Bathymetry Roulette generation implementation notes

Documentation index · Generation guide · Generation methods · Natural Earth data

Outcome and feasibility

Stage 4.5 is implemented as the projection-aware bathymetry-roulette pass. It combines the original twelve-color Natural Earth blue ramp with a second, independent form encoding: a progressively more complex Izzi roulette family for each depth threshold. Every roulette is an even-odd-filled form at 30% opacity. Each family expands into an explicit overlapping field whose nearby cells share a deterministic projected-page Voronoi assignment rather than displaying one canonical symbol on a uniform grid. The pass writes one layered SVG for every production projection and can export the corresponding PDF and PNG review artifacts.

The design is feasible without another geographic dataset. The existing Natural Earth renderer already loads the twelve nested 1:10m bathymetry polygons, repairs and clips them at projection cuts, preserves holes, and projects them on all six map frames. Izzi’s a60-svg-curves-roulette.h, explored by izzi/examples/curves-roulette.cc, supplies deterministic closed epitrochoid and hypotrochoid paths for the visual vocabulary.

The canonical public name is bathymetry-roulette. Generation profiles also accept the requested bathymetry-rolette spelling and the earlier ledger name art-agua-roulette as aliases. Output filenames always use the canonical spelling.

Confirmed depth catalogue

Each row is the representative base style for one depth family. R:r is the fixed-to-rolling radius ratio, d/r is point distance divided by rolling radius, and the closure period is the number of rolling-circle turns sampled before the path closes. The 0 m form starts exactly at d/r = 1, the cycloid boundary; no form is below it. Depth alone raises d/r strictly to 5.00. Every level uses even-odd fill and the matching color from Natural Earth’s ordinary bathymetry scheme.

Every turn has 128 line samples. The table describes the representative base curve shown in the key; it is not a single symbol stamped unchanged across the map. Each base curve expands into twelve deterministic layout variations:

• diameter factors range from 0.74 to 1.36 around a 2.15-unit base diameter;
• phases step from 0 through 11/12 of a turn;
• centers move by up to 0.22 cells in both axes; and
• alternating rows are offset by half a cell.

Point distance is deliberately not a layout variation: all cells at one depth retain that depth’s exact d/r. Cell spacing is 1.10 page units. Even the smallest 1.591-unit curve is wider than that spacing, so neighboring roulettes overlap and their clipped forms read as a continuous field instead of a regular icon grid. Fill and stroke both use the depth blue at exactly 30% opacity; stroke width begins at 0.014 units and varies slightly between layout families. The common opaque ground is rgb(239,245,243). Thus shape, density from overlap, and the restored blue ramp all communicate depth without making any one cue carry the interpretation alone.

Layering and clipping model

The generator turns each already projected Natural Earth depth geometry into an SVG clipPath. For each depth it then paints an opaque full-frame ground through that clip and generates an explicit staggered page-space mosaic. Twenty-four deterministically jittered sites form a 6-by-4 projected-page Voronoi partition. Every field-cell center is assigned to its nearest site; each site selects one of twelve layout variations, so each variation owns exactly two regions at every depth. Neighboring cells consequently share diameter, phase, and offset behavior over broad areas. The roulette curves are not hard-clipped to the planar Voronoi boundaries: their overlapping edges can cross a region boundary and produce softer transitions and moiré. Natural Earth depth geometry remains the only geographic clip. All coordinates are written into the SVG and collected into twelve semantic variation groups. There is no SVG <pattern> element or reused canonical curve in the field.

This follows the compositional model of the historical ocean pass: establish a clipped geographic region, distribute related motif variations through a mosaic, paint the region ground, and draw the varied motif linework above it. Unlike that pass’s geographic 5°/10° cells, the roulette mosaic is registered in projected page space. Curves therefore keep a consistent physical scale across projections while their offsets, sizes, phases, and Voronoi neighborhoods break the old symbol grid. The depth’s d/r does not vary spatially.

The twelve depth groups paint shallow to deep, matching the source nesting order. Because each depth paints the same opaque ground before its linework, a deeper threshold replaces the shallower field beneath it and the visible result is a set of exclusive bands without an expensive polygon-difference pass. Projection-safe geographic clipping still comes from the shared Natural Earth pipeline, including even-odd polygon and hole behavior. Star-X retains the same unfolded-ocean topology used by the water pass.

The SVG layer contract is:

bathymetry-roulette-metadata
defs
  12 bathymetry-roulette-clip-* clip paths
bathymetry-roulette
  bathymetry-0m
    bathymetry-0m-roulette-ground
    12 bathymetry-0m-roulette-variation-* groups
  bathymetry-200m
  ...
  bathymetry-10000m
bathymetry-roulette-key

Every variation group contains one explicit path with all assigned cell subpaths and records its instance count, diameter factor, exact depth d/r, phase, two center offsets, and its two Voronoi site numbers. The root metadata records the 6-by-4 nearest-site assignment, absence of hard Voronoi clipping, page-space cell size, base diameter, row stagger, variation count, 30% opacity, minimum d/r, accepted-moiré policy, per-depth cell count, and total curve-instance count. For example, Cahill-Keyes contains 1,269 cells per depth and 15,228 explicit curve instances overall. The visible four-column key shows the representative base curve and blue for every depth with its abbreviated kind, radius ratio, and d/r value.

Products and commands

Generate all six layered SVGs with:

make generate-bathymetry-roulette

generate-bathymetry-roulette-projections is an equivalent family target. Use generate-bathymetry-roulette-PROJECTION for one map, or export every SVG, PDF, and 3840-pixel-long-side PNG with:

make generate-bathymetry-roulette-artifacts

The links below are immutable v14 release references. They show the blue, filled, Voronoi-grouped implementation documented above; the older v12 references retained the pre-Stage-13 monochrome algorithm. Local focused review uses assets.generated/cahill-keyes/png/bathymetry-roulette-ck-44-22.png.

The pass is also selectable through generation-profile.json as bathymetry-roulette or either compatibility alias.

Verification and interpretation limits

make check validates the twelve-entry depth catalogue and twelve-entry field variation catalogue, d/r >= 1, strict depth growth, all-filled paint rule, unique closed base and varied paths, equal 24-site distribution, unique IDs, sample counts, exact 30% opacity, and one-, two-, and seven-turn closure periods. Each generator then reopens its SVG and checks the projection view box, Voronoi-field metadata and counts, twelve clip paths, 144 variation groups, depth paint order, ground/clip references, hole-preserving clip rules, sufficient projected geometry, finite output, absence of SVG pattern definitions, and presence of every original Natural Earth bathymetry blue.

The explicit variation paths are intentionally large XML nodes. External libxml2 validation should therefore use xmllint --huge --noout; ordinary mode may stop at its node-size guard even though the document is well formed.

The fields encode categorical Natural Earth thresholds, not continuous seafloor elevation or uncertainty. Roulette shape does not imply current, direction, geology, or measured roughness. Curves are intentionally clipped into partial, overlapping arcs at coastlines and depth boundaries. Dense fills, interference between adjacent curves, and moiré at some display or export scales are intentional properties of the confirmed artwork; they should not be read as additional bathymetric data. Every field instance is serialized rather than referenced, so SVG/PDF size and rendering cost are deliberately not bounded as part of this generative pass.