Function Repository Resource:

Circle3D

Source Notebook

Represent a circle in 3D

Contributed by: Erik Mahieu

ResourceFunction["Circle3D"][]

represents a circle in 3D of radius 1, centered at the origin and perpendicular to the x-axis.

ResourceFunction["Circle3D"][{r_y,r_z}]

represents an ellipse in 3D with semiaxes lengths r_y and r_z, centered at the origin and perpendicular to the x-axis.

ResourceFunction["Circle3D"][{x,y,z},{r_y,r_z},ψ,ζ]

represents a circle in 3D with semiaxes lengths r_y and r_z, centered at {x,y,z} and rotated by angles ψ and ζ around 3D vectors parallel to y- and z-axes respectively.

Details and Options

ResourceFunction["Circle3D"] can be used as a 3D graphics primitive and be used in Graphics3D.

ResourceFunction["Circle3D"] takes the Line-primitives generated by the ellipse ParametricPlot3D[{0,aSin[t],bCos[t]},{t,-π,π}], translates and rotates them as specified by the function’s parameters {x,y,z},ψ,ζ.

Examples

Basic Examples (2)

A unit circle in 3D:

In[1]:=

Out[1]=

An ellipse in 3D:

In[2]:=

Out[2]=

Scope (1)

We can use a Manipulate to explore all the parameters of the function Circle3D:

In[3]:=

$Manipulate[ Graphics3D[{Red, Thickness[.01], ResourceFunction["Circle3D"][{x, y, z}, {a, b}, \[Psi], \[Zeta]]}, Axes -> True, PlotRange -> 2, ImageSize -> Small], {{a, 1.5, "semi-major axis"}, .1, 2, ImageSize -> Tiny}, {{b, 1, "semi-minor axis"}, .1, 2, ImageSize -> Tiny}, {{\[Psi], 0, "y-axis rotation"}, -\[Pi], \[Pi], ImageSize -> Tiny}, {{\[Zeta], 0, "z-axis rotation"}, -\[Pi], \[Pi], ImageSize -> Tiny}, {{x, 0, Subscript["x", "center"]}, -1, 1, ImageSize -> Tiny}, {{y, 0, Subscript["y", "center"]}, -1, 1, ImageSize -> Tiny}, {{z, 0, Subscript["z", "center"]}, -1, 1, ImageSize -> Tiny}, ControlPlacement -> Left]$