Classification of Points On A Surface
- At elliptical points, both principal curvatures have the same sign, and the surface is locally convex.
- At umbilic points, both principal curvatures are equal and every tangent vector can be considered a principal direction. These typically occur in isolated points.
- At hyperbolic points, the principal curvatures have opposite signs, and the surface will be locally saddle shaped.
- At parabolic points, one of the principal curvatures is zero. Parabolic points generally lie in a curve separating elliptical and hyperbolic regions.
- At flat umbilic points both principal curvatures are zero. A generic surface will not contain flat umbilic points. The monkey saddle is one surface with an isolated flat umbilic.
Read more about this topic: Principal Curvature
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