  The basic goal of quantization for probability distribution is to reduce the
number of values, which is typically uncountable, describing a probability
distribution to some finite set and thus to make an approximation of a
continuous probability distribution by a discrete distribution. It has broad
application in signal processing and data compression. In this paper, first we
define the uniform distributions on different curves such as a line segment, a
circle, and the boundary of an equilateral triangle. Then, we give the exact
formulas to determine the optimal sets of $n$-means and the $n$th quantization
errors for different values of $n$ with respect to the uniform distributions
defined on the curves. In each case, we further calculate the quantization
dimension and show that it is equal to the dimension of the object; and the
quantization coefficient exists as a finite positive number. This supports the
well-known result of Bucklew and Wise (1982), which says that for a Borel
probability measure $P$ with non-vanishing absolutely continuous part the
quantization coefficient exists as a finite positive number
