{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.line-shape","code":"thing-line-shape","url":"https://ver.cy/models/thing/line-shape/","name":"line","alternateNames":["lip","band","belt","carousel","carrousel","luggage carousel","luggage carrousel","clinch","clench","conveyer belt","conveyor belt","conveyer"],"kind":"thing","status":"published","version":"0.1.0-research.1","language":"en","classifiers":{"family":"Thing Registry","category":"Physical world and living systems","entryKind":"noun.shape","plane":"PHY","domain":["PHY.OBJ"],"industry":[],"navPath":"","tags":[],"facets":{"substance":"form","origin":"conceptual","agency":"inert","mobility":"not-applicable","scale":"not-applicable","affordances":["observable"]}},"whatItIs":"A line is a one-dimensional geometric magnitude - length without breadth or thickness - whose extremities, when it has any, are points, equivalently the locus traced by a point moving in space.","purpose":"Enable an AI agent to recognise a line, assess whether its geometry and continuity support an intended use, and decide which measurements or transformations are valid.","scope":{"in":["Straight and curved lines, with finite, one-sided unbounded or two-sided unbounded extent","Endpoints, closure, continuity and self-intersection","Length, direction, curvature and changes of direction where defined","Placement within a plane, surface or three-dimensional space","Geometric representations and their approximation limits","Operations that preserve or deliberately change line geometry"],"out":["The width, thickness, material and colour of a drawn stroke, wire or other physical carrier","Surfaces and regions, including the interior a closed line may bound","Movement speed, elapsed time and the identity of an object following a trajectory","Network routing, flow and connectivity semantics beyond geometric incidence","Text lines, queues, product lines and other non-geometric meanings of line"],"boundaries":[]},"distinguishingFeatures":["A line records extension along its course without assigning intrinsic breadth or thickness; a visible stroke or wire has a cross-section belonging to its carrier.","A line has a course beyond a single location; an isolated point or a collapsed zero-length representation needs explicit treatment as a degenerate case.","A closed line records its boundary course without including the enclosed region.","Curvature does not disqualify a shape under this registry definition; the narrower mathematical meaning of an infinite straight line is only one possible case.","A geometric line does not require a traversal time or speed; those distinguish a motion trajectory from its underlying trace."],"structure":{"bundles":[{"id":"course-and-extent","name":"Course and extent","description":"Establish what geometric course the line denotes and how far that course extends.","layers":[{"id":"geometric-identity","name":"Geometric identity","description":"Identify the line's defining course independently of its visible carrier.","findings":[{"id":"defining-course","name":"Defining course","description":"Record whether the course is straight, curved or composed of portions, and what definition or observation establishes it.","questions":[{"text":"What rule, construction or observed trace identifies this particular straight or curved course?","id":"defining-course-q01","kind":"definition"},{"text":"Is the record intended to identify the occupied geometric points alone, or does it also distinguish traversal order and repeated passage?","id":"defining-course-q02","kind":"boundary"}]}]},{"id":"extent-and-ends","name":"Extent and ends","description":"Separate actual terminations from limits imposed by a drawing, sample or measurement window.","findings":[{"id":"endpoint-and-domain-status","name":"Endpoint and domain status","description":"Record finite or unbounded extent, endpoint inclusion and any restriction to a selected portion.","questions":[{"text":"Which apparent ends are actual endpoints, and which are clipping or sampling limits?","id":"endpoint-and-domain-status-q01","kind":"boundary"},{"text":"What evidence establishes whether the line terminates, continues indefinitely or has an unresolved continuation?","id":"endpoint-and-domain-status-q02","kind":"provenance"}]}]}]},{"id":"length-and-local-shape","name":"Length and local shape","description":"Describe distance along the line and how its direction changes.","layers":[{"id":"along-course-distance","name":"Along-course distance","description":"Establish the domain and method for measuring length along the line.","findings":[{"id":"arc-length-assessment","name":"Arc length assessment","description":"Record length for a specified portion, including whether the available representation supports a finite value.","questions":[{"text":"Between which locations or parameter limits is arc length being measured, and in what units?","id":"arc-length-assessment-q01","kind":"measurement"},{"text":"Is