STL Tile Approach (Printable Earth)

This document captures how model-render-print turns the GDEM data on the shared /datasets volume into STL models that load into a slicer and print on a 3D printer. It is a decision log; mark each option decided with a date and reason.

Goal

Printable 3D models of the Earth’s surface from the ETOPO 2022 dataset (/datasets/dataset-etopo-2022/, 15-arcsecond GeoTIFF tiles, ~6 GB). The surface of the globe is divided into roughly equal-size tiles along lines of latitude and longitude; each tile is an STL file that: - loads into OrcaSlicer / PrusaSlicer (binary STL, millimeters, watertight), - prints on a common FDM printer (each tile fits the bed, flat bottom down), - has a flat bottom so it sits against the printer bed, - mates with its neighbors along the top surface, so the assembled set shows the whole globe.

Source data

• ETOPO 2022 — global relief model combining land elevation and seafloor bathymetry at 15-arcsecond (~450 m) resolution, as 350 GeoTIFF tiles.
• Maintained and versioned by the model-elevation-earth project; the manifest is /datasets/manifest.yml (etopo-2022).
• Read-only consumption: this project never writes to /datasets; derived tiles go in dataflow.out/stl/.

Candidate approaches

1. Spherical patch tiles — CHOSEN (decided 2026-08-26)
   • Each tile is the solid piece of a globe: the top surface is the sphere at radius R + relief, the bottom is a flat chord plane, and the side walls are vertical in the tile’s local frame. Tiles placed bottom-down print flat; the top surfaces are the exact spherical surface, so the assembled outside of a set is the globe.
2. Flattened relief plaques — rejected (decided 2026-08-26)
   • Each tile is a flat map projection extruded with relief on top (the common “terrain plate” approach). Simpler, but the pieces are flat plaques that cannot assemble into a globe; the task names the surface of the globe, so the pieces must carry the sphere’s curvature.
3. Full solid globe / slice stack — deferred (decided 2026-08-26)
   • Print the whole globe (possibly in stacked rings) in one model. Larger prints than the bed allows at useful sizes; the task asks for lat/lon tiles.

Tiling scheme

• Latitude bands of equal height band_degrees (default 30).
• Within a band, longitude is split into N = round(360 · cos(mid_lat) / band) tiles, so each tile covers roughly equal surface area.
• The highest and lowest bands are a single round tile each (the polar caps, spanning the full 360 degrees of longitude). Decided 2026-08-26: the task allows “the highest latitude can be a single (round) tile”; both poles get the same treatment for symmetry.
• Defaults (band 30): south cap 1 + 8 + 12 + 12 + 8 + north cap 1 = 42 tiles. Band 15 gives 180 tiles (regional detail).

Geometry (per tile)

• Globe radius R (default 100 mm → 200 mm globe; fits a 220 mm bed).
• Tile-local frame: up is the sphere normal at the tile center; east and north complete the frame.
• Top surface: for each sample (lat, lon), the point is (R + h) · r̂ where h is the mapped elevation and r̂ the unit radial vector; the point is expressed in the tile-local frame.
• Elevation mapping: h = base + relief · (e − e_min) / (e_max − e_min) with the global ETOPO range (so neighboring tiles share absolute scale). Defaults: base 3 mm, relief 20 mm → Everest ≈ 23 mm above the bed, Challenger Deep ≈ 3 mm.
• Bottom: a flat plane at the local z of the shallowest top point minus base, translated so the plane is z = 0 (the bed plane in the STL).
• Side walls: chamfered. Each wall quad is bounded above by the top-surface boundary edge and below by the radial projection of that edge onto the bottom plane, so every wall plane contains the globe center. In the assembled globe each shared edge pair therefore lies in one common wall plane (no wedge gaps), and the walls flare slightly outward going up (a trivially printable overhang).
• Underside mark: the tile id (e.g. N30E045) is engraved as recessed grooves on the underside (z stays 0; the grooves cut upward into the base). Engraved, not raised, so the tile still sits flat on the bed.
• Key socket: a rectangular recess cut into the centre of the underside, 6 mm (tile east) × 4 mm (tile north) × 2 mm deep, centred on the tile centre. It receives the support ring’s tab (see the ring lattice below); the engraved id sits in the lower rows of a taller, still centred label box so the socket stays clear.
• The tile is watertight: top quads (fan at the pole), chamfered wall strips, engraved bottom face (ring fan around the label grid).
• Units: millimeters; the STL’s z = 0 is the bed plane, so slicers can “lay on face” without translation.

