  Uniform distribution of the points has been of interest to researchers for a
long time and has applications in different areas of Mathematics and Computer
Science. One of the well-known measures to evaluate the uniformity of a given
distribution is Discrepancy, which assesses the difference between the Uniform
distribution and the empirical distribution given by putting mass points at the
points of the given set. While Discrepancy is very useful to measure
uniformity, it is computationally challenging to be calculated accurately. We
introduce the concept of directed Discrepancy based on which we have developed
an algorithm, called Directional Discrepancy, that can offer accurate
approximation for the cap Discrepancy of a finite set distributed on the unit
Sphere, $\mathbb{S}^2.$ We also analyze the time complexity of the Directional
Discrepancy algorithm precisely; and practically evaluate its capacity by
calculating the Cap Discrepancy of a specific distribution, Polar Coordinates,
which aims to distribute points uniformly on the Sphere.
