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8.1.3.1 Curvature plots

For a planar curve, an inflection point occurs at a point where the curvature changes sign (see Sect. 2.2). Note that a vanishing curvature does not necessarily imply inflections, e.g. consider the curve $ y=x^{4}$ at $ x=0$ . Using curvature plots, which consist of segments normal to the curve emanating from a number of points on the curve and whose lengths are proportional to the magnitude of the curvature given in (2.25) at the associated point, inflection points and the variation of curvature can be easily identified as illustrated in Fig. 8.3.

Figure 8.3: Curvature plot of a planar curve with inflections
\begin{figure}\centerline{\psfig{figure=fig/bottle_curvat_plot.ps,height=2.5in}}\end{figure}


December 2009