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29
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 640 (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.
ReTiling Polygonal Surfaces
 Computer Graphics
, 1992
"... This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speed ..."
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Cited by 445 (3 self)
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This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speedingup the offline rendering of complex scenes. Unfortunately, generating these levels of detail is a timeconsuming task usually left to a human modeler. This paper shows how a new set of vertices can be distributed over the surface of a model and connected to one another to create a retiling of a surface that is faithful to both the geometry and the topology of the original surface. Themain contributions of this paper are: 1) a robust method of connecting together new vertices over a surface, 2) a way of using an estimate of surface curvature to distribute more new vertices at regions of higher curvature and 3) a method of smoothly interpolating between models that represent the same object at different levels of detail. The key notion in the retiling procedure is the creation of an intermediate model called the mutual tessellation of a surface that contains both the vertices from the original model and the new points that are to become vertices in the retiled surface. The new model is then created by removing each original vertex and locally retriangulating the surface in a way that matches the local connectedness of the initial surface. This technique for surface retessellation has been successfully applied to isosurface models derived from volume data, Connolly surface molecular models and a tessellation of a minimal surface of interest to mathematicians. CRCategoriesandSubjectDescriptors: I.3.3 [ComputerGraph ics]: Picture/Image Generation  Display algorithms
Survey of Polygonal Surface Simplification Algorithms
, 1997
"... This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons ..."
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Cited by 227 (3 self)
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This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons
Simplification Envelopes
"... We propose the idea of simplification envelopes for generating a hierarchy of levelofdetail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a userspecifiable distance # from the original model and that all points of the original m ..."
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Cited by 206 (17 self)
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We propose the idea of simplification envelopes for generating a hierarchy of levelofdetail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a userspecifiable distance # from the original model and that all points of the original model are within a distance # from the approximation. Simplificationenvelopes provide a general framework within which a large collection of existing simplification algorithms can run. We demonstrate this technique in conjunction with two algorithms, one local, the other global. The local algorithm provides a fast method for generating approximations to large input meshes (at least hundreds of thousands of triangles). The global algorithm provides the opportunity to avoid local "minima" and possibly achieve better simplifications as a result. Each approximation attempts to minimize the total number of polygons required to satisfy the above # constraint. The key advantages of our approach are...
Efficient algorithms for geometric optimization
 ACM Comput. Surv
, 1998
"... We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear progra ..."
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Cited by 114 (10 self)
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We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear programming and related problems, and LPtype problems and their efficient solution. We then describe a variety of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other querytype problems.
Multiresolution Modeling for Fast Rendering
 PROCEEDINGS OF GRAPHICS INTERFACE
, 1994
"... Three dimensional scenes are typically modeled using a single, fixed resolution model of each geometric object. Renderings of such a model are often either slow or crude, however: slow for distant objects, where the chosen detail level is excessive, and crude for nearby objects, where the detail lev ..."
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Cited by 113 (5 self)
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Three dimensional scenes are typically modeled using a single, fixed resolution model of each geometric object. Renderings of such a model are often either slow or crude, however: slow for distant objects, where the chosen detail level is excessive, and crude for nearby objects, where the detail level is insufficient. What is needed is a multiresolution model that represents objects at multiple levels of detail. With a multiresolution model, a rendering program can choose the level of detail appropriate for the object's screen size so that less time is wasted drawing insignificant detail. The principal challenge is the development of algorithms that take a detailed model as input and automatically simplify it, while preserving appearance. Multiresolution techniques can be used to speed many applications, including real time rendering for architectural and terrain simulators, and slower, higher quality rendering for entertainment and radiosity. This paper surveys existing multiresolutio...
Hierarchical Geometric Approximations
, 1994
"... This dissertation explores some techniques for automatic approximation of geometric objects. My thesis is that using and extending concepts from computational geometry can help us in devising efficient and parallelizable algorithms for automatically constructing useful detail hierarchies for geometr ..."
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Cited by 38 (4 self)
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This dissertation explores some techniques for automatic approximation of geometric objects. My thesis is that using and extending concepts from computational geometry can help us in devising efficient and parallelizable algorithms for automatically constructing useful detail hierarchies for geometric objects. We have demonstrated this by developing new algorithms for two kinds of geometric approximation problems that have been motivated by a single driving problem  the efficient computation and display of smooth solventaccessible molecular surfaces. The applications of these detail hierarchies are in biochemistry and computer graphics. The smooth solventaccessible surface of a molecule is useful in studying the structure and interactions of proteins, in particular for attacking the proteinsubstrate docking problem. We have developed a parallel lineartime algorithm for computing molecular surfaces. Molecular surfaces are equivalent to the weighted ffhulls. Thus our work is pot...
Temporal Continuity of Levels of Detail in Delaunay Triangulated Terrain
 In Proc. Visualization ’96
, 1996
"... The representation of a scene at different levels of detail is necessary to achieve realtime rendering. In aerial views only part of the scene that is close to the viewing point needs to be displayed with a high level of detail, while more distant parts can be displayed with a low level of detail. ..."
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Cited by 27 (0 self)
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The representation of a scene at different levels of detail is necessary to achieve realtime rendering. In aerial views only part of the scene that is close to the viewing point needs to be displayed with a high level of detail, while more distant parts can be displayed with a low level of detail. However, when the sequence of images is generated and displayed in realtime, the transition between different levels of detail causes noticeable temporal aliasing. In this paper, we propose a method, based on object blending, that visually softens the transition between two levels of Delaunay triangulation. We present an algorithm that establishes, in an offline process, a correspondence between two given polygonal objects. The correspondence enables online blending between two representations of an object, so that one representation (level of detail) progressively evolves into the other. 1 INTRODUCTION Terrain data is used by many computer graphics applications, including flight simulato...
Generating Levels of Detail for LargeScale Polygonal Models
, 1995
"... We present an efficient algorithm for generating various levelsofdetail approximations for a given polygonal model. Our algorithm guarantees that all points of an approximation are within a userspecifiable distance ffl from the original model and all points of the original model are within a dist ..."
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Cited by 6 (0 self)
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We present an efficient algorithm for generating various levelsofdetail approximations for a given polygonal model. Our algorithm guarantees that all points of an approximation are within a userspecifiable distance ffl from the original model and all points of the original model are within a distance ffl from the approximation. Each approximation attempts to minimize the total number of polygons required to satisfy the previous constraint. We show how the problem of generating levelsof detail approximations reduces to the classic set partition problem. The various approximations are guaranteed to be topologically consistent with the input polygonal model. The approximations can be constrained by the user to preserve any desired edges of the input model. We also propose a method to compute an estimate of the quality of the approximation generated by our algorithm with respect to the optimal approximation satisfying the same constraints. We have implemented our algorithm and have obt...