Line of curvature

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Definition

Symbol-free definition

A curve on a regular surface is termed a line of curvature if it satisfies the following conditions:

  • At every point on the curve the tangent vector to the curve is a principal vector (i.e. is in one of the principal directions) to the surface.
  • The derivative of the standard unit normal to the surface along the curve, is a scalar function times the unit tangent vector to the curve
  • The geodesic torsion of the curve vanishes everywhere

Facts

Rodrigues' formula

Further information: Rodrigues' formula