{"uid":"cap_Elf-YWJeSoGMTzXoY7nfd","slug":"exact-rational-segment-arrangement-dcel-with-face-hole-topology-8d353234","name":"Exact Rational Segment Arrangement DCEL with Face/Hole Topology","description":"Recover the complete exact planar subdivision induced by supplied closed segments, including overlap splitting, twin/next incidence, disconnected components, bounded faces and inner boundary components; not segment clipping or intersection counting.","url":"https://detect.halowerk.com/v1/F-TD2000-DATASTRUCTURES-10/exact-rational-segment-arrangement-dcel-face-hole-topology?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","$defs":{"json":{"anyOf":[{"type":"null"},{"type":"boolean"},{"type":"number"},{"type":"string","maxLength":6000},{"type":"array","items":{"$ref":"#/properties/input/properties/body/properties/artifact/%24defs/json"},"maxItems":512},{"type":"object","maxProperties":128,"additionalProperties":{"$ref":"#/properties/input/properties/body/properties/artifact/%24defs/json"}}]}},"required":["arrangement"],"properties":{"arrangement":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["segments"],"properties":{"segments":{"type":"array","items":{"$ref":"#/properties/input/properties/body/properties/artifact/%24defs/json"},"maxItems":512}},"additionalProperties":false},"claim":{"$ref":"#/properties/input/properties/body/properties/artifact/%24defs/json"}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_Br-kVTvwbrwn62kAJsJg8","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the complete planar subdivision (DCEL) induced by a set of closed line segments, returning all half-edges, faces, bounded regions, inner boundary components, and connectivity incidence with overlap splitting.","exampleAgentPrompt":"Take these 12 closed line segments and compute the full exact planar subdivision they induce — I need the complete DCEL with all half-edge twin/next incidence, every bounded face, and all inner boundary (hole) components, including any disconnected parts.","exampleUseCases":[{"title":"Architectural floor plan topology recovery","prompt":"I have the wall segments of a floor plan as closed line segments — can you compute the complete planar subdivision they form, with all rooms (bounded faces), holes, and half-edge connectivity so I can traverse adjacency between rooms?"},{"title":"Validating claimed polygon arrangement","prompt":"I submitted a planar arrangement claim for these 20 closed segments. Can you recover the exact DCEL including all face/hole topology and check whether the claimed structure matches what the segments actually induce, including any overlapping splits?"},{"title":"Circuit board region decomposition","prompt":"Here are the closed boundary segments of a PCB layout. I need the full planar subdivision with every bounded face, inner boundary component, and twin/next half-edge incidence — including properly split overlapping segments — so I can enumerate all enclosed copper regions."}],"resultDescription":"Returns the complete doubly-connected edge list (DCEL) for the planar arrangement induced by the input segments, including: all half-edges with twin and next pointers, bounded and unbounded faces, inner boundary (hole) components, and disconnected components. Overlap segments are properly split. The topology is computed with exact rational arithmetic.","failureModes":["Malformed or non-closed segments in input array causing rejection","Exceeding the 512-segment array limit resulting in schema validation error","Invalid or inconsistent arrangement claim leading to mismatch error","Degenerate input (e.g. all collinear segments) producing unexpected face structure","Ill-formed JSON artifact structure causing request failure"],"whenToPreferThis":"Use this endpoint when you need the full exact planar topology — not just intersection counts or clipped segments — but the complete DCEL with face enumeration, hole detection, and half-edge incidence for a set of closed line segments. It is the right choice for applications that must traverse face adjacency, enumerate bounded regions, detect holes, or verify a topological claim about a planar arrangement. Prefer it over intersection-only APIs when downstream processing requires walking the half-edge structure.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:32:51.020Z","isFirstParty":false,"canonicalSlug":"exact-rational-segment-arrangement-dcel-with-face-hole-topology-8d353234"}