yes, but but A-B is a straight!

so you can

• define the catenary(chain- curve) in 2D space
• linear_extrude it to 3D space
• use multmatrix to skew it on the way  from AB to C
• mirror-copy the result as you probably only get half of the riangle

On Fri, Jun 28, 2024 at 11:49 AM Dan Perry via Discuss <
discuss@lists.openscad.org> wrote:

The catenary is from A to the midpoint of BC.

On Fri, Jun 28, 2024 at 6:13 AM Guenther Sohler via Discuss <
discuss@lists.openscad.org> wrote:

The OP said "approximate".  I would think that a catenary would be more of
an "exact" solution.

IMO, an approximation would simply be a large radius arc-segment.

On Fri, Jun 28, 2024 at 11:00 AM David Phillip Oster via Discuss <
discuss@lists.openscad.org> wrote:

I would agree on this, but as far as I remember from long ago in
Engineering School, the catenary only describes the shape of the rope if:

• It's density is homogeneous (which is almost always implied, when not
  stated otherwise),

• we are in an homogeneous gravitational field (which is even more
  implied, if we don't have an awful long rope and the extremes are very
  far away).

• the rope is subject to its own weight only, which in this case doesn't
  seem to apply.

On 28/06/2024 18:11, Joe H via Discuss wrote:

I think if the wind is uniform across the sail hitting it straight on it
would have pretty much the same effect as gravity on a rope. The catenary
formula comes from balancing  tension along the rope with gravity and
integrating. There is a function in NopSCADlib to make one:
https://github.com/nophead/NopSCADlib/tree/master?tab=readme-ov-file#catenary

On Fri, 28 Jun 2024 at 17:36, Andreas Croci via Discuss <
discuss@lists.openscad.org> wrote:

looks to me a shape like this:

[image: Screenshot 2024-06-28 at 10.54.30 PM.png]

On Fri, 28 Jun 2024 at 15:20, Dan Perry via Discuss <
discuss@lists.openscad.org> wrote:

I found a solution:
[image: image.png]

I used the bezier functions in BOSL2.  Adjusting the center_z and edge_z
parameters is a quick way to tweak the shape of the sail.  My solution to
turn the zero thickness bezier patch into a 1 unit thick shape is
inelegant, hopefully the BOSL2 team can explain a better way.

include <BOSL2/std.scad>
include <BOSL2/beziers.scad>

$fs = 0.2;
$fa = 1.0;

center_z = 20;
edge_z = 8;

patch = [
[[0,  50, 0], [25,  33.3, edge_z], [50,  16.7, edge_z], [75, 0, 0]],
[[0,  0, 0], [25,  0, center_z], [50,  0, center_z-5], [75, 0, 0]],
[[0, -50, 0], [25, -33.3, edge_z], [50, -16.7, edge_z], [75, 0, 0]]
];
// debug_bezier_patches(patches=[patch], size=1, showcps=false);
vnf = bezier_vnf([
patch,
up(1, patch),
]);

difference() {
hull() vnf_polyhedron(vnf);
translate([0, 0, -1]) scale([1.01, 1.01, 1.00]) hull() vnf_polyhedron
(vnf);
}

On Fri, Jun 28, 2024 at 10:49 AM Dan Perry dan.p3rry@gmail.com wrote: