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International audience; Roundness and cylindricity evaluations are among the most important problems in computational metrology, and are based on sets of surface measurements (input data points). A recent approach to such evaluations is based on a linear-programming approach yielding a rapidly converging solution. Such a solution is determined by a fixed-size subset of a large input set. With the intent to simplify the main computational task, it appears desirable to cull from the input any point that cannot provably define the solution. In this note we present an analysis and an efficient solution to the problem of culling the input set. For input data points arranged in cross-sections under mild conditions of uniformity, this algorithm runs in linear time.

The assumption of real-number arithmetic, which is at the basis of conventional geometric algorithms, has been seriously challenged in recent years, since digital computers do not exhibit such capability. A geometric predicate usually consists of evaluating the sign of some algebraic expression. In most cases, rounded computations yield a reliable result, but sometimes rounded arithmetic introduces errors which may invalidate the algorithms. The rounded arithmetic may produce an incorrect result only if the exact absolute value of the algebraic expression is smaller than some (small) varepsilon, which represents the largest error that may arise in the evaluation of the expression. The threshold varepsilon depends on the structure of the expression and on the adopted computer arithmetic, assuming that the input operands are error-free. A pair (arithmetic engine,threshold) is an "arithmetic filter". In this paper we develop a general technique for assessing the efficacy of an arithmetic filter. The analysis consists of evaluating both the threshold and the probability of failure of the filter. To exemplify the approach, under the assumption that the input points be chosen randomly in a unit ball or unit cube with uniform density, we analyze the two important predicates "which-side" and "insphere". We show that the probability that the absolute values of the corresponding determinants be no larger than some positive value V, with emphasis on small V, is Theta(V) for the which-side predicate, while for the insphere predicate it is Theta(V^(2/3)) in dimension 1, O(sqrt(V)) in dimension 2, and O(sqrt(V) ln(1/V)) in higher dimensions. Constants are small, and are given in the paper., Comment: 22 pages 7 figures Results for in sphere test inproved in cs.CG/9907028

Special issue on sketch based modeling; International audience; We present a new method for interactively creating garments for dressing virtual characters. The user draws an outline of the front and back of the garment, and the system makes reasonable geometric inferences about the overall shape of the garment (ignoring constraints arising from physics). Both the garment's shape and the way the character is wearing it are determined at once. We use the distance from the 2D garment silhouette to the character model to infer the variations of the distance between the remainder of the garment and the character in 3D. The garment surface is generated from the silhouette and border lines and this varying distance information, using a distance field to the character's body. This method is integrated in an interactive system in which the user sketches the garment over the 3D model of the character. Our results show that the system can be used to create a broad range of clothes that may be worn in a variety of ways.