A method of decoding point cloud data comprises obtaining a bitstream that includes an arithmetically encoded syntax element indicating a vertical point position offset within a node of a tree that represents 3-dimensional positions of points in a point cloud represented by the point cloud data; and decoding the vertical point position offset, wherein decoding the vertical point position offset comprises: determining a laser index of a laser candidate in a set of laser candidates, wherein the determined laser index indicates a laser beam that intersects the node; determining a context index based on whether the laser beam is above a first distance threshold, between the first distance threshold and a second distance threshold, between the second distance threshold and a third distance threshold, or below the third distance threshold; and arithmetically decoding a bin of the vertical point position offset using a context indicated by the determined context index.