In this chapter, we extend the findings of Chap. 3 to 2-D kinesthetic data. For this, we again design an appropriate experimental setup and record the responses of several users to piecewise constant haptic signals. In order to predict the labels of the responses, we have used the Weber, level crossing, and conic section-based classifiers. It has been found that similar to 1-D haptic signal, the level crossing classifier performs better than the Weber classifier for all users. Thus, the level crossing classifier-based sampler turns out to be a good candidate for perceptually adaptive sampling mechanism for 2-D haptic data also. Further, we study the possible structures of the perceptual deadzone for 2-D haptic data and examine whether the deadzone depends on the direction of the kinesthetic force stimulus. The level crossing classifier defines the best fit deadzone around a reference vector to be circular, while the Weber classifier makes the radius a function of its current magnitude. A competing conic section-based classifier makes the kinesthetic deadzone directionally sensitive. It is demonstrated that the kinesthetic perception is circularly symmetric and is independent of the direction of the force stimulus. Hence, a user does not have any directional preference while perceiving any change in the kinesthetic stimulus. © 2018, Springer Nature Singapore Pte Ltd.