The Differential Geometry of curves is described by means of the Frenet-Serret formulas, which cast first, second and third order derivatives into curvature and torsion. While in usual vector calculus these quantities are usually considered to be scalar values, formulating the Frenet-Serret equations in the framework of Geometric Algebra exhibits that they are best described by a bivector for t...

In this paper we obtain, for the first time, explicit formulae for integral invariants for curves in 3D with respect to the special and the full affine groups. Using an inductive approach we first compute Euclidean integral invariants and use them to build the affine invariants. The motivation comes from problems in computer vision. Since integration diminishes the effects of noise, integral in...

2 Separation of variables and the complete integral 5 2.1 Separation of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The envelope of a family of curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The complete integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Determining the characteristic strips from t...