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intersection (geometry)

vr.tr.intersection-geometry · thing-q1364910

Let an agent explain geometric intersections, relay methods and formulas from geometry and computational geometry sources, describe the cases the registry aliases name, distinguish geometric intersection from set intersection generally and from the metacentre as a naval concept, and explain tangency as an intersection at a shared point of contact.

Thing Registry Cross-cutting context XCT.QLT
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources

Bundle → Layer → Finding → Questions Filled

4 bundles · 8 layers · 8 findings · 16 questions

Understand What a geometric intersection is.

Definition

Definition.

Definition

Definition.

  1. What is an intersection in geometry, and how does it differ from set intersection, tangency and the metacentre? definition
  2. Is the question about theory, a formula, computation or naval architecture? boundary

Cases

Named cases.

Cases

Cases.

  1. What are line-plane, line-sphere, line segment and polyhedron-line intersections and intersection curves? definition
  2. Which entry fits the specific case? action
Methods Methods.

Analytic

Analytic methods.

Analytic

Analytic.

  1. How are intersections found with equations and vectors? provenance
  2. Which references are standard? provenance

Computational

Computational geometry.

Computational

Computational.

  1. How do algorithms such as Bentley-Ottmann find intersections efficiently? provenance
  2. Which sources are cited? provenance
Applications Applications.

Graphics

Graphics and CAD.

Graphics

Graphics.

  1. How are intersections used in ray tracing, collision detection and CAD? provenance
  2. Which entry fits collision detection? action

Naval

Metacentre.

Naval

Naval.

  1. What is the metacentre, and why does it matter for ship stability? provenance
  2. Which entry fits metacentric height? action
Context Algebraic geometry and history.

Algebraic

Intersection theory.

Algebraic

Algebraic.

  1. What is intersection theory in algebraic geometry, such as Bezout s theorem? provenance
  2. Which entry fits Bezout s theorem? action

History

History.

History

History.

  1. How did Descartes coordinate geometry make intersections computable? provenance
  2. Which entry fits analytic geometry? action

Classifiers Filled

Family
Thing Registry
Category
Cross-cutting context
Entry kind
thing
Plane
XCT
Domain
XCT.QLT
Other names and narrower kinds
metacenter, intersection curve, line-plane intersection, intersection of a polyhedron with a line, line segment intersection, line–sphere intersection, meridian-parallel intersection, plane–sphere intersection, sphere–cylinder intersection, point of tangency, surface–surface intersection

What it is Filled

In geometry, the set of points common to two or more figures, such as the point where two lines meet, the line where two planes meet, the intersection curve of two surfaces, line-plane, line-sphere and line segment intersections and the intersection of a polyhedron with a line; the registry aliases also include the metacentre, a point in naval architecture defined by intersecting lines of buoyancy, which is a specific application.

Why it exists Filled

Let an agent explain geometric intersections, relay methods and formulas from geometry and computational geometry sources, describe the cases the registry aliases name, distinguish geometric intersection from set intersection generally and from the metacentre as a naval concept, and explain tangency as an intersection at a shared point of contact.

Distinguishing features Filled

  • Common points
  • Dimension-dependent results
  • Computational algorithms
  • Applications in graphics

What robots and AI may and may not do Filled

Must not

  • Report numerically unstable intersections as exact.
  • Exclude a shared point from an intersection merely because it is a point of tangency.
  • File the metacentre in the registry aliases as a general geometric intersection.
  • Use unchecked intersection results in safety-critical design.

Only with a human decision

  • Human review is required when using computed intersections in structural or ship stability design.

May

  • Compute intersections of lines, planes, surfaces and solids with stated tolerances.
  • Identify tangential intersections and distinguish them from crossings in results.

Moral aspects Filled

  • Errors in geometry can propagate into unsafe designs.
  • Ship stability depends on the metacentre, which is safety-critical.

Who is affected

  • Engineers and designers
  • Students
  • Users of designed objects

Owners Filled

Steward

Nobody owns the concept; it belongs to mathematics.

Links to other meta-models Filled

parent

  • Q17141489 - registry parent class
  • Q211548 - registry parent class

related

  • intersection - in registry terms
  • locus - in registry terms
  • ray tracing
  • metacentric height - in naval architecture

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.intersection-geometry
  • Wikidata: Q1364910 (https://www.wikidata.org/wiki/Q1364910)

Direct properties not applicable Not applicable

  • two lines in a plane: one point, none or infinitely many note
  • line-sphere: solve a quadratic note
  • Bentley-Ottmann algorithm: 1979 year - segment intersections

Plane XCT: no invented physical properties.

Recognition optional Filled

  • Common points of geometric figures
  • Intersection curve, line-plane, line-sphere, line segment and polyhedron-line intersections; metacentre
  • Set intersection is general; tangency is touching without crossing; the metacentre is a ship stability point
  • Not a visible object; points or curves where figures meet.

Capabilities and actions required Filled

  • explain the concept
  • relay methods
  • describe named cases
  • distinguish related concepts

Hazards and failure modes required Filled

  • Numerical instability can affect computed intersections.
  • Treating tangency as separate from intersection can omit shared points.
  • The registry alias metacentre names a distinct applied concept.

Standards and interfaces required Filled

  • No regulation

Context of use required Filled

  • Not applicable; a geometric concept.
  • line-line and line-plane intersections
  • line-sphere and ray-surface intersections
  • intersection curves of surfaces
  • segment intersection problems
  • polyhedron-line intersections
  • applied cases such as the metacentre

Sources Filled

  1. Wikidata item Q1364910: intersection (geometry) - identity and sense of the item
  2. Wikipedia: Intersection (geometry) - general description of the item

Open questions

  • Should the metacentre be linked as a separate entry?
  • How should geometry sources be linked?
  • The registry entry has merged aliases naming specific cases; should they be grouped?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q1364910/spec.json