Curvature ( $κ$ )

Curvature measures the rate at which a curve or surface normal changes. A plane circle of radius

R

has curvature

1/ R

.

Table of contents
- Signed curvature of a plane graph Curvature

Signed curvature of a plane graph ( $κ = \frac{u _{xx}}{( 1 + u _{x}^{2} ) ^{3/2}}$ )

For an oriented plane curve written locally as the graph

(x, u (x))

, its signed curvature is

κ = \frac{u _{xx}}{( 1 + u _{x}^{2} ) ^{3/2}} .

κ = 0

describes straight lines, while

κ = 1/ R

describes consistently oriented arcs of circles of radius

R

.

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