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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: 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. 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. 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

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

Sam Carrettie

Sam Carrettie, Freelancer

Posted 11 years ago

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]

POSTED BY: Sam Carrettie

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]

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

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 11 years ago

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.

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

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 11 years ago

POSTED BY: Gianluca Gorni

Ray Hill

Posted 11 years ago

Attachments:

POSTED BY: Ray Hill

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 11 years ago

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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