  We consider the construction of a polygon $P$ with $n$ vertices whose turning
angles at the vertices are given by a sequence $A=(\alpha_0,\ldots,
\alpha_{n-1})$, $\alpha_i\in (-\pi,\pi)$, for $i\in\{0,\ldots, n-1\}$. The
problem of realizing $A$ by a polygon can be seen as that of constructing a
straight-line drawing of a graph with prescribed angles at vertices, and hence,
it is a special case of the well studied problem of constructing an \emph{angle
graph}.
  In 2D, we characterize sequences $A$ for which every generic polygon
$P\subset \mathbb{R}^2$ realizing $A$ has at least $c$ crossings, for every
$c\in \mathbb{N}$, and describe an efficient algorithm that constructs, for a
given sequence $A$, a generic polygon $P\subset \mathbb{R}^2$ that realizes $A$
with the minimum number of crossings.
  In 3D, we describe an efficient algorithm that tests whether a given sequence
$A$ can be realized by a (not necessarily generic) polygon $P\subset
\mathbb{R}^3$, and for every realizable sequence the algorithm finds a
realization.
