Hi everyone

I have a really complex (for me) problem that I can't seem to solve. It is a
subproblem of an attempt to extrude a 2d shape along a bezier curve.

I have a list of (programmatically generated) polygons stored as vectors,
shown below.

poly1 = [
[0,0,0],
[0, 40,  0],
[30, 20, 0],
[50, 30, 0],
[50, 0, 0]
];

poly2 = [
[0,0,10],
[0, 50,  10],
[30, 30, 10],
[50, 20, 10],
[50, 0, 10]
];

shape = [poly1, poly2, ..., polyN];

What I want is to make these into a solid shape. poly1 forms the bottom,
polyN forms the top, the edges of the rest work to define the walls of the
polygons.

The number of vertices in all polygons is the same, in this example 5 (in
the real world a lot higher).
And the vertices are corresponding (ie the first vertex of first polygon is
to be connected with the first of the second, see below.) The z coordinate
is always the same for all vertices in each polygon. So a list of flat
faces.

Perhaps a picture makes it more clear. I have drawn in a few triangles in
red and blue. Essentially the whole shape should be covered by them to make
a solid.

http://forum.openscad.org/file/n11326/layers.png

Code:

planes = [[[-1, 0, 0], [125, 0, 0], [125, 235, 0], [125, 235, 0], [126.808,
257.216, 0], [132.264, 275.928, 0], [141.416, 291.232, 0], [154.312,
303.224, 0], [171, 312, 0], [171, 312, 0], [-1, 312, 0]], [[-1, 0, 31.2],
[145.624, 0, 31.2], [145.624, 235, 31.2], [145.624, 235, 31.2], [147.432,
257.216, 31.2], [152.888, 275.928, 31.2], [162.04, 291.232, 31.2], [174.936,
303.224, 31.2], [191.624, 312, 31.2], [191.624, 312, 31.2], [-1, 312,
31.2]], [[-1, 0, 62.4], [165.655, 0, 62.4], [165.655, 235, 62.4], [165.655,
235, 62.4], [167.463, 257.216, 62.4], [172.919, 275.928, 62.4], [182.071,
291.232, 62.4], [194.967, 303.224, 62.4], [211.655, 312, 62.4], [211.655,
312, 62.4], [-1, 312, 62.4]], [[-1, 0, 93.6], [184.703, 0, 93.6], [184.703,
235, 93.6], [184.703, 235, 93.6], [186.511, 257.216, 93.6], [191.967,
275.928, 93.6], [201.119, 291.232, 93.6], [214.015, 303.224, 93.6],
[230.703, 312, 93.6], [230.703, 312, 93.6], [-1, 312, 93.6]], [[-1, 0,
124.8], [202.305, 0, 124.8], [202.305, 235, 124.8], [202.305, 235, 124.8],
[204.113, 257.216, 124.8], [209.569, 275.928, 124.8], [218.721, 291.232,
124.8], [231.617, 303.224, 124.8], [248.305, 312, 124.8], [248.305, 312,
124.8], [-1, 312, 124.8]], [[-1, 0, 156], [217.843, 0, 156], [217.843, 235,
156], [217.843, 235, 156], [219.651, 257.216, 156], [225.107, 275.928, 156],
[234.259, 291.232, 156], [247.155, 303.224, 156], [263.843, 312, 156],
[263.843, 312, 156], [-1, 312, 156]], [[-1, 0, 187.2], [230.446, 0, 187.2],
[230.446, 235, 187.2], [230.446, 235, 187.2], [232.254, 257.216, 187.2],
[237.71, 275.928, 187.2], [246.862, 291.232, 187.2], [259.758, 303.224,
187.2], [276.446, 312, 187.2], [276.446, 312, 187.2], [-1, 312, 187.2]],
[[-1, 0, 218.4], [238.665, 0, 218.4], [238.665, 235, 218.4], [238.665, 235,
218.4], [240.473, 257.216, 218.4], [245.929, 275.928, 218.4], [255.081,
291.232, 218.4], [267.977, 303.224, 218.4], [284.665, 312, 218.4], [284.665,
312, 218.4], [-1, 312, 218.4]], [[-1, 0, 249.6], [239.742, 0, 249.6],
[239.742, 235, 249.6], [239.742, 235, 249.6], [241.55, 257.216, 249.6],
[247.006, 275.928, 249.6], [256.158, 291.232, 249.6], [269.054, 303.224,
249.6], [285.742, 312, 249.6], [285.742, 312, 249.6], [-1, 312, 249.6]],
[[-1, 0, 280.8], [226.617, 0, 280.8], [226.617, 235, 280.8], [226.617, 235,
280.8], [228.425, 257.216, 280.8], [233.881, 275.928, 280.8], [243.033,
291.232, 280.8], [255.929, 303.224, 280.8], [272.617, 312, 280.8], [272.617,
312, 280.8], [-1, 312, 280.8]], [[-1, 0, 312], [130.91, 0, 312], [130.91,
235, 312], [130.91, 235, 312], [132.718, 257.216, 312], [138.174, 275.928,
312], [147.326, 291.232, 312], [160.222, 303.224, 312], [176.91, 312, 312],
[176.91, 312, 312], [-1, 312, 312]]];

//      plane_extrude()
//      extrudes a face to make it visible for debugging
module plane_extrude(face, height=1) {
translate([0, 0, face[0][2]])
linear_extrude(height=height)
polygon([for (i=face) [ i[0], i[1] ] ]);
}

// debug
for (i=planes) {
plane_extrude(i);
}

On side note, it would be nice if echo() formatted vectors differently when
they are nested. For example by printing each sub-vector on a new line.

