Three-dimensional scanning, data reduction and modelling are important elements in the reverse engineering process and in the rapid prototyping cycle as a whole. In order to achieve accurate reconstructed products, points are sampled at high density. For reconstruction, however, conventional methods usually reduce the data homogeneously without preserving the shape. As a result, essential characteristic details may be lost. In addition, multilevel-of-detail models, which are essential for design and manufacturing, do not exist in conventional methods where only one level of reduced data is created. In this paper, continuous and discrete methods for reconstructing progressive models are proposed. Through these methods, the reconstructed geometric model is represented by hierarchical levels of detail. The main advantage of the approach is that sampled points are significantly reduced to several levels of abstraction, while the geometric behaviour is preserved at each level. That is, even at lower resolution levels, critical details are preserved. The method is also extended to progressive volumetric geometric models, simulation and layered manufacturing.
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