## Experimental Results  
### Offline Encoding  
This set of experiments highlights different results obtained by running the offline encoding tool provided by PRISMIN framework on ASCII datasets (Comma-separated values--CSV) recorded for a past public event (\"TourismA\" 2018 in Florence, Italy). The main goal of these experiments was to assess the compression ratios and accuracy of spatial attributes, in this case, locomotion of HMD users (\(S_{p}(u,t)\)). We compared the data size and accuracy results to binary formats (using different precision) and existing lossless approaches. We also evaluated discrepancies and quantization effects by employing different bit-depths for QSAs. The original recording for the original CSV dataset  
Figure 6: Examples of QSAs generated by prisms attached to a volume to track spatial attributes over time (**left**) and standalone (**right**). used A timestep of 0.1 s to capture user states: in general this is a good temporal interval to capture spatial attributes (like location in the virtual environment) while the VR session is running. The 3D scene considered is an IVE already used by CNR ISPC in several past projects [36; 37]. In order to consider only meaningful sessions, the original locomotion data were first filtered using a set of acceptance policies for sessions performed in this specific IVE: radius (R), variance (\(s^{2}\)) and duration (D). The session radius (R) represents the bounding sphere of all locomotion data for a given user: we set a minimum of 5.0 m to accept the session. Regarding variance (\(s^{2}\)) for locomotion data, a minimum of 5.0 for at least one the three dimensions was set. Finally, a minimum of 20 s for (D) was set to accept the session. At this point, several tests on filtered VR sessions were performed to assess data size and accuracy, including raw binary and image-based encoding (Section 3). First, a session volume \(V_{0}\) with extents (50.28 m \(\times\) 76.46 m \(\times\) 10.0 m) was deployed: due to voxel quantization (see Definition 4 in Section 3.1) the location maximum error for each dimension is \(e\) = \(<\pm\) 9 cm, \(\pm\) 14.9 cm and \(\pm\) 1.9 cm \(>\). A second volume \(V_{1}\) (25.27 m \(\times\) 12.85 m \(\times\) 8.28 m) was added to the 3D scene to encode finer users locomotion on a selected area (stairs) with maximum quantization error \(e\) = \(<\pm\) 4.9 cm, \(\pm\) 2.5 cm and \(\pm\) 1.6 cm \(>\). A size comparison of the original CSV locomotion dataset (2.86 Mb) with lossless binary (double precision and single byte) and QSA (PNG format, bit-depth 8, lossless) was performed. As expected, binary encoding (double and single byte precision) resulted in great compression ratios (21% and 5% respectively) compared to the original CSV (see Figure 7). We applied the image-based model to the same locomotion data using lossless PNG format (bit-depth 8), obtaining a very compact QSA (20.1 kb) that encodes all locomotion sessions for all users. In order to assess image quantization effects, we performed multiple encoding tests using different bit-depths for QSA, decreasing data  
Figure 7: Top: data size comparison (Kb) between original dataset (CSV) and binary (double and byte precision). Bottom: comparison between binary (byte) and QSA (lossless PNG with bit-depths 8, 6 and 4). size but obviously increasing quantization errors for 3D location decoding. The locomotion data encoding using QSA with bit-depth = 8 led to the following compression ratios: 0.68% (CSV/QSA); 3.19% (binary double precision/QSA); 12.77% (binary byte precision/QSA). The latter employs the same quantization (each 3D location is represented by 3 bytes) and can be used for direct comparison between datasets using same accuracy. As a reference, a lossless encoding scheme for 3D points [38] reports compression ratios of 16.10% and 26.27%, furthermore the encoding/decoding routines in that case depend on previous point (distance-based predictors) and it is more computationally intensive.