Tuesday, August 15, 2006
Offsetting and sharp points
Ignore the inner offset triangle and quadrilateral for the moment; just stick with the outside edges. We have six lines A...F that are infinitely long and are considered half-planes solid on their sides with the black dots. Using . for intersection and + for union, the boolean expression that describes the outer shape is
This is exactly how the RepRap Java code (subversion repository - start here) solves the offset problem.
Anyway, it still seems like it would have a problem with the seams. Move D down a bit more.. allow 4 or 5 threads widths between the interior angle and the bottom..? I suspect you will still have a triangle and quadralateral. Tracing a perimeter in this case might cause two problems:
1. You would be trying to squish too much material as you traced the inset E and F as it approached D.
2. Subsequent layers would print the perimeter identically. I suspect if you squeezed the two ears at the top together, the piece would have a tendency to fracture along the seam created between E and F. I think you'd also be able to observe the seam on side D.
Again, I'm not sure if this would be common in things to be printed, on a reprap, and maybe it's more a mathematical curiosity than any problem with the extrusion path.
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