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17
Face Fixer: Compressing polygon meshes with properties
 In SIGGRAPH’00 Conference Proceedings
, 2000
"... Most schemes to compress the topology of a surface mesh have been developed for the lowest common denominator: triangulated meshes. We propose a scheme that handles the topology of arbitrary polygon meshes. It encodes meshes directly in their polygonal representation and extends to capture face grou ..."
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Cited by 85 (18 self)
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Most schemes to compress the topology of a surface mesh have been developed for the lowest common denominator: triangulated meshes. We propose a scheme that handles the topology of arbitrary polygon meshes. It encodes meshes directly in their polygonal representation and extends to capture face groupings in a natural way. Avoiding the triangulation step we reduce the storage costs for typical polygon models that have group structures and property data.
Dynamic ViewDependent Multiresolution on a ClientServer Architecture
 CAD Journal
, 2000
"... We consider the problem of transmitting huge triangle meshes in the context of a Weblike clientserver architecture. Approximations of the original mesh are transmitted by applying selective refinement. A multiresolution geometric model is maintained by the server. A client may query the server for ..."
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Cited by 13 (3 self)
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We consider the problem of transmitting huge triangle meshes in the context of a Weblike clientserver architecture. Approximations of the original mesh are transmitted by applying selective refinement. A multiresolution geometric model is maintained by the server. A client may query the server for a mesh at an arbitrary, continuously variable, level of detail. The client makes repeated queries over time with different query parameters. The server answers to queries by traversing the multiresolution model and transmitting updates to the client, which uses them to progressively modify a current mesh. We study this problem in the context of a vertexbased multiresolution model, which is a special instance of the MultiTriangulation [Pup96, DFPM97], based on vertex insertion and removal. We define a compact data structure for such a model which exploits the specific update rule. We propose a dynamic algorithm for selective refinement and we discuss in detail its implementation as a...
Towards InPlace Geometric Algorithms and Data Structures
 In Proceedings of the Twentieth ACM Symposium on Computational Geometry
, 2003
"... For many geometric problems, there are ecient algorithms that surprisingly use very little extra space other than the given array holding the input. For many geometric query problems, there are ecient data structures that need no extra space at all other than an array holding a permutation of the ..."
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Cited by 13 (4 self)
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For many geometric problems, there are ecient algorithms that surprisingly use very little extra space other than the given array holding the input. For many geometric query problems, there are ecient data structures that need no extra space at all other than an array holding a permutation of the input. In this paper, we obtain the rst such spaceeconomical solutions for a number of fundamental problems, including threedimensional convex hulls, twodimensional Delaunay triangulations, xeddimensional range queries, and xeddimensional nearest neighbor queries.
Facility location on terrains
 PROC. 9TH INTERNATIONAL SYMPOSIUM OF ALGORITHMS AND COMPUTATION, VOLUME 1533 OF LECTURE NOTES COMPUT. SCI
, 1998
"... Given a terrain defined as a piecewiselinear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. The distance is measured as the length of the Euclidean shortest path along the terrain. To simpli ..."
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Cited by 12 (2 self)
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Given a terrain defined as a piecewiselinear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. The distance is measured as the length of the Euclidean shortest path along the terrain. To simplify the problem somewhat, we extend the terrain to (the surface of) a polyhedron. To compute the optimum placement, we compute the furthestsite Voronoi diagram of the sites on the polyhedron. The diagram has maximum combinatorial complexity Θ(mn²), and the algorithm runs in O(mn² log² mlogn) time.
Progressive TINs: Algorithms and Applications
 In Proceedings 5th ACM workshop on Advances in geographic information systems, Las Vegas
, 1997
"... Transmission of geographic data over the Internet, rendering at different resolutions /levels of detail, or processing at unnecessarily fine detail pose interesting challenges and opportunities. In this paper we explore the applicability to GIS of the notion of progressive meshes, introduced by H ..."
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Cited by 8 (2 self)
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Transmission of geographic data over the Internet, rendering at different resolutions /levels of detail, or processing at unnecessarily fine detail pose interesting challenges and opportunities. In this paper we explore the applicability to GIS of the notion of progressive meshes, introduced by Hoppe [13] to the field of computer graphics. In particular, we describe progressive TINs as an alternative to hierarchical TINs, design algorithms for solving GIS tasks such as selective refinement, point location, visibility or line of sight queries, isoline/contour line extraction and provide empirical results which show that our algorithms are of considerable practical relevance. Moreover, the selective refinement data structure and refinement algorithm solves a question posed by Hoppe.
Compressing Triangulated Irregular Networks
 Geoinformation
, 1999
"... We address the problem of designing compact data structures for encoding a Triangulated Irregular Network (TIN). In particular, we study the problem of compressing connectivity, i.e., the information describing the topological structure of the TIN, and we propose two new compression methods which ha ..."
