A Method for Determining the Curvature of Natural Forms and its Application to Certain Tail Feathers of the Superb LyrebirdMenura novaehollandiae

Abstract

SummarySmith, L.H. (1990). A method for determining the curvature of natural forms and its application to certain tail feathers of the Superb Lyrebird Menura novaehollandiae. Emu 90, 231–240.A method for determining the curvature pattern of a two-dimensional curve is described and demonstrated by its application to three types of tail feathers of the Superb Lyrebird. Assuming that the curve is part of a circle, the straight line AB joining the ends A and B of the curve is a chord of that circle. The perpendicular bisector of the chord AB passes through the centre of the circle 0 and meets the curve (circle) at C, and at D, a distance of 2R from C, where R is the radius of the circle. Because DOC is a diameter of a circle, angle DAC (= angle DBC) equals 90 degrees (Euclidean theorem) and AC (= BC = L)/2R = Cos θ, where θ is the angle between AC and DOC. Thus, R = L/2 Cos θ. The paper describes how L and θ are measured. Extension of the method to the shorter elements resulting from the first step enables a curvature pattern for the entire curve (feather) to be determined. The plain median rectrix of a Superb Lyrebird, and the median and lyrate rectrices of a mature male Superb Lyrebird, were all more highly curved at the distal end.