A triangulation-based object reconstruction method

Reconstructing the shape of a 3D object from a digital scan of its surface has a range of applications, such as reverse engineering, authoring 3D synthetic worlds, shape analysis, 3D faxing and tailor-fit modeling. Input data might come in dfierent forms, depending on the scanning device used. It is usually comprised of the location (zI, yl, zi) of points on the surface of the object, and at times additional topological and geometric information, as well as measures of other physical properties. The sampling provided by recent scanning devices (such as the Lzser range scanner) is dense, in the sense that the resolution is much smaller than the sise of shape features of interest. Often multiple scans are required to capture the entire object’s surface. We make no assumptions on spatiaJ relations among sample points, and assume that the input is a large, but unorganized, collection of measurements. Our goal is to reconstruct a boundary representation of the object, based on implicit polynomial surface patches of low degree, that has the tiesired geometric continuity and approximates the data within a user-specified parameter E. For a discussion of related prior work the reader is referred to [6]. In [I], we presented a method based on alpha-shapes, to build an initial piecewise-linear reconstruction, followed by an incremental, adaptive piecewise polynomial fitting of the signed distance function defined by the alpha-shape. The method relied on the user to select a good a-value. The final reconstructed model was represented as a collection of C] -smooth implicit algebraic patches. A more up-to-date, detailed description of the algorithm can be found in [2]. In this paper, and the accompanying video presentation,