Rotating 3D plots can produce reflections?

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.

[Matt J]

I've attached each of the figures as .fig files, in case anyone wants to try to reproduce the effect.

Answer 1

[Mike Garrity]

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.

[Matt J]

Hi Mike,

Can you tell me what you did to "add some perspective"?

[Mike Garrity]

You just do this:

set(gca,'Projection','perspective')

In those pictures, I exaggerated by increasing the CameraViewAngle.

surf(peaks)
ax = gca;
cp = ax.CameraPosition;
ct = ax.CameraTarget;
ax.Projection = 'perspective';
ax.CameraViewAngle = 45;
ax.CameraPosition = ct + .25*(cp - ct);

But it's easy to get carried away with that.

ax.CameraViewAngle = 120;
ax.CameraPosition = ct + .0625*(cp - ct);

[Matt J]

Thanks, Mike.

The other part of my question, though, was how to systematically avoid such perspective illusions, so that I can tell the spatial relationships between the objects as if actually viewing them in 3D space. Not sure if you had any suggestions for that. One method I found was to insert an arrow into the inside of the arc, showing the sense of its curl,

Now, when I tilt the plot upward, I can still tell, because of the opaqueness of the arc point markers that the arc is in the foreground and that the red arrow is in the background. Thus, there's no confusion about which way the arc curls.

[Mike Garrity]

Yes, that's a good idea. Most computer graphics textbooks will include some asymmetric object in the scene to provide this sort of help.

Another option is to have something opaque with a standard color pattern. For example, a cube with a different color on each face. After a while, you learn the colors and know which side you're looking at. That generally doesn't help other people much though.