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Surface reconstruction from unorganized points
 COMPUTER GRAPHICS (SIGGRAPH ’92 PROCEEDINGS)
, 1992
"... We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be know ..."
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Cited by 651 (8 self)
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We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance — all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from twodimensional slices, and interactive surface sketching.
Decimation of triangle meshes
 Computer Graphics (SIGGRAPH '92 Proceedings
, 1992
"... The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software. ..."
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Cited by 569 (2 self)
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The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software.
Arrangements and Their Applications
 Handbook of Computational Geometry
, 1998
"... The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arr ..."
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Cited by 76 (20 self)
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The arrangement of a finite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arrangements to problems in motion planning, visualization, range searching, molecular modeling, and geometric optimization. Some results involving planar arrangements of arcs have been presented in a companion chapter in this book, and are extended in this chapter to higher dimensions. Work by P.A. was supported by Army Research Office MURI grant DAAH049610013, by a Sloan fellowship, by an NYI award, and by a grant from the U.S.Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR9122103 and CCR9311127, by a MaxPlanck Research Award, and by grants from the U.S.Israeli Binational Science Foundation, the Israel Science Fund administered by the Israeli Ac...
Using Generic Programming for Designing a Data Structure for Polyhedral Surfaces
 Comput. Geom. Theory Appl
, 1999
"... Appeared in Computational Geometry  Theory and Applications 13, 1999, 6590. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, ..."
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Cited by 46 (5 self)
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Appeared in Computational Geometry  Theory and Applications 13, 1999, 6590. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedral surfaces and evaluate edgebased representations with respect to our design goals. A design for polyhedral surfaces in a halfedge data structure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and facebased structures. Key words: Library design; Generic programming; Combinatorial data structure; Polyhedral surface; Halfedge data structure 1 Introduction Combinatorial structures, such as planar maps, are fundamental in computational geometry. In order to be useful in practice, a solid library for compu...
The Design and Implementation of Planar Maps in CGAL
 Special Issue, selected papers of the Workshop on Algorithm Engineering (WAE
, 1999
"... this paper has been supported in part by ESPRIT IV LTR Projects No. 21957 (CGAL) and No. 28155 (GALIA), by the USAIsrael Binational Science Foundation, by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), by ..."
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Cited by 39 (17 self)
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this paper has been supported in part by ESPRIT IV LTR Projects No. 21957 (CGAL) and No. 28155 (GALIA), by the USAIsrael Binational Science Foundation, by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), by a FrancoIsraeli research grant "factory of the future" (monitored by AFIRST/France and The Israeli Ministry of Science), and by the Hermann Minkowski  Minerva Center for Geometry at Tel Aviv University
A realtime GPU subdivision kernel
 ACM Trans. Graph
, 2005
"... Figure 1: CatmullClark surfaces fully reevaluated (40 patches, depth 5) at 21 fps on an ATi 9700 mobile graphics chip. By organizing the control mesh of subdivision in texture memory so that irregularities occur strictly inside independently refinable fragment meshes, all major features of subdivis ..."
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Cited by 37 (4 self)
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Figure 1: CatmullClark surfaces fully reevaluated (40 patches, depth 5) at 21 fps on an ATi 9700 mobile graphics chip. By organizing the control mesh of subdivision in texture memory so that irregularities occur strictly inside independently refinable fragment meshes, all major features of subdivision algorithms can be realized in the framework of highly parallel stream processing. Our implementation of CatmullClark subdivision as a GPU kernel in programmable graphics hardware can model features like semismooth creases and global boundaries; and a simplified version achieves nearrealtime depthfive reevaluation of moderatesized subdivision meshes. The approach is easily adapted to other refinement patterns, such as Loop, DooSabin or √ 3 and it allows for postprocessing with additional shaders.
Matchmaker: Manifold BReps for nonmanifold rsets
 Proceedings of the ACM Symposium on Solid Modeling
, 1999
"... Many solid modeling construction techniques produce nonmanifold rsets (solids). With each nonmanifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each nonmanifold edge of N with 2k incident faces will be ..."
