It is not a simple task to find whether a consistent winding is reversed or
not. The only way I have found was to compute the polyhedron volume by:

function polyhedron_volume(v,f) =
//  based on
https://iconline.ipleiria.pt/bitstream/10400.8/1433/1/artigo-7.pdf
let( crx = [for(fi=f, j=[1:1:len(fi)-2])
let( v0=v[fi[0]],
v1=v[fi[j]],
v2=v[fi[(j+1)%len(fi)]] )
(cross(v1-v0, v2-v0)*((v0+v1+v2).x)).x ] )
-sum(crx)/6;

where sum() computes the sum of the vectors in a list. If
polyhedron_volume() is negative, the winding is reversed. It works provided
the winding is consistent.

It seems that a consistent wrong orientation is being handled. At least if
you do a Boolean operation on a purple object and a regular one or on two
purple objects you don't get a CGAL error.

The only miracle is indeed that:
scale([1,1,-1])
cube(100);

like other regular (cylinder() or xxx_extrude()) objects aren't display
purple by F12. I guess that F12 just ignores them.

Ronaldo wrote

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On 2/20/2020 8:04 AM, Parkinbot wrote:

I built a cube with polyhedron() and mirrors and negative scales don't
turn it purple.  When I flip one of the faces, it's consistently purple
across the various reflections.

It seems like it would be easy enough to fix a polyhedron after an
arbitrary scale(); you'd just reverse the winding order of all of the
faces if there were an odd number of negative scales.

I expect that you could derive the same information from a
transformation matrix, but right now I'm not up to the math to do it.

I've reverted my change to the manual, restoring the "same direction" /
"prefers clockwise" version.

Did we ever get an authoritative resolution on the negative scale question?

A 4x4 transformation matrix includes some sort of mirroring if its
determinant is less than 0. If the determinant is zero, the
transformation is a projection on a lower dimension space and may or may
not include a mirroring. It seems that multmatrix doesn't computes the
matrix determinant or, at least, ignores if it is zero and does a
projection on a lower dimension space but considers it a 3D object!

multmatrix( [ [1,0,0,0], [1,0,0,0],[0,0,-1,0]]) cube(10);
square();

An exploit of the sign of the determinant of the multmatrix would be an
explanation.

JordanBrown wrote

the ultimate authority is always the compiler ;-)
another place to check is the source code ...

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On 2/20/2020 10:03 AM, Parkinbot wrote:

Not so much for "sometimes produces bad results" problems.  Better to
have somebody (or some documentation) that says "X is expected to work
and Y is expected to be unreliable".

Yeah, maybe, if you speak C++ and you understand how the 3D guts all
interact.

But, looking at it with my very marginal C++ knowledge, it sure looks
like all mirror() does is to set up a transformation matrix.

https://github.com/openscad/openscad/blob/master/src/transform.cc#L171

... which suggests that negative scale and the multmatrix equivalents
would be fine.

On 2/20/2020 2:51 PM, Parkinbot wrote:

Everybody seems to agree that negative scales are OK, so I removed that
note from the manual.