Originally Posted by
Jimbo
I always make a distinction between smooth and sharp personally. Though I do agree that they both need to achieve some kind of minimum level before you can call an edge properly honed.
But dichotomies like "properly/improperly" hide a lot of nuance and variation. Sharp and smooth lie on a continuum, and so their interaction does too.
So anyway, to me sharp is a measure related to the inverse of the distance between the two sides of the bevel (ie the smaller the distance, the higher the sharpness). The measure might actually be important: consider two possible measures - mean distance and maximum distance (over the entire edge, bevel width will vary so we need a summary measure unless we start delving into sharpness as a function of distance from heel or something, and that's just going way too complicated IMO).
Smooth, on the other hand, to me is a measure of the variability of the distances along the edge. Highly variable bevel distances will not give a smooth edge, whereas homogeneity will.
So, for the average distance measure things might get a little rough because as we all know with means, they are made up of, potentially, large and small values. So an edge with a highish sharpness (low average distance) could very well feel rough because that mean distance value comprises highly variable "peaks and troughs".
On the other hand, if you defined sharpness in terms of maximum distance, then something with a high sharpness is by definition guaranteed to be smooth because all other points along the edge must be less than the maximum, of course.
I don't know if that makes sense to people, but that's how I look at it. Feel free to ignore as you see fit! :)
James.