This is your code. It uses two rotations, one around the y axis and the other one around the x axis. You can play with the vectors. X = [3, -2, .10]; Y = [2, 0, 3]; vector(X, .02, "red"); vector(Y, .02, "blue"); x = X/norm(X); // 1st rotation X_ = mmult(rotxz(x), [X]); // rot X by X projected to xz Y1 = mmult(rotxz(x), [Y]); // rot Y by X projected to xz y = Y1/norm(Y1); // second rotation Y_ = mmult(rotyz(y), [Y1]); // rot Y1 by Y1 projected to yz vector(X_, 0.02, "black"); vector(Y_, 0.02, "white"); function rotxz(d) = [[d[0], 0, d[2]], [0, 1, 0], [-d[2], 0, d[0]]]; function rotyz(d) = [[1, 0, 0], [0, d[1], d[2]], [0, -d[2], d[1]]]; function mmult(X, Y) = len(X) != len(Y[0])? undef: [for(i=[0:len(Y)-1]) [for(j=[0:len(X[0])-1]) X[j]*Y[i]]][0]; module vector(p1=[100,100], r=undef, color=undef, reverse=false) { t = reverse?p1:[0,0,0]; s = reverse?-1:1; r = r==undef?norm(p1)/100:r; translate(t)scale(s) if(color) color(color) vec(); else vec(); module vec() { l = norm(p1); v = p1/l; hull() { sphere(r); translate((l-5*r)*v) sphere(r); } hull() { translate((l-5*r)*v) sphere(2*r); translate(p1) sphere(r/10); } } } -- Sent from: http://forum.openscad.org/

Hi Parkinbot, Thanks, but it doesn't do what I want. I've built a whole structure, and I want to rotate the structure so it will lay horizontally according to the 2 vectors, but the structure itself must stay unchanged. If I feed in these vectors in your script: X = [1, 1, 1]; Y = [0, 0, 1]; The angle between X and Y changes. Or do I interpret your script wrongly? Rogier Wolff gives a hint of how to do it, but it is not a complete solution unfortunately... Maurice >This is your code. It uses two rotations, one around the y axis and the other >one around the x axis. >You can play with the vectors. > >X = [3, -2, .10]; >Y = [2, 0, 3]; > >vector(X, .02, "red"); >vector(Y, .02, "blue"); > >x = X/norm(X); // 1st rotation > >X_ = mmult(rotxz(x), [X]); // rot X by X projected to xz >Y1 = mmult(rotxz(x), [Y]); // rot Y by X projected to xz >y = Y1/norm(Y1); // second rotation >Y_ = mmult(rotyz(y), [Y1]); // rot Y1 by Y1 projected to yz > >vector(X_, 0.02, "black"); >vector(Y_, 0.02, "white"); > >function rotxz(d) = > [[d[0], 0, d[2]], > [0, 1, 0], > [-d[2], 0, d[0]]]; > >function rotyz(d) = > [[1, 0, 0], > [0, d[1], d[2]], > [0, -d[2], d[1]]]; > >function mmult(X, Y) = len(X) != len(Y[0])? undef: > [for(i=[0:len(Y)-1]) > [for(j=[0:len(X[0])-1]) > X[j]*Y[i]]][0]; > > >module vector(p1=[100,100], r=undef, color=undef, reverse=false) >{ > t = reverse?p1:[0,0,0]; > s = reverse?-1:1; > r = r==undef?norm(p1)/100:r; > > translate(t)scale(s) > if(color) color(color) vec(); > else vec(); > module vec() > { > l = norm(p1); > v = p1/l; > hull() > { > sphere(r); > translate((l-5*r)*v) sphere(r); > } > hull() > { > translate((l-5*r)*v) sphere(2*r); > translate(p1) sphere(r/10); > } > } >} > > > >-- >Sent from: http://forum.openscad.org/ > >_______________________________________________ >OpenSCAD mailing list >Discuss@lists.openscad.org >http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org

Sorry, there must be a bug choosing the rotations The usual solution is to create an orthogonal base and use it as transformation. So try this: X = [1, 1, 1]; Y = [0, 0, 1]; vector(X, .02, "red"); vector(Y, .02, "blue"); x = X/norm(X); // unit length y_ = Y/norm(Y); // unit length y = y_-x*(x*y_); // orthogonal to x z = cross(x,y); // orthogonal to x and y X1 = mmult([x,y,z], [X]); Y1 = mmult([x,y,z], [Y]); vector(X1, 0.02, "black"); vector(Y1, 0.02, "white"); function mmult(X, Y) = len(X) != len(Y[0])? undef: [for(i=[0:len(Y)-1]) [for(j=[0:len(X[0])-1]) X[j]*Y[i]]][0]; -- Sent from: http://forum.openscad.org/

and last but not least: I forgot to unify the lenght of y and z. So the proper coordinate system is: x = X/norm(X); // y_ = Y/norm(Y); // y1 = y_-x*y_*x; // orthogonal to x y = y1/norm(y1); z1 = cross(x,y); // orthogonal to x and y z = z1/norm(z1); -- Sent from: http://forum.openscad.org/

> The rotated points P1', P2' and P3' are not in the X - Y plane, but that is no problem, the slicer will fix that. A simple translate(-P1) before the hull leaves the result on the XY plane. On Mon, 17 Dec 2018 at 01:39, Parkinbot <rudolf@digitaldocument.de> wrote: > and last but not least: I forgot to unify the lenght of y and z. So the > proper coordinate system is: > > > x = X/norm(X); // > y_ = Y/norm(Y); // > y1 = y_-x*y_*x; // orthogonal to x > y = y1/norm(y1); > z1 = cross(x,y); // orthogonal to x and y > z = z1/norm(z1); > > > > > -- > Sent from: http://forum.openscad.org/ > > _______________________________________________ > OpenSCAD mailing list > Discuss@lists.openscad.org > http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org >