curve
Let an agent handle curves by definition, representation, properties and application, from geometry to data plots and maps.
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.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent handle curves by definition, representation, properties and application, from geometry to data plots and maps.
A continuous line, straight or bent, in a plane or in space; in mathematics, the image of a continuous map from an interval, and in applied use, lines such as contour lines, isodose lines or rotation curves.
What it is for: Describing shapes, trajectories and relationships in data and maps.
It can be define it, by equation or parameters; draw and plot it; compute length, curvature and area under it; fit it, to data.
Distinguishing features
One-dimensional continuous object
Can be closed or open, smooth or not
Represented by equations, parameters or data points
Applied curves represent measured relationships
What it looks like
A line on a graph, map or drawing; contour lines on maps, cooling curves on charts.
How it is recognised
Lines on plots and maps
Equations such as y = f(x) or parametric forms
Named curves such as parabola or catenary
Related models
is a kind of - geometric object
is studied by - geometry
has property - arc length
is used in - isolines and plots
In practice
Families and kinds
algebraic curves: lines, conics
transcendental curves
parametric and spline curves
data curves: cooling curves, rotation curves
isolines: contour, isoseismal, isodose lines
Standards and regulation
ISO 80000-2 notation
Cartographic conventions for contour lines
Failure modes and hazards
Overfitting curves to data
Misreading axes and scales
Extrapolating beyond data
Also called
+159
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.curve
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Definition What curve.
A curve needs a definition.
Form
Equation or data.
Form
How the curve is defined.
- How is the curve defined: equation, parameters or data? definition
- Over what domain? definition
Type
Named class.
Type
Curve class.
- Which class of curve is it? definition
- Is it closed or open? definition
Properties Measures and shape.
Properties describe behaviour.
Measures
Length, curvature.
Measures
Computed measures.
- What are its length and curvature? measurement
- Where are its extrema? measurement
Smoothness
Continuity.
Smoothness
Smoothness.
- Is it smooth everywhere? boundary
- Where are corners or cusps? boundary
Data Fitted curves.
Data curves need honest fitting.
Fit
Model fit.
Fit
Fit quality.
- How well does the curve fit the data? measurement
- Is it overfitted? boundary
Extrapolation
Beyond data.
Extrapolation
Extrapolation risk.
- Is the curve used beyond the data range? boundary
- What justifies that? provenance
Presentation Plots and maps.
Presentation affects interpretation.
Axes and scale
Plot reading.
Axes
Axes and scale.
- What are the axes, units and scale? definition
- Is a log scale used? boundary
Isolines
Contour meaning.
Isolines
Meaning of isolines.
- What value does each isoline represent? definition
- What is the interval? measurement
What the second pass must settle
- Should named curves be separate entries?
- How should data curves link to their datasets?
- How should isolines be modelled?