I wrote a routine to make round-edged holes in cylindrical shells.  For
example:

http://forum.openscad.org/file/t2477/ehole.png

It seems to work a lot of the time.  The above example renders without a
hitch.  But I have a mystery that sometimes I get a CGAL error.  What I
don't understand is that if I render the mask (the thing that I cut away to
make the hole) then CGAL issues no error and everything appears OK.  (The
mask is a union of two objects and I have also got a cube in there for good
measure, so CGAL is activated.)  The case I was really interested in was to
create a slot in a cylinder, so here is the mask, which renders OK:

http://forum.openscad.org/file/t2477/hmask.png

No CGAL error yet.  But when I difference it from the cylindrical shell as
follows, I get a CGAL error below.  I wonder about the "non coplanar faces".
I didn't think my model had any such thing.

Rendering Polygon Mesh using CGAL...
PolySet has nonplanar faces. Attempting alternate construction
ERROR: CGAL error in CGALUtils::applyBinaryOperator difference: CGAL ERROR:
assertion violation! Expr: itl != it->second.end() File:
/mxe/usr/x86_64-w64-mingw32.static.posix/include/CGAL/Nef_3/SNC_external_structure.h
Line: 1152
Geometries in cache: 19
Geometry cache size in bytes: 2719400
CGAL Polyhedrons in cache: 3
CGAL cache size in bytes: 43133288
Total rendering time: 0 hours, 1 minutes, 52 seconds
Top level object is a 3D object:
Simple: yes
Vertices: 264
Halfedges: 792
Edges: 396
Halffacets: 272
Facets: 136
Volumes: 3
Rendering finished.

Preview looks like this:

http://forum.openscad.org/file/t2477/cslot.png

So why can I take two valid objects, take their difference and the result is
invalid?  Under what circumstances can this occur?

Code that produces the examples:

include<BOSL2/std.scad>
include<BOSL2/skin.scad>

$fn=64;//4;//128;

function cylhole(r, path, offset=0) =
[for(point=path)
cylindrical_to_xyz(concat([r+offset],xscale(360/(2PIr),p=point)))];

// r is center radius of cylindrical shell, thickness is shell thickness,
path is path for hole to cut (2d)
module cylholemask(r,thickness,path)
{
cutout = cylhole(r,path);
cutout_tangent = path_tangents(cutout);
cutout_normal = [for(i=idx(cutout)) cross(cutout_tangent[i], [cutout[i].x,
cutout[i].y,0])];
minangle = min(subindex(path,0))360/(2PIr);
maxangle = max(subindex(path,0))360/(2PIr);

innerplane1 = plane_from_points(
[(r-thickness/2)[cos(minangle), sin(minangle),0],
(r-thickness/2)[cos(minangle), sin(minangle),1],
(r-thickness/2)*[cos(maxangle), sin(maxangle),0]]);
outerplane = concat(select(innerplane1,0,2), [r+thickness]);
innerplane = concat(select(innerplane1,0,2), [innerplane1[3]-thickness]);

farpts = scale([1.1,1.1,1],p=cutout);

inner = [for(i=idx(cutout)) plane_line_intersection(innerplane,
[farpts[i],cutout[i]])];
outer = [for(i=idx(cutout)) plane_line_intersection(outerplane,
[farpts[i],cutout[i]])];

skin([inner, outer], slices=0,convexity=10);
path_sweep((cmask(thickness/2)), cutout, closed=true, method="manual",
normal=cutout_normal);
}

function cmask(r) =
let(eps=0.1)
fwd(r+.01,p=
[
[r+eps,0],
each arc(r=r, angle=[0, 180]),
[-r-eps,0],
[-r-eps, r+eps],
[r+eps, r+eps]
]);

slot=reverse(turtle(["move",4,"arcleft", .5, "move", 5, "arcright", 1,
"arcleft", .5,180, "move", 3+4,
"arcleft", .5, 180, "arcright", 1, "move", 5,
"arcleft",.5]));

difference(){
up(1.25)cyl(r=10.5, h=10);
up(1.25)cyl(r=9.5, h=11);
cylholemask(10,1.05, subdivide_path(simplify_path(slot),475,exact=false));
// This fails
//  cylholemask(10, 1.05, apply(xscale(3),circle(r=3, $fn=128)));    // This
works
}

right(75)cube([1,1,1]);

--
Sent from: http://forum.openscad.org/

The problem of CGAL objecting to my model doesn't seem to be specifically
correlated to the non-coplanar faces that it notes.  I changed the model a
bit and that went away.  I also tried explicitly triangulating the only
faces that aren't triangles.  (Note that these faces were constructed by
intersecting lines with a plane, so they can't be non-coplanar.)  None of
this fixed anything.

It seems like the issue of rounding gets raised repeatedly as an explanation
for CGAL errors, generally in situations where it is not relevant.  I did
finally encounter this, so it does actually happen.  It happens in one of
my models when points are closer together in my model than 1.3e-6.  The
model above has a modest spacing of facets and shouldn't have any points so
close together.  (And yes, if I increase the points to larger than 1.3e-6,
like say 1.4e-6 then the CGAL error in that case vanishes.)

I'm kind of puzzled about when/how CGAL decides to examine my shape, though.
I tried unioning my mask shape with a cube and got the CGAL error.  But my
mask shape is already the union of two shapes that overlap each other.  Why
doesn't this trigger a CGAL evaluation and the error?  Why do I have to
separately union with a cube to get the error?  In any case, this produces a
better explanation of what is going wrong: something is somehow amiss with
the polyhedron that defines my roundover.  The other shape (which cuts the
hole) doesn't seem to produce the error when unioned with a cube.

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