Results 1  10
of
107
An optimal algorithm for intersecting line segments in the plane
 J. ACM
, 1992
"... Abstract. Themain contribution ofthiswork is an O(nlogr ~ +k)timeal gorithmfo rcomputingall k intersections among n line segments in the plane, This time complexity IS easdy shown to be optimal. Within thesame asymptotic cost, ouralgorithm canalso construct thesubdiwslon of theplancdefmed by the se ..."
Abstract

Cited by 161 (2 self)
 Add to MetaCart
Abstract. Themain contribution ofthiswork is an O(nlogr ~ +k)timeal gorithmfo rcomputingall k intersections among n line segments in the plane, This time complexity IS easdy shown to be optimal. Within thesame asymptotic cost, ouralgorithm canalso construct thesubdiwslon of theplancdefmed by the segments and compute which segment (if any) lies right above (or below) each intersection and each endpoint. The algorithm has been implemented and performs very well. The storage requirement is on the order of n + k in the worst case, but it is considerably lower in practice. To analyze the complexity of the algorithm, an amortization argument based on a new combinatorial theorem on line arrangements is used.
Exact polyhedral visual hulls
 In British Machine Vision Conference
, 2003
"... We propose an exact method for efficiently and robustly computing the visual hull of an object from image contours. Unlike most existing approaches, ours computes an exact description of the visual hull polyhedron associated to polygonal image contours. Furthermore, the proposed approach is fast and ..."
Abstract

Cited by 63 (11 self)
 Add to MetaCart
We propose an exact method for efficiently and robustly computing the visual hull of an object from image contours. Unlike most existing approaches, ours computes an exact description of the visual hull polyhedron associated to polygonal image contours. Furthermore, the proposed approach is fast and allows realtime recovery of both manifold and watertight visual hull polyhedra. The process involves three main steps. First, a coarse geometrical approximation of the visual hull is computed by retrieving its viewing edges, an unconnected subset of the wanted mesh. Then, local orientation and connectivity rules are used to walk along the relevant viewing cone intersection boundaries, so as to iteratively generate the missing surface points and connections. A final connection walkthrough allows us to identify the planar contours for each face of the polyhedron. Implementation details and results with synthetic and real data are presented. 1
Planar Separators and Parallel Polygon Triangulation
, 1992
"... We show how to construct an O( p n)separator decomposition of a planar graph G in O(n) time. Such a decomposition defines a binary tree where each node corresponds to a subgraph of G and stores an O( p n)separator of that subgraph. We also show how to construct an O(n ffl )way decomposition tree ..."
Abstract

Cited by 51 (7 self)
 Add to MetaCart
We show how to construct an O( p n)separator decomposition of a planar graph G in O(n) time. Such a decomposition defines a binary tree where each node corresponds to a subgraph of G and stores an O( p n)separator of that subgraph. We also show how to construct an O(n ffl )way decomposition tree in parallel in O(log n) time so that