boat propeller customizable - OpenSCAD nSpline() library with show cases

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nSpline last update 2019-03-14: Works well with OpenSCAD 2019.01 RC3 and older versions down to OpenSCAD 2015.3. To upgrade your version, visit OpenSCAD snapshots. With this post, I'm releasing my splines library. The main function is nSpline(), which performs interpolation over a series of m-dimensional vectors describing 2D shapes and calculates intermediate values with arbitrary precision. The programming technique behind it is quite versatile, so you may find it useful for your projects as well. For example, feed the function with seven 4D-vectors given as a 7x4 array and ask it to return a 100x4 array. It will interpolate each of the four dimensions over the series of hundred vectors. You could also feed it with a 10x8 array and receive a 200x8 array, where each of the eight dimensions is interpolated. The m-dimensional vectors can be interpreted in any way you like, which means you need to provide a generator function that does that. Typically, this function uses part of the vector to generate a parametrized 2D shape and another part to translate, rotate, scale, or even colorize this 2D shape along some trajectory in three-dimensional space. This is similar to linear_extrude(), but with more freedom - at the price of greater self-responsibility. When using sweep() on any series of 2D shapes, it's crucial that no polygon describing a 2D shape intersects itself and no two 2D shapes within the series intersect each other. Two 2D shapes should not even share a common vertex. OpenSCAD does not check the result of a sweep (which ultimately executes a polyhedron call) and currently allows exporting non-manifold STLs in some cases, so using this very powerful scheme requires walking a tightrope. I have successfully tested it with numerous projects, primarily in blade design, but also beyond. I mainly use it for extrusion with my own sweep() function provided in the Naca_Sweep library. You can also use it without modification with the new skin() function currently under evaluation by the development team as a future language feature. // Usage scheme: n-dimensional natural cubic spline interpolation A = [[...], [...], [...]]; // Define Mxm matrix, M > 2, m > 1 B = nSplines(A, N); // Get interpolated Nxm matrix C = gen_dat(B); // Interpret data as sequence of 2D-shapes // and generate trajectory sweep(B); // Extrude by knitting polyhedron object As a testament to the power of this approach, I have designed a customizable boat propeller in boatprop.scad that uses airfoil data and some realistic modeling of twist, camber, and pitch. The basic setup consists of four well-placed slices only, as shown in the second image reveals - the fourth slice is too small to be visible. The parameters necessary to generate 2D airfoil data for these four polygons make up part of the primary data fed into nSpline(), with the other part used to describe affine operations (translation and rotation) for three-dimensional placement. A horn in horn.scad as part of an instrument. The code uses a Boolean difference operation of an outer and an inner skin object. For further code examples, see the more basic knot() example in the splines.scad file (slow CGAL rendering) and http://forum.openscad.org/Rendering-fails-difference-between-F5-and-F6-tp15041p15100.html http://forum.openscad.org/general-extrusion-imperfect-tp14740p14752.html. Extrusion functions give you a lot of freedom, but also place responsibility on you: avoid self-intersection of the extruded path. If self-intersection at some point is unavoidable, try to split the array, sweep all parts separately, and use union().