fundamental theorem of space curves
Let be a regular, parameterized space curve, without points of inflection. Let be the corresponding curvature and torsion functions. Let be a Euclidean isometry. The curvature and torsion of the transformed curve are given by and , respectively.
Conversely, let be continuous functions, defined on an interval , and suppose that never vanishes. Then, there exists an arclength parameterization of a regular, oriented space curve, without points of inflection, such that and are the corresponding curvature and torsion functions. If is another such space curve, then there exists a Euclidean isometry such that
|Title||fundamental theorem of space curves|
|Date of creation||2013-03-22 13:23:28|
|Last modified on||2013-03-22 13:23:28|
|Last modified by||rmilson (146)|