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In this paper, we present a novel proxy-based method of the adaptive haptic rendering of a variable density 3D point cloud data at different levels of detail without pre-computing the mesh structure. We also incorporate features like rotation, translation, and friction to provide a better realistic experience to the user. A proxy-based rendering technique is used to avoid the pop-through problem while rendering thin parts of the object. Instead of a point proxy, a spherical proxy of a variable radius is used, which avoids the sinking of proxy during the haptic interaction of sparse data. The radius of the proxy is adaptively varied depending upon the local density of the point data using kernel bandwidth estimation. During the interaction, the proxy moves in small steps tangentially over the point cloud such that the new position always minimizes the distance between the proxy and the haptic interaction point (HIP). The raw point cloud data re-sampled in a regular 3D lattice of voxels are loaded to the haptic space after proper smoothing to avoid aliasing effects. The rendering technique is validated with several subjects, and it is observed that this functionality supplements the user's experience by allowing the user to interact with an object at multiple resolutions.