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Use ParametricPlot3D to plot a general circular cylinder?

Mohammad Amir Khan

Mohammad Amir Khan, Retired

Posted 7 years ago

Hello everyone, How do I parametrise and use ParametricPlot3D to plot a general circular cylinder with general as axis and radius R?

POSTED BY: Mohammad Amir Khan

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Christopher Young

Christopher Young, CYInsight

Posted 6 years ago

Attachments: Plotting cylinde...nb

POSTED BY: Christopher Young

John Guenther

Posted 6 years ago

There seems to be an easier answer. ParametricPlot3D[{Cos[u], Sin[u], t}, {u, 0, 2 Pi}, {t,0,5}] (has radius of 1} ParametricPlot3D[{2Cos[u], 2Sin[u], t}, {u, 0, 2 Pi}, {t,0,5}] (has radius of 2} It shouldn't be to hard (I think) to figure our how to do Cylinders with different orientations.

POSTED BY: John Guenther

Hans Milton

Posted 7 years ago

Another variant of getting the coordinate axes: getMatrix[axis_ /; Norm[axis] != 0] := Module[ {v2, v3}, v2 = {x, y, z} /. First@FindInstance[ Dot[axis, {x, y, z}] == 0 && Norm@{x, y, z} != 0, {x, y, z}, Reals ]; v3 = Cross[axis, v2]; Normalize /@ {axis, v2, v3} ]

Another variant of getting the coordinate axes:

getMatrix[axis_ /; Norm[axis] != 0] := Module[
    {v2, v3},
    v2 = {x, y, z} /. First@FindInstance[
        Dot[axis, {x, y, z}] == 0 && Norm@{x, y, z} != 0, {x, y, z}, Reals
    ];
    v3 = Cross[axis, v2];
    Normalize /@ {axis, v2, v3}
]

POSTED BY: Hans Milton

John McGee

John McGee, Wolfram Research

Posted 7 years ago

POSTED BY: John McGee

John McGee

John McGee, Wolfram Research

Posted 7 years ago

The problem is with my oversimplified Orthogonalize. The other two vectors should be nearly perpendicular to "axis", as in Orthogonalize[{1,10,0},{0,1,0},{0,0,1}].

POSTED BY: John McGee

John McGee

John McGee, Wolfram Research

Posted 7 years ago

Given an axis vector "axis" and a radius "r". You first need to construct an orthonormal set of coordinate axes. {vz, vx, vy} = Chop@Orthogonalize[{axis, {1, 0, 0}, {0, 1, 0}}] Now, given a base point "b" and a height "h" the plot can be constructed with: Show[ParametricPlot3D[b+zvz+rCos[\[Theta]]vx+rSin[\[Theta]]vy,{z,0,h},{\[Theta],0,2\[Pi]},PlotStyle->Directive[Opacity[0.7],Orange]], Graphics3D[{Blue,PointSize[0.02],Point[b],Arrow[{b,b+hvz}], Magenta,Arrow[{b,b+rvx}],Green,Arrow[{b,b+rvy]}]] This will also show the cylinder axis in blue, with the other two axes in Magenta and Green.

Given an axis vector "axis" and a radius "r". You first need to construct an orthonormal set of coordinate axes.

{vz, vx, vy} = Chop@Orthogonalize[{axis, {1, 0, 0}, {0, 1, 0}}]

Now, given a base point "b" and a height "h" the plot can be constructed with:

Show[ParametricPlot3D[b+z*vz+r*Cos[\[Theta]]*vx+r*Sin[\[Theta]]*vy,{z,0,h},{\[Theta],0,2\[Pi]},PlotStyle->Directive[Opacity[0.7],Orange]],
Graphics3D[{Blue,PointSize[0.02],Point[b],Arrow[{b,b+h*vz}], Magenta,Arrow[{b,b+r*vx}],Green,Arrow[{b,b+r*vy]}]]

This will also show the cylinder axis in blue, with the other two axes in Magenta and Green.

POSTED BY: John McGee

Mohammad Amir Khan

Mohammad Amir Khan, Retired

Posted 7 years ago

Thank you so much John McGee. When I use the axis as {1,10,0) , the base point as {0,0,1} and h=5 I get a blank plot. What could be he reason?

POSTED BY: Mohammad Amir Khan

Christopher Young

Christopher Young, CYInsight

Posted 6 years ago

Are you sure you made the coordinate box big enough? I get a cylinder that's cut off by the plot boundary. But I think that John McGee's method just using Orthogonalize[ ] should work as long as the axis and the other two vectors are linearly independent. Otherwise, you'd have to choose different 2nd and 3rd vectors. Attachments: Plotting cylinde...nb