Search results for "Frenet–Serret formulas"
showing 3 items of 3 documents
Differential Geometry of Curves and Surfaces
2001
The goal of this article is to present the relation between some differential formulas, like the Gauss integral for a link, or the integral of the Gaussian curvature on a surface, and topological invariants like the linking number or the Euler characteristic.
Pappus type theorems for hypersurfaces in a space form
2002
In order to get further insight on the Weyl’s formula for the volume of a tubular hypersurface, we consider the following situation. Letc(t) be a curve in a space formM λ n of sectional curvature λ. LetP 0 be a totally geodesic hypersurface ofM λ n throughc(0) and orthogonal toc(t). LetC 0 be a hypersurface ofP 0. LetC be the hypersurface ofM λ n obtained by a motion ofC 0 alongc(t). We shall denote it byC PorC Fif it is obtained by a parallel or Frenet motion, respectively. We get a formula for volume(C). Among other consequences of this formula we get that, ifc(0) is the centre of mass ofC 0, then volume(C) ≥ volume(C),P),and the equality holds whenC 0 is contained in a geodesic sphere or…
Geometric Properties of the 3D Spine Curve
2003
Through a 3D reconstruction of the human back surface using structured light techniques, we study the properties of spine curve by means of a set of parameters related to measures commonly applied in medicine. In this way, descriptors for measuring the abnormalities in the projections of the front and sagittal planes can be computed. We build the spine curve in 3D and analyse the behaviour of the Frenet frame when along the curve the deformation processes in idiophatic scoliosis appear.