

Here's something I'm having trouble understanding, if someone can help
me understand I'd be very appreciative.
Here's a nifty way of drawing a cube with cut off corners.
But, it fails on the mirror of the corner at [1,1,1].
module corner(wid) {
corner_points = [[0,0,0],[1,0,0],[0,1,0],[0,0,1]];
corner_faces = [[0,3,1],[0,2,3],[0,1,2],[1,3,2]];
polyhedron(wid*corner_points, corner_faces);
}
module cornercube(wid, cornerwid) {
cube_vertices = [[0,0,0],[0,0,1],[0,1,0],[0,1,1],
[1,0,0],[1,0,1],[1,1,0],[1,1,1]];
difference() {
cube(wid);
for (v = cube_vertices) {
#translate(wid*v) mirror(v) corner(cornerwid);
}
}
}
cornercube(20,5);
This code fixes things by handling that corner as a special case.
Can someone explain to me what's different about the one corner?
And is there some transformation that will work on all eight corners?
module cornercube2(wid,cornerwid) {
cube_vertices7 = [[0,0,0],[0,0,1],[0,1,0],[0,1,1],
[1,0,0],[1,0,1],[1,1,0]];
cube_vertices1 = [[1,1,1]];
difference() {
cube(wid);
for (v = cube_vertices7) {
translate(wid*v) mirror(v) corner(cornerwid);
}
for (v = cube_vertices1) {
#translate(wid*v) rotate([180,90,0]) corner(cornerwid);
}
}
}
cornercube2(20,5);
_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


Something is wrong with your logic.
Intuitively, I would expect that a rotation and translation is needed to position each corner. You are using a mirror and a translation.
It's been a while since I studied matrix transformations, but it seems to me that a rotation can *sometimes* be implemented using a mirror, but not in the general case. So maybe you are getting lucky, and a mirror just happens to be sufficient to perform the rotation in 7 of the 8 cases?
_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


It's indeed a special case. If you transfer the original corner (red color)
DIRECTLY to its position (i.e., w/o mirror()), and compare its relationship
with the one that is mirrored (teal color), you can see from the graph how
it is a special case :
< http://forum.openscad.org/file/t602/180804_4_corner_mirroring_1.png>
Instead of mirroring 7 times to all corners, mirroring application like this
can be better achieved by mirroring the original one (C0) to [x,0,0] corner
 make it C1. Then, mirror BOTH C0C1 to [0,y,0], generating 4 corners,
than again onto [0,0,z] to generate 8 corners:
module corners(wid=20, cornerwid=5)
{
module mirror_dir(d)
{
mps = [[1,0,0],[0,1,0],[0,0,1]];
children(); //<==== original copy
translate( wid*mps[d]) mirror( mps[d] ) children(); //<==== mirrored
copy
}
mirror_dir(2)
mirror_dir(1)
mirror_dir(0)
corner(cornerwid);
}
< http://forum.openscad.org/file/t602/180804_4_corner_mirroring_2.png>
This would be a very good general mirroring module for future 8corner
mirroring.

$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer ); $ Tips ; $ Snippets

Sent from: http://forum.openscad.org/_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


On 04. aug. 2018 16:38, doug moen wrote:
> Another way to cut corners off a cube is to intersect it with an
> octahedron. I think the logic for this would be easier.
Indeed. The solution is trivial if you write a module defining an
octahedron with vertices on the main axes, distanced "size" from origin,
i.e. module octahedron(size);
Then you can do
module cornercube(wid,cornerwid)
{
intersection()
{
octahedron(size=wid*sqrt(2)cornerwid/2);
cube(size:wid,center=true);
}
}
Carsten Arnholm
_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


Yeah Carsten,
a more convenient way to code this would be:
cornercube(20,5);
module octahedron(d = 10)
scale(d*sqrt(3))
{
cylinder(r1=1, r2=0, h=sqrt(3)*.5, $fn=4);
scale([1,1,1])cylinder(r1=1, r2=0, h=sqrt(3)*.5, $fn=4);
}
module cornercube(d=20, d1=5)
intersection()
{
cube(d, true);
octahedron(dd1);
}

Sent from: http://forum.openscad.org/_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


On 20180807 13:05, Parkinbot wrote:
> Sorry, I miscalculated the height of the octahedron. It is as easy as
> this:
>
> module octahedron(d = 10)
> {
> scale(d*sqrt(3))
> {
> cylinder(r1=1, r2=0, h=1, $fn=4);
> scale([1,1,1])cylinder(r1=1, r2=0, h=1, $fn=4);
> }
> }
Yes, you can do it this way, although it is "cheating" as it relies on
the OpenSCAD discretization of a cylinder instead of defining the
polyhedron explicitly. It is more compact, but less readable.
I used a different approach in my own code (not openSCAD), realising
that any convex polyhedron can be defined from just an array of vertex
coordinates. An octahedron is just one of many in this category
https://gist.github.com/arnholm/c71852301b56b318a83a59c20bb29fe8Carsten Arnholm
_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


I don't think that using language primitives is "cheating", but I understand
what you mean. The main problem with the code given by the threadstarter is
that the cube is not centered. With a centered cube everything is clear and
easy.
Btw, there was another calculation error in my octahedron. I hope this the
final version:
module octahedron(d = 10)
{
x = d * 2 *sqrt(5)/3;
scale(x)
{
cylinder(r1=1, r2=0, h=1, $fn=4);
scale([1,1,1])cylinder(r1=1, r2=0, h=1, $fn=4);
}
}

Sent from: http://forum.openscad.org/_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


Em ter, 7 de ago de 2018 12:27, Carsten wrote:
I used a different approach in my own code (not openSCAD), realising
that any convex polyhedron can be defined from just an array of vertex
coordinates.
A similar approach in OpenSCAD language might be:
module octahedron(r=1) { verts = [ [r,0,0], [0,r,0], [r,0,0], [0, r,0], [0,0,r], [0,0,r] ] ; hull( polyhedron(verts, [0,1,2,3,4,5]) ); }
_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


> Yes, you can do it this way, although it is "cheating" as it relies on
> the OpenSCAD discretization of a cylinder instead of defining the
> polyhedron explicitly. It is more compact, but less readable.
I agree on the readability, but I wouldn't consider it cheating. It's a well
defined behaviour, it's not just some random effect of how it currently
works.

Sent from: http://forum.openscad.org/_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org


On 20180809 07:50, Troberg wrote:
>> Yes, you can do it this way, although it is "cheating" as it relies on
>> the OpenSCAD discretization of a cylinder instead of defining the
>> polyhedron explicitly. It is more compact, but less readable.
>
> I agree on the readability, but I wouldn't consider it cheating. It's a
> well
> defined behaviour, it's not just some random effect of how it currently
> works.
That is why is said "cheating" (with quotes). It relies on
implementation details such as the discretization of a cylinder (or a
cone rather) plus it also relies on implicit union of 2 such objects.
Granted, this is well known current OpenSCAD behavior, but still.
It is also a special case that works only for creating an octahedron. If
you wanted a different kind of convex polyhedron you would be out of
luck with this approach.
But for sure it solved the original problem as presented.
Carsten Arnholm
_______________________________________________
OpenSCAD mailing list
[hidden email]
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org