Have a nice day,
Bananapeel :)

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Splitting up the polygons to handles concave regions was a good idea. Apart
from that that I'm not quite sure what you're suggesting here (I'll take a
closer look). In general I can't use hull() because the polygons are
concave. If I split my polygons into convex regions and use hull() I don't
see where the spheres come in.

:)

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Assuming points are nearest-neighbour ordered and len(poly1)==len(poly2), the
following may serve your purpose:

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I see what you're doing now, and indeed it was my first attempt (except I
used linear extrude() instead of spheres).

It doesn't work with concave objects. And frankly I think subdividing the
polygons is more work than solving the problem directly.

Indeed I had some code for the simplest case (only two polygons "hulled"
together) that I thought was working perfectly, until I tried it on
different polygons and found all the faces to be inside out, and some
structural problems.

Code:

poly1 = [
[0,0,0],
[0, 40,  0],
[30, 20, 0],
[50, 30, 0],
[50, 0, 0]
];

poly2 = [
[0,0,10],
[0, 50,  10],
[30, 30, 10],
[50, 20, 10],
[50, 0, 10]
];

plane1 = [
[-1, 0, 0], [125, 0, 0], [125, 235, 0], [125, 235, 0], [125.162,
242.038, 0], [125.65, 248.755, 0], [126.464, 255.154, 0], [127.606, 261.236,
0], [129.077, 267.004, 0], [130.879, 272.461, 0], [133.012, 277.61, 0],
[135.479, 282.453, 0], [138.279, 286.993, 0], [141.416, 291.232, 0],
[144.889, 295.173, 0], [148.701, 298.818, 0], [152.853, 302.171, 0],
[157.345, 305.233, 0], [162.179, 308.008, 0], [167.357, 310.497, 0], [171,
312, 0], [-1, 312, 0]
];

plane2 = [
[-1, 0, 312], [130.91, 0, 312], [130.91, 235, 312], [130.91, 235,
312], [131.073, 242.038, 312], [131.56, 248.755, 312], [132.374, 255.154,
312], [133.516, 261.236, 312], [134.987, 267.004, 312], [136.789, 272.461,
312], [138.922, 277.61, 312], [141.389, 282.453, 312], [144.19, 286.993,
312], [147.326, 291.232, 312], [150.8, 295.173, 312], [154.612, 298.818,
312], [158.763, 302.171, 312], [163.255, 305.233, 312], [168.089, 308.008,
312], [173.267, 310.497, 312], [176.91, 312, 312], [-1, 312, 312]
];

/* pair_mksolid(a, b)
Connect two 3d planes with corresponding vertices into one solid
a: bottom polygon
b: top polygon
/
function pair_mksolid_orange(a, b) = [
concat(a,b), / add points /
concat( [ / add planes as faces /
[for (i=[0:len(a)-1]) i],
[for (i=[0:len(b)-1]) i+len(a)]
],
/ divide space between vertex 0 and 1 into two triangles /
/ i is the vertex on plane a, i+len(a) is the corresponding vertex
on plane b */
[for (i=[0:len(a)-1])  [i, (i+1)%len(a), i+len(a)]]
,[for (i=[0:len(a)-2]) [i+1, (i+len(a)+1)%(len(a)*2), i+len(a)]]
,[[0, len(a), len(a)*2-1]]
)
];

   // Simple example almost works (bottom inside out)

poly3d = pair_mksolid_orange(poly1, poly2);
// Complex example does not work (inside out and wrong near
concave-ness)
//poly3d = pair_mksolid_orange(plane1, plane2);
echo(poly3d[0]);
echo("");
echo ( poly3d[1]);
polyhedron(points=poly3d[0], faces=poly3d[1]);

:)

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Turns out the input data was a little bit broken. All faces clockwise and an
duplicated vertex. However, I still get these mysterious purple "flaps".

http://forum.openscad.org/file/n11334/gullwing.png

Code:

poly1 = [[-1.0,312.0,0.0],
//[171.0,312.0,0.0],
[171.0,312.0,0.0],
[136.375,284.0,0.0],
[125.0,235.0,0.0],
[125.0,235.0,0.0],
[125.0,0.0,0.0],
//[-1.0,0.0,0.0]
];

poly2 = [[-1.0,312.0,30.0],
//[191.624,312.0,30.0],
[191.624,312.0,30.0],
[156.999,284.0,30.0],
[145.624,235.0,30.0],
[145.624,235.0,30.0],
[145.624,0.0,30.0],
//[-1.0,0.0,30.0]
];

for (i=[0:-1+len(poly1)] ) color([1, i0.1, 0]) translate(poly1[i])
sphere(r=5);
for (i=[0:-1+len(poly2)] ) color([0, i0.1, 1]) translate(poly2[i])
sphere(r=5);

poly1to2=concat(poly1,poly2);
echo(poly1to2);
poly1to2_faces=[ [for(i=[len(poly1)-1:-1:0]) i]
,[for(j=[len(poly1):len(poly1)+len(poly2)-1]) j]
];
poly1to2_faces_between1=[for(k=[0:len(poly1)-1]) [k,k+1,k+len(poly1)]];
poly1to2_faces_between2=[for(k=[0:len(poly1)-1])
[k+len(poly1),k+len(poly1)-1,k]];

echo(poly1to2_faces);
echo(poly1to2_faces_between1);
echo(poly1to2_faces_between2);

polyhedron(points=poly1to2

,faces=concat(poly1to2_faces,poly1to2_faces_between1,poly1to2_faces_between2));

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See https://github.com/openscad/list-comprehension-demos

..and try this:
use <list-comprehension-demos/skin.scad>
skin([poly1,poly2]);

-Marius