  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.
