ONDULO > The curvature

When the curvature defines the defect.

An appearance defect is defined by a fast variation in the local slope across a short distance, depending on the altitude and the wavelength.
These information allows to characterize the appearance defect by the spatial derivative of its slope, or the second derivative of its altitude, namely the curvature.
The information Altitude is so not enough relevant if it's not linked with the wavelenght.
To colour, a defect with a depth of 50µm and a wavelenght of 50mm will be less visible than a defect with a depth of 20µm and a wavelenght of 20 mm because the local curvature is smaller for the first defect.

From slope to curvature.

Locally, the surface can be defined by the function z = f(x,y) and the slopes by its components dz/dx et dz/dy.
The slope variation from one point to the other is described by the two components d²z/dx²and d²z/dy²(the slope derivatives) and by the cross-derivative d²z/dxdy (the torsion), which is not taken into account.
The spatial derivatives of the slopes correspond to the local curvatures at one point M(x,y).
The information 'Local slope' is so essential to characterize, by numerical derivation, the surface in terms of curvature variations.
More information.

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