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Cited by 5 (2 self)
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We address the problem of designing compact data structures for encoding a Triangulated Irregular Network (TIN). In particular, we study the problem of compressing connectivity, i.e., the information describing the topological structure of the TIN, and we propose two new compression methods which have different purposes. The goal of the first method is to minimize the number of bits needed to encode connectivity information: it encodes each vertex once, and at most two bits of connectivity information for each edge of a TIN; algorithms for coding and decoding the corresponding bitstream are simple and efficient. A practical evaluation shows compression rates of about 4.2 bits per vertex, which are comparable with those achieved by more complex methods. The second method compresses a TIN at progressive levels of detail and it is based on a strategy which iteratively removes a vertex from a TIN according to an errorbased criterion. Encoding and decoding algorithms are presented and c...
Tight bounds for connecting sites across barrieres
 in Proc. 22nd SoCG, ACM
, 2006
"... Given m points (sites) and n obstacles (barriers) in the plane, we address the problem of finding a straightline minimum cost spanning tree on the sites, where the cost is proportional to the number of intersections (crossings) between tree edges and barriers. If the barriers are infinite lines the ..."
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Cited by 5 (2 self)
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Given m points (sites) and n obstacles (barriers) in the plane, we address the problem of finding a straightline minimum cost spanning tree on the sites, where the cost is proportional to the number of intersections (crossings) between tree edges and barriers. If the barriers are infinite lines then there is a spanning tree where every barrier is crossed by O ( √ m) tree edges (connectors), and this bound is asymptotically optimal (spanning tree with low stabbing number). Asano et al. showed that if the barriers are pairwise disjoint line segments, then there is a spanning tree such that every barrier crosses at most 4 tree edges and so the total cost is at most 4n. Constructionswith3crossings per barrier and 2n total cost provide a lower bound. We obtain tight bounds on the minimum cost spanning tree in the most exciting special case where the barriers are interior disjoint line segments that form a convex subdivision and there is a point in every cell. In particular, we show that there is a spanning tree such that every barrier is crossed by at most 2 tree edges, and there is a spanning tree of total cost 5n/3. Both bounds are tight.
Selecting Independent Vertices For Terrain Simplification
, 1998
"... In this paper we investigate decimation algorithms for simplifying triangulated terrain models in order to support progressive transmission of GIS terrain models over the web. We report on experiments with heuristics that select an independent set of vertices to be deleted, while trying to preser ..."
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Cited by 5 (0 self)
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In this paper we investigate decimation algorithms for simplifying triangulated terrain models in order to support progressive transmission of GIS terrain models over the web. We report on experiments with heuristics that select an independent set of vertices to be deleted, while trying to preserve terrain characteristics.
Compressing TINs
 In Proceedings of the 6th ACM Symposium on Advances in Geographic Information Systems
, 1998
"... We address the problem of designing compact data structures for encoding a Triangulated Irregular Network (TIN) as a sequential bitstream. In particular, we study the problem of compressing connectivity, i.e., the information describing the topological structure of the TIN and we propose two new com ..."
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Cited by 4 (1 self)
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We address the problem of designing compact data structures for encoding a Triangulated Irregular Network (TIN) as a sequential bitstream. In particular, we study the problem of compressing connectivity, i.e., the information describing the topological structure of the TIN and we propose two new compression methods which have different purposes. The goal of the first method is to minimize the number of bits needed to encode connectivity information: it encodes each vertex once, and requires two bits of connectivity information for each edge of a TIN. We present efficient algorithms for coding and decoding the corresponding bitstream and show some practical evaluation of the method. The second method compresses a TIN at progressive levels of detail and is based on a strategy which iteratively removes a vertex from a TIN according to an errorbased criterion. Encoding and decoding algorithms are presented and compared with other approaches to progressive compression. 2 Introduction Hug...
Compression and Streaming of Polygon Meshes
, 2005
"... Polygon meshes provide a simple way to represent threedimensional surfaces and are the defacto standard for interactive visualization of geometric models. Storing large polygon meshes in standard indexed formats results in files of substantial size. Such formats allow listing vertices and polygons ..."
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Cited by 3 (0 self)
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Polygon meshes provide a simple way to represent threedimensional surfaces and are the defacto standard for interactive visualization of geometric models. Storing large polygon meshes in standard indexed formats results in files of substantial size. Such formats allow listing vertices and polygons in any order so that not only the mesh is stored but also the particular ordering of its elements. Mesh compression rearranges vertices and polygons into an order that allows more compact coding of the incidence between vertices and predictive compression of their positions. Previous schemes were designed for triangle meshes and polygonal faces were triangulated prior to compression. I show that polygon models can be encoded more compactly by avoiding the initial triangulation step. I describe two compression schemes that achieve better compression by encoding meshes directly in their polygonal representation. I demonstrate that the