Extrude Along Path

OpenSCAD script to generate the polyhedron that is formed by extruding a polygon along a specified path. List comprehensions allow the path and polygon points to be specified parametrically.

Instructions

This is a native OpenSCAD implementation of path extrusion.

A polygon is specified as a set of points in 2D space, and a path is specified as a set of points in 3D space. The extrusion script copies the 2D origin-centred polygon along each of the points along the path, rotating each copy around the origin to face the next point on the path, and to be oriented in such a way that a unit vector perpendicular to the normal angle polygon matches up (as close as possible) with the same vector on the next copy.

See the script 'path_extrude.scad' for the most recent version, implementing the above algorithm. The latest version is also available in a revision-controlled format from here.

Updates from 2018 code:

• Essentially a code re-write from a blank state, but preserving the function signature
• Fixed up the polygon rotation / gimball lock issue by shifting a few negative signs around in the rotation function
• Tweening between two polygons with equal path lengths via 'exShape2' argument. This allows for a simple linear scaling as well (i.e. just make the second shape larger or smaller).

• Explicit scale and rotation options are available for simple tweaks of the polygons at each location Preparation:
  put path_extrude.scad into the same directory as your OpenSCAD code,
  and add "use ;" to the top of your OpenSCAD code.

  Syntax:

  module path_extrude(exPath, exShape, exShape2=[],
  exRots = [0], exScale = [1], merge=false)

  Creates an extruded path object by translating and rotating the shape described byexShape along the path described byexPath.

  Arguments:

*exPath - 3D path through which shape will be extruded *exShape - 2D shape to extrude along the path *exShape2 [optional] - 2D shape to morph exShape into over the course of the extrusion *exRots [optional] - Additional rotation to be applied at each path point. If this is shorter than the length of the path, then it will be recycled. *exScale [optional] - Scale factor to be applied at each path point. If this is shorter than the length of the path, then it will be recycled. *merge - set to true if the extruded path should be closed between the end and start point (i.e. a closed tube with no end covers) Constraints:

• exPath should be a vector of 3D vectors of at least length 3
• exShape should be a vector of 2D vectors of at least length 3
• exShape should be a single closed polygon
• exShape2 should be a single closed polygon
• exShape2 should have the same number of points as exShape
• exRots should be a vector of at least length 1
• exScale should be a vector of at least length 1 OpenSCAD Code examples

Pentagon spiral

use ; myPoints = [ for(t = [0:72:359]) [cos(t-18),sin(t-18)] ]; myPath = [[-1,0,0],[1,0,0],[2,1,0.5],[2,3,1.5], [1,4,2],[-1,4,3],[-2,3,3.5],[-2,1,4.5],[-1,0,5]]; path_extrude(exShape=myPoints, exPath=myPath);Double rotated spiral

use ; pi=3.14159; myPoints = [ for(t = [0:90:359]) [cos(t+45),sin(t+45)] ]; myPath = [ for(t = [0:3.6:360]) [5cos(2t),5sin(2t), (t<90)?0:((t-90) 4pi/180)] ]; path_extrude(exShape=myPoints, exPath=myPath);Trefoil knot spinning top

This uses the Wikipedia trefoil knot equation, with a bit of squash on the X and Y direction to improve printability:
[https://en.wikipedia.org/wiki/Trefoil\_knot ]

use ; myPoints = [ for(t = [0:18:359]) 2.5[cos(t),sin(t)] ]; // https://en.wikipedia.org/wiki/Trefoil\_knot myPath = [ for(t = [0:3.6:359]) [ 4(sin(t) + 2sin(2t)), 4(cos(t) - 2cos(2t)), 5(-sin(3*t))] ]; path_extrude(exPath=myPath, exShape=myPoints, merge=true); cylinder(d1=10, d2=2, h=10, $fn=50); translate([0,0,9.8]) sphere(d=2, $fn=48);Double Helix

use ; shift=0; pi=3.14159; for(shift = [0, 360/15]){ myPoints = [ for(t = [0:72:359]) [cos(t),sin(t)] ]; myPath = [ for(t = [0:5:359]) [ (10+1.212pisin(5t))cos(t+shift), (10+1.212pisin(5t))sin(t+shift), 1.212picos(5*t) ] ]; path_extrude(exShape=myPoints, exPath=myPath, merge=true); } This is intended to simulate a right-handed DNA backbone with major/minor groove width of {1/3,2/3}, 5 turns per loop, 10 bases per turn, helix radius of 1/3.3 times the arc length of a single turn. The ring radius was 15 in this example.

M16 Bolt

see [ https://en.wikipedia.org/wiki/ISO\_metric\_screw\_thread ]

Note that for the bolt thread to extrude properly, I need to bypass the rotation correction algorithm. The slight double twist in a screw thread is enough to eventually twist the curve around on its extrusion axis. I'm not happy with this fudge, as I expect there could be situations in which it doesn't work. As a future TODO, I think I'd like to include a parameter which indicates where the reference vector should try to point at each path point (e.g. for a screw thread, that target would be the centre of the bolt, at the same height as the path point).

use ; length=30; P=2; // pitch H=sqrt(3)/2 P; // height of triangle R=H/(P/2); ppr=20; // points per revolution loops=length/P; D=16; xw=0.4; // extrude width myPoints = [ [-H/2-xw+0.1R,-P/2+0.1], [1/4H-xw,-P/8], [1/4H-xw,P/8], [-H/2-xw+0.1R,P/2-0.1] ]; myPath = [ for(t = [-(180/loops):(360/(pprloops)):360+(180/loops)]) [(D/2)cos(loopst),(D/2)sin(loopst), P(loopst)/360] ]; difference(){ union(){ translate([0,0,-xw]) rotate(180) cylinder(h=length+xw2, r=D/2-3/8H-xw/2, $fn=ppr); path_extrude(exShape=myPoints, exPath=myPath, preRotate=false); translate([0,0,-7]) minkowski(){ rotate(180) cylinder(r=(24 / cos(30) - xw)/2-1, h=6, $fn=6); sphere(r=1, $fn=8); } } translate([0,0,length-2]) rotate_extrude($fn=60) polygon([[D/2-4,4],[D/2+4,4],[D/2+4,-2]]); } M16 Nut

use ; length=8; P=2; // pitch H=sqrt(3)/2 P; // height of triangle R=H/(P/2); ppr=30; // points per revolution loops=length/P; D=16; xw=0.4; // extrude width myPoints = [ [-H/2+xw+0.1R,-P/2+0.1], [1/4H+xw,-P/8], [1/4H+xw,P/8], [-H/2+xw+0.1R,P/2-0.1] ]; myPath = [ for(t = [-(180/loops):(360/(pprloops)):360+(180/loops)]) [(D/2)cos(loopst),(D/2)sin(loopst), P(loopst)/360] ]; difference(){ translate([0,0,1]) minkowski(){ rotate(180) cylinder(r=(24 / cos(30) - xw)/2-1, h=length-2, $fn=6); sphere(r=1, $fn=8); } translate([0,0,-xw]) rotate(180) cylinder(r=D/2-3/8H+xw, $fn=ppr, h=length+xw2); translate([0,0,length-xw2]) cylinder(r1=D/2-3/8H+xw, r2=D/2+4+xw, $fn=ppr, h=4); translate([0,0,-4+xw2]) cylinder(r1=D/2+4+xw, r2=D/2-3/8H+xw, $fn=ppr, h=4); path_extrude(exShape=myPoints, exPath=myPath, exRots=[180]); }