How to a make a curved sheet (cube) in OpenSCAD? - curve

Question

How can I curve a sheet (cube)? I'd like to control the angle of the bend/curve.
e.g.
cube([50,50,2]);

Answer 1

You can rotate_extrude() an rectangle with the parameter angle. This requires the openscad version 2016.xx or newer, see documentation.
It is necessary to install a development snapshot, see download openscad
$fn= 360;
width = 10; // width of rectangle
height = 2; // height of rectangle
r = 50; // radius of the curve
a = 30; // angle of the curve
rotate_extrude(angle = a) translate([r, 0, 0]) square(size = [height, width], center = true);
looks like this:
The curve is defined by radius and angle. I think it is more realistic, to use other dimensions like length or dh in this sketch
and calculate radius and angle
$fn= 360;
w = 10; // width of rectangle
h = 2; // height of rectangle
l = 25; // length of chord of the curve
dh = 2; // delta height of the curve
module curve(width, height, length, dh) {
// calculate radius and angle
r = ((length/2)*(length/2) - dh*dh)/(2*dh);
a = asin((length/2)/r);
rotate_extrude(angle = a) translate([r, 0, 0]) square(size = [height, width], center = true);
}
curve(w, h, l, dh);
Edit 30.09.2019:
considering comment of Cfreitas, additionally moved the resulting shape to origin, so dimensions can be seen on axes of coordinates
$fn= 360;
w = 10; // width of rectangle
h = 2; // height of rectangle
l = 30; // length of chord of the curve
dh = 4; // delta height of the curve
module curve(width, height, length, dh) {
r = (pow(length/2, 2) + pow(dh, 2))/(2*dh);
a = 2*asin((length/2)/r);
translate([-(r -dh), 0, -width/2]) rotate([0, 0, -a/2]) rotate_extrude(angle = a) translate([r, 0, 0]) square(size = [height, width], center = true);
}
curve(w, h, l, dh);
and the result:
Edit 19.09.2020: There was a typo in the last edit: In the first 'translate' the local 'width' should be used instead of 'w'. Corrected it in the code above.

Answer 2

I can do it this way but it would be better if you could specify the bend/curve in #degrees as an argument to the function:
$fn=300;
module oval(w, h, height, center = false) {
scale([1, h/w, 1]) cylinder(h=height, r=w, center=center);
}
module curved(w,l,h) {
difference() {
oval(w,l,h);
translate([0.5,-1,-1]) color("red") oval(w,l+2,h+2);
}
}
curved(10,20,30);

Answer 3

Using the concept used by a_manthey_67, corrected the math and centered (aligned the chord with y axis) the resulting object:
module bentCube(width, height, length, dh) {
// calculate radius and angle
r = (length*length + 4*dh*dh)/(8*dh);
a = 2*asin(length/(2*r));
translate([-r,0,0]) rotate([0,0,-a/2])
rotate_extrude(angle = a) translate([r, 0, 0]) square(size = [height, width], center = true);}

Answer 4

Or, if you just want something with a fixed length, and a certain bent angle do this:
module curve(width, height, length, a) {
if( a > 0 ) {
r = (360 * (length/a)) / (2 * pi);
translate( [-r-height/2,0,0] )
rotate_extrude(angle = a)
translate([r, 0, 0])
square(size = [height, width], center = false);
} else {
translate( [-height/2,0,width] )
rotate( a=270, v=[1,0,0] )
linear_extrude( height = length )
square(size = [height, width], center = false);
}
}
The if (a > 0) statement is needed to make an exception when the bending angle is 0 (which, if drawing a curved surface, would result in an infinite radius).
Animated GIF here