New control massic polygon of a \(B\)-rational curve resulting from a homographic change of parameter
The authors call massic vector what \textit{H. Grassmann} [Die Ausdehnungslehre (1844)] used to call extensive quantity of step 1, i.e. the vector space generated by sums of points and vectors. They have developed an extensive theory of approximations using this vector space [cf. the first two authors, Courbes et surfaces rationnelles. Applications à la CAO (1989; Zbl 0713.68095)]. Rational Bézier curves are a subset of their BR-curves because they are based on point control only. These BR-curves allow infinitely far control on the same level as that through finite points. In this paper, they discuss four ways of computing projective changes of parameter for BR-approximations, using algorithms previously developed for operations on BR-curves. Each way is illustrated by explicit computation for the folium of Descartes and the trisectrix of MacLaurin.
scientific article; zbMATH DE number 553670
scientific article