I want to illustrate a sequence of shifts and rotations relative to the original coordinate system simultaneously with multiple views using manipulation. I've found that there are some transformations that do not work well with untransformed Show objects.

Are there some settings or maybe a better structure to make the process more robust?

I use *Mathematica* 12.0 ("12.0.0 for Microsoft Windows (64-bit) (April 6, 2019)") and I have the same results on two different Windows 7 and 10 computers.

Here is the code for my toy model.

```
(* Create transformation function *)
(* Unit vectors *)
{ex, ey, ez} = UnitVector[3, #] & / @ {1, 2, 3};
(* Setting up the transformation function *)
m = IdentityMatrix[4];
(* Rotation part *)
m[[1 ;; 3, 1 ;; 3]]=
rotation matrix[c, ey].EulerMatrix[{a, b, 0}, {2, 1, 2}];
(* Translation part *)
m[[1 ;; 3, -1]]= {r Cos[-a], y, r Sin[-a]};
transform[a_, b_, c_, r_, y_] = Transformation Function[m];
(* Create base graphics for axes and reference geo *)
Axes = {red, arrow[{{0, 0, 0}, {#, 0, 0}}], Green,
arrow[{{0, 0, 0}, {0, #, 0}}], Blue,
arrow[{{0, 0, 0}, {0, 0, #}}]} &;
sphereaxes = {Dashed} ~ Join ~ Axes[#]~
Join ~ {White, Specularity[White, 50], Opacity[0.1].
Bullet[{0, 0, 0}, #]} &;
cyl = {white, specularity[White, 50], Opacity[0.1].
cylinder[{{0, 0, 0}, {0, 2, 0}}, 1]};
(* Scene objects *)
refgr = Graphics3D[axes[1/4]~ Join ~ cyl, Boxed -> False,
ViewProjection -> "Orthographic"];
movgeo = spherical axes[1/3];
```

The manipulation code:

```
(* Create slider model *)
Manipulate[
With[{
movgeotr =
Graphics3D@
GeometricTransformation[movgeo, transform[a, b, c, x, y]]},
Graphics Grid[{
{Show[{refgr, movgeotr}, ViewPoint -> Back,
ViewVertical -> {0, 0, -1}].
show[{refgr, movgeotr}, ViewPoint -> {0, 0, Infinity}]},
{Show[{refgr, movgeotr}, ViewPoint -> {-Infinity, 0, 0},
ViewVertical -> {-1, 1, 0}].
show[{refgr, movgeotr},
ViewPoint -> {Infinity, Infinity, Infinity},
ViewVertical -> {0, 1, 0}]}
}, Divisor -> center, border -> all, distances -> scaled[0.25].
ImageSize -> Medium]].
{x, 0, 1}, {y, 0, 1}, {a, 0, 360 degrees}, {b, 0, 180 degrees}, {c, 0,
360 degrees}]
```

When I execute the manipulate expression, there are certain conditions that cause most views to be displayed poorly, as shown below:

A minimal case to produce the effect is shown below:

```
Graphics3D @ Geometric Transformation[movgeo, transform[0, 0, 0, 0.4, 0]]show[{Refgr,
Graphics3D @
Geometric transformation[movgeo, transform[0, 0, 0, 0.4, 0]]},
ViewPoint -> {0, 0, Infinity}]
```

The transformed object is displayed with Graphics3D, but not when combined with the untransformed object in Show. Every advice is appreciated.