# Exact Rational Segment Arrangement DCEL with Face/Hole Topology

> Exact Rational Segment Arrangement DCEL with Face/Hole Topology is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

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.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-DATASTRUCTURES-10/exact-rational-segment-arrangement-dcel-face-hole-topology?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/exact-rational-segment-arrangement-dcel-with-face-hole-topology-8d353234
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Elf-YWJeSoGMTzXoY7nfd

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability exact-rational-segment-arrangement-dcel-with-face-hole-topology-8d353234 -d '<json body>'
```

Example prompt: 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.

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

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.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/exact-rational-segment-arrangement-dcel-with-face-hole-topology-8d353234/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)