The spherical indicatrix of curvature of a 3D curve is the trajectory (included in the sphere with center O and radius 1) of the point P such that where is the tangent (unit) vector of the curve under consideration.
If the indicatrix is parametrized by the curvilinear abscissa s, then the speed of the point P is equal to the curvature: (see the notations); therefore, the curvilinear abscissa of the indicatrix of curvature is the angle of curvature j.
The indicatrix of curvature is a circle iff the curve is a helix.

The spherical indicatrix of torsion of a 3D curve is the trajectory (included in a sphere with center O and radius 1) of the point Q such that where is the binormal (unit) vector of the curve under consideration.
If the indicatrix is parametrized by the curvilinear abscissa s, then the speed of the point Q is equal to the torsion: ; therefore, the curvilinear abscissa of the indicatrix of torsion is the angle of curvature y.
 

next curve

previous curve

2D curves

3D curves

surfaces

fractals

polyhedra

© Robert FERRÉOL  2018