Real Rational Curves are not `Unit Speed'

Computer Aided Geometric Design, Elsevier, Vol 8, pp.151-157, 1991

MESHING
RESEARCH
CORNER

Rida T. Farouki
IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA

Takis Sakkalis
Department of Mathematical Sciences, Oakland University, Rochester, MI 48309, USA

Abstract
We prove that it is impossible to parameterize any real plane curve, other than a straight line, by rational functions of its arc length. The proof extends in a straightforward manner to real space curves of any dimension d >= 3.