In weld symbols one can specify the finish of the weld. In flush weld, for example, one needs to level the weld into a flat surface. I can imagine when this is needed: if something is required to rest flat on the welded surface, an uneven weld might get in the way.
But why do we have a symbol for a convex finish? When is it required that the weld "sticks out" like that? Similarly, why the concave? If I do a concave fillet weld for example, isn't the resulting weld less strong than intended in the weld size since it is slightly smaller due to the concave shape?