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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 192 (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 171 (16 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...
Variational shape approximation
 ACM Trans. Graph
, 2004
"... Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage and that copies show this notice on the first page or initial screen of a display alon ..."
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Cited by 157 (4 self)
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Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee.
Discrete Geometric Shapes: Matching, Interpolation, and Approximation: A Survey
 Handbook of Computational Geometry
, 1996
"... In this survey we consider geometric techniques which have been used to measure the similarity or distance between shapes, as well as to approximate shapes, or interpolate between shapes. Shape is a modality which plays a key role in many disciplines, ranging from computer vision to molecular biolog ..."
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Cited by 126 (10 self)
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In this survey we consider geometric techniques which have been used to measure the similarity or distance between shapes, as well as to approximate shapes, or interpolate between shapes. Shape is a modality which plays a key role in many disciplines, ranging from computer vision to molecular biology. We focus on algorithmic techniques based on computational geometry that have been developed for shape matching, simplification, and morphing. 1 Introduction The matching and analysis of geometric patterns and shapes is of importance in various application areas, in particular in computer vision and pattern recognition, but also in other disciplines concerned with the form of objects such as cartography, molecular biology, and computer animation. The general situation is that we are given two objects A, B and want to know how much they resemble each other. Usually one of the objects may undergo certain transformations like translations, rotations or scalings in order to be matched with th...
Multiresolution Modeling: Survey & Future Opportunities
, 1999
"... For twenty years, it has been clear that many datasets are excessively complex for applications such as realtime display, and that techniques for controlling the level of detail of models are crucial. More recently, there has been considerable interest in techniques for the automatic simplificati ..."
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Cited by 118 (7 self)
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For twenty years, it has been clear that many datasets are excessively complex for applications such as realtime display, and that techniques for controlling the level of detail of models are crucial. More recently, there has been considerable interest in techniques for the automatic simplification of highly detailed polygonal models into faithful approximations using fewer polygons. Several effective techniques for the automatic simplification of polygonal models have been developed in recent years. This report begins with a survey of the most notable available algorithms. Iterative edge contraction algorithms are of particular interest because they induce a certain hierarchical structure on the surface. An overview of this hierarchical structure is presented,including a formulation relating it to minimum spanning tree construction algorithms. Finally, we will consider the most significant directions in which existing simplification methods can be improved, and a summary of o...
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 94 (12 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.
Hierarchical Triangulation for Multiresolution Surface Description
 ACM Transactions on Graphics
, 1995
"... A new hierarchical trianglebased model for representing surfaces over sampled data is proposed, which is based on the subdivision of the surface domain into nested triangulations, called a Hierarchical Triangulation (HT). The model allows compression of spatial data and representation of a surface ..."
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Cited by 88 (16 self)
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A new hierarchical trianglebased model for representing surfaces over sampled data is proposed, which is based on the subdivision of the surface domain into nested triangulations, called a Hierarchical Triangulation (HT). The model allows compression of spatial data and representation of a surface at successively finer degrees of resolution. An HT is a collection of triangulations organized in a tree, where each node, except for the root, is a triangulation refining a face belonging to its parent in the hierarchy. We present a topological model for representing an HT, and algorithms for its construction and for the extraction of a triangulation at a given degree of resolution. The surface model, called a Hierarchical Triangulated Surface (HTS), is obtained by associating data values with the vertices of triangles, and defining suitable functions that describe the surface over each triangular patch. We consider an application of a piecewiselinear version of the HTS to interpolate topo...
Approximation Algorithms For Geometric Problems
, 1995
"... INTRODUCTION 8.1 This chapter surveys approximation algorithms for hard geometric problems. The problems we consider typically take inputs that are point sets or polytopes in two or threedimensional space, and seek optimal constructions, (which may be trees, paths, or polytopes). We limit attent ..."
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Cited by 82 (1 self)
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INTRODUCTION 8.1 This chapter surveys approximation algorithms for hard geometric problems. The problems we consider typically take inputs that are point sets or polytopes in two or threedimensional space, and seek optimal constructions, (which may be trees, paths, or polytopes). We limit attention to problems for which no polynomialtime exact algorithms are known, and concentrate on bounds for worstcase approximation ratios, especially bounds that depend intrinsically on geometry. We illustrate our intentions with two wellknown problems. Given a finite set of points S in the plane, the Euclidean traveling salesman problem asks for the shortest tour of S. Christofides' algorithm achieves approximation ratio 3 2 for this problem, meaning that it always computes a tour of length at most threehalves the length of the optimal tour. This bound depends only on the triangle inequality, so Christofides' algorit
Approximation Algorithms for Geometric Tour and Network Design Problems (Extended Abstract)
"... ..."
Representation and Visualization of Terrain Surfaces at Variable Resolution
, 1997
"... We present a new approach for managing the multiresolution representation of discrete topographic surfaces. A Triangulated Irregular Network (TIN) representing the surface is built from sampled data by iteratively refining an initial triangulation that covers the whole domain. The refinement process ..."
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Cited by 69 (10 self)
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We present a new approach for managing the multiresolution representation of discrete topographic surfaces. A Triangulated Irregular Network (TIN) representing the surface is built from sampled data by iteratively refining an initial triangulation that covers the whole domain. The refinement process generates triangulations of the domain corresponding to increasingly finer approximations of the surface. Such triangulations are embedded into a structure in a three dimensional space. The resulting representation scheme encodes all intermediate representations that were generated during refinement. We propose a data structure and traversal algorithms that are oriented to the efficient extraction of approximated terrain models with an arbitrary precision, either constant or variable over the domain. 1. Introduction The search for multiresolution representation schemes has recently become very popular. Major applications involve generic surfaces embedded in 3D space 16;8;27 , terrains i...