June, 30 - updated Naca_sweep.scad and Naca4.scad

The STL designs shown along with this thing are not really meant for printing, rather to visually demonstrate the power of a special programming technique based on new features of OpenSCAD 2015 that will allow you to do really wicked stuff. Also I verify a promise given in a previous post NACA Airfoils - 4 digit fully parametric OpenSCAD library, where I introduced some very flexible airfoil calculation functionality.

To give you an overview where this programming technique applies: As long as a wing, fin, blade or fuselage design does not exceed the (scalable) range of a single NACA airfoil type almost all requirements will be accomplished by juggling around with the mighty OpenSCAD operators linear_extrude() and rotate_extrude().

Whenever a specific (e.g. non-linear) trajectory and/or a transition between different airfoil types, say between a NACA1480 and a NACA1510 is demanded, one is stumped with this tools. In cases, where convexity is granted for all shapes, the hull() operator maybe helpful. I have demonstrated this technique in my Springs, helicoils, elliptic rings post. Concave stuff by contrast is always more resistive.

With this post I show the implementation of a sweep operator that connects a set of 2D "slices" placed on a trajectory in 3D space into a single polyhedron. Each slice must be derived from a non-self-intersecting polygon describing a 2D shape, like an airfoil (or any other shape) and have the same number of points as all others. Transformed into a 3D point set, Euclidean transformations are applied to correctly place it on the trajectory in 3D space sweep() builds an object of.

My two examples present two techniques to generate trajectory hull objects with transitions:

1. Slice objects built of two (or more) 2D shapes and composed by union(). This approach is easier, but CGAL (F6) rendering can take a lot of time.
2. Polyhedron objects built from a vector of 2D shapes. This approach needs a function to generate the vector set and has the advantage of CGAL rendering being very fast.

The code for central module sweep(dat, convexity){ } is just a few lines. You call it with a fully prepared vector of 3D points set vectors.

To be be able to freely place a 2D shape within 3D space, I added a bunch of functions operating over points sets and providing translation, rotation and scaling functionality.

Use functions

• v3D to expand a 2D point set vector [[X1, Y1], ... , [Xn, Yn]] into the 3D point set vector [[X1, Y1, 0], ... , [Xn, Yn, 0]]
• T_(x=0, y=0, z=0, v) to translate a point set vector v in all three dimensions.
• R_(x=0, y=0, z=0, v) to rotate a point set vector v in all three dimensions.
• S_(x=1, y=1, z=1, v) to scale a point set vector v in all three dimensions.
• Tx(x=0, v), Ty(y=0, v), Tz_(z=0, v) as shortcuts to translate a point set vector v in one dimension.
• Rx(x=0, v), Ry(y=0, v), Rz_(z=0, v) as shortcuts to rotate a point set vector v in one dimension.
• Sx(x=1, v), Sy(y=1, v), Sz_(z=1, v) as shortcuts to scale a point set vector v in one dimension.

A last hint: Use F12 to check whether triangle orientation in the polyhedron is correct and has no self-intersections. If you see any purple triangles after F5, there is a problem and the result will be rejected by CGAL or at least cause trouble when applying any Boolean operations.
If everything is purple, you can either

• reverse your tracjectory by changing the sign of the path variable.
• or reverse the vertex order in all your polygons

Have fun!