HCI researchers have long recognized the significant effects of movement direction on human performance, and this factor has been carefully addressed to benefit user interface design. According to our previous study (2012), the weights of the two target dimensions, width W and height H, in the extended index of difficulty (ID) for 2D pointing tasks are asymmetric and appear to vary periodically based on movement direction (θ), following a cosine function. However, this periodic effect of movement direction is uncertain for direct 2D touch pointing tasks, and a thorough understanding of the effects of movement direction on direct pointing tasks, such as on touch input surfaces, is still lacking. In this paper, we conducted two experiments on a 24-inch touch screen, with tilted and horizontal orientations respectively, to confirm the periodic effect in the context of direct pointing and illustrate its variations across different pointing tasks. At the same time, we propose a quantification formula to measure the real differences in task difficulty caused by the direction factor. To the best of our knowledge, this is the first study to do so. Using this formula, the ID values in different directions can be unified to the same scale and compared, providing a new perspective for understanding and evaluating human performance in different interaction environments.