Abstract: Many applications of geometry processing and computer vision rely on geometric
properties of curves, particularly their curvatures and torsions. This paper proposes some methods
to estimate the curvature and the torsion, based on some algorithms for weighted least-squares
fitting and local arc-length approximation in order to eliminate noises. By Maple procedure,
statistical analysis of some selected common curves is carried out to get partial values of their
curvatures and torsions, and then an approximate interval about ideal curvatures and ideal torsions
is put forward. Furthermore, several test models for embedding specific ideal curvature or ideal
torsion in crafts are taken into account.

Key words: curvature estimation algorithm, torsion estimation algorithm, ideal curvature and
torsion, embedded craft