o paper: add remap and performance figures; expand architecture/cross-section sections; update both drafts

Author: Rajeev Jain

paper/images/performance.svg

@@ -67,6 +67,19 @@ We compare UXarray to adjacent tools and libraries (e.g., generic mesh readers,
 
 # Implementation
 
+## Architecture and design
+
+We organize UXarray around a core Grid abstraction paired with Xarray-backed UxDataArray/UxDataset containers. Accessors (subset, remap, cross_section, plot) provide mesh-aware operations that preserve dimensions and coordinate semantics while normalizing disparate I/O formats into a minimal UGRID-consistent contract. Figures above depict the architecture and data flow.
+
+## Cross-sections
+
+Great-circle sampling uses pyproj.Geod on WGS84 to compute intermediate lon/lat along the geodesic, which are then mapped to unit-sphere Cartesian coordinates for face lookup. Constant latitude/longitude modes sample uniform steps along parallels/meridians. Values are gathered via nearest-face selection and returned with a new steps dimension plus along-track lat/lon coordinates.
+
+Caveats and design notes:
+- For integer-typed inputs, NaN representation requires upcasting to float when samples fall outside the mesh.
+- Current implementation materializes the backing array; future work will preserve dask laziness where supported.
+- Face selection depends on get_faces_containing_point behavior and grid coverage.
+
 - Core abstractions: Grid and UxDataArray, with UncachedAccessor-based extensions.
 - I/O across multiple formats with normalization to a common topology representation.
 - Cross-sections via geodesic and constant-lat/lon sampling with nearest-neighbor face selection.
@@ -87,6 +100,8 @@ cs = uxds["psi"].cross_section(start=(-45, -45), end=(45, 45), steps=200)
 
 ![Cross-section modes](images/cross_section_modes.svg)
 
+![Remap pipeline](images/remap_pipeline.svg)
+
 # Use cases
 
 - Cross-section analysis along great-circle arcs and along constant parallels/meridians, including event-centric slices (e.g., cyclones, fronts).
@@ -98,6 +113,8 @@ cs = uxds["psi"].cross_section(start=(-45, -45), end=(45, 45), steps=200)
 
 # Quality control
 
+![Illustrative performance](images/performance.svg)
+
 Continuous integration, unit tests, style and linting (pre-commit, ruff), and multi-platform testing. Target Python 3.10+.
 
 # Acknowledgements

paper/images/remap_pipeline.svg

@@ -103,6 +103,10 @@ examples of UXarray usage (with attribution) once gathered.
   <img src="images/cross_section_modes.svg" alt="Cross-section modes" width="800" />
   <figcaption>Figure 4: Cross-section modes supported: geodesic (great-circle), constant latitude, constant longitude.</figcaption>
 </figure>
+<figure>
+  <img src="images/remap_pipeline.svg" alt="Remap pipeline" width="800" />
+  <figcaption>Figure 5: Remapping pipeline and diagnostics.</figcaption>
+</figure>
 
 <h3>Conclusions</h3>
 <p>