Sampling

• Per-tile mesh grid at sample_degrees (default 0.25) in latitude.
• Longitude spacing scales by 1 / cos(mid_lat) so the physical vertex spacing stays roughly constant across the globe (a polar cap is not over-built at 360-degree density).
• Average resampling via GDAL from the source VRT; a coarse global grid supplies the elevation range used for the mapping.

Toolchain

• GDAL 3.8.4 on the build host (gdalbuildvrt for the source VRT, osgeo.gdal.Warp for per-tile sampling) plus Python 3 with osgeo/numpy. Verified on the build host 2026-08-26.

Assembly (superseded: internal frame)

• An earlier plan added an internal hub-and-strut frame. It is dropped: the glued seams need help, but a central hub with one strut per tile is too hard to assemble and align (see the decision log below).

Assembly (superseded: rib + hemispheres)

• An intermediate plan assembled each hemisphere from a full-diameter reinforcing rib that seated the first row of tiles, with tile-to-ring sockets and between-tile wall keys. The ribs, the sockets and the wall keys are dropped (see the decision log below).

Assembly (tiles only: STEP export for CAD)

• The interior solid with the through-bore is dropped. The tile set can be exported as STEP (AP214) with make step (scripts/tiles_step.py) for editing in a CAD tool such as OnShape:
  • dataflow.out/step/tiles-all.step — all 42 tiles in assembled orientation (each solid at its world position in the globe, with its own local frame, exactly as it sits when the printed tiles are glued), as one product holding 42 separately named solids, so a CAD import gives one part studio with 42 bodies in place;
  • dataflow.out/step/tiles/tile-<id>.step — one file per tile, for editing a single tile. Millimetres are declared through the geometric representation context, so CAD tools import at the right scale. --hemisphere north|south takes one hemisphere and --tile <id> (repeatable) takes named tiles; the tiles are meshed at 5 degrees by default because the STEP is a faceted B-rep and a finer grid multiplies the file size.

Assembly (current: support ring lattice)

• The globe is larger than the print bed, so the internal support is printed in sections and assembled inside the tiles: 3 horizontal rings + 12 meridian arcs + 1 cap stem = 16 pieces per hemisphere, rendered by make rings (scripts/rings_build.py) into dataflow.out/rings/.
• Horizontal rings: one flat washer per latitude band, at the band centres (15° / 45° / 75° N; -15° / -45° / -75° for the south). The washer is 8 mm thick radially and 6 mm tall, and its top and bottom faces lie in planes parallel to the equator’s — the outer and inner faces are vertical cylinders — so it stands on its whole annular face and prints flat. Its outer top rim just reaches the sphere of radius tiles_radius - 0.6 mm, so it hugs the tiles without touching them, and the washer hangs from that rim toward the equator. A ring carries a tab over every tile centre of its band (12 on the equatorial ring, 8 on the temperate ring): the tab is 5.6 × 3.6 mm and runs along the tile’s up axis into the tile’s 6 × 4 × 2 mm centre socket, 1.8 mm deep and 0.2 mm clear per side. Building each tab in the tile’s own frame is what lets a flat ring key a tilted tile; a tab’s root sits inside the ring wall, so the two fuse into one printed piece.
• Cap ring: the 75°-band ring has no tabs — the polar cap tile centres on the pole, not on the ring — so it is the structural ring that the meridian arcs and the cap stem tie into.
• Meridian arcs: 12 arcs, each running from the equator up to the cap ring, 8 mm thick × 6 mm wide. Each arc’s radius is interpolated so that it either passes inside a ring’s bore or passes it on the key side, whichever keeps it nearer the ring, always with 0.6 mm of clearance. At every crossing the arc carries a key — a 5.6 mm wide box that seats in a 6 mm wide notch in the ring face the arc arrives at, 2.8 mm deep with 0.2 mm of slack, and runs back past the ring’s bore into the arc’s body so the two fuse. The meridians sit at 0° / 30° / … / 330°: those longitudes are the equatorial band’s tile seams, so a notch never lands on a tab (the equatorial tiles centre on 15° + 30°k and the temperate tiles on 22.5° + 45°k, both at least 7.5° away).
• Cap stem: a 6 × 4 mm post on the polar axis from the cap ring’s spokes up into the polar cap tile’s socket (0.2 mm tip clearance), plus two crossed spoke bars that run from the axis into the cap ring’s wall. The spokes sit on the diagonals, so they clear the meridians’ keys, and in the half of the wall the keys do not use. The post rises from the spokes’ plane, so the piece stands on its cross when printed.
• Bed fit: the 15° ring is the largest piece at Ø189.6 mm, leaving ~15 mm on a 220 mm bed; the meridian arcs are ~105 × 105 × 6 mm and the cap stem ~28 × 28 × 8 mm. print_ready lays every piece flat (meridian planes rotated horizontal, southern pieces rolled over so their up side is up) with z = 0 on the bed.
• Verification: tests/05-rings-math.sh is a portable (no GDAL) check that each ring’s horizontal faces lie only at its bottom, its top or the notch roof, that each ring stands on a whole annulus, that the tabs seat inside the sockets in the tile’s own frame, that the meridians never enter a ring’s material but their keys reach into their bodies, that the south mirrors the north, that the cap stem reaches the pole socket and its spokes land in the cap ring’s wall, and that every print-ready piece stands flat and fits the bed. The rendered STLs are checked separately for watertightness, positive volume and z = 0.

