Curvature - Definition

In Shape Design & Styling, the curvature is related to the radius of curvature of a shape.
The radius of curvature of a curve at one point is the radius Rmax (in millimeters) of the circle (C) in contact with that curve at that point, biggest as possible. The line (red colored here) which represents this radius is normal to the tangent at the same point.

At this point, the Curvature is the number which attests to the rate of turn of the curve and it can be calculated as following:

                                                                          Curvature = 1 / Rmax (value in mm)

Specific values

LINE
The radius of curvature of a line is constant and equal to ∞. Its curvature is also constant and equal to 0.
Radius: R = Cst = ∞
Curvature: C = 0

CIRCLE

The radius of curvature of a circle is constant and equal to the radius of the circle. Its curvature is also constant and equal to 1/R.
Radius: R = Cst
Curvature: C = 1 / R = Cst

Curvature - Graphical Representation

This is evolution of the radius or the curvature value all along a curve. Curvature or Radius values along the curve can be represented through a graphic comb.
Depending on the context, the graphical evolution comb can represent the Radius values or the curvature Values. It also can be displayed with positive or negative side.

Then that means the  evolution of a curve can be displayed through 4 graphical ways as following:

• Area with a small curvature value = nearly flat area (nearly like a curve)
• Area with curvature value which becomes bigger = area of curvature acceleration
• Point where the curvature value is equal to 0 and then in the other direction = inflexion point

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