From rectilinear line to curve: graphic constructions to transform a polyline in a curved line

Abstract

Which curves can better describe a polyline? Circle and ellipse are the simplest curves and the only  ones used in this paper. An elliptical line is more complex than circumference: in fact many graphic softwares can’t use it in polylines. The best solution is certainly the "simulation" of elliptical shapes using only circular arcs.
The final construction included in this paper shows the possibility of constructing, point to point, a pseudo-elliptical curve with an original type of transformed curve: the conjunction by polar transformation. This function is analyzed in its both graphic and numerical aspects in order to completely map its behavior, beyond the contingent utility of architectural drawing.