Bezier Library for OpenScad
by ckirby, published
Updated 5/10/13--fixed triangle winding in centered BezWall; use polyhedron for variable-height BezArc.
I wanted a bezier library that could handle an arbitrary number of control points. When working on thingiverse.com/thing:77586, I also wanted to rotate extrude a "wall" defined by a bezier path and a width.
BezWall is the workhorse function. The "ctlPts" parameter accepts between 1-8 bezier control points.
The parameters "width" and "height" accept static values (e.g., 5) specifying the width and height of the wall. If height is 0, it will generate a 2d object you can extrude yourself.
The alternate parameters "widthCtls" and "heightCtls" accept an array of values that will be bezier-interpolated along the length of the wall.
If the "centered" parameter is "true", the wall is centered on the path defined by "ctlPts". Otherwise, one edge of the wall is defined by "ctlPts".
At the moment, there is no documentation! But there is a test file that runs through most of the available features.
I'd previously done some work writing coffeescript code to generate bezier interpolation functions that accept an arbitrary number of control points, and I'd written some coffeescript to generate openscad code. It occurred to me that I could use coffeescript to automate a lot of the tedium in writing openscad functions. So, the coffeescript file in this thing will generate openscad functions to handle bezier interpolation with a varying number of control points. The attached BezierScad.scad file can deal with up to 8 control points, but you can easily modify orderMax in the coffeescript file to have it generate functions that can deal with higher or lower orders.
The BezLine function is simpler than BezWall and offers a subset of the BezWall functionality.
BezLine takes an array of 1-8 control points and an array of 1-8 width values, which will be bezier interpolated as widths for the resulting line.
BezLine doesn't accept a "steps" parameter. Rather, it takes a "resolution" parameter of between 2-6. The resulting line will have (2**resolution) segments.
BezArc returns a shape similar to that generated by WilliamAAdams' BezQuadCurve function.