Here's an X shape formed by cutting some ellipses out of a cube.
I would like to smooth the sharp corners on the sides by subtracting
a shape that will be tangent to the side ellipsis and the side of
the cube, as per the red markup in the attached image.

How can I calculate that shape, or otherwise smooth the sharp edge?

$fn=30;

ZZ=5;
WW=42;
HH=100;

difference() {
cube([WW,HH,ZZ]);
// top and bottom
translate([WW/2,0,0])  scale([1,2.5 ,1]) cylinder(ZZ,d=WW-(10));
translate([WW/2,HH,0]) scale([1,2.5,1]) cylinder(ZZ,d=WW-(10));
// sides
translate([0,HH/2,0]) scale([1,1.8,1]) cylinder(ZZ,r=WW/4);
translate([WW,HH/2,0]) scale([1,1.8,1]) cylinder(ZZ,r=WW/4);
// smooth the arms
// ???
}

Hm, better start in 2D and then try to use offset() for things like this.

ZZ=5;
WW=42;
HH=100;
os = 15;

linear_extrude(ZZ)
intersection()
{
square([WW,HH]);
difference()
{
offset(-os)offset(os)
{
translate([WW/2,0])  scale([1,2.5]) circle(d=WW);
translate([WW/2,HH,0]) scale([1,2.5,1]) circle(d=WW);
}
translate([WW/2,0])  scale([1,2.5]) circle(d=WW-(10));
translate([WW/2,HH,0]) scale([1,2.5,1]) circle(d=WW-(10));
}
}

--
Sent from: http://forum.openscad.org/

I use this handy little snippet for rounding corners in 2d:

module polyround(radius){
//Inside corners
offset(r=-radius)
offset(delta=radius)
//Outside corners
offset(r=radius)
offset(delta=-radius)
children();
}

//Sample code
//One sample shape
module poly(outer,inner){

polygon([[-outer,0],[-inner,inner],[0,outer],[inner,inner],[outer,0],[inner,-inner],[0,-outer],[-inner,-inner]]);
}

//Another sample shape
module poly2(){
translate([220,0,0])
difference(){
square([200,200], center=true);
square([100,100], center=true);
}
}

//First shape with rounded corners
polyround(10)
poly(100,30);

//Shape without rounded corners, for reference
translate([0,0,-1])
color("red")
poly(100,30);

//Second shape with rounded corners
polyround(10)
poly2();

//Shape without rounded corners, for reference
translate([0,0,-1])
color("red")
poly2();

--
Sent from: http://forum.openscad.org/