Frenet Frames of Trigonometric B'ezier Curves

Quaternion Frenet Frames: Making Optimal Tubes and Ribbons from Curves

Andrew J. Hanson Computer Science Department Indiana University Bloomington, IN 47405 [email protected] } Introduction } Our purpose here is to show how the quaternion formalism can be applied with great success not only to the interpolation between coordinate frames, but also to a remarkably elegant description of the evolving coordinate-frame geometry of curves. Speci c applications of th...

Frenet Frames and Toda Systems

It is shown that the integrability conditions of the equations satisfied by the local Frenet frame associated with a holomorphic curve in a complex Grassmann manifold coincide with a special class of nonabelian Toda equations. A local moving frame of a holomorphic immersion of a Riemann surface into a complex Grassmann manifold is constructed and the corresponding connection coefficients are ca...

Bezier curves

i=0 aix , ai ∈ R. We will denote by πn the linear (vector) space of all such polynomials. The actual degree of p is the largest i for which ai is non-zero. The functions 1, x, . . . , x form a basis for πn, known as the monomial basis, and the dimension of the space πn is therefore n + 1. Bernstein polynomials are an alternative basis for πn, and are used to construct Bezier curves. The i-th Be...

Stationary acceleration of Frenet curves

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curve...

5 Rational Bezier Curves Andrelief