A continuous mapping which preserves the orientation of a Jordan curve is called sense-preserving or orientation-preserving. If on the other hand a mapping reverses the orientation, it is called sense-reversing.
An example of sense-preserving mapping is any conformal mapping . If you however look at the mapping , then that is a sense-reversing mapping. In general if is a smooth mapping then the Jacobian in fact is defined as , and so a mapping is sense preserving if the modulus of the partial derivative with respect to is strictly greater then the modulus of the partial derivative with respect to .
|Date of creation||2013-03-22 14:08:01|
|Last modified on||2013-03-22 14:08:01|
|Last modified by||jirka (4157)|