Row diameters

• The horizontal (small-circle) diameter of the base sphere at the latitude rows between the 30-degree bands, for R = 100 mm:
  • 0° (equator, N00 ↔︎ S30 join): 2·R·cos 0° = 200.0 mm
  • 30° (N00 ↔︎ N30, S30 ↔︎ S60 joins): 2·R·cos 30° = 173.2 mm
  • 60° (N30 ↔︎ cap, S60 ↔︎ cap joins): 2·R·cos 60° = 100.0 mm
• With relief, the local diameter at any point is 2·(R + h)·cos φ, up to ~220 / 190.5 / 110 mm where the topography is highest.

Open questions

• Print calibration: relief/base defaults tuned against a real print on the Elegoo Centauri Carbon (0.4 mm nozzle).
• Larger fidelity: finer sample spacing (e.g. 0.1 degree) and/or smaller band heights for regional tiles; watch STL size per tile.

Decision log

• 2026-08-26 — Approach: spherical patch tiles (candidate 1). Reason: tiles carry the globe’s curvature and assemble along the top surface; flattened plaques (candidate 2) cannot assemble and the task names the globe’s surface.
• 2026-08-26 — Tiling: 30-degree bands, longitude split by cos(mid_lat), single polar cap tiles. Reason: roughly equal surface area per tile, 42 tiles for the whole globe, round polar caps.
• 2026-08-26 — Globe size: R = 100 mm (200 mm diameter). Reason: fits a common 220 mm bed while keeping 30-degree tiles ~52 mm across.
• 2026-08-26 — Solid construction: top surface + flat bottom + vertical local walls, watertight per tile; bottom translated to z = 0. Reason: prints flat on the bed; slicers need watertight solids. Superseded the same day: the walls are now chamfered (below).
• 2026-08-26 — Elevation mapping: global ETOPO range, base 3 mm + relief 20 mm. Reason: consistent absolute scale across tiles; print-friendly relief; deepest ocean floor still clears the base plate.
• 2026-08-26 — Sampling: 0.25-degree default, longitude spacing scaled by 1/cos(mid_lat). Reason: ~0.4 mm vertex spacing at the 200 mm globe (matches the 0.4 mm nozzle); polar caps are not over-built.
• 2026-08-26 — Output: binary STL + manifest.json in dataflow.out/stl/. Reason: compact, universally accepted by slicers; the manifest carries parameters and provenance for make check and the dashboard.
• 2026-08-26 — Toolchain: GDAL 3.8.4 + Python 3 with osgeo/numpy. Reason: available on this host (verified 2026-08-26); no custom reader needed.
• 2026-08-26 — Oceans: flat for now (--oceans-flat on the standard run). Reason: the near-term prints are land-focused; seafloor relief is deferred. Flat oceans clamp water-covered cells to 0 m elevation, so all ocean cells map to one sea-level plateau height above the base and the coastline rim stays visible; a flush-to-base variant remains possible.
• 2026-08-26 — Chamfered walls through the globe center. Each wall quad’s plane contains the globe center, so every shared edge pair lies in one common plane in the assembled globe and the wedge gaps disappear. Reason: the vertical walls left per-tile wedge gaps when tiles were tilted up and joined; the chamfer makes the mating walls coplanar.
• 2026-08-26 — Underside id: engraved (recessed) tile id on the underside. Reason: the user asked for an identifying mark to aid assembly; engraving keeps z = 0 so the tile still sits flat on the bed.
• 2026-08-26 — Verification: watertightness (edge-manifold), flat bottom at z = 0, expected bounds, positive signed volume via make check. Reason: these are the properties slicers rely on.