the reported length exact, estimated from samples, infinite or undetermined, and what supports that assessment?","id":"arc-length-assessment-q02","kind":"measurement"}]}]},{"id":"direction-and-bending","name":"Direction and bending","description":"Describe tangents, curvature and exceptional locations along the course.","findings":[{"id":"local-shape-regularity","name":"Local shape regularity","description":"Record straight portions, smooth bends, corners and cusps without assigning tangents or curvature where they are undefined.","questions":[{"text":"Where are tangent direction and curvature defined, and what construction or estimation method supplies them?","id":"local-shape-regularity-q01","kind":"measurement"},{"text":"Which changes of direction are intended corners or cusps, and which may be sampling artefacts?","id":"local-shape-regularity-q02","kind":"provenance"}]}]}]},{"id":"continuity-and-incidence","name":"Continuity and incidence","description":"Establish how the course connects to itself and meets other geometry.","layers":[{"id":"course-continuity","name":"Course continuity","description":"Assess uninterrupted connection and return to the starting location.","findings":[{"id":"gaps-and-closure","name":"Gaps and closure","description":"Record known gaps and whether closure is exact, tolerance-based or unresolved.","questions":[{"text":"Can the intended course be followed continuously, and where do actual or suspected gaps occur?","id":"gaps-and-closure-q01","kind":"boundary"},{"text":"Does the course close exactly or only within a stated tolerance, and how was that tested?","id":"gaps-and-closure-q02","kind":"measurement"}]}]},{"id":"crossings-and-shared-portions","name":"Crossings and shared portions","description":"Distinguish geometric intersection, touching, retracing and overlap.","findings":[{"id":"incidence-classification","name":"Incidence classification","description":"Record where courses meet or coincide in the actual embedding, separately from apparent contact in a projection.","questions":[{"text":"Which contacts are intersections in the line's coordinate space, and which arise only in a projected view?","id":"incidence-classification-q01","kind":"measurement"},{"text":"At each contact, do the courses cross, touch or share a portion, and does any claimed junction meaning belong to another model?","id":"incidence-classification-q02","kind":"boundary"}]}]}]},{"id":"representation-and-geometric-actions","name":"Representation and geometric actions","description":"Connect the ideal line to its recorded representation and constrain changes by the intended geometric result.","layers":[{"id":"embedding-and-fidelity","name":"Embedding and fidelity","description":"Record the space, representation method and uncertainty needed to interpret the line.","findings":[{"id":"representation-basis","name":"Representation basis","description":"Identify coordinate frame, units, supporting geometry and how an equation, control-point construction or sample represents the intended course.","questions":[{"text":"In what coordinate frame and units is the line defined, and is it constrained to a plane or surface?","id":"representation-basis-q01","kind":"definition"},{"text":"How was the representation obtained, and what positional error or unresolved interpolation exists between recorded points?","id":"representation-basis-q02","kind":"provenance"}]}]},{"id":"operation-conditions","name":"Operation conditions","description":"State the conditions and preservation requirements for a proposed geometric operation.","findings":[{"id":"permitted-geometric-change","name":"Permitted geometric change","description":"Record whether an operation changes the intended course or only its representation, together with the geometric properties that must remain valid.","questions":[{"text":"For the proposed trim, join, extension, transformation or simplification, which endpoints, lengths, incidences or closure properties must be preserved?","id":"permitted-geometric-change-q01","kind":"action"},{"text":"What construction rule and error allowance make the operation determinate, and how will the resulting course be checked?","id":"permitted-geometric-change-q02","kind":"action"}]}]}]},{"id":"evidence-and-external-alignment","name":"Evidence and external alignment","description":"What the world already says about this thing, gathered so the model can be checked against it.","layers":[{"id":"reported-evidence","name":"Reported evidence","description":"Findings from the breadth pass, kept separate from the structural claims.","findings":[{"id":"evidence-kinds","name":"Kinds and varieties","description":"Reported by the breadth pass; each item needs checking against its source before it becomes normative.","questions":[{"text":"Which of these kinds and varieties hold for the sense of line this model covers, and on what evidence?","id":"evidence-kinds-q01","kind":"provenance"}]},{"id":"evidence-identifiers","name":"Identifiers