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 I agree that Boolean operations, offset e minkovski of objects defined by points has its own interested. However, my point when I started this thread was the inefficiency of the projection() operator. I consider brute force to approach the projection by simply joining polygons by Boolean union. Something better would be expected but it seems that is the way OpenSCAD does projection as you can see by this small example:\$fn=400;tw=180;sc=0.01;projection()union(){  linear_extrude(20,twist=tw,scale=sc)    circle(30);   mirror([0,0,1])     linear_extrude(20,twist=tw,scale=sc)      circle(30);}It took more than 7 min. in my computer to find a circle with 400 vertices at the end. Even with tw=0 and sc=0.8, it required 8 sec.I think the union of polygons is one of the worst strategy to projection despite its conceptual simplicity. The border of the projection of a polyhedron is contained in the projection of its vertical silhouette edges namely and loosely those edges whose adjacent faces are one facing upward and the other, downward. Usually the set of silhouette edges is a small fraction of the total number. After finding the silhouette edges and projecting them a sweep algorithm may be used to connect the segments and define a polygon. To those that may be interested, here is a reference: It is not an easy task to implement in OpenSCAD language but it would be far easier and faster than polygon union. Anyway, I am not interested here in native language implementations of projection but to have a faster built-in one. _______________________________________________ OpenSCAD mailing list [hidden email] http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org
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