On 17. mai 2017 12:01, Eric Buijs wrote:

Yes, do not create non-manifold topology in the first place :-) That is
in fact what you are doing with those shapes. You have solids that share
only single edges with neighbour objects. That is 1-manifold and not
2-manifold.

You can tweak those shapes into creating 2 manifold intersections with
each other simply by adding a small offset to the polygon:

=======

a = 1;
b = 1;

m = 7/6  ;

n1 = 0.3;
n2 = 0.3;
n3 = 0.3;

radius = 30;

range_multiplier = 6;

function superformula(theta) = pow(pow(abs(1 / a * cos(m/4theta)),n2)+
pow(abs(1 / a * sin(m/4theta)),n3), 1 / n1);

function supershape(range_multiplier) = [for (theta = [0:1:360 *
range_multiplier]) [radius/superformula(theta) * cos(theta),
radius/superformula(theta) * sin(theta)] ];

linear_extrude(3.2)
offset(r=0.001)
polygon(supershape(range_multiplier));
cylinder(r=radius,h=1);

Carsten Arnholm

On 17. mai 2017 13:09, Carsten Arnholm wrote:

By the way, after closer inspection it looks like you are creating a
complex shape using a single highly self-intersecting polygon. That is
something I would expect to cause failure either way.

Carsten Arnholm

This is a very interesting case. The polygonal line that defines the
polygon is not a 1-manifold due to self-intersections. The polygon is not
simple. There are a few interpretation alternatives what is inside of a
non-simple polygon. The one OpenSCAD/CGAL seems to choose may result in a
non-2-manifold when extruded. One example where the extrusion of non-simple
polygon is accepted as 2-manifold by CGAL follows:

function circle(r) = [for(a=[0:10:360]) r*[cos(a), sin(a)]];
function reverse(p) = [for(i=[len(p)-1:-1:0]) p[i]];

linear_extrude(2)
polygon(concat(circle(20),reverse(circle(10))));
cube(30);

It generates a 2-manifold even if the reverse() is excluded in the polygon
definition. However, if this last polygon is taking as an input shape for
sweep.scad the resulting polyhedron will be refused as a 2-manifold.

BTW, different slicers choose different ways to interpret similar
situations and the 3D printing from them will be different.

2017-05-17 9:15 GMT-03:00 Eric Buijs ebuijs@mac.com:

On 17. mai 2017 16:57, Ronaldo Persiano wrote:

This is a polygon with 74 edges in a single loop. Edge 37 runs from
[20,0] (vertex37) to [10,0] (vertex38) and the final edge 74 runs from
[10,0] (vertex74) to [20,0] (vertex01).

There are coinciding vertices (37/01 and 38/74) and coinciding edges
(37/74 , parallel and overlapping). It is a classic "2*PI problem". I
would classify that as a self intersecting polygon.

If the polygon had been defined with an inner and outer loop instead, it
would be well defined.

It ultimately falls into "undefined behaviour" category when you have a
polygon with either intersecting non-parallel edges or overlapping
parallel edges.

The model by Eric Buijs that "worked" with an offset was in effect also
relying on undefined behaviour for this reason.

Carsten Arnholm

The polygon I have defined will have different nature if the reverse
operation is removed. As is, the polygon is not simple but "well defined"
in the sense that it has a well defined interior. Its regularization (
regularization(P) = closure(interior(P)) ) would be identical to the one
with inner and outer loops. However, if the reverse operation is removed,
it will have a boundary cross and then its interior is not well defined
anymore and no regularization would be possible.

2017-05-17 14:33 GMT-03:00 Carsten Arnholm arnholm@arnholm.org:

ok thinking in my limited mathmatically way, I can see there might be an
issue with nearly parallel triangles....

but it kinda seems like I dunno am I missing something to do with the
issues...

On 17/05/17 21:03, Eric Buijs wrote:

Chris,

Eric Buijs issue has not anything in common with nearly parallel triangles.
It is a non-manifold issue like the one where two cubes have one edge in
common.

cube(10);
translate([10,10,0]) cube(10);

2017-05-17 19:49 GMT-03:00 Mr C Camacho chris@bedroomcoders.co.uk: