I am looking for a way, given a 2D object and a cut line that is known to
cut the object into two parts, to generate those two parts as 2D objects in
a predictable way. I would like the object to be any 2D object, and the cut
line to be specified as a vector. The only way I can see of doing it at the
moment is to specify the cut as a region that is known to enclose one of
the parts, but this is a bit clunky for what I want. Can anyone help?

(The application is a sheet material folding module I am working on:
https://github.com/highfellow/openscad-sheet-folder )

Thanks for any help with this.

Andrew Baxter

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​Andrew,

The following code may be a starting point to do what you want. For sake
of completeness I included a module ( boundingRect() ) that computes the
bounding rectangle of a 2D shape.

// the extent of the children projection on x axis
module xExtent()
hull() translate([0,1/2])
projection() rotate([90,0,0])
linear_extrude(1) children();

// the left extreme of the xExtent of children
module leftExtreme() difference() {
xExtent() children();
translate([1,0]) scale([1,1.1])xExtent() children();
}

// the lower left "point" of the children bounding rectangle
module lowerLeft() minkowski() {
leftExtreme() children(); // X
rotate(90) leftExtreme() rotate(-90) children(); // Y
}

// the positive part of the xExtent of children
module halfExtent(){
difference() {
xExtent() children();
hull(){
translate([-1/2,0]) square(1,center=true);
lowerLeft() xExtent() children();
}
}
}

// a bounding rectangle of the part of children
// that has positive ordinate x
module halfBoundRect() offset(-1/2) minkowski() {
halfExtent() children();
rotate(-90) xExtent() rotate(90) children();
}

// the bounding rectangle of children
module boundingRect() offset(-1/2) minkowski() {
xExtent() children();
rotate(-90) xExtent() rotate(90) children();
}

// a test shape
module shape() translate([2.5,0]){
rotate(0) square(10,center = true);
rotate(45) square(10,center = true);
}

%scale([1,1,0.1]) shape();
// the shape positive part
color("red")
intersection(){
shape();
halfBoundRect() shape();
}

​

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// fold operator.
// A, B are two points on cutting line, rightside controls which side is
shown. maxsize controls cube size
module fold(A=[0,0], B=[1,1], rightside = true, maxsize=10000){
// construct cube from vector defined by points A, B
v = (B-A)/norm(B-A);
w = [v[1], -v[0]];
dir = rightside?1: -1;
C1 = A+maxsize/2v;
C2 = A-maxsize/2v;
C3 = A+dirwmaxsize - maxsize/2v;
C4 = A+dirwmaxsize + maxsize/2v;
p = [C1, C2, C3, C4];
intersection()
{
polygon(p);
union() children();
}
}

fold(A = [0, 6], B = [6, 3], rightside= true)
{
circle(10);
square(18, center = true);
}

Ronaldo's code was just a hint, how you do it by use of an automated
boundingbox operator. The rest would be vector calculation stuff, which is
trivial.
Here is a solution that intersects with a dumb (but parametrized) square. Is
it this what you are looking for? Otherwise, please show us a drawing of
what you mean.

Hi Parkinbot,

The problem with that code is it doesn't deal with cases where the
extension of the fold line intersects other parts of the shape that you
don't want folded. This could happen either because the perimeter of the
shape is not convex, or because the region to be folded lies inside an
internal hole in the shape. I want my module to be able to handle these
cases. I know that it would be possible to specify the part of the shape to
be folded by passing the module a polygon enclosing that part, but this
would make it complicated to use and I would like to avoid it if possible.
It would be neat to be able to specify the folds just as a list of lines to
fold along, specified as a pair of points.

I have a reasonable idea of how I want to write most of the module - see
https://github.com/highfellow/openscad-sheet-folder . I am just stuck on
how to split a 2D object into two along a line. If anyone knows how to do
this that would be great; otherwise I'll have to use a less elegant way of
specifying which part of the shape to fold.

Andy,

That is not the same problem you state at this thread beginning. And
it is not a well defined problem. It is clear to me that the cut line
is not the only input data you need to solve the problem. But it is by
no means clear what else would be needed. If a half-space defined by a
line is not satisfactory, an input polygon seems to be the more
adequate alternative. Or are you searching for an artificial
intelligence algorithm to do it?

2017-09-09 16:18 GMT+01:00 andy <site@highfellow.org
mailto:site@highfellow.org>:

 Hi Parkinbot,

 The problem with that code is it doesn't deal with cases where the
 extension of the fold line intersects other parts of the shape
 that you don't want folded. This could happen either because the
 perimeter of the shape is not convex, or because the region to be
 folded lies inside an internal hole in the shape. I want my module
 to be able to handle these cases. I know that it would be possible
 to specify the part of the shape to be folded by passing the
 module a polygon enclosing that part, but this would make it
 complicated to use and I would like to avoid it if possible. It
 would be neat to be able to specify the folds just as a list of
 lines to fold along, specified as a pair of points.

 I have a reasonable idea of how I want to write most of the module
 - see https://github.com/highfellow/openscad-sheet-folder
 <https://github.com/highfellow/openscad-sheet-folder> . I am just
 stuck on how to split a 2D object into two along a line. If anyone
 knows how to do this that would be great; otherwise I'll have to
 use a less elegant way of specifying which part of the shape to fold.

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