Normal smooth sharpening - is that possible?

Here’s what i think of.


3 edges, extrude points connecting the edges at another direction relative to the center edge, if in same direction, build a quad, else subdivide new edges and center edge and connect new points, then build two quads. two edges of new quads are x and y axis, and another two should be subdivided and resulting points coordinates in x,y including center point, filtered by square root. then x,y coordinates is quad between edge and duplicate of another edge, and x- is first center edge vert and x- is the second, y+ is positive bump and y- is negative. So is that possible? And is that possible in GLSL?
Of course, direction and length of the edges should be passed as vertex normal.

Your drawing and explanation are both quite hard to grip. Please use thinner and cleaner lines, annotations and separated steps when doing this kind of diagram and don’t make a rushed explanation.