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

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more