Fausto Bernardini

Automatic reconstruction of surfaces and scalar fields from 3D scans

We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. A possible application is the rapid computer model reconstruction of an existing part or prototype from a three dimensional (3D) points scan of its surface. Color, texture or some scalar material property of the physical part, define natural scalar fields over the surface of the CAD model. Our reconstruction algorithm does not impose any convexity or differentiability restrictions on the surface of the original physical part or the scalar field function, except that it assumes that there is a sufficient sampling of the input point data to unambiguously reconstruct the CAD model. Compared to earlier methods our algorithm has the advantages of simplicity, efficiency and uniformity (both CAD model and scalar field reconstruction). The simplicity and efficiency of our approach is based on several novel uses of appropriate sub-structures (alpha shapes) of a three-dimensional Delaunay Triangulation, its dual the three-dimensional Voronoi diagram, and dual uses of trivariate Bernstein-Bezier forms. The boundary of the CAD model is modeled using implicit cubic Bernstein-Bezier patches, while the scalar field is reconstructed with functional cubic Bernstein-Bezier patches. CR

Automatic Reconstruction of 3D CAD Models from Digital Scans

We present an approach for the reconstruction and approximation of 3D CAD models from an unorganized collection of points. Applications include rapid reverse engineering of existing objects for use in a virtual prototyping environment, including computer aided design and manufacturing. Our reconstruction approach is flexible enough to permit interpolation of both smooth surfaces and sharp features, while placing few restrictions on the geometry or topology of the object. Our algorithm is based on alpha-shapes to compute an initial triangle mesh approximating the surface of the object. A mesh reduction technique is applied to the dense triangle mesh to build a simplified approximation, while retaining important topological and geometric characteristics of the model. The reduced mesh is interpolated with piecewise algebraic surface patches which approximate the original points. The process is fully automatic, and the reconstruction is guaranteed to be homeomorphic and error bounded with respect to the original model when certain sampling requirements are satisfied. The resulting model is suitable for typical CAD modeling and analysis applications.

Reconstructing Surfaces and Functions on Surfaces from Unorganized Three-Dimensional Data

Abstract. Creating a computer model from an existing part is a common problem in reverse engineering. The part might be scanned with a device like the laser range scanner, or points might be measured on its surface with a mechanical probe. Sometimes, not only the spatial location of points, but also some associated physical property can be measured. The problem of automatically reconstructing from this data a topologically consistent and geometrically accurate model of the object and of the sampled scalar field is the subject of this paper. The proposed algorithm can deal with connected, orientable manifolds of unrestricted topological type, given a sufficiently dense and uniform sampling of the objects surface. It is capable of automatically reconstructing both the model and a scalar field over its surface. It uses Delaunay triangulations, Voronoi diagrams, and α-shapes for efficiency of computation and theoretical soundness. It generates a representation of the surface and the field based on Bernstein—Bézier polynomials, with the surface modeled by implicit patches (A-patches), that are guaranteed to be smooth and single-sheeted.

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,

Scientific problem solving in a distributed and collaborative multimedia environment

We describe a distributed and collaborative environment for cooperative scientific problem solving. SHASTRA is a highly extensible, distributed and collaborative design and scientific manipulation environment. At its core is a powerful collaboration substrate - to support synchronous multi-user applications, and a distribution substrate - which emphasizes distributed problem solving. The design of SHASTRA is the embodiment of the following idea - scientific manipulation toolkits can abstractly be thought of as objects that isolate and provide specific functionality. At the system level, SHASTRA dictates architectural guidelines and provides communication facilities that let toolkits cooperate to utilize the functionality they offer. At the application level, it provides collaboration and multimedia facilities that let users cooperate. A synergistic union of these two elements yields a sophisticated problem solving environment.