You can linear_extrude() a polygon to make a flat polyhedron that can be
placed in 3D space.

On 11 October 2017 at 21:39, thomas-hn thomas-hn@gmx.de wrote:

Thomas,

You can only define polygons in 2d space, but this shouldn’t be too much of a limitation. All points in a polygon must be on the same plane, so if you defined it in 3d space, it would be easy to have an invalid polygon.

The best way to do what you want is probably:
Given your set of 3d points, compute a transform so they all lay on the plane
Use polygon() to render that set of points
Use linear_extrude() to create a 3d shape from those points
Apply the inverse of the original transform to put the 3d shape into place

Maybe let's start my question in another way. For example, we have four
vertices [2, 2, 2], [2, 8, 8], [7, 2, 2], [7, 8, 8] and let's create a face
between them and "linearextrude" this.
It is important to have such four vertices at exact the mentioned positions.

How would you create the 3D object? Please also consider that it is not
ensured that all four vertices are placed so "friendly" as in the example,
they could also be somehow rotatet in space.

Is there a way to create the 3D object which has its four bottom vertices at
the given coordinates without a lot of calculations and
transforming/rotating a cube?

fred_dot_u wrote

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

This sounds like an interesting solution, thanks
However, has anyone an even simpler solution?

Hypher wrote

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

Well, if you don't mind the extra faces, this is pretty simple:

hull()
for(p=[[2,2,2], [2,8,8], [7,2,2], [7,8,8]])
translate(p) cube(0.000002, true);

Something funny. My first try was without the for, and it worked with cubes
as small as 1E-99, but with the for loop, it doesn't work with cubes of
size 1E-6.

2017-10-11 23:30 GMT+02:00 thomas-hn thomas-hn@gmx.de:

--
Regards from Spain,
Antonio

A polygon in OpenSCAD is always a 2D shape on the XY plane. You should not
apply geometric transformations on it that take it away from the XY plane
or you will be in trouble. For instance:

linear_extrude(40)
rotate([90,0,0])
square(20);

Additionally, you are allowed to linear_extrude 2D polygons only.

Following @Appletree, you should define your polygon in the XY plane,
extrude it and then move/rotate the 3D shape to the position you want it.
You can't avoid geometric transformations in this case. If you find the
normal vector of the plane containing the input 3D points ( a cross
product) the geometric transformations will be simple to compute:

// input points
p=[[2,2,2], [2,8,8], [7,8,8], [7,2,2]];

nrm = normal(p);
rot = frotFromTo(nrm,[0,0,1]); // compute the rotation to the XY plane
pxy = [for(pi=p) rot*pi]; // rotate the points to XY plane
p2d = [for(pxyi=pxy) [pxyi[0],pxyi[1]]]; // projects on 2D

rotFromTo([0,0,1], nrm)
linear_extrude(20)
polygon(p2d);

// normal to the triangle [ p[0], p[1], p[2] ]
function normal(p) = cross(p[1]-p[0], p[2]-p[1]);
// matrix of the transformation of mirroring along a direction
function fmirror(v) =
norm(v)==0 ? [[1,0,0],[0,1,0],[0,0,1]] :
let(u = v/norm(v))
[ [1,0,0] - 2*u[0]u, [0,1,0] - 2u[1]u, [0,0,1] - 2u[2]*u ];
// matrix of the minimum rotation that brings the vector di to the
direction do
function frotFromTo(di,do) =
norm(di-do)==0 || norm(di)==0 || norm(do)==0 ?
[[1,0,0],[0,1,0],[0,0,1]] :
fmirror(do/norm(do)+di/norm(di)) * fmirror(di);
// the minimum rotation that brings the vector di to the direction do
module rotFromTo(di,do)
if( norm(di-do)==0 || norm(di)==0 || norm(do)==0 )
children();
else
mirror(do/norm(do)+di/norm(di)) mirror(di) children();

This code does not check if the input points are coplanar. Anyway, it
generates a valid solid provided the first three input points are not
colinear.

2017-10-11 17:39 GMT-03:00 thomas-hn thomas-hn@gmx.de:

On 2017-10-11 22:39, thomas-hn wrote:

As others have indicated, a polygon is a 2d entity that by definition in
OpenSCAD exists in the XY plane. This could be seen as a specialization
of the mathematical term "polygon".

You may perhaps want to look at OpenSCAD polyhedron instead, which uses
3d coordinates. It is supposed to have flat faces that are in fact
mathematical polygons.

Carsten Arnholm