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Marching Intersections: an Efficient Resampling Algorithm for Surface Management
 In Proceedings of Shape Modeling International (SMI
, 2001
"... The paper presents a simple and efficient algorithm for the removal of small topological inconsistencies and high frequency details from surface models. The method, called Marching Intersections (MI), adopts a volumetric approach and acts as a resampling filter: all the intersection points between t ..."
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Cited by 15 (0 self)
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The paper presents a simple and efficient algorithm for the removal of small topological inconsistencies and high frequency details from surface models. The method, called Marching Intersections (MI), adopts a volumetric approach and acts as a resampling filter: all the intersection points between the input model and the lines of a user selected 3D reference grid are located and then, beginning from these intersections, an output surface is reconstructed. MI, which presents good characteristics in terms of efficiency, compactness, and quality of the output models, can be also used: for the conversion between different representation schemes; to perform logical operations on geometric models; for the topological simplification of surfaces; and for the simplification of huge meshes, i.e. meshes too large to be allocated in main memory during the simplification process. All these aspects are discussed in the paper and timing and graphic results are presented.
Fixing Geometric Errors on Polygonal Models: A Survey
 J. COMPUT SCI
"... Polygonal models are popular representations of 3D objects. The use of polygonal models in computational applications often requires a model to properly bound a 3D solid. That is, the polygonal model needs to be closed, manifold, and free of selfintersections. This paper surveys a sizeable literatu ..."
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Cited by 9 (1 self)
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Polygonal models are popular representations of 3D objects. The use of polygonal models in computational applications often requires a model to properly bound a 3D solid. That is, the polygonal model needs to be closed, manifold, and free of selfintersections. This paper surveys a sizeable literature for repairing models that do not satisfy this criteria, focusing on categorizing them by their methodology and capability. We hope to offer pointers to further readings for researchers and practitioners, and suggestions of promising directions for future research endeavors.
ThreeDimensional Shape Representation via Shock Flows
 BROWN UNIVERSITY
, 2003
"... We address the problem of representing 3D shapes when partial and unorganized data is obtained as an input, such as clouds of point samples on the surface of a face, statue, solid, etc., of regular or arbitrary complexity (freeform), as is commonly produced by photogrammetry, laser scanners, comput ..."
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Cited by 7 (2 self)
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We address the problem of representing 3D shapes when partial and unorganized data is obtained as an input, such as clouds of point samples on the surface of a face, statue, solid, etc., of regular or arbitrary complexity (freeform), as is commonly produced by photogrammetry, laser scanners, computerized tomography, and so on. Our starting point is the medial axis (MA) representation which has been explored mainly for 2D problems since the 1960's in pattern recognition and image analysis. The MA makes explicit certain symmetries of an object, corresponding to the shocks of waves initiated at the input samples, but is itself difficult to directly use for recognition tasks and applications. Based on previous work on the 2D problem, we propose a new representation in 3D which is derived from the MA, producing a graph we call the shock scaffold. The nodes of this graph are defined to be certain singularities of the shock flow along the MA. This graph can represent exactly the MA  and the original inputs  or approximate it, leading to a hierarchical description of shapes. We develop accurate and efficient algorithms to compute for 3D unorganized clouds of points the shock scaffold, and thus the MA, as well as its close cousin the Voronoi diagram. One computational method relies on clustering and visibility constraints, while the other simulates wavefront propagation on a 3D grid. We then propose a method of splitting the shock scaffold in two subgraphs, one of which is related to the (a priori unknown) surface of the object under scrutiny. This allows us to simplify the shock scaffold making more explicit coarse scale object symmetries, while at the same time providing an original method for the surface interpolation of complex datasets. In the last part of this talk, we address extensions of the shock scaffold by studying the case where the inputs are given as collections of unorganized polygons. Keywords: 3D shape representation, medial axis, Voronoi diagram, maximal contact spheres and shocks, directed graphs (digraphs), shock scaffold hierarchy (5 levels), wave propagation, eikonal equation, Euclidean distance maps, Lagrangian versus Eulerian computations, deterministic celullar automata, Huygens versus Fermat's optical principles, visibility constraints, unorganized generators, point clouds, polygonal clouds, quadrics, quartics, octics, Groebner bases and hybrid elimination methods, surface interpolation and meshing, ribs and ridges.
An Algorithm For Projecting Points Onto A Patched CAD Model
 In Proceedings, 10th International Meshing Round Table
, 2001
"... We are interested in building structured overlapping grids for geometries de ned by computeraideddesign (CAD) packages. Geometric information de ning the boundary surfaces of a computation domain is often provided in the form of a collection of possibly hundreds of trimmed patches. The rst step ..."
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Cited by 5 (0 self)
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We are interested in building structured overlapping grids for geometries de ned by computeraideddesign (CAD) packages. Geometric information de ning the boundary surfaces of a computation domain is often provided in the form of a collection of possibly hundreds of trimmed patches. The rst step in building an overlapping volume grid on such a geometry is to build overlapping surface grids. A surface grid is typically built using hyperbolic grid generation; starting from a curve on the surface, a grid is grown by marching over the surface. A given hyperbolic grid will typically cover many of the underlying CAD surface patches. The fundamental operation needed for building surface grids is that of projecting a point in space onto the closest point on the CAD surface. We describe a fast algorithm for performing this projection, it will make use of a fairly coarse global triangulation of the CAD geometry. We describe how to build this global triangulation by rst determining the connectivity of the CAD surface patches. This step is necessary since it often the case that the CAD description will contain no information specifying how a given patch connects to other neighbouring patches. Determining the connectivity is dicult since the surface patches may contain mistakes such as gaps or overlaps between neighbouring patches.
2009. Repairing and meshing imperfect shapes with Delaunay refinement
 In SPM ’09: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
"... As a direct consequence of software quirks, designer errors, and representation flaws, often threedimensional shapes are stored in formats that introduce inconsistencies such as small gaps and overlaps between surface patches. We present a new algorithm that simultaneously repairs imperfect geometr ..."
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Cited by 3 (0 self)
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As a direct consequence of software quirks, designer errors, and representation flaws, often threedimensional shapes are stored in formats that introduce inconsistencies such as small gaps and overlaps between surface patches. We present a new algorithm that simultaneously repairs imperfect geometry and topology while generating Delaunay meshes of these shapes. At the core of this approach is a meshing algorithm for input shapes that are piecewise smooth complexes (PSCs), a collection of smooth surface patches meeting at curves nonsmoothly or in nonmanifold configurations. Guided by a user tolerance parameter, we automatically merge nearby components while building a Delaunay mesh that has many of these errors fixed. Experimental evidence is provided to show the results of our algorithm on common computeraided design (CAD) formats. Our algorithm may also be used to simplify shapes by removing small features which would require an excessive number of elements to preserve them in the output mesh. Categories andSubjectDescriptors
Compression Techniques for Distributed Use of 3D Data: An Emerging Media Type on the Internet
"... 3D data is being processed in a number of application domains such as, engineering design, manufacture, architecture, ..."
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3D data is being processed in a number of application domains such as, engineering design, manufacture, architecture,
Shape Operators and Mechanical Criteria in the Preparation of Components for Engineering Analysis
, 2008
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