Real rational curves are not ’unit speed’

Rida T. Farouki; Takis Sakkalis

doi:10.1016/0167-8396(91)90040-I

Computer Aided Geometric Design

Paper

01 Jan 1991

Real rational curves are not 'unit speed'

View publication

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. © 1991.

Paper

Algebraically rectifiable parametric curves

Takis Sakkalis, Rida T. Farouki

Computer Aided Geometric Design

Paper

Computing with barycentric polynomials

Rida T. Farouki

The Mathematical Intelligencer

Paper

Pythagorean-hodograph space curves

Rida T. Farouki, Takis Sakkalis

Advances in Computational Mathematics

Paper

Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves

Rida T. Farouki, Jairam Manjunathaiah, et al.

CAD Computer Aided Design

View all publications

Abstract

Related

Algebraically rectifiable parametric curves

Computing with barycentric polynomials

Pythagorean-hodograph space curves

Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves