RDFXML2SVG: fix the force layout's asymptotics and physics

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The Fruchterman–Reingold positioning in RDFXML2SVG.xsl was unusable beyond a few dozen nodes. This rebuilds the machinery around the same force model and fixes five genuine defects in the physics found along the way.

Performance

Wall clock incl. ~1.1s npx/SEF-compile startup; SaxonJS 3.0.0-beta2, default 30 steps, synthetic flat RDF/XML graphs (~1.3 edges/node):

Input	master	this branch
50 nodes	8.5 s	1.7 s
100 nodes	506 s	3.1 s (~165×)
250 nodes	extrapolates to hours	16.8 s
500 nodes	—	67.5 s

What changed:

• positions live in one map keyed by node id (O(1) lookups where the sequence-of-maps predicate scans $seq[?node-id eq $id] made every step O(n³)); adjacency and the circle seed are computed once, and the O(n²) non-adjacent-ids lists are gone along with the per-edge map rebuild + regroup dance;
• hot-path map parameters are declared as="map(*)", not the precise map(xs:string, map(*)) — SaxonJS validates a declared deep map type entry by entry on every call and parameter binding; on the tunneled positioning pass this alone cost 8.6 s of fixed time at n=250 (the single largest measured share);
• each step buckets nodes into a spatial grid (0.7 spring lengths per cell, built with for-each-group — map:merge 'combine' re-copies a packed cell's list per node) and repels against a deterministic, spatially stratified sample of the 3×3 neighborhood (≤3 per cell, ≤16 total) — the customary ~2k-cutoff grid approximation of FR;
• the per-node displacement is a single XPath expression with sqrt-free Δ·k²/d² repulsion (per-pair XSLT instructions dominated the profile).

Correctness

Layouts differ from the old output beyond the sampling approximation, because the old physics had defects:

• repulsion was scaled by node degree — the edge-record regrouping summed a node's repulsion displacement once per incident edge record;
• attraction acted twice per adjacent pair (the edge list carried both directions and each record pulled both endpoints); it now acts once, as the cited paper defines;
• the canvas clamp was broken math — it mixed the axes (width²/4 − y² is a circle, not the width×height ellipse), took abs() of negative sqrt arguments, and fed the already re-shifted x into the y clamp; now a rectangular frame clamp followed by a radial projection onto the inscribed ellipse;
• coincident nodes could stick forever (zero distance contributed zero force); they now separate along a deterministic direction derived from id order;
• line clipping divided by zero for horizontally aligned nodes (the acknowledged TO-DO), emitting NaN coordinates — reproduced on a 100-node graph; now a unit-vector walk-back with no case analysis. Plus the literal-line x-diff=0/y-diff=0 branch set y2 from $x2 (typo).

Scope and verification

The RDF-side patterns are untouched — the contract stays Jena's RDFXML_PLAIN, now spelled out in the header note. $spring-stiffness was never used by the force model, before or now; it stays for signature compatibility. The positioning internals (ac:SVGPositioningLoop, ac:force-step, the ac:SVGPositioning tunnel) have no external dependents in Web-Client or LinkedDataHub.

Verified: identical node/line/viewBox inventory against the old output on 50/100-node graphs; no NaN; byte-identical positions across repeated runs (the hsl() type-coloring was never run-stable under SaxonJS's random-number-generator and still is not); side-by-side visual check on a small ontology.

🤖 Generated with Claude Code

https://claude.ai/code/session_01FJSsKMVPsAKPVvpLYoK7SS