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EN
In this paper an algorithm for the representation of 3D models is described and experimentally evaluated. Three-dimensional objects are becoming very popular recently and they are processed in various ways - analysed, retrieved, recognised, and so on. Moreover, they are employed in various aplications, such as virtual reality, entertainment, Internet, Computer Aided Design, or even in biometrics or medical imaging. That is why the development of appropriate algorithms for the representation of 3D objects is so important recently. These algorithms - so called 3D shape descriptors - are assumed to be invariant to particular transformations and deformations. One of the possible approaches is based on the projections of a 3D object into planar shapes and representation of them using a 2D shape descriptor. An algorithm realising this idea is described in this paper. Its first stage is based on the rendering of 20 2D projections, from various points of view. Later, the obtained projections are stored in a form of bitmaps and the Curvature Scale Space algorithm is applied for the description of the planar shapes extracted from them. The proposed approach is experimentally compared with several other 3D shape representation methods.
EN
In the paper we deal with the problem of three-dimensional shape reconstruction when its two-dimensional projections from selected directions are available. This situation corresponds e.g. to the trial of digitalizing the shape from photographs. We propose a methods for creating the mesh, projecting the shape keeping the information about light and perspective. On this basis we use SA technique to modify this shape in a controlled way in order to reproduce the initially assumed one best.
EN
In the context of developing automated optical inspection system, this work brings into focus the aspect of de-velopment of evaluation algorithms for thickness distribution extraction from the object model reconstructed after surface scanning. Within this work an algorithm for the evaluation of local differences between two triangle meshes is presented. The pair of triangular meshes is representing the front and backside of a scanned 3D-object. The resulting array of differences vector corresponds to the shortest local distances (i.e. local thickness) between sides of object.
EN
This paper presents general survey of subdivision schemes using for modeling 3D object of arbitrary topological type. The way of analyzing main properties of subdivision surfaces is also presented. This mathematical set of tools allow to use subdivision as well defined predict block in multiresolution analysis of surface meshes by second generation wavelet.
PL
Artykuł prezentuje przegląd metod modelowania obiektów 3D za pomocą podpodziału powierzchni. Został przedstawiony sposób analizy głównych właściwości powierzchni, które powstały w wyniku zastosowania schematów podpodziału. Ten zestaw matematycznych narzędzi pozwala na użycie schematów podpodziału jako bloku predykcji w wielorozdzielczej analizie siatek powierzchni za pomocą falek drugiej generacji.
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