figure
a combination of points and lines and planes that form a visible palpable shape
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
recalled by Codex without web access - no source was read
Researched by: Codex
Purpose and description
Enable an agent to recognise, describe, compare and assess permissible changes to a physically manifested figure through its points, lines, surfaces and spatial relationships.
A figure is a spatial configuration of points, lines, curves, or surfaces that defines a discernible shape, here understood through its visible or tangible physical realization.
It can be Trace and annotate constituent points, contours, edges and surfaces.; Measure dimensions, angles and curvature with stated uncertainty.; Compare two figures for congruence, similarity or a specified geometric resemblance.; Identify gaps, intersections, holes and disconnected components.; Assess how bending, cutting, joining or scaling would change the configuration.; Select additional views or tactile observations needed to resolve hidden geometry..
Distinguishing features
The referent is a spatial configuration that can be observed visually or by touch, rather than a numerical value or person.
Its description identifies geometric elements and their arrangement, rather than only naming the material or function of its bearer.
An outline seen from one viewpoint is distinguished from the complete shape when depth or hidden surfaces affect the configuration.
A physically realised circle, polygon or solid is distinguished from its ideal mathematical description by measurable departures and observation limits.
Calling the figure human-shaped describes its geometry and does not make this entry a model of a person or an artwork.
Scope
+ Points, edges, curves, faces and surfaces that compose a physical shape
+ Connections, intersections, boundaries, openings and enclosed regions
+ Dimensions, proportions, curvature and symmetry
+ The relationship between the shape and its physical bearer
+ Observed shape condition and changes relative to a stated reference
- Purely abstract geometric objects without a physical manifestation
- The material composition and complete lifecycle of the object bearing the shape
- Charts, numbered illustrations and their informational content
- People, numerical values and rhetorical figures
- Manufacturing processes and equipment used to produce the shape
Characteristics
- Geometric extent
- Predominantly linear, surface-like or volumetric; assessment scale stated Determines whether length, area, volume or several of these are needed to describe the figure.
- Component arrangement
- Identified points, curves, edges and surfaces with incidence and adjacency relations Distinguishes figures with similar overall dimensions but different internal arrangements.
- Boundary and closure
- Open or closed contours; bounded or unbounded model extent; enclosed regions identified Prevents an open trace from being treated as an enclosed region or solid.
- Dimensions and proportions
- Lengths in mm or m, angles in degrees or radians, and dimensionless ratios; reference frame stated Supports size-sensitive decisions and comparisons independent of absolute scale.
- Curvature and planarity
- Curve curvature in inverse length, radius in length units, and departure from a fitted plane in length units Separates straight or planar features from curved ones without assuming ideal geometry.
- Symmetry
- Reflection, rotation, other specified symmetry or none established; tolerance stated Supports recognition and detection of departures from an expected arrangement.
- Physical bearer
- Object, surface marking, relief or other identified physical manifestation Connects the figure to what must actually be inspected or changed.
- Departure from reference shape
- Within tolerance, outside tolerance or undetermined; reference and comparison method identified Makes condition judgements depend on an explicit intended or prior configuration.
Analytical facets
- substance
- form
- origin
- conceptual
- agency
- inert
- mobility
- not-applicable
- scale
- not-applicable
- affordances
- observable
Also called
+58
Where this came from
oewn:2024 · CC BY 4.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 5 bundles · 9 layers · 13 findings · 21 questions.
Figure identity and manifestation Establishes which physical configuration is being described and separates it from its bearer and representations.
A figure can be confused with an entire object, its outline or an ideal geometry; these distinctions control what the model describes.
Referent and bearer
Locates the figure in a physical manifestation and defines the selected extent.
Selected physical configuration
Record the spatial configuration selected as the figure and identify the physical entity that bears it.
- Is the figure the complete shape of an object, a surface marking, a relief or another physical configuration? definition
- Where does the selected figure end and the remainder of its bearer begin? boundary
Observed and ideal shape
Separates physical observations from geometric approximations.
Geometric interpretation
Record any ideal shape used to describe the figure without treating the idealisation as an exact observation.
- Which geometric description, if any, is being used as an approximation to this figure? definition
- Which observations support that description, and which departures have been measured? provenance
Geometric composition and connectivity Describes the elements forming the figure and how they meet or enclose space.
Arrangement and connectivity distinguish shapes that share dimensions or silhouettes.
Constituent elements
Identifies meaningful vertices, contours, edges, faces and curved surfaces.
Element decomposition
Record a decomposition appropriate to the observation scale, distinguishing physical features from construction lines and fitted subdivisions.
- Which points, lines, curves and surfaces are needed to describe this figure at the selected scale? definition
- Which element boundaries are physically observable, and which were introduced by the geometric representation? boundary
Connections and enclosures
Describes component contact, contour closure and openings.
