A coder decodes, from a bitstream, quality unit information indicating: an occupancy tree representing a partition of a volume of a point cloud geometry, and quality units corresponding to nodes of the occupancy tree. Based on the occupancy tree, an occupied quality unit is from the quality units. The occupied quality unit contains a portion of the point cloud geometry and corresponds to a set of occupied leaf nodes of the occupancy tree. Positions of triangle vertices of the set of occupied leaf nodes are decoded from the bitstream. The coder dequantizes the positions of triangle vertices based on at least one local quality parameter associated with the occupied quality unit. The coder reconstructs the portion of the point cloud geometry based on the dequantized positions of triangle vertices.