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Graphing 2D circles in 3D

Posted 9 years ago

Hi all,

I imagine the solution to this is simple, though I've had a hell of a time figuring out what it is.

I'm just trying to plot an equation for a circle in 3D (arbitrarily oriented). I will ultimately be trying to plot more than one, and simple shapes in 3D. I am trying to avoid parameterizing, if possible. Any advice is appreciated! I am quite new to mathematica.

Thanks.

8 Replies

enter image description here

POSTED BY: Simon Cadrin

enter image description here

POSTED BY: Simon Cadrin

enter image description here

POSTED BY: Simon Cadrin

Thank you all for the suggestions. I actually just ended up parameterizing, though I've learned a lot from your input.

You can simulate a circle in 3D by a very thin cylinder. Use something like Cylinder[{x,y,z+.001,},{x,y,z}}.r]. You might then need to rotate it into the desired orientation.

POSTED BY: S M Blinder

The Presentations Application sold through my web site had Circle3D and Disk3D routines. These date back to about Mathematica 6 but still are convenient. One specifies the location, orientation and radius along with possible options.

<< Presentations`
$PlotTheme = "Classic";
Draw3DItems[
 {Opacity[0.8],
  {FaceForm[Lighter@Brown],
   Disk3D[{2, 2, 2}, {2, 0, 2}, 1, Mesh -> None],
   Thick,
   Circle3D[{2, 2, 2}, {2, 0, 2}, 1]},
  Circle3D[{0, 0, 0}, {0, 0, 1}, 2],
  Arrow3D[{0, 0, 0}, {0, 0, 1}, {0.3}],
  Arrow3D[{2, 2, 2}, {2, 2, 2} + Normalize[{2, 0, 2}], {0.3}]},
 NeutralLighting[0, 0.5, 0.1],
 NiceRotation,
 PlotRange -> All,
 Axes -> True,
 ImageSize -> 400]

enter image description here

Some non parametrized options:

DiscretizeRegion[TransformedRegion[Circle[], AffineTransform[{{1, 0}, {0, 1}, {0, 0}}]]]

Graphics3D[Point[Append[#, 0] & /@ CirclePoints[250]]]

Graphics3D[{FaceForm[], Polygon[Append[#, 0] & /@ CirclePoints[50]]}]

Graphics3D[BSplineCurve[Append[#, 0] & /@ CirclePoints[7], SplineClosed -> True]]
POSTED BY: Vitaliy Kaurov
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