How does "mirror" symmetry really work?

[allmhuran]

In general, creating a mirror image of something cannot be done by a rotation. Mirror symmetry really means pulling something "inside out" through the mirror. There's no way to rotate your left hand to make it match your right hand.

However, there is an exception to this rule. If the object is already symmetrical, then you can rotate it to produce a "mirrored" copy. But then way you need to rotate it depends on which way it is oriented.

And there is a third possibility: if the part's plane of mirror symmetry is the same as the plane by which you are trying to mirror it, then you need to translate (not rotate) the part along the axis through that plane.

In the image below, you will see an example of this. The cockpit geometry (but not the texture!) is itself symmetrical: In its "natural" orientation You can cut it vertically lengthwise down the middle and produce two halves that are the same. So we can in fact produce a "mirrored" copy in the construction facility by performing the appropriate rotatin or translation.

Note: in principle, the game could theoretically create a true mirror. It could examine the model and textures and invert all of the coordinates along the axis through the desired symmetry plane, effectively creating a "new" (virtual) part. But the game doesn't appear to be doing this, because note how the cockpit door texture is not, in fact, mirrored. The part has been rotated.

But how does the game figure out which way to do the rotation? It depends on where the plane of symmetry of original shape is in its natural orientation, as well as depending on how I have subsequently rotated it before placing it onto the craft.

The reason why I ask is because I am making some custom "welded" parts, and ideally I would like to make them so that the game can correctly place them with mirror symmetry. But at the moment some of the parts end up being rotated the wrong way. Is there something in a part config file that can be set to tell the game what the "natural" plane of symmetry is (if any)?

Edited February 24, 2016 by allmhuran

[Crzyrndm]

https://github.com/Crzyrndm/B9-PWings-Fork/blob/master/GameData/B9_Aerospace_ProceduralWings/Parts/Aero_Wing_Procedural/wing_procedural_typeA.cfg#L42

Basically, a unit vector that tells KSP which axis to rotate the model around (and in this case, to turn it inside out by applying a negative scale factor)

[AlextheBodacious]

Something about how its plane is, as the part is going left/right relative to itself.

P.S. Here's the image OP's showing

Edited February 24, 2016 by AlextheBodacious

[allmhuran]

7 hours ago, Crzyrndm said:

https://github.com/Crzyrndm/B9-PWings-Fork/blob/master/GameData/B9_Aerospace_ProceduralWings/Parts/Aero_Wing_Procedural/wing_procedural_typeA.cfg#L42

Basically, a unit vector that tells KSP which axis to rotate the model around (and in this case, to turn it inside out by applying a negative scale factor)

Thanks very much, perfect answer and exactly the kind of thing I was expecting. I don't think I've ever seen that line in a config file I was playing with, perhaps because the welding mod drops it out! Super useful info!

[Crzyrndm]

That'd probably be because most parts can just use the default one (which I can't remember off the top of my head)