ISO TC 211 Geographic information/Geomatics

# ISO/TC 211 Geolexica

## Concept “curvature vector <differential geometry>”

Term ID

2041

source

ISO 19107:2019, (E), 3.19

eng

### curvature vector <differential geometry>

second derivative of a curve parameterized by arc length, at a point

Note to entry: If c(s) = (x(s), y(s), z(s)) is a curve in a 3D Cartesian space (bbb"E"^3), and s is the arc length along c(s), then the unit tangent vector is dot c(s) = (dot x(s), dot y(s), dot z(s)), i.e. the derivative of the coordinate values of c with respect to s. The curvature vector is ddot c(s) = (ddot x(s), ddot y(s), ddot z(s)). The curvature vector can be approximated by the inverse of the radius of a circle through any 3 nearby points on the curve (pointed from the curve to towards the centre of the circle)

ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)

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info

• status: valid
• classification: preferred
• date accepted: 2019-12-02

Review

last review performed:
(2019-12-02)
status:
final
decision:
accepted
decision event:
Normal ISO processing
notes:
Publication of document ISO 19107:2019(E)