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319
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 458 (0 self)
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The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
Teddy: A sketching interface for 3d freeform design
, 1999
"... We present a sketching interface for quickly and easily designing freeform models such as stuffed animals and other rotund objects. The user draws several 2D freeform strokes interactively on the screen and the system automatically constructs plausible 3D polygonal surfaces. Our system supports seve ..."
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Cited by 371 (33 self)
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We present a sketching interface for quickly and easily designing freeform models such as stuffed animals and other rotund objects. The user draws several 2D freeform strokes interactively on the screen and the system automatically constructs plausible 3D polygonal surfaces. Our system supports several modeling operations, including the operation to construct a 3D polygonal surface from a 2D silhouette drawn by the user: it inflates the region surrounded by the silhouette making wide areas fat, and narrow areas thin. Teddy, our prototype system, is implemented as a Java ™ program, and the mesh construction is done in realtime on a standard PC. Our informal user study showed that a firsttime user typically masters the operations within 10 minutes, and can construct interesting 3D models within minutes.
Unstructured lumigraph rendering
 In Computer Graphics, SIGGRAPH 2001 Proceedings
, 2001
"... We describe an image based rendering approach that generalizes many image based rendering algorithms currently in use including light field rendering and viewdependent texture mapping. In particular it allows for lumigraph style rendering from a set of input cameras that are not restricted to a pla ..."
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Cited by 224 (12 self)
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We describe an image based rendering approach that generalizes many image based rendering algorithms currently in use including light field rendering and viewdependent texture mapping. In particular it allows for lumigraph style rendering from a set of input cameras that are not restricted to a plane or to any specific manifold. In the case of regular and planar input camera positions, our algorithm reduces to a typical lumigraph approach. In the case of fewer cameras and good approximate geometry, our algorithm behaves like viewdependent texture mapping. Our algorithm achieves this flexibility because it is designed to meet a set of desirable goals that we describe. We demonstrate this flexibility with a variety of examples. Keyword ImageBased Rendering 1
Asrigidaspossible shape manipulation
 ACM Trans. Graph
, 2005
"... We present an interactive system that lets a user move and deform a twodimensional shape without manually establishing a skeleton or freeform deformation (FFD) domain beforehand. The shape is represented by a triangle mesh and the user moves several vertices of the mesh as constrained handles. The ..."
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Cited by 126 (16 self)
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We present an interactive system that lets a user move and deform a twodimensional shape without manually establishing a skeleton or freeform deformation (FFD) domain beforehand. The shape is represented by a triangle mesh and the user moves several vertices of the mesh as constrained handles. The system then computes the positions of the remaining free vertices by minimizing the distortion of each triangle. While physically based simulation or iterative refinement can also be used for this purpose, they tend to be slow. We present a twostep closedform algorithm that achieves realtime interaction. The first step finds an appropriate rotation for each triangle and the second step adjusts its scale. The key idea is to use quadratic error metrics so that each minimization problem becomes a system of linear equations. After solving the simultaneous equations at the beginning of interaction, we can quickly find the positions of free vertices during interactive manipulation. Our approach successfully conveys a sense of rigidity of the shape, which is difficult in spacewarp approaches. With a multiplepoint input device, even beginners can easily move, rotate, and deform shapes at will.
Optimistic parallelism requires abstractions
 In PLDI
, 2007
"... Irregular applications, which manipulate large, pointerbased data structures like graphs, are difficult to parallelize manually. Automatic tools and techniques such as restructuring compilers and runtime speculative execution have failed to uncover much parallelism in these applications, in spite o ..."
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Cited by 120 (20 self)
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Irregular applications, which manipulate large, pointerbased data structures like graphs, are difficult to parallelize manually. Automatic tools and techniques such as restructuring compilers and runtime speculative execution have failed to uncover much parallelism in these applications, in spite of a lot of effort by the research community. These difficulties have even led some researchers to wonder if there is any coarsegrain parallelism worth exploiting in irregular applications. In this paper, we describe two realworld irregular applications: a Delaunay mesh refinement application and a graphics application that performs agglomerative clustering. By studying the algorithms and data structures used in these applications, we show that there is substantial coarsegrain, data parallelism in these applications, but that this parallelism is very dependent on the input data and therefore cannot be uncovered by compiler analysis. In principle, optimistic techniques such as threadlevel speculation can be used to uncover this parallelism, but we argue that current implementations cannot accomplish this because they do not use the proper abstractions for the data structures in these programs. These insights have informed our design of the Galois system, an objectbased optimistic parallelization system for irregular applications. There are three main aspects to Galois: (1) a small number of syntactic constructs for packaging optimistic parallelism as iteration over ordered and unordered sets, (2) assertions about methods in class libraries, and (3) a runtime scheme for detecting and recovering from potentially unsafe accesses to shared memory made by an optimistic computation. We show that Delaunay mesh generation and agglomerative clustering can be parallelized in a straightforward way using the Galois approach, and we present experimental measurements to show that this approach is practical. These results suggest that Galois is a practical approach to exploiting data parallelism in irregular programs.
