On Thu, Jun 6, 2024 at 3:28 PM William F. Adams via Discuss < discuss@lists.openscad.org> wrote: > My thanks to everyone's input and thoughts. > … > It seems to me that for the three planes: > > - XY > - XZ > - ZY > > it should be possible to have three Bézier curves (left-most/right-most > or front-back or top/bottom for two, and a mid-line for the third), so any > given region should be definable by: > > 3 * planes * 3 * Bézier curves * (2 on-curve points + 2 off-curve > points) == 36 coordinate pairs > > which is a marked contrast to representations such as: > > https://github.com/DavidPhillipOster/Teapot > Thanks for taking a look at my work. I was surprised to find no instances of the Newell Teapot <https://en.wikipedia.org/wiki/Utah_teapot> on thingiverse. I took a 1986 publication of the Newell Teapot and ported it to OpenSCAD with BOSL2. I cut the original in half by taking advantage of its symmetry about the Y axis and using the OpenSCAD primitive: mirror. Next steps for me is taking advantage of the radial symmetry of the lid and body by using rotate_extrude to make manifold shapes of the teapot lid and body. bezier_vnf already works with a bezier patch defined as 16 control points, or 48 floats, smaller than the 36 coordinate pairs (72 floats) you propose. For a square patch, bezier_vnf works with just 4 control points. For a planar patch, where the boundary is a cubic bezier, 8 control points it interprets as two layers of 4 points each. It would be nice if there were something like https://github.com/butcherg/wxpolygon that worked with Apple Vision Pro that let you work with 3D models in with your hands and eyes to reach into the simulated 3D space and grab a control point to move it slightly in 3D space, writing back to a prepared .scad file. In the same way wxpolygon doesn't work with arbitrary .scad files but it does let you work with its text files that are compatible with OpenSCAD.