### Local coordinate systems in OpenSCAD

Here's a small snippet for setting a local coordinate system. You need to know the location to treat as origin as well as the direction vectors to treat as X and Y.

// Take a position vector (p) and 3 direction vectors (uvw) // and create a transformation matrix. The origin is transformed to p, // and xyz point along uvw. // Normally, the caller will ensure that uvw are orthogonal unit vectors function puvw(p, u, v, w) = [ [u[0], v[0], w[0], p[0]], [u[1], v[1], w[1], p[1]], [u[2], v[2], w[2], p[2]]]; // Take a position vector (p) and 2 direction vectors (uv) which should be // orthogonal but need not be unit vectors. Calculate the unit vectors as well // as the third vector and return the resulting matrix function puv(p, u, v) = let(nu = u / norm(u), nv = v / norm(v), nw = cross(nu, nv)) puvw(p, nu, nv, nw); // Operate in a local coordinate system where the origin is the point p, // x points along u, y points along v, and z points along the normal vector // to uv. x and y should be orthogonal but need not be unit vectors. module puv(p, u, v) { multmatrix(puv(p, u, v)) children(); }

For instance, suppose you want to lay out some feature relative to a cone 100mm in diameter and 500mm tall. It's convenient to set the origin to the intersection of the cone base with the +x axis, +x be the direction from the base of the cone to the tip, +y be the direction tangential to the cone, and +z be the direction 'out' from the cone. You might invoke puv like so (corr is a factor to make the flats of the faceted cone exactly touch the 100mm diameter circle):

effen = 16; // 16, 32, 64, ... corr = 1 / cos(180/effen); for(i=[0:45:360]) rotate(i) puv([100,0,0], [-100, 0, 500], [0, -1, 0]) linear_extrude(height=1) square([25, 4], center=true); %rotate(45/4) cylinder(d1=200*corr, d2=0, h=500, $fn=effen);

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