Delaunay Refinement Algorithms for Triangular Mesh Generation
 Computational Geometry: Theory and Applications
, 2001
"... Delaunay refinement is a technique for generating unstructured meshes of triangles for use in interpolation, the finite element method, and the finite volume method. In theory and practice, meshes produced by Delaunay refinement satisfy guaranteed bounds on angles, edge lengths, the number of tria ..."
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Cited by 101 (0 self)
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Delaunay refinement is a technique for generating unstructured meshes of triangles for use in interpolation, the finite element method, and the finite volume method. In theory and practice, meshes produced by Delaunay refinement satisfy guaranteed bounds on angles, edge lengths, the number of triangles, and the grading of triangles from small to large sizes. This article presents an intuitive framework for analyzing Delaunay refinement algorithms that unifies the pioneering mesh generation algorithms of L. Paul Chew and Jim Ruppert, improves the algorithms in several minor ways, and most importantly, helps to solve the difficult problem of meshing nonmanifold domains with small angles.
Topological Noise Removal
"... Meshes obtained from laser scanner data often contain topological noise due to inaccuracies in the scanning and merging process. This topological noise complicates subsequent operations such as remeshing, parameterization and smoothing. We introduce an approach that removes unnecessary nontrivial to ..."
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Cited by 98 (3 self)
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Meshes obtained from laser scanner data often contain topological noise due to inaccuracies in the scanning and merging process. This topological noise complicates subsequent operations such as remeshing, parameterization and smoothing. We introduce an approach that removes unnecessary nontrivial topology from meshes. Using a local wave front traversal, we discover the local topologies of the mesh and identify features such as small tunnels. We then identify nonseparating cuts along which we cut and seal the mesh, reducing the genus and thus the topological complexity of the mesh.
Active Blobs
, 1998
"... A new regionbased approach to nonrigid motion tracking is described. Shape is defined in terms of a deformable triangular mesh that captures object shape plus a color texture map that captures object appearance. Photometric variations are also modeled. Nonrigid shape registration and motion trackin ..."
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Cited by 89 (4 self)
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A new regionbased approach to nonrigid motion tracking is described. Shape is defined in terms of a deformable triangular mesh that captures object shape plus a color texture map that captures object appearance. Photometric variations are also modeled. Nonrigid shape registration and motion tracking are achieved by posing the problem as an energybased, robust minimization procedure. The approach provides robustness to occlusions, wrinkles, shadows, and specular highlights. The formulation is tailored to take advantage of texture mapping hardware available in many workstations, PC's, and game consoles. This enables nonrigid tracking at speeds approaching video rate. 1 Introduction A key open problem in tracking is that of encoding and comparing shapes as they undergo nonrigid deformation. Simply providing robustness to nonrigid deformation is insufficient, because deformation often provides important information about how shapes are related. To make things worse, tracking must also ...
Computing MinimumWeight Perfect Matchings
 INFORMS
, 1999
"... We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the ..."
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Cited by 83 (2 self)
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We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dualchange � for each tree. As a benchmark of the algorithm’s performance, solving a 100,000node geometric instance on a 200 Mhz PentiumPro computer takes approximately 3 minutes.
Viewdependent displacement mapping
 ACM Transactions on Graphics
, 2003
"... Displacement mapping was originally created as a rendering tool to provide smallscale modulation of an underlying smooth surface. However, it has now emerged as a sculpting tool, to the extent that complex geometry can effectively be added to a scene at rendering time. The attendant complexity of d ..."
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Cited by 68 (1 self)
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Displacement mapping was originally created as a rendering tool to provide smallscale modulation of an underlying smooth surface. However, it has now emerged as a sculpting tool, to the extent that complex geometry can effectively be added to a scene at rendering time. The attendant complexity of displacement maps is placing increased demands on rendering systems, from quality, performance, and memory perspectives. While adequate solutions exist within scanline rendering architectures, good general solutions have been difficult to come by in raytraced or hardwarebased environments, or in situations in which a complete displaced surface is desired. We present an approach to the rendering of displacement mapped surfaces that scales with the complexity of the displacement map, with an eye to minimizing the amount of additional geometry generated by the mapping process. We perform a feature analysis of displacement maps, aggregate these features, and map them onto geometry in space. This approach affords a significant degree of complexity control, it permits featurebased tessellation of surfaces, and it is amenable to use in raytraced, scanline, or hardware accelerated settings. This kind of feature analysis naturally applies to other classes of texture mapping as well. 1