By Michael S. Floater (auth.), Roberto Cipolla BA(Hons), MSE, MEng, DPhil, Ralph Martin MA, PhD, FIMA, CMath, MBCS, CEng (eds.)

These complaints acquire the papers authorised for presentation on the bien nial IMA convention at the arithmetic of Surfaces, held within the collage of Cambridge, 4-7 September 2000. whereas there are lots of foreign con ferences during this fruitful borderland of arithmetic, special effects and engineering, this can be the oldest, the main common and the single one to concen trate on surfaces. participants to this quantity come from twelve diversified nations in european rope, North the USA and Asia. Their contributions mirror the vast range of present-day functions which come with modelling components of the human physique for scientific reasons in addition to the creation of vehicles, plane and engineer ing parts. a few functions contain layout or building of surfaces through interpolating or approximating info given at issues or on curves. Others think of the matter of 'reverse engineering'-giving a mathematical descrip tion of an already built item. we're fairly thankful to Pamela Bye (at the Institue of Mathemat ics and its purposes) for assist in making preparations; Stephanie Harding and Karen Barker (at Springer Verlag, London) for publishing this quantity and to Kwan-Yee Kenneth Wong (Cambridge) for his heroic support with com piling the court cases and for facing a number of technicalities coming up from huge and diverse machine documents. Following this Preface is an inventory of the programme committee who with the aid of their colleagues did a lot paintings in refereeing the papers for those proceedings.

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11. The first 5 images show some of the identically labeled topologicial regions of the test objects. The bottom right image shows the disturbed area between regions Fig. 12. Segmentation results. The segmentation algorithm is based on the simplified computation of mean and Gaussian curvature Computation of local differential parameters on irregular meshes 33 References 1. J. C. Jain (1986) Invariant Surface Characteristics for 3D Object Recognition in Range Images. Journal of Computer Vision, Graphics, and Image Processing 33, 33-80 2.

XN} C n ~ JR2 together with a set {Yl, ... , YN} C JR3 such that Yj = F(xj) for all j, 1 ~ j ~ N, either exactly or approximately. Again, the nonparametric setting specializes to the case Yj = (Xj, f(xj», 1 ~ j ~ N. In general, derivative values can be specified, but we skip over such extensions here. More serious are qualitative data like "smoothness", "good shape" or whatever the user may prescribe. Here, we ignore everything except smoothness, and we shall restrict the latter to the classical mathematical definition.

Furthermore, if exact reconstruction at the data locations is required, and if the user wants to avoid solving non-local linear systems, there is no way around localized Langrange-type interpolation formulae. Thus two instances of such techniques are studied in some detail: • interpolation by weighted local Lagrangians based on radial basis functions and • moving least squares. While the former is much more simple than the latter, it still has some deficiencies in theory and practice. Moving least squares, if equipped with certain additional features, turn out to be widely satisfactory, even in difficult cases.