On 09. april 2016 22:18, Carsten Arnholm wrote:

This restriction applied to AngelScript CSG as well, but it is easily
removed. An OpenSCAD trivial base case serves as an example:

module sph1() { translate([0,100,0])sphere(30); }
sph1();
mirror([1,1,0])sph1();

As the manual says, it "Mirrors the child element on a plane through the
origin". However, restricting the mirror plane to go through the origin
only is unnecessary.

A couple of AngelScript CSG snippets of the same case follow. First, the
same "OpenSCAD-style mirroring" around origin:

solid@ sph1 = translate(0,100,0)*sphere(30);
solid@ sph2 = mirror(1,1,0)*sph1;

second, same as above, just using explicit vector argument for the
mirror normal, the mirror plane point still defaults to origin:

solid@ sph2 = mirror(vec3d(1,1,0))*sph1;

third, same plane normal, but using mirror plane point different from
origin:

solid@ sph2 = mirror(vec3d(1,1,0),pos3d(100,100,0))*sph1;

The third case obviously gives a different result than the two first
cases, sph2 ends up at x=100,y=200. This is a useful and practical
scenario that I think isn't quite as easily expressed in OpenSCAD, so it
might be something to consider.

Carsten Arnholm

Carsten said: "Regarding mirror transformations, the more interesting thing
is that it unnecessarily restricted to perform mirroring only through the
origin. Mirroring through an arbitrary point is useful."

This is equally true for rotate, scale and shear transformations. If a
shape has its own local origin, then often you want to transform it
relative to its local origin.

In OpenSCAD, the standard idiom for transforming relative to a shape's
local origin is:
translate(origin) rotate(R) translate(-origin) shape

In OpenSCAD2, transformations will be values, so it will be possible to
encapsulate this idiom using a function:

at(origin,transform)(shape) =
translate(origin) transform translate(-origin) shape;

at(origin, rotate(R)) shape

On 9 April 2016 at 16:18, Carsten Arnholm arnholm@arnholm.org wrote:

On 10. april 2016 18:22, doug moen wrote:

For rotate, yes you must do that, if rotation around the shape local
origin is what you want, or if you want to rotate around some other point.

For a mirror plane through an arbitrary point, both the the location of
the mirror plane and the shape matters. The position specified with
mirror transformation isn't a local transformation origin though, it is
any point in the mirror plane, there are infinitely many such points for
the same transformation.

Using my previous example
solid@ sph1 = translate(0,100,0)*sphere(30);

The following gives identical mirror transformations, using different
points in the same mirror plane:
solid@ sph2 = mirror(vec3d(1,1,0),pos3d(100,100,0))*sph1;
solid@ sph3 = mirror(vec3d(1,1,0),pos3d(0,200,0))*sph1;
solid@ sph4 = mirror(vec3d(1,1,0),pos3d(-100,300,0))*sph1;

I am not quite sure how your OpenSCAD2 idiom will handle this case.
Perhaps it will work the same. Building it into the mirror
transformation directly is relatively straightforward and the standard
method I have encountered elsewhere, so it seems natural to me.

Carsten Arnholm

Yes, I understand why your interface to mirror() could be considered more
natural.

But it's still true that in OpenSCAD, you use
translate(origin) mirror(vec) translate(-origin) shape
to mirror a shape using a reflection plane passing through 'origin'. It
will often be the case that the 'origin' will be located relative to the
shape being reflected.

On 10 April 2016 at 14:23, Carsten Arnholm arnholm@arnholm.org wrote: