The form defects quality needs methods to express allowable deviations. We propose a new language for form defects expression. This one is based on natural mode shapes of a discretized feature. The finite element method is used in order to compute those modes. Then a basis of defects is built with the natural modes. A defect is projected in this basis and thus the coordinates (modal coefficient) represent it. Hence, tolerancing is possible, by limiting those coordinates. The methods proposed in the literature can be applied on elementary geometries or there is a need to express the set of possible features (explicit geometry). Our method is versatile because it is based on the discretization of the feature (implicit geometry). The modal tolerancing method proposes two ways to express specifications of form defects: (1) The spectral tolerancing shows the modal coordinates and their limits in a bar chart graph by drawing the limits. In this method, we can see the decomposition of the measured feature and express tolerancing on each coordinate. (2) When a specification needs to link coordinates, we propose the modal domain method. An inclusion test of the feature coordinates gives the result of the metrology. Those methods are presented in an example.

. Tolerance analysis and synthesis by means of deviation domains, axi-symmetric cases. J Davidson. Models for computer aided tolerancing in design and manufacturing, springer, pp. 84-94, 2007, engineering, <10.1007/1-4020-5438-6_10>.

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International audienceReflectance Transformation Imaging is a recent technique allowing for the measurement and the modeling of one of the most influential parameters on the appearance of a surface, namely the angular reflectance, thanks to the change in the direction of the lighting during acquisition. From these photometric stereo images (discrete data), the angular reflectance is modeled to allow both interactive and continuous relighting of the inspected surface. Two families of functions, based on polynomials and on hemispherical harmonics, are cited and used in the literature at this aim, respectively, associated to the PTM and HSH techniques. In this paper, we propose a novel method called Discrete Modal Decomposition (DMD) based on a particular and appropriate Eigen basis derived from a structural dynamic problem. The performance of the proposed method is compared with the PTM and HSH results on three real surfaces showing different reflection behaviors. Comparisons are made in terms of both visual rendering and of statistical error (local and global). The obtained results show that the DMD is more efficient in that it allows for a more accurate modeling of the angular reflectance when light-matter interaction is complex such as the presence of shadows, specularities and inter-reflections

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Controlling surface appearance has become essential in the supplier/customer relationship. In this context, many industries have implemented new methods to improve the sensory inspection, particularly in terms of variability. A trend is to develop both hardware and methods for moving towards the automation of appearance inspection and analysis. If devices inspired from dimensional control solutions generally allow to identify defects far apart the expected quality of products, it do not allow to quantify finely appearance anomalies, and decide on their acceptance. To adress this issue, new methods devoted to appearance modelling and rendering have been implemented, such as the Reflectance Transformation Imaging (RTI) technique. By varying the illumination positions, the RTI technique aims at enriching the classical information conveyed by images. Thus each pixel is described by a set of values rather than one value classically; each value corresponding to a specific illumination position. This set of values could be interpolated or approximated by a continuous model (function), associated to the reflectance of the pixel, generally based on a second order polynomial (namely, Polynomial Texture Mapping Technique). This paper presents a new approach to evaluate this information from RTI acquisitions. A modal projection based on dynamics (Discrete Modal Decomposition) is used to estimate surface reflectance on each measurement point. After presenting the acquisition device, an application on an industrial surface is proposed in order to validate the approach, and compare it to the more classical polynomial transformation. Results show that the proposed projection basis not only provides closer assessment of surface reflectance (modelling) but also yields to a more realistic rendering.

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