Practical ducting layout in process plants needs to satisfy a number of on-site constraints. The search for an optimal flow path around the obstructions is a multi-parameter problem and is computationally prohibitively expensive. In this study, authors proposed a rapid and efficient methodology for the optimal linkage of arbitrarily oriented fluid flow ducts using a single-parameter quadratic/cubic Bézier curves in two/three dimensions to describe the centreline of the curved duct. A smooth interconnecting duct can then be generated by extruding the duct face along the curve. By varying the parameter either along the angular bisector or along the axes of the ducts, a family of Bézier curves is generated. Computational fluid dynamics simulations show that the relationship between pressure drop and the adjustable parameter is a unimodal curve and the optimal connecting duct is the one which has the least pressure drop while satisfying on-site constraints can be used for linking the ducts. The efficacy of the method is demonstrated by applying it to some cases of practical interest. © 2015, DESIDOC.