Existing techniques for 3D action recognition are sensitive to viewpoint variations because they extract features from depth images which are viewpoint dependent. In contrast, we directly process pointclouds for cross-view action recognition from unknown and unseen views. We propose the Histogram of Oriented Principal Components (HOPC) descriptor that is robust to noise, viewpoint, scale and action speed variations. At a 3D point, HOPC is computed by projecting the three scaled eigenvectors of the pointcloud within its local spatio-temporal support volume onto the vertices of a regular dodecahedron. HOPC is also used for the detection of Spatio-Temporal Keypoints (STK) in 3D pointcloud sequences so that view-invariant STK descriptors (or Local HOPC descriptors) at these key locations only are used for action recognition. We also propose a global descriptor computed from the normalized spatio-temporal distribution of STKs in 4-D, which we refer to as STK-D. We have evaluated the performance of our proposed descriptors against nine existing techniques on two cross-view and three single-view human action recognition datasets. The Experimental results show that our techniques provide significant improvement over state-of-the-art methods.