Topological arrangement
Record connected components, intersections, closed contours and holes with enough evidence to distinguish contact from projected overlap.
- Which elements actually meet, and which merely overlap in the available view? boundary
- How many disconnected components, closed contours and openings can be established at the stated resolution? measurement
Dimensions and shape comparison Captures metric geometry and the criteria used to compare figures.
Shape comparison requires separating size, proportion, orientation and departures from ideal form.
Metric description
Measures the figure using an explicit reference frame and suitable geometric quantities.
Dimensions, angles and curvature
Record the measurements needed to distinguish the figure, including thickness or depth when a planar approximation may hide relevant geometry.
- Which lengths, angles, areas, depths or curvature measurements determine the figure for the intended task? measurement
- What reference frame, units and measurement uncertainty apply to those quantities? measurement
Equivalence and symmetry
Defines which transformations and deviations a comparison permits.
Comparison criterion
Record whether comparison concerns congruence, similarity, symmetry or another explicitly defined relationship.
- May comparison ignore translation, rotation, reflection or uniform scaling, and which differences must remain significant? definition
- What tolerance determines whether the figures match or the claimed symmetry holds? measurement
Observation and shape change Connects the available evidence to shape condition and proposed geometric interventions.
Hidden geometry and changes to contours or connectivity can invalidate recognition and alter what actions are appropriate.
Observation coverage
Records how the figure was observed and which geometric features remain unresolved.
Visible and palpable evidence
Distinguish measured geometry from features inferred through occlusion, perspective or limited tactile access.
- Which views, scans, traces or tactile observations establish the figure's contours and surfaces? provenance
- What additional observation would distinguish a true opening, recess or contact from an appearance caused by viewpoint? action
Geometric condition and intervention
Assesses departures from a reference and predicts the shape consequences of an intervention.
Shape change assessment
Record geometric changes separately from their material causes, and relate proposed changes to constraints supplied by the bearer's model.
- Which contours, dimensions or connections differ from the intended or previously observed figure? measurement
- Would the proposed bend, cut or join preserve the required shape relationships, and what bearer constraints govern whether it may be performed? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Check these first
Recalled without web access and unsourced; every item is a lead to verify.
- The supplied sense overlaps strongly with geometric figure; verify whether the registry intends physical realizations only or also abstract geometric configurations.
- Points, lines, and planes are idealizations; physical realizations have thickness, surface irregularities, and finite measurement precision.
- No universal identifier scheme, characteristic size range, or regulation is asserted for this broad category.
- Which of these check these first hold for the sense of figure this model covers, and on what evidence? provenance
Kinds and varieties
Recalled without web access and unsourced; every item is a lead to verify.
- Plane figures
- Solid figures
- Open figures
- Closed figures
- Polygonal figures
- Curvilinear figures
- Which of these kinds and varieties hold for the sense of figure this model covers, and on what evidence? provenance
Real-world use
Recalled without web access and unsourced; every item is a lead to verify.
- Representing spatial relationships in drawings and diagrams.
- Defining profiles and forms in design and manufacturing.
- Teaching geometry using drawn figures and tangible models.
- Describing and comparing shapes in visual recognition.
- Which of these real-world use hold for the sense of figure this model covers, and on what evidence? provenance
Typical measurements
Recalled without web access and unsourced; every item is a lead to verify.
- Length or perimeter - Scale-dependent; no characteristic range - m
- Area - Scale-dependent; applicable to specified regions or surfaces - m²
- Enclosed volume - Scale-dependent; applicable to figures enclosing a three-dimensional region - m³
- Angle - Depends on the geometric configuration - ° or rad
- Which of these typical measurements hold for the sense of figure this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Recalled without web access and unsourced; every item is a lead to verify.
- geometric figure - A geometric figure is an ideal mathematical configuration; this sense concerns a visible or tangible realization of such a configuration.
- shape - Shape is the spatial form a figure has; a figure is the configuration exhibiting that form.
- physical object - A physical object has material properties and identity beyond its form; a figure describes its spatial configuration or a configuration represented on it.
- diagram - A diagram communicates information through a representation; a figure in this sense need not communicate anything.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of figure this model covers, and on what evidence? provenance
What the second pass must settle
- Does the registry require a figure to be both visible and palpable, or does either form of physical observation suffice?
- Does the reference to planes restrict this entry to planar components, or are curved surfaces and general three-dimensional shapes intended?
- Where does this entry's ownership end relative to any existing world model of shape, form or geometric configuration?
- Should surface markings and disconnected arrangements count as figures under this registry definition?
- Which application-specific tolerances determine when physical irregularities change figure classification or identity?