loops: implied closed loops from loose LINE and ARC chains (#1906)

* loops: implied closed loops from loose LINE and ARC chains

LOOPS is a read-only inquiry command that chains LINE and ARC endpoints
meeting within a tolerance. Closed loops report their member handles,
perimeter, area and winding (exact with arcs, like SHAPES); open chains
report the endpoint gap, where it is and their length; branch junctions
(three or more ends at one point) are reported but excluded from the
chains rather than resolved.

The tolerance defaults to 1e-9 x the extents diagonal and is an option.
The quadratic endpoint pairing is capped (maxPairs, 1,000,000 by default)
and reports capped/pairTestsNeeded instead of guessing from a partial
pairing. Degenerate lines and arcs are counted under skipped; full-circle
arcs close on their own. The command is read-only.

Fixes #1437

* loops: cap maxPairs at 100,000,000 so a caller can't ask for unbounded work

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

---------

Co-authored-by: Brandon Thomas <echelon@gmail.com>
Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

docs/mcp.md

@@ -43,6 +43,7 @@ Example client configuration (Claude Code / Claude Desktop):
 | `inspect_drawing {entities?, limit?}` | Counts, extents, layers, styles, blocks, layouts, selection, undo history and entities. |
 | `query_entities {type?, layer?, window?, crossing?, limit?, offset?}` | Filtered entities with handles and geometry. `window` `[[x0,y0],[x1,y1]]` finds objects whose geometry is inside it or crosses it (`crossing: false`: entirely inside). `count` is every match, `returned` the page (`offset`, `limit`, default 500). |
 | `execute {"command": "shapes", "params": {type?, layer?, window?, crossing?, limit?, offset?, tolerance?}}` | Facts about the closed shapes — closed polylines, circles, full ellipses, closed splines: perimeter, area, centroid, winding, the first self-intersection and coincident vertices, exact with arcs and bulges. Other matches are counted under `skipped` with the reason. |
+| `execute {"command": "loops", "params": {tolerance?, maxPairs?, limit?, offset?}}` | Implied closed loops from loose LINE and ARC chains: each closed loop with its member handles, perimeter, area and winding, exact with arcs; each open chain with the endpoint gap, its location (`at`, `ends`) and length; and branch junctions (three or more ends meeting), reported but not resolved. `tolerance` defaults to 1e-9 × the extents diagonal; the quadratic endpoint pairing stops at `maxPairs` (default 1,000,000) and reports `capped` with `pairTestsNeeded` instead of guessing from a partial pairing. |
 | `query_entities {type?, layer?, selected?, window?, crossing?, limit?, offset?}` | Filtered entities with handles and geometry. `selected: true` restricts results to the current selection in the active space; an empty selection returns no entities. Omitted/false queries all entities in that space. Filters combine before paging. `window` `[[x0,y0],[x1,y1]]` finds objects whose geometry is inside it or crosses it (`crossing: false`: entirely inside). `count` is every match, `returned` the page (`offset`, `limit`, default 500). |
 | `render {width?, height?, fit?, window?}` | A PNG image of the drawing, or of just the area `window` `[[x0,y0],[x1,y1]]` (one sheet or room of a large drawing; 1600 px wide with the window's shape unless sized). |
 | `find_text {contains?, layer?, window?, limit?, offset?}` | The readable texts — TEXT, MTEXT without formatting codes, block attributes, multileaders — with text, insertion point, height, rotation, style, layer and handle; filtered by content (any case), layer and a window around the insertion points. Read-only (the `texts` command). |