MATLAB: Rotating 3D plots can produce reflections

3d plotcameraperspective

I am using a 3D plot to visualize the relationship among some vectors and an arc of points. The initial plot is as below. Note that the arc has a directionality to it, which is shown by labeling certain points in the sequence of arc points with increasing numbers 1,35,..137.
The thing that is puzzling me is that, when using the rotation tool on the figure toolbar
I find that I can re-orient the perspective so that it looks like the following
The second perspective appears not to be a rigid rotation of the first. Note that in the first version, the right-handed curl of the arc is around an axis aligned with the cyan v-Vector. Conversely, in the second version, the arc curls right-handedly around the negative of the v-vector. Additionally, in the first perspective, it appears that the triple product
   dot(cross(u,v),w)>0
is positive, whereas in the second perspective, it appears to be negative.
In light of these observations, it appears that points have been transformed by some sort of reflection, in addition to rotation. So my question is, is this a natural thing and is there a way to change the graphics properties so that the apparent relative orientation of vectors and points are preserved — as if all the graphics elements form a rigid body — when the rotation tool is used.

Best Answer

I think that's just an optical illusion because of the orthographic projection.
Here's what I get if I load them and add some perspective.
Initial - View = 126.2344, 82.6943
Rotated - View = -18.8486, -72.8486
As you can see, you've rotated around Z by about 180 degrees and then tipped the front up.
Related Question