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How do I show a cheese (segment) from a flattish 3D cylinder (or tube)

Ray Hill
Posted 11 years ago

For someone this is probably too simple! However I have spent hours trawling through documentation and examples to find my answer, without success.

So:

  1. Say I want to draw: cylinder[{{0,.1,0},{0,.4,0}} ,2] I then want to cut away or hide the whole volume from 2pi/6 to pi/6 and just leave the wedge showing.
  2. This is just one component of an engine in a far larger set, so whatever is done must not interfere with existing objects or later additions.
  3. I have also looked high and low to find find a way of doing simple things like drawing a solid hemisphere, so apart from plot regions etc which have global effects, so far zilch!

I sure wish there were slice object, twist object and taper object commands (I guess thats a progressive scale),the last one can in fact be done with tubes around BSplinecurves quite well but cannot find a way to do cuboids.

Many thanks in advance for any input.
POSTED BY: Ray Hill
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Ray Hill
Ray Hill
Posted 11 years ago

Thanks Sam, that got me a bit closer (file attached), now I need to work on turning that into a full 3D object which I can position with everything else, so I can rotate it as part of the whole Manipulation. I have started to fiddle further and found it incompatible with Graphics3D, so maybe I need a table that combines Graphics3D and RegionPlot commands. Well thats nearly half a day gone, thankfully I am now retired, if I was being paid to develop commercially at this rate I'd have been fired long ago ;(. I guess ideally if I could turn what you have given me into a 3D primitive I think I'd be there.

Am trying to get a similarity to the mass balances on this: http://en.wikipedia.org/wiki/Radial_engine#/media/File:TwinWaspConRods.jpg

Attachments:
POSTED BY: Ray Hill

Take a look at regions. Probably something like:

R = DiscretizeRegion[
  RegionProduct[
   DiscretizeRegion[Disk[{0, 0}, 1, {0 , 11 Pi/6}], 
    MaxCellMeasure -> .01], Line[{{0.}, {2.}}]]]
RegionPlot3D[R]

enter image description here
POSTED BY: Sam Carrettie
Ray Hill
Ray Hill
Posted 11 years ago

Gianluca, one thing can thing can you please point out where the radius is set, but very many thanks, I think you have just invented a new primitive, Wolfram should publish it in their code! You used some functions and techniques that I had never come across before.

I have parameterized it as follows: (* a cheesy wedge provided by Gianluca Gorni and parameterised by Ray \ Hill set z= height required, set startangle and endangle, interesting games \ when playing with zscale *)

wedge = Module[{k = 3, circ, n, twoCircs, cyl, z = 0.2, 
    startangle = Pi/3, endangle = Pi - Pi/3, zscale = 0}, 
   circ = Table[{Cos[t], Sin[t], zscale}, {t, startangle, endangle, 
      Pi/(6 k)}];
   n = Length[circ];
   twoCircs = Join[circ, Map[# + {0, 0, z} &, circ]];
   cyl = GraphicsComplex[twoCircs, 
     Polygon[Table[{m, m + 1, m + n + 1, m + n}, {m, n - 1}]], 
     VertexNormals -> twoCircs];
   N@{Polygon[Join[{{0, 0, 0}}, circ]], 
     Translate[
      Polygon[Join[{{0, 0, 0}}, circ]], {0, 0, z}], {EdgeForm[], cyl},
      Polygon[{circ[[1]], {0, 0, 0}, {0, 0, z}, 
       circ[[1]] + {0, 0, z}}], 
     Polygon[{circ[[-1]], {0, 0, 0}, {0, 0, z}, 
       circ[[-1]] + {0, 0, z}}]}];
Graphics3D[wedge]
POSTED BY: Ray Hill

You can do it with Graphics3D primitives this way:

myObject = Module[{k = 3, circ, n, twoCircs, cyl},
   circ = 
    Table[{Cos[t], Sin[t], 0}, {t, 2 Pi/6, 2 Pi + Pi/6, Pi/(6 k)}];
   n = Length[circ];
   twoCircs = Join[circ, Map[# + {0, 0, 2} &, circ]];
   cyl = GraphicsComplex[twoCircs, 
     Polygon[Table[{m, m + 1, m + n + 1, m + n}, {m, n - 1}]], 
     VertexNormals -> twoCircs];
   N@{Polygon[Join[{{0, 0, 0}}, circ]], 
     Translate[Polygon[Join[{{0, 0, 0}}, circ]], {0, 0, 2}],
     {EdgeForm[], cyl}, 
     Polygon[{circ[[1]], {0, 0, 0}, {0, 0, 2}, 
       circ[[1]] + {0, 0, 2}}], 
     Polygon[{circ[[-1]], {0, 0, 0}, {0, 0, 2}, 
       circ[[-1]] + {0, 0, 2}}]}];
Graphics3D[myObject]

You can apply geometric transformations to it.
POSTED BY: Gianluca Gorni

Nice animation! I am glad that I could help.
POSTED BY: Gianluca Gorni
Ray Hill
Ray Hill
Posted 11 years ago

Very many thanks Gianluca. I probably would not have got this far without your help.

