Curvature of singular Bézier curves and surfaces

This paper presents a general approach for finding the limit curvature at a singular endpoint of a rational Bézier curve and the singular corner of a rational Bézier surface patch. Conditions for finite Gaussian and mean limit curvatures are expressed in terms of the rank of a matrix.

► Limit curvature at a singular endpoint of a rational Bézier curve.
► Limit curvature at singular corner of a rational Bézier surface patch.
► In general, limit curvature at a singular point is infinite.
► Conditions are presented for finite, unique limit curvature.