Description
This book brings together recent research results in the design and use of curve and surface methods, as applied to engineering design and analysis problems, and as used by computer vision scientists for description of image and scene features. The papers are by both academics and industrialists and range from pure mathematics to experiences with the use of surface representations. The main sections of the book are: (i) mathematics of surfaces, (ii) surface modelling, (iii) curves and curve modelling, and (iv) computer vision applications. This book is intended for postgraduate students, research workers in industry, mathematics, computer science, engineering science, and engineering.Table of ContentMathematics of Surfaces, J.K. Johnstone and C.K. Shene; Dupin cyclides as blending surfaces for cones, R. Morris; A new method for drawing algebraic surfaces, B. van-Brunt; Weingarten surfaces, Surface Modelling, A.A. Ball; Towards a geometric characterization of shape, B.P. Butler, M.G. Cox and A.B. Forbes; The reconstruction of workpiece surface from probe co-ordinate data, W.L.F. Degen; Nets with plane silhouettes, M. Eck; Degree reduction of Bezier surfaces, E.F. Eisele; Best approximations of some parametric surfaces by Bezier surfaces, H. Hagen; Variational principles in curve and surface design, G. Liden and A.A. Ball; Intersection techniques for assessing surface quality, P. Malraison; The Shell Game; Surface modeling with a non-manifold solid modeller, J.C. Owen and S.A. Reid; Intersecting engineering surfaces using silhouettes, A.R.M. Piah; Data reduction on simple closed smooth surfaces, M.J. Pratt; B 'ezier surface blending in solid modelling, M. Schichtel; Shape preserving lifting of B-spline curves with an extension to surfaces, J. Warren; Multi-sided rational surface patches with independent boundary control, F. Yamaguchi and M. Niizeki; A proposal for geometric processing of rational polynomial curves; Curves and Curve Modelling, R.T. Farouki and J.K. Johnstone; Computing point/curve and curve/curve bisectors, T. Lyche and K. Strom; Knot insertion for natural splines, J.J. Malosse; Parametrization of implicit elliptic curves by rational function, G. Renner; Interpolation with G 2 cubic curves; Computer Vision Applications, L.D. Cai; Scale space behaviour of small shape features on the KH sign image of surfaces, D.A. Forsyth; The outline of an algebraic surface yields the surface, P.J. Giblin, J.E. Rycroft and F.E. Pollick; Moving surfaces, G. Taubin; Algebraic curves and surfaces in 3D computer vision, E. Trucco and R.B. Fisher; Preserving shape at boundaries in diffusion smoothing, M. Umusuthan and A.M. Wallace; A comparative analysis of algorithms for fitting planar curves and surfaces defined by implicit polynomials.
