  In this paper, first we have defined a uniform distribution on the boundary
of a regular hexagon, and then investigated the optimal sets of $n$-means and
the $n$th quantization errors for all positive integers $n$. We give an exact
formula to determine them, if $n$ is of the form $n=6k$ for some positive
integer $k$. We further calculate the quantization dimension, the quantization
coefficient, and show that the quantization dimension is equal to the dimension
of the object, and the quantization coefficient exists as a finite positive
number. Then, we define a mixture of two uniform distributions on the boundary
of a semicircular disc, and obtain a sequence and an algorithm, with the help
of which we determine the optimal sets of $n$-means and the $n$th quantization
errors for all positive integers $n$ with respect to the mixed distribution.
Finally, for a uniform distribution defined on an elliptical curve, we
investigate the optimal sets of $n$-means and the $n$th quantization errors for
all positive integers $n$.
