A path algebra approach to the computation of exact rational parametrisations for CAD/CAM applications

This paper describes a method for the construction of rational polynomial paths that does not require the apriori specification of either vertices or weights. An algebra of rational paths is developed within which paths with positive weights can be generated from more elementary paths with the same property. Case studies demonstrate that the path algebra can provide a simple means of obtaining exact rational representations of paths defined in non‐rational terms.