Burrman,
I had looked at your post in which you included results from Rhino's UnrollSrf command.
(MoI's edge = 18.7470243394886 / Rhino's unrolled edge = 18.7500218509622) I guess I looked at that and decided it was close enough for me. But I don’t want to imply that I don’t appreciate people who strive for more precision.
In the model which I posted earlier, I used 15 points of correspondence: The results were:
38.1236928 for the edge of the solid and
38.1219458 for the curve derived by the Curve Through Points method.
In the next model using the same form, I simply increased the number of points of correspondence to 30:
The results were closer:
38.1236928 for the edge of the solid and
38.1235415 for the curve derived by the Curve Through Points method.
I also laid the first curve (derived from 15 points) over the second curve (derived from 30 points) and zoomed in close to examine to amount of divergence. I snapped a few lines from various points on one line to the other resulting in lengths of:
0.006009, 0.0005429, 0.0010549
I would assume that if one increased the number of points of correspondence towards infinity (a true curve) the length of the derived curve would approach the true length of the curved surface’s edge. That gets into calculus which makes my head hurt.
Those tools describing the relationship of length to radians to degrees are interesting. I will have to examine them when I get a chance. To be honest I never understood why there should be another way of measuring angles besides degrees. I dismissed radians without really trying to understand their practical use. Thanks
- Dan