Signed Curvature
The sign of the signed curvature k indicates the direction in which the unit tangent vector rotates as a function of the parameter along the curve. If the unit tangent rotates counterclockwise, then k > 0. If it rotates clockwise, then k < 0.
The signed curvature depends on the particular parametrization chosen for a curve. For example the unit circle can be parametrised by (cos(θ),sin(θ)) (counterclockwise, with k > 0), or by (cos(−θ),sin(−θ)) (clockwise, with k < 0). More precisely, the signed curvature depends only on the choice of orientation of an immersed curve. Every immersed curve in the plane admits two possible orientations.
Read more about this topic: Curvature, Curvature of Plane Curves
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