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Reconstructing Visible Regions From Visible Segments
, 1986
"... An algorithm is presented for reconstructing visible regions from visible edge segments in object space. This has applications in hidden surface algerithms operating on polyhedral scenes (e.g.W.R. Franklin, "A linear time exact hidden surface algorithm," ACM Computer Graphics 14(3), 117 ..."
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Cited by 4 (3 self)
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An algorithm is presented for reconstructing visible regions from visible edge segments in object space. This has applications in hidden surface algerithms operating on polyhedral scenes (e.g.W.R. Franklin, "A linear time exact hidden surface algorithm," ACM Computer Graphics 14(3), 117123, 1980). A special case of reconstruction can be formulated as a graph problem: "Determine the faces of a straightedge planar graph given in terms of its edges." This is accomplished in O (n log n) time using linear space for a graph with n edges, and is worstcase optimal. (The graph may have separate components but the components must not contain each other.) The general problem of reconstruction is then solved by applying our algorithm to each component in the containment relation.
On the Complexity of Some Geometric Intersection Problems
 Journal of Computing and Information
, 1995
"... : A classification of polygons is proposed together with a new class of connected polygons, called ordinary polygons. Ordinary polygons include simple polygons possibly with holes. The determination of the intersection of a line segment and an ordinary polygon with N edges requires\Omega\Gamma N lo ..."
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Cited by 2 (1 self)
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: A classification of polygons is proposed together with a new class of connected polygons, called ordinary polygons. Ordinary polygons include simple polygons possibly with holes. The determination of the intersection of a line segment and an ordinary polygon with N edges requires\Omega\Gamma N log N) time in the worst case. A lineartime algorithm is given, however, if a planar subdivision of the polygon in trapezoids is allowed as a preprocessing. As the minimal trapezoidal subdivision of an ordinary polygon is NPcomplete, we propose a subdivision that, although not minimal, has at most 3N vertices and 5N edges, and can be computed in optimal \Theta(N log N) time in the worst case. The intersection of an Medge ordinary polygon with an Nedge ordinary polygon can be obtained in \Theta(M log M + MN + N log N) time, which is also worstcase optimal. Applications to worstcase optimal clipping and scanconversion algorithms and efficient hiddenline and hiddensurface algorithms th...
Assessment of Mesh Simplification Algorithm Quality
, 2002
"... This paper describes a method to compare an original mesh and its simplified representation. Meshes considered here contain geometric features as well as other surface attributes such as material colors, texture, temperature, and radiation, etc. Many simplification algorithms have been presented in ..."
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Cited by 1 (0 self)
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This paper describes a method to compare an original mesh and its simplified representation. Meshes considered here contain geometric features as well as other surface attributes such as material colors, texture, temperature, and radiation, etc. Many simplification algorithms have been presented in literature. In this paper we present a new method to assess mesh simplification algorithm quality according to the appearance attributes. This assessment allows the appreciation of local quality and the computation of global quality statistics of a simplified mesh. The method can be easily and quickly used. We present a fast algorithm to sample the surface of a triangular mesh. The sampling technique increases the assessment resolution and the statistic precision.
Nearest Point Query on 184,088,599 Points in E 3 with a Uniform Grid
, 2006
"... Nearpt3 is an algorithm and implementation to preprocess more than 10 8 fixed points in E 3 and then perform nearest point queries against them. With fixed and query points drawn from the same distribution, Nearpt3’s expected preprocessing and query time are θ(1), per point, with a very small consta ..."
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Nearpt3 is an algorithm and implementation to preprocess more than 10 8 fixed points in E 3 and then perform nearest point queries against them. With fixed and query points drawn from the same distribution, Nearpt3’s expected preprocessing and query time are θ(1), per point, with a very small constant factor. The data structure is a uniform grid in E 3, typically with the same number of grid cells as points. The storage budget for Nearpt3, in addition to the space to store the points themselves, is only 4 bytes per grid cell plus 4 bytes per point. Running on a laptop computer, Nearpt3 can process these
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"... This paper describes a method to compare an original mesh and its simplified representation. Meshes considered here contain geometric features as well as other surface attributes such as material colors, texture, temperature, and radiation, etc. Many simplification algorithms have been presented in ..."
Abstract
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This paper describes a method to compare an original mesh and its simplified representation. Meshes considered here contain geometric features as well as other surface attributes such as material colors, texture, temperature, and radiation, etc. Many simplification algorithms have been presented in literature. In this paper we present a new method to assess mesh simplification algorithm quality according to the appearance attributes. This assessment allows the appreciation of local quality and the computation of global quality statistics of a simplified mesh. The method can be easily and quickly used. We present a fast algorithm to sample the surface of a triangular mesh. The sampling technique increases the assessment resolution and the statistic precision.