Line of curvature: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A curve on a [[regular surface]] is termed a '''line of curvature''' if | 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== | ==Facts== | ||
Latest revision as of 19:48, 18 May 2008
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