Skip to main content

graphics3d - Is there a way to increase the smoothness of a cylinder?


I am using Cylinder to produce wide flat disks (in Mathematica 8). This works just fine except that the circular base of such a cylinder turns out to be really just a 40-gon which is simply too coarse an approximation to a circle for what I have in mind. Is there a way to convince Mathematica to use say a 200-gon as a circular base for a cylinder?


Here is an example of the kind of picture that I am trying to create. Zoom in to see how coarse the cylinders' curved surfaces pan out.


Graphics3D[{Cylinder[{{0, 0, 0}, 0.0011 {0.`, 0.`, -0.9510565162951536`}}, .1], 
  Cylinder[{{0, 0, 0}, 0.0011 {0.`, 0.`, 0.9510565162951536`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.85065080835204`, 0.`, -0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 

    0.0011 {0.85065080835204`, 0.`, 0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.6881909602355868`, -0.5`, -0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.6881909602355868`, 0.5`, -0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.6881909602355868`, -0.5`, 0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.6881909602355868`, 0.5`, 0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 

    0.0011 {-0.2628655560595668`, -0.8090169943749475`, \
-0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.2628655560595668`, 
      0.8090169943749475`, -0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.2628655560595668`, -0.8090169943749475`, 
      0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.2628655560595668`, 0.8090169943749475`, 

      0.42532540417601994`}}, .1], 
  Cylinder[{{0, 0, 0}, 0.0011 {0.`, 0.`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 0.0011 {0.`, 0.`, 1.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.42532540417602`, 0.3090169943749474`, 
      0.8506508083520399`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.7236067977499789`, 0.5257311121191336`, 
      0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 

    0.0011 {0.16245984811645317`, 0.5`, 0.8506508083520399`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.2628655560595668`, 0.8090169943749473`, 
      0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.27639320225002106`, 0.8506508083520399`, 
      0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.42532540417602`, -0.3090169943749474`, 
      0.8506508083520399`}}, .1], 

  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.7236067977499789`, -0.5257311121191336`, 
      0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.85065080835204`, 0.`, 0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.16245984811645317`, -0.5`, 0.8506508083520399`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.27639320225002106`, -0.8506508083520399`, 
      0.4472135954999579`}}, .1], 

  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.2628655560595668`, -0.8090169943749473`, 
      0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.5257311121191336`, 0.`, 0.8506508083520399`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.8944271909999159`, 0.`, 0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.6881909602355868`, -0.5`, 0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 

    0.0011 {0.6881909602355868`, 0.5`, 0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.7236067977499789`, -0.5257311121191336`, \
-0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.42532540417602`, -0.3090169943749474`, \
-0.8506508083520399`}}, .1], 
  Cylinder[{{0, 0, 0}, 0.0011 {0.`, 0.`, -1.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.2628655560595668`, -0.8090169943749473`, \

-0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.16245984811645317`, -0.5`, -0.8506508083520399`}}, .1],
   Cylinder[{{0, 0, 0}, 
    0.0011 {-0.27639320225002106`, -0.8506508083520399`, \
-0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.7236067977499789`, 
      0.5257311121191336`, -0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 

    0.0011 {0.42532540417602`, 
      0.3090169943749474`, -0.8506508083520399`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.85065080835204`, 0.`, -0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.27639320225002106`, 
      0.8506508083520399`, -0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.16245984811645317`, 0.5`, -0.8506508083520399`}}, .1], 
  Cylinder[{{0, 0, 0}, 

    0.0011 {0.2628655560595668`, 
      0.8090169943749473`, -0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.8944271909999159`, 0.`, -0.4472135954999579`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.5257311121191336`, 0.`, -0.8506508083520399`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.6881909602355868`, 0.5`, -0.5257311121191336`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.6881909602355868`, -0.5`, -0.5257311121191336`}}, .1], 

  Cylinder[{{0, 0, 0}, 0.0011 {0.`, 1.`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.5877852522924731`, 0.8090169943749473`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.9510565162951535`, 0.3090169943749474`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.9510565162951535`, -0.3090169943749474`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {-0.5877852522924731`, -0.8090169943749473`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 0.0011 {0.`, -1.`, 0.`}}, .1], 

  Cylinder[{{0, 0, 0}, 
    0.0011 {0.5877852522924731`, -0.8090169943749473`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.9510565162951535`, -0.3090169943749474`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.9510565162951535`, 0.3090169943749474`, 0.`}}, .1], 
  Cylinder[{{0, 0, 0}, 
    0.0011 {0.5877852522924731`, 0.8090169943749473`, 0.`}}, .1]}]

Answer



You can fix this problem by using the following Option in Graphics3D:



Method -> {"CylinderPoints" -> {200, 1}}

Adjust 200 to match your requirements. (Indeed the default is 40.)


Edit: I don't know exactly what the second parameter does, but using the single parameter form shown in the documentation linked below results in a big slow-down. I could guess that it is points in the other direction but that doesn't seem to make sense. Anyway I can't tell the visual difference between {200, 1} and {200, 200} but the former is much faster than the latter. ("CylinderPoints" -> 200 is apparently equivalent to "CylinderPoints" -> {200, 200}.)


You can make the change permanent with the Option Inspector by changing this value in the Graphics3DBoxOptions:


enter image description here


From Three-Dimensional Graphics Primitives:



Even though Cone, Cylinder, Sphere, and Tube produce high-quality renderings, their usage is scalable. A single image can contain thousands of these primitives. When rendering so many primitives, you can increase the efficiency of rendering by using special options to change the number of points used by default to render Cone, Cylinder, Sphere, and Tube. The "ConePoints" Method option to Graphics3D is used to reduce the rendering quality of each individual cone. Cylinder, sphere, and tube quality can be similarly adjusted using "CylinderPoints", "SpherePoints", and "TubePoints", respectively.




40 points:


enter image description here


200 points:


enter image description here


Comments

Post a Comment

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more