||This task will show you how to define areas on a mesh along
the curvatures or curvature radii.
There are five
The geometric construction of the maximum and minimum
curvatures is the following:
let be a plane containing the normal to the surface in a given point.
This plane cuts the surface along a curve that has a given curvature in this
If this plane rotates around the normal, the curvatures of the curves
the surface will vary between two utmost values.
These two values are the maximum (KM) and the minimum (Km) curvatures.
The mean curvature is equal to (KM+Km)/2.
The utmost values appear where the surface is the most warped.
The mean curvature is largely used to detect irregularities on the surface.
A minimal surface is characterized by a null mean curvature.
The gaussian curvature is equal to KM.Km.
It describes the local shape of a surface in one point:
- if it is positive, the point is elliptic,
i.e. the surface has locally the shape of an ellipsoid around that point,
- if it is negative, the surface is hyperbolic in this points,
i.e. the local shape is a horse saddle,
- it it is null, the surface is parabolic in this point,
i.e. one of the maximum or minimum curvatures is null in this point.
The cone and the cylinder are two surfaces where all points are parabolic.
The absolute curvature is equal to |KM|+|Km|.
It is used to detect the surface areas where the surface is locally almost
(the absolute curvature is almost null).
The curvature radii are the inverse of the corresponding
Only the maximum and the minimum radii are relevant.