The systems and methods discussed herein implement a volumetric approach to point cloud representation, compression, decompression, communication, or any suitable combination thereof. The volumetric approach can be used for both geometry and attribute compression and decompression, and both geometry and attributes can be represented by volumetric functions. To create a compressed representation of the geometry or attributes of a point cloud, a suitable set of volumetric functions are transformed, quantized, and entropy-coded. When decoded, the volumetric functions are sufficient to reconstruct the corresponding geometry or attributes of the point cloud.