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15
Piecewise smooth surface reconstruction
, 1994
"... We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of t ..."
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Cited by 303 (13 self)
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We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data. A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.
Automatic reconstruction of Bspline surfaces of arbitrary topological type
 SIGGRAPH'96
, 1996
"... Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners in ..."
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Cited by 173 (0 self)
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Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product Bspline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single Bspline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of Bspline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the Bspline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy userspecified error tolerances, and demonstrate our method on both synthetic and real data.
Surface Approximation and Geometric Partitions
 IN PROC. 5TH ACMSIAM SYMPOS. DISCRETE ALGORITHMS
, 1994
"... Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Si ..."
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Cited by 100 (14 self)
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Motivated by applications in computer graphics, visualization, and scientific computation, we study the computational complexity of the following problem: Given a set S of n points sampled from a bivariate function f(x; y) and an input parameter " ? 0, compute a piecewise linear function \Sigma(x; y) of minimum complexity (that is, a xymonotone polyhedral surface, with a minimum number of vertices, edges, or faces) such that j\Sigma(x p ; y p ) \Gamma z p j "; for all (x p ; y p ; z p ) 2 S: We prove that the decision version of this problem is NPHard . The main result of our paper is a polynomialtime approximation algorithm that computes a piecewise linear surface of size O(K o log K o ), where K o is the complexity of an optimal surface satisfying the constraints of the problem. The technique
Automatic Reconstruction of 3D CAD Models from Digital Scans
 International Journal of Computational Geometry and Applications
, 1999
"... 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 synthetic computer environment, including computer aided design and manufacturing. Our reconstruc ..."
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Cited by 40 (10 self)
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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 synthetic computer 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 alphashapes to compute an initial triangle mesh approximating the object's surface. 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 respec...
A Galvez, Functional Networks for BSpline Surface Reconstruction
 Future Generation Computer Systems
, 2004
"... Recently, a new extension of the standard neural networks, the socalled functional networks, has been described [E. Castillo, ..."
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Cited by 7 (2 self)
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Recently, a new extension of the standard neural networks, the socalled functional networks, has been described [E. Castillo,
Modeling Physical Fields for Interrogative Visualization
, 1997
"... Interrogative visualization refers to the process of interactive computer graphics display and accurate quantitative querying of physical data. Quantitative querying includes search for metric, combinatorial and topological information. To support this paradigm, we build uniform, compact, coregis ..."
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Cited by 5 (2 self)
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Interrogative visualization refers to the process of interactive computer graphics display and accurate quantitative querying of physical data. Quantitative querying includes search for metric, combinatorial and topological information. To support this paradigm, we build uniform, compact, coregistered representations (spline models) of multiple physical data fields over the same domain. Dense, unstructured volumetric scalar fields are approximated by C 1 continuous trivariate polynomial spline functions of low degree. Additionally, these spline functions are also used to model scattered scalar fields sampled over a manifold surface in the volume. Using both implicit polynomial spline surfaces and trivariate polynomial spline functions allows for model representations of both manifold and associated scalar fields over the same spatial decomposition. Quantitative querying is made efficient by utilizing various search structures over the modeled field data. 1 Introduction I...
Reverse Engineering FreeForm Shapes Ph.D. Dissertation written by Volker
, 2001
"... Hungarian Academy of Sciences The reports of the opponents and the protocol of the defence can be found at the Deanery ..."
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Hungarian Academy of Sciences The reports of the opponents and the protocol of the defence can be found at the Deanery
Adaptive Reconstruction of Surfaces and Scalar Fields from Dense Scattered Trivariate Data •
, 1995
"... In this paper, we propose an approach to model a set oftrivariate dense and scattered dalaon an unknown manifold by the zero contour of the a l piecewise triquadratic or tricubic polynomial. The 0 1function approximates the data over an octrec·like mesh in an adaptive fashion. At the same time, an ..."
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In this paper, we propose an approach to model a set oftrivariate dense and scattered dalaon an unknown manifold by the zero contour of the a l piecewise triquadratic or tricubic polynomial. The 0 1function approximates the data over an octrec·like mesh in an adaptive fashion. At the same time, and applying the sllme techniques. a scalar field (scalar values associated with the sampled surface points) is also modeled as a C 1 piecewise polynomial function defined on the reconstructed surface. The reconstructed surface and field can be used to visualize and interact with the data in a variety of ways. 1
Abstract Springmass model application to engineering NURBS surface reconstruction
"... reconstruction from point clouds is described. In last few years springmass models have been largely and successfully applied in Computer Animation for cloth simulation, but their application has been limited to nonEngineering fields. Following the physical metaphor of laying a cloth over a nonst ..."
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reconstruction from point clouds is described. In last few years springmass models have been largely and successfully applied in Computer Animation for cloth simulation, but their application has been limited to nonEngineering fields. Following the physical metaphor of laying a cloth over a nonstructured set of spatial points and yielding an optimised collision detection algorithm, a C++ code, named CloSReEng (Cloth Simulation Reverse Engineering) has been developed and tested. During the reconstruction procedure a springmass network (NURBS surface where control points have masses self connected with springs) is pushed on point cloud by forces on masses. Once a part of the network gets in contact with a point, the cloth is constrained to this point and the procedure is stopped when the whole network has gained the equilibrium status. Several tests of CloSReEng software have demonstrated the high quality of surface reconstruction (1/1000 error maximum) with acceptable computing time. Thus the proposed method could be considered an interesting alternative to classical techniques.
Interactive Visualization Of Multidimensional Data
, 1995
"... Interactive data visualization concerns the real time manipulation of sampled and computed data for comprehensive display. The goal of the visualization is to bring to the user a deeper understanding of the data as well as the underlying physical laws and properties. In this survey paper I focus on ..."
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Interactive data visualization concerns the real time manipulation of sampled and computed data for comprehensive display. The goal of the visualization is to bring to the user a deeper understanding of the data as well as the underlying physical laws and properties. In this survey paper I focus on two problem areas relating to interactive data visualization. The first is in data reduction and dealing with the computation of errorbounded reduced detail meshes with topological correctness. The second is in data reconstruction from scattered point scans and dealing with accurate spline models which support interactive querying and manipulation. For each of these problem areas I survey some of the related research and simultaneously present some of our own recent results. 1 Introduction Interactive data visualization concerns the real time manipulation of sampled and computed data for comprehensive display. The goal of the visualization is to bring to the user a deeper understanding of ...