We know for vector bundles on smooth projective curve we have a HN filtration. Let $0=E_0 \leq E_1 ... \leq E_n=E$ be such a filtration of $E$. Then we can construct a convex polygon with lattice point vertices where for each $E_i$ we mark the point $(r_i,d_i)$ corresponding to its rank and degree.
Given any such convex polygon with lattice point vertices can we produce a vector bundle whose Harder Narasimhan polygon is exactly that one?
Edit : After the counterexample posted in the comments I am refining my polygon. I am starting with a convex polygon in the first quadrant such that origin is a vertex. I also require the slopes to be decreasing (slopes of each edge from the left to right as the HN filtration needs that decreasing slopes criteria.
Now can I say such a polygon comes from a HN filtration?
I am not sure I really understand your question. Here is an example. $(1,0),(2,-1),(4,-2)$. These cannot come from a Harder-Narasimhan filtration since the $\mu$ sequence is $0,-1, -1/2$ and $-1<-1/2$.