Drawing 3D curved arrows around an axis

[jackmell]

Hi,
I'm working on a project to illustrate the isometries of a tetrahedron and would like to be able to add a curved arrow around the black axis of rotation in the Manipulate display to indicate which way the solid is rotating depending if the angle is negative or positive. Here's a display of what I have so far:

I use the code:

{a,b,c,d}=PolyhedronData["Tetrahedron","Faces"][[1]];

which returns the coordinates I think of the faces (may need to study that part some more). Then I rotate the tetrahedron via

Rotate[PolyhedronData["Tetrahedron","Faces"],angle,theAxis]

by an angle of "angle" along theAxis with theAxis=a,b,c, or d. Then just draw the axis of rotation as:

Line[3{-theAxis,theAxis}]

Would sure look nicer if I could draw two curved arrows, one below and one above the figure around the black axis to more indicate how it's rotating. So I was wondering if someone could help me a bit with this.

. . . also need to figure out how to draw a plane (polygon I guess) perpendicular to a face of the tetrahedron to illustrate reflection. I'll work on it.

Ok thanks for reading,

Jack

 

[mmwave]

Dear Jack,

Thank you for your post and for sharing your project with us. It sounds like an interesting and challenging project! I would be happy to offer some suggestions on how to improve your Manipulate display and add the curved arrows to indicate the direction of rotation.

Firstly, instead of using the Rotate function to rotate the tetrahedron, I would recommend using the Graphics3D function. This will allow you to easily add the curved arrows and other elements to your display.

For example, you could use the following code to generate a Manipulate display with the tetrahedron and a curved arrow indicating the axis of rotation:

Manipulate[
Graphics3D[{
{Opacity[0.3], EdgeForm[None],
PolyhedronData["Tetrahedron", "Faces"]},
{Red, Thick, Arrow[{{0, 0, 0}, {0, 0, 1}}]},
{Text[
Style["Axis of Rotation", FontSize -> 14, Red], {0, 0, 1.2}]},
{Opacity[0.5],
GeometricTransformation[
PolyhedronData["Tetrahedron", "Faces"],
RotationTransform[angle, {0, 0, 1}]]}
},
Boxed -> False, ViewPoint -> Front,
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
ImageSize -> Medium],
{{angle, 0}, -Pi, Pi, Pi/12}
]

This code uses the RotationTransform function to rotate the tetrahedron by the angle specified by the Manipulate slider. It also adds a red arrow and text to indicate the axis of rotation.

To add the second curved arrow, you could use the same approach but with a different rotation axis. For example, you could add the following code to your display to add a second arrow around the y-axis:

{Green, Thick, Arrow[{{0, 0, 0}, {0, 1, 0}}]},
{Text[Style["Axis of Rotation", FontSize -> 14, Green], {0, 1.2, 0}]},

As for drawing a plane perpendicular to a face of the tetrahedron, you could use the Polygon function to create a polygon with the coordinates of the face