  We generalize the construction of the bracelet and bangle bases defined by
Musiker, Schiffler and Williams, and the band basis defined by D. Thurston to
cluster algebras arising from orbifolds. We prove that the bracelet bases are
positive, and the bracelet basis for the affine cluster algebra of type
$C_n^{(1)}$ is atomic. We also show that cluster monomial bases of all
skew-symmetrizable cluster algebras of finite type are atomic.
