Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, end-user comprehensibility of the results, non-presumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate clusters in large high dimensional datasets.

Generating optimal NC code to drive milling machines for models defined by freeform trimmed surfaces is a difficult problem. In practice, Two main approaches are used to generate toolpaths for surfaces, neither of which is optimal, in general. The first exploits the parametric representation and generates isocurves that are uniformly distributed across the parametric domain. This approach is not optimal if the surface mapping into Euclidean space is not isometric. The second approach contours the models by intersecting the surfaces with planes equally spaced in Euclidean space, resulting in a piecewise linear toolpath approximation which is nonadaptive to the local surface geometry. Furthermore, the toolpath generated by contouring is suitable for 3 axis milling but is inappropriate for 5 axis milling. In this paper, an algorithm developed to adaptively extract isocurves for rendering [9] is adapted and enhanced to generate milling toolpaths for models consisting of trimmed surfaces, a...

this paper we present a new method of feature recognition that works entirely on set-theoretic geometric models, and which allows features to be found when there are small geometrical deviations

This paper describes a new algorithm for computing Minkowski sums of set-theoretic geometric models. The algorithm uses a variation on Woodwark's method for feature recognition. At the end of the paper we present results from an implementation of the algorithm running on twodimensional data, and from a more experimental version raytracing into three-dimensional Minkowski sums to render a picture. Introduction Consider a cube and a small sphere. Allow the centre of the sphere (which we shall call the sphere's reference point) to move everywhere in the cube, and take the union of all the resulting infinite number of spheres. The solid formed by that union would be a cube bigger than the original by the radius of the sphere, but with rounded corners. This shape is a Minkowski or vector sum of the cube and the sphere, written cube \Phi sphere [2]. The Minkowski sum of any two solid shapes is a well-defined set. The reference point for the shape that moves about doesn't have to be its cent...

Voronoi diagrams and their applications. In Computational Geometry and its Applications, Lecture Notes in Computer Science 333, Springer-Verlag (1988), 148-157. Other: extended abstract. [2344.2, KAVDA -CGA-88] 1577 R. Klein. Concrete and Abstract Voronoi Diagrams, Lecture Notes in Computer Science 400, Springer-Verlag (1989). Keywords: book. [2452, K-CAVD-SV-89] 1578 R. Klein. Voronoi diagrams in the Moscow metric. Technical Report 7, Inst. Inform., Univ. Freiburg (1987). [2344.1, K-VDMM-UF-87] 1579 R. Klein. Walking an unknown street with bounded detour. In Proc. 32nd Annu. IEEE Sympos. Found. Comput. Sci. (1991), 304-313. [2803, K-WUSBD-32FOCS-91] 1580 R. Klein, K. Mehlhorn and S. Meiser. On the construction of abstract Voronoi diagrams II. In Proc. 1st Annu. SIGAL Internat. Sympos. Algorithms, Lecture Notes in Computer Science 450, Springer-Verlag (1990), 138-154. [2466, KMM-CAVDI-1SIGALISA-90] 1581 R. Klein, O. Nurmi, T. Ottmann and D. Wood. A dynamic fixed windowing problem. Repo...

This paper describes the Virtual Manufacturing System| a virtual world consisting of a machine shop in which engineering components can be made. The mechanisms and processes of their manufacture are recorded so that those mechanisms and processes can be carried out subsequently on real computer-numerically-controlled machine tools. This Virtual Manufacturing System makes heavy demands on the geometric modeller that is required to support it. At the moment the one in use is the Svlis set-theoretic modeller. This has a number of special abilities that make it suitable for the task, and those abilities are described in detail. Introduction The natural instinct of an engineer who wants to make a new device is to go to a workshop, nd some scrap aluminium or mild steel, and to machine up what is required. The engineer will do this by eye where dimensions are not critical, and by measurement where they are. He or she will make mistakes of course|holes may be drilled in the wrong ...