I have now got what I need, it'll now just take some fine tuning of positions to drop it into my larger model.

wedge1[turnit_] := With[{\[Theta] = turnit},
   (* Set radius, z for thickness and startangle and endangles, 
   extendfactor creates a coneshell, 
   or part of*){Gray, 
    Rotate[Translate[
      Rotate[Module[{radius = 1, k = 3, circ, n, twoCircs, cyl, 
         extendfactor = 0, z = .2, startangle = Pi/4, 
         endangle = 3 Pi/4}, 
        circ = Table[{radius Cos[t], radius Sin[t], 
           extendfactor}, {t, startangle, endangle, Pi/(6 k)}];

        (* Outside face *)
        n = Length[circ];
        twoCircs = Join[circ, Map[# + {0, 0, z} &, circ]];
        cyl = 
         GraphicsComplex[twoCircs, 
          Polygon[Table[{m, m + 1, m + n + 1, m + n}, {m, n - 1}]], 
          VertexNormals -> twoCircs];
        N@{Polygon[Join[{{0, 0, 0}}, circ]], 
          Translate[
           Polygon[Join[{{0, 0, 0}}, circ]], {0, 0, z}], {EdgeForm[], 
           cyl},

          (* Inside faces*)

          Polygon[{circ[[1]], {0, 0, 0}, {0, 0, z}, 
            circ[[1]] + {0, 0, z}}], 
          Polygon[{circ[[-1]], {0, 0, 0}, {0, 0, z}, 
            circ[[-1]] + {0, 0, z}}]}], Pi/2, {1, 0, 0}], {0, -1.5, 
       0.5}], \[Theta], {0, 1, 0}]}];

wedge2[turnit_] := With[{\[Theta] = turnit},
   (* Set radius, z for thickness and startangle and endangles, 
   extendfactor creates a coneshell, or part of*)
   {Gray,
    Rotate[
     Translate[
      Rotate[Module[{radius = 1, k = 3, circ, n, twoCircs, cyl, 
         extendfactor = 0, z = .2, startangle = Pi/4, 
         endangle = 3 Pi/4}, 
        circ = Table[{radius Cos[t], radius Sin[t], 
           extendfactor}, {t, startangle, endangle, Pi/(6 k)}];

        (* Outside face *)
        n = Length[circ];
        twoCircs = Join[circ, Map[# + {0, 0, z} &, circ]];
        cyl = 
         GraphicsComplex[twoCircs, 
          Polygon[Table[{m, m + 1, m + n + 1, m + n}, {m, n - 1}]], 
          VertexNormals -> twoCircs];
        N@{Gray, Polygon[Join[{{0, 0, 0}}, circ]], 
          Translate[
           Polygon[Join[{{0, 0, 0}}, circ]], {0, 0, z}], {EdgeForm[], 
           cyl},

          (* Inside faces*)


          Polygon[{circ[[1]], {0, 0, 0}, {0, 0, z}, 
            circ[[1]] + {0, 0, z}}], 
          Polygon[{circ[[-1]], {0, 0, 0}, {0, 0, z}, 
            circ[[-1]] + {0, 0, z}}]}], -Pi/2, {1, 0, 
        0}], {0, .3, -.5}], \[Theta], {0, 1, 0}]}];

rods[turnit_] := With[{\[Theta] = turnit}, 
   Rotate[
    {{Gray, Cuboid[{-.1, -1.5, -.2}, {.1, -1.7, 1}]},
     {Gray, Cuboid[{-.1, .3, .2}, {.1, .5, -1}]}}, \[Theta], {0, 1, 
     0}]];

shaft = {Gray, Cylinder[{{0, -1.8, 0}, {0, .6, 0}}, .1]};

(end of initialisation cell )

Manipulate[
 Graphics3D[{wedge1[turnit], wedge2[turnit], rods[turnit], shaft}, 
  Axes -> True, AxesLabel -> {"x", "y", "z"}, 
  PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}, {-2.5, 2.5}}], {{turnit, 0, 
   "run engine"}, 0, 2 \[Pi], .01, ControlType -> Animator, 
  AnimationRunning -> False}]

File attached

Attachments:
POSTED BY: Ray Hill

The radius is implicitly set to 1 in the definition of circ. You can set it to any value r with

circ = Table[{r Cos[t], r Sin[t], zscale}, {t, startangle, endangle, 
      Pi/(6 k)}]
POSTED BY: Gianluca Gorni
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