• 2026-08-27 — Ribs and between-tile alignment keys deleted; the assembly approach is under revision. The reinforcing ribs (with the tile-to-ring underside sockets) and the wall fin/groove keys are removed from the tile build, the site (the rib page is gone) and this document; the previous state was tagged in git for reference. Row diameters of the base sphere (R = 100 mm) at the 0/30/60-degree rows are 200.0 / 173.2 / 100.0 mm.
• 2026-08-27 — Interior support dropped; the tiles are exported as a STEP file instead. The interior-solid-and-bore support did not match what was wanted, so it is removed entirely; the tiles remain the deliverable. An AP214 STEP file with one solid per tile at its world position is written for editing in OnShape or FreeCAD, with the sample density parameterized to keep the file size practical.
• 2026-09-23 — STEP export: the whole tile set, in assembly, with millimetre units (make step, scripts/tiles_step.py). Reason: the request was for STEP files of all tiles in their assembled orientation for OnShape. The earlier exporter wrote one hemisphere with no unit context, so a CAD import could land at the wrong scale; the rewritten writer declares a millimetre geometric representation context and puts every solid in one product (a part studio with 42 placed bodies), and also writes a file per tile. tests/06-step-export.sh walks the STEP reference graph and checks that each solid sits inside its own tile’s patch of the globe.
• 2026-09-23 — Support: horizontal rings keyed into the tile centres, vertical meridian arcs keyed into the rings (the user’s plan). Reason: the support must print on a 220 mm bed while the assembled globe is 200 mm across, so it is printed in sections (16 pieces per hemisphere) and assembled inside the tiles. The ring’s tab goes into a 6 × 4 × 2 mm socket cut into each tile’s underside centre; the socket is 0.4 mm larger than the tab in both lateral directions and 0.2 mm deeper, so the parts drop together after printing.
• 2026-09-23 — Meridians sit on the equatorial tile seams (0° + 30°k). Reason: the first draft put the meridians at the equatorial tile centres (15° + 30°k), where a ring would then need a groove and a tab at the same longitude — geometrically impossible. At the seams, no crossing lands on a tab (nearest tab 7.5° away), so every meridian keeps a key at all three ring crossings.
• 2026-09-23 — The rings are flat washers, not sphere-hugging bands. Reason: the user asked for the rings’ sides to be parallel to the equator’s plane so they print flat. A band tilted to follow the sphere stands on a circular edge (the 75-degree band nearly on edge); a washer whose faces are horizontal stands on its whole annulus. The cost is that a swept profile can no longer carry the tiles’ tabs — the tiles are tilted relative to the ring — so each tab is now built in the tile’s own frame as a box rooted in the ring wall, and the meridians key into a notch in the ring face they arrive at instead of a tongue-in-groove. Southern rings and the southern stem are rolled over by print_ready, so both hemispheres print the same way up.
• 2026-09-23 — Ring lattice verified by a portable math test (tests/05-rings-math.sh) plus STL checks (watertight, positive volume, z = 0, ≤ 220 mm). Reason: the ring geometry is easy to get subtly wrong (the first render silently built every ring at twice its radius, and the cap ring at latitude 90°), so the checks assert the tile-frame fit and the assembled radii numerically rather than by eye.