Two Ways to Construct a Smooth Piecewise Rational Curve Original Research Article

Two approaches to constructing piecewise rational curves are compared and contrasted. One involves projecting a piecewise polynomial curve whose polynomial segments are joined according to given totally positive connection matrices. The other, which is discussed in more detail, constructs the Bézier points of the rational segments by successively cutting corners of a given control polygon. The smoothness and total positivity properties of the resulting curves are also discussed.