



          Manipulate[
          
 RegionPlot3D[(x^2 + ((1 + b)*y)^2 + z^2 - 1)^3 - x^2*z^3 - 
          
    a*y^2*z^3 <= 0, {x, -scale, scale}, {y, -scale, 
          
   scale}, {z, -scale, scale}, Mesh -> None, Axes -> None, 
          
  Boxed -> False, 
          
  PlotStyle -> Directive[Red, Opacity[0.8], Specularity[White, 30]], 
          
  PlotPoints -> ControlActive[Automatic, 40]], {{a, .1}, .0001, 
          
  1}, {{b, 1}, .00001, 5}, {{scale, 1.25}, 1, 5}, 
          
 SynchronousUpdating -> False]








          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Feb 14 at 16:38









          Chip HurstChip Hurst

          22.2k15791




          22.2k15791












          • $begingroup$
            That's much nicer!
            $endgroup$
            – orome
            Feb 14 at 16:40




















          • $begingroup$
            That's much nicer!
            $endgroup$
            – orome
            Feb 14 at 16:40


















          $begingroup$
          That's much nicer!
          $endgroup$
          – orome
          Feb 14 at 16:40






          $begingroup$
          That's much nicer!
          $endgroup$
          – orome
          Feb 14 at 16:40













          2












          $begingroup$

          Adding the ContourPlot3D option PlotPoints -> n where n is some number greater than or equal to 100 improved things considerably for me. There is still a very faint ring around the lower portion of the heart when I do this, but it's a considerable improvement.



          The PlotPoints argument tells Mathematica how many points to use when initially sampling the plot. Many functions (including 2D functions like DensityPlot) accept this argument. For whatever reason, the default is often quite low for functions/plots with rapid changes or singularities.



          Demo:



          First, without any additional argument:
          enter image description here



          Then with PlotPoints -> 200.
          with argument






          share|improve this answer











          $endgroup$













          • $begingroup$
            That doesn't do anything for me.
            $endgroup$
            – orome
            Feb 14 at 16:38










          • $begingroup$
            @orome I bet you place the option in the Directive again.
            $endgroup$
            – xzczd
            Feb 14 at 16:39










          • $begingroup$
            @xzczd: Yep! (God I hate Mathematica's inadequate syntax checking!)
            $endgroup$
            – orome
            Feb 14 at 16:42










          • $begingroup$
            @orome I'm also surprised that Mathematica doesn't give any warning in this case :D
            $endgroup$
            – xzczd
            Feb 14 at 16:43












          • $begingroup$
            It shows improvement now, but still shows (as you point out) artifacts that ruin it.
            $endgroup$
            – orome
            Feb 14 at 16:46
















          2












          $begingroup$

          Adding the ContourPlot3D option PlotPoints -> n where n is some number greater than or equal to 100 improved things considerably for me. There is still a very faint ring around the lower portion of the heart when I do this, but it's a considerable improvement.



          The PlotPoints argument tells Mathematica how many points to use when initially sampling the plot. Many functions (including 2D functions like DensityPlot) accept this argument. For whatever reason, the default is often quite low for functions/plots with rapid changes or singularities.



          Demo:



          First, without any additional argument:
          enter image description here



          Then with PlotPoints -> 200.
          with argument






          share|improve this answer











          $endgroup$













          • $begingroup$
            That doesn't do anything for me.
            $endgroup$
            – orome
            Feb 14 at 16:38










          • $begingroup$
            @orome I bet you place the option in the Directive again.
            $endgroup$
            – xzczd
            Feb 14 at 16:39










          • $begingroup$
            @xzczd: Yep! (God I hate Mathematica's inadequate syntax checking!)
            $endgroup$
            – orome
            Feb 14 at 16:42










          • $begingroup$
            @orome I'm also surprised that Mathematica doesn't give any warning in this case :D
            $endgroup$
            – xzczd
            Feb 14 at 16:43












          • $begingroup$
            It shows improvement now, but still shows (as you point out) artifacts that ruin it.
            $endgroup$
            – orome
            Feb 14 at 16:46














          2












          2








          2





          $begingroup$

          Adding the ContourPlot3D option PlotPoints -> n where n is some number greater than or equal to 100 improved things considerably for me. There is still a very faint ring around the lower portion of the heart when I do this, but it's a considerable improvement.



          The PlotPoints argument tells Mathematica how many points to use when initially sampling the plot. Many functions (including 2D functions like DensityPlot) accept this argument. For whatever reason, the default is often quite low for functions/plots with rapid changes or singularities.



          Demo:



          First, without any additional argument:
          enter image description here



          Then with PlotPoints -> 200.
          with argument






          share|improve this answer











          $endgroup$



          Adding the ContourPlot3D option PlotPoints -> n where n is some number greater than or equal to 100 improved things considerably for me. There is still a very faint ring around the lower portion of the heart when I do this, but it's a considerable improvement.



          The PlotPoints argument tells Mathematica how many points to use when initially sampling the plot. Many functions (including 2D functions like DensityPlot) accept this argument. For whatever reason, the default is often quite low for functions/plots with rapid changes or singularities.



          Demo:



          First, without any additional argument:
          enter image description here



          Then with PlotPoints -> 200.
          with argument







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Feb 14 at 16:48

























          answered Feb 14 at 16:36









          user16054user16054

          1,606417




          1,606417












          • $begingroup$
            That doesn't do anything for me.
            $endgroup$
            – orome
            Feb 14 at 16:38










          • $begingroup$
            @orome I bet you place the option in the Directive again.
            $endgroup$
            – xzczd
            Feb 14 at 16:39










          • $begingroup$
            @xzczd: Yep! (God I hate Mathematica's inadequate syntax checking!)
            $endgroup$
            – orome
            Feb 14 at 16:42










          • $begingroup$
            @orome I'm also surprised that Mathematica doesn't give any warning in this case :D
            $endgroup$
            – xzczd
            Feb 14 at 16:43












          • $begingroup$
            It shows improvement now, but still shows (as you point out) artifacts that ruin it.
            $endgroup$
            – orome
            Feb 14 at 16:46


















          • $begingroup$
            That doesn't do anything for me.
            $endgroup$
            – orome
            Feb 14 at 16:38










          • $begingroup$
            @orome I bet you place the option in the Directive again.
            $endgroup$
            – xzczd
            Feb 14 at 16:39










          • $begingroup$
            @xzczd: Yep! (God I hate Mathematica's inadequate syntax checking!)
            $endgroup$
            – orome
            Feb 14 at 16:42










          • $begingroup$
            @orome I'm also surprised that Mathematica doesn't give any warning in this case :D
            $endgroup$
            – xzczd
            Feb 14 at 16:43












          • $begingroup$
            It shows improvement now, but still shows (as you point out) artifacts that ruin it.
            $endgroup$
            – orome
            Feb 14 at 16:46
















          $begingroup$
          That doesn't do anything for me.
          $endgroup$
          – orome
          Feb 14 at 16:38




          $begingroup$
          That doesn't do anything for me.
          $endgroup$
          – orome
          Feb 14 at 16:38












          $begingroup$
          @orome I bet you place the option in the Directive again.
          $endgroup$
          – xzczd
          Feb 14 at 16:39




          $begingroup$
          @orome I bet you place the option in the Directive again.
          $endgroup$
          – xzczd
          Feb 14 at 16:39












          $begingroup$
          @xzczd: Yep! (God I hate Mathematica's inadequate syntax checking!)
          $endgroup$
          – orome
          Feb 14 at 16:42




          $begingroup$
          @xzczd: Yep! (God I hate Mathematica's inadequate syntax checking!)
          $endgroup$
          – orome
          Feb 14 at 16:42












          $begingroup$
          @orome I'm also surprised that Mathematica doesn't give any warning in this case :D
          $endgroup$
          – xzczd
          Feb 14 at 16:43






          $begingroup$
          @orome I'm also surprised that Mathematica doesn't give any warning in this case :D
          $endgroup$
          – xzczd
          Feb 14 at 16:43














          $begingroup$
          It shows improvement now, but still shows (as you point out) artifacts that ruin it.
          $endgroup$
          – orome
          Feb 14 at 16:46




          $begingroup$
          It shows improvement now, but still shows (as you point out) artifacts that ruin it.
          $endgroup$
          – orome
          Feb 14 at 16:46


















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