and schemes","description":"Reported by the breadth pass; each item needs checking against its source before it becomes normative.","questions":[{"text":"Which of these identifiers and schemes hold for the sense of line this model covers, and on what evidence?","id":"evidence-identifiers-q01","kind":"provenance"}]},{"id":"evidence-standards-and-regulation","name":"Standards and regulation","description":"Reported by the breadth pass; each item needs checking against its source before it becomes normative.","questions":[{"text":"Which of these standards and regulation hold for the sense of line this model covers, and on what evidence?","id":"evidence-standards-and-regulation-q01","kind":"provenance"}]},{"id":"evidence-real-world-use","name":"Real-world use","description":"Reported by the breadth pass; each item needs checking against its source before it becomes normative.","questions":[{"text":"Which of these real-world use hold for the sense of line this model covers, and on what evidence?","id":"evidence-real-world-use-q01","kind":"provenance"}]},{"id":"evidence-measurements","name":"Typical measurements","description":"Reported by the breadth pass; each item needs checking against its source before it becomes normative.","questions":[{"text":"Which of these typical measurements hold for the sense of line this model covers, and on what evidence?","id":"evidence-measurements-q01","kind":"provenance"}]},{"id":"evidence-failure-modes-and-hazards","name":"Failure modes and hazards","description":"Reported by the breadth pass; each item needs checking against its source before it becomes normative.","questions":[{"text":"Which of these failure modes and hazards hold for the sense of line this model covers, and on what evidence?","id":"evidence-failure-modes-and-hazards-q01","kind":"provenance"}]},{"id":"evidence-regional-variation","name":"Regional variation","description":"Reported by the breadth pass; each item needs checking against its source before it becomes normative.","questions":[{"text":"Which of these regional variation hold for the sense of line this model covers, and on what evidence?","id":"evidence-regional-variation-q01","kind":"provenance"}]},{"id":"evidence-neighbours","name":"Neighbouring kinds and how to tell them apart","description":"Reported by the breadth pass; each item needs checking against its source before it becomes normative.","questions":[{"text":"Which of these neighbouring kinds and how to tell them apart hold for the sense of line this model covers, and on what evidence?","id":"evidence-neighbours-q01","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Construct, measure and transform lines in drawings and models it is authorized to change.","State the tolerance and units used when reporting a length or position."],"mustNot":["Report a measured length without its units, tolerance or method.","Change a dimension on a drawing others build from without recording the change.","Treat an idealized line as identical to a real edge with width and roughness."],"requiresHuman":["Approving dimensions on a drawing used for manufacture or construction."]},"ethics":{"considerations":["Dimension errors in drawings lead to parts and structures that fail.","Clear geometry teaching gives people access to technical work."],"affectedParties":["Builders and manufacturers","Users of the finished product","Students"]},"owners":{"steward":"Nobody owns the concept; the owner of each drawing or model answers for its lines.","roles":[],"masterSystems":[]},"relations":[{"target":"oewn-00028005-n","type":"parent","note":"registry parent class"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.line-shape","Open English WordNet: oewn-13886392-n"]},"properties":{"applicability":"required","items":["Geometric form: straight | curved | piecewise straight | mixed | undetermined","Extent: finite | unbounded in one direction | unbounded in both directions | undetermined","Arc length: length units with measured domain; finite value | infinite | undetermined","Endpoint status: endpoint locations and inclusion status, or no endpoints; distinguish geometric endpoints from display cuts","Closure: open | closed | undetermined, with any closure tolerance","Continuity and regularity: continuous portions, gaps, corners, cusps and locations where a tangent is undefined","Curvature: inverse length where defined, with location and estimation method","Geometric embedding: coordinate frame, dimension, units and any supporting plane or surface","Intersection and overlap: self or other-line intersection locations, shared portions and unresolved near contacts","Representation fidelity: positional error bound in length units, or unknown, with reference geometry and method"]},"recognition":{"applicability":"not-applicable","items":[]},"capabilities":{"applicability":"required","items":["Measure distance along a specified portion and compare it with straight endpoint separation.","Locate points, tangents and local bending where these are defined.","Test closure, continuity, intersections and coincidence under an explicit tolerance.","Trim, split, extend or join portions while recording changes to endpoints and continuity.","Translate, rotate, scale or project the line and assess the resulting geometric changes.","Sample, fit or simplify its representation against an explicit error allowance."]},"hazards":{"applicability":"required","items":["Missing tolerances make a drawing unbuildable or unsafe.","Unit confusion between millimetres and inches causes expensive errors."]},"interfaces":{"applicability":"required","items":["ISO 128, Technical product documentation, International Organization for Standardization."]},"context":{"applicability":"required","items":["A line is used in geometry to describe paths, boundaries and relationships between points.","In mathematical modelling and technical drawing, it supports reasoning about length, direction, intersection and continuity."]}},"sources":[{"title":"Euclid, Elements, Book I, Definitions (Dionysius Lardner edition, 1855), Trinity College Dublin","url":"https://www.maths.tcd.ie/~dwilkins/Euclid/Elements_Lardner1855/BookI/EuclidElementsBk01Definitions_Lardner1855.php","note":"Classical definition of a line as length without breadth; extremities are points; right line as that which lies evenly between its extremities; generation of a mathematical line as the trace of a moving point."},{"title":"Proclus and related ancient commentators on Euclid I, cited in Introduction, Springer (ch. citing Friedlein 1873 / Morrow 1992)","url":"https://link.springer.com/chapter/10.1007/978-3-030-95817-6_1","note":"Line as length without breadth, as the flowing of a point, and as magnitude extended in one direction; Aristotle on a moving point generating a line; straight line as uniform undeviating flow."},{"title":"Geometry, Encyclopædia Britannica, 11th edition (1911), Encyclopædia Britannica / Wikisource","url":"https://en.wikisource.org/wiki/Page:EB1911_-_Volume_11.djvu/697","note":"A line as the one-dimensional object with length only; the path of a moving point is a line; boundaries of a line are points."},{"title":"line (Q37105), Wikidata","url":"https://www.wikidata.org/wiki/Q37105","note":"Stable identifier and labels for the infinite non-curved (straight) line; language contrast such as English line / Spanish recta / Chinese 直线."},{"title":"ISO 80000-3:2019 Quantities and units - Part 3: Space and time, International Organization for Standardization","url":"https://standards.iteh.ai/catalog/standards/iec/f0b04329-37ca-4e6f-81d6-94adffcb8ed2/iso-80000-3-2019","note":"Length need not be measured along a straight line; path length / arc length of a rectifiable curve; distance as shortest path length; some curves (e.g. fractals) are not rectifiable."},{"title":"Geometric primitive, Wikipedia","url":"https://en.wikipedia.org/wiki/Geometric_primitive","note":"Line or curve as the one-dimensional geometric primitive in CAD, GIS and vector graphics, commonly stored as polylines or parametric curves."},{"title":"11 Lines, geometry course notes, Steve J. Trettel","url":"https://geometry.stevejtrettel.site/plane/lines/","note":"Modern metric characterization of a (straight) line as a curve whose every finite segment is length-minimizing."},{"title":"Open English WordNet 2024, synset oewn-13886392-n","url":"https://en-word.net/id/oewn-13886392-n","note":"sense and gloss of the concept"},{"title":"Wiktionary: line","url":"https://en.wiktionary.org/wiki/line","note":"word senses and usage"}],"openQuestions":["Does this registry entry include rays, disconnected collections of curve portions and branched traces, or should some of these belong to neighbouring models?","Should two traces occupying the same geometric points count as the same line when their traversal order or repeated coverage differs?","How should zero-length degeneracies and non-rectifiable curves be represented without treating them as ordinary measurable lines?","Which application-specific tolerances should govern closure, coincidence and continuity, and how should conflicting tolerances be reconciled?","When a line is inferred from a physical stroke or wire, what extraction rule establishes its course and uncertainty?"],"resources":{"spec":"/models/things/publications/thing-line-shape/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-line-shape/spec.json"],"providers":["Codex","Grok"],"researchStatus":"unreviewed","generatedAt":"2026-09-07T10:22:02Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"filled","interaction.recognition":"not-applicable","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-07T10:10:25+00:00: completeness 1.00; sense: WordNet gloss; 6 live sources; review by codex: pass","interaction.recognition":"An ideal geometric line is abstract and cannot be perceived directly, although visible marks can represent it."},"score":1.0}}