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Cited by 37 (18 self)
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Many solid modeling construction techniques produce nonmanifold rsets (solids). With each nonmanifold model N we can associate a family of manifold solid models that are infinitely close to N in the geometric sense. For polyhedral solids, each nonmanifold edge of N with 2k incident faces will be replicated k times in any manifold model M of that family. Furthermore, some nonmanifold vertices of N must also be replicated in M, possibly several times. M can be obtained by defining, in N, a single adjacent face TA(E,F) for each pair (E,F) that combines an edge E and an incident face F. The adjacency relation satisfies TA(E,TA(E,F))=F. The choice of the map A defines which vertices of N must be replicated in M and how many times. The resulting manifold representation of a nonmanifold solid may be encoded using simpler and more compact datastructures, especially for triangulated model, and leads to simpler and more efficient algorithms, when it is used instead of a nonmanifold repre...
Designing a Data Structure for Polyhedral Surfaces
 In Proc. 14th Annu. ACM Sympos. Comput. Geom
, 1998
"... Design solutions for a program library are presented for combinatorial data structures in computational geometry, such as planar maps and polyhedral surfaces. Design issues considered are genericity, flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedr ..."
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Cited by 31 (2 self)
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Design solutions for a program library are presented for combinatorial data structures in computational geometry, such as planar maps and polyhedral surfaces. Design issues considered are genericity, flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedral surfaces. Edgebased representations for polyhedrons are evaluated with respect to the design goals. A design for polyhedral surfaces in a halfedge data structure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and facebased structures managing holes in facets. 1 Introduction Combinatorial structures, such as planar maps, are fundamental in computational geometry. In order to use computational geometry in practice, a solid library must provide generic and flexible solutions as one of its fundamental cornerstones. Other design criteria are time and space efficiency. Easeofuse is necessar...
Fast Rendering of Subdivision Surfaces
, 1996
"... Subdivision surfaces provide a curved surface representation that is useful in a number of applications, including modeling surfaces of arbitrary topological type [5], fitting scattered data [6], and geometric compression and automatic levelofdetail generation using wavelets [8]. Subdivision sur ..."
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Cited by 25 (1 self)
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Subdivision surfaces provide a curved surface representation that is useful in a number of applications, including modeling surfaces of arbitrary topological type [5], fitting scattered data [6], and geometric compression and automatic levelofdetail generation using wavelets [8]. Subdivision surfaces also provide an attractive representation for fast rendering, since they can directly represent complex surfaces of arbitrary topology. This direct representation contrasts with traditional approaches such as trimmed NURBS, in which tesselating trim regions dominates rendering time, and algebraic implicit surfaces, in which rendering requires resultants, root finders, or other computationally expensive techniques. We present a method for subdivision surface triangulation that is fast, uses minimum memory, and is simpler in structure than a naive rendering method based on direct subdivision. These features make the algorithm amenable to implementation on dedicated geometry eng...
XFastMesh: Fast Viewdependent Meshing from External Memory
, 2002
"... We present a novel diskbased multiresolution triangle mesh data structure that supports paging and viewdependent rendering of very large meshes at interactive frame rates from external memory. Our approach, called XFastMesh, is based on a viewdependent mesh simplification framework that represent ..."
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Cited by 24 (0 self)
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We present a novel diskbased multiresolution triangle mesh data structure that supports paging and viewdependent rendering of very large meshes at interactive frame rates from external memory. Our approach, called XFastMesh, is based on a viewdependent mesh simplification framework that represents halfedge collapse operations in a binary hierarchy known as a mergetree forest. The proposed technique partitions the mergetree forest into socalled detail blocks, which consist of binary subtrees, that are stored on disk. We present an efficient external memory data structure and file format that stores all detail information of the multiresolution triangulation method using significantly less storage then previously reported approaches. Furthermore, we present a paging algorithm that provides efficient loading and interactive rendering of large meshes from external memory at varying and viewdependent levelofdetail. The presented approach is highly efficient both in terms of space cost and paging performance.