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'

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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.

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

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Abstract

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The bisector of a point and a plane parametric curve

Self-consistent Monte Carlo simulation of the cathode fall including treatment of negative-glow electrons

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

Approximation by Interval Bezier Curves