# Manipulate Cuboid for Rotation

Using the example code from the cuboid:

Graphics3D[{Opacity[0.3], EdgeForm[],Table[{ColorData["Rainbow"][Rescale[c, {0, 2 Pi}]],GeometricTransformation[Cuboid[],RotationTransform[c, {-1, 2, -3},{1.5, 0, 0}]]}, {c, 0, 2 Pi, 2 Pi/12}]}]


I'm trying to manipulate it so it shows one image after the other. I changed it in this way:

Manipulate[Graphics3D[{Opacity[0.3],EdgeForm[], {ColorData["Rainbow"][Rescale[a, {0, 2 Pi}]],GeometricTransformation[Cuboid[],RotationTransform[a, {-1, 2, -3}, {1.5, 0, 0}]]}}], {a, 0, 2 Pi}]


But that doesn't keep the same scale, I wanted to show one cube at a time but in the way displayed in the first code.

Here's a simple trick that does what you want. We can include a transparent sphere in our scene that is large enough that MMA does not zoom in on each successive the cuboid. We can do that by adding Opacity[0],Sphere[center,radius] to our list of graphics directives, but what center and what radius should we use?

A check of the documentation for RotationTransformation shows that the rotation is about an axis through the anchor point {1.5,0,0}, so we can use that as our center. How big should the sphere be? Maybe a 1.5 radius, maybe a little bigger. We don't want to make it too big.

A little experimentation gives the following code with a radius of 2, which seems to work well.

Manipulate[Graphics3D[{
Opacity[0.03], Sphere[{1.5, 0, 0}, 2],
Opacity[0.3], EdgeForm[], {
ColorData["Rainbow"][Rescale[a, {0, 2 Pi}]],
GeometricTransformation[Cuboid[],
RotationTransform[a, {-1, 2, -3}, {1.5, 0, 0}]]
}}],
{a, 0, 2 Pi}]


Your Manipulate works pretty good. In the above, the sphere shows faintly, just so we can see it. Change its opacity to zero for complete transparency.

• What a simple solution! Worked perfectly, thank you! – Joseph Dec 6 '16 at 22:21