Dereck S. Meek

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Approximations to the surface normal and to the Gaussian curvature of a smooth surface are often required when the surface is defined by a set of discrete points. The accuracy of an approximation can be measured using asymptotic analysis. The errors of several approximations to the surface normal and to the Gaussian curvature are compared.  2000 Elsevier(More)
Arc splines, i.e. G 1 curves made of circular arcs and straight-line segments, are important, as they are the paths that are used by automatically controlled cutting machinery. Many algorithms for approximately representing discrete data by a polygon have been published. In the paper, simple modifications of two of those algorithms are applied to the(More)
Arc splines are G continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which(More)
Consumer products such as ping-pong paddles, can be designed by blending circles. To be visually pleasing it is desirable that the blend be curvature continuous without extraneous curvature extrema. Transition curves of gradually increasing or decreasing curvature between circles also play an important role in the design of highways and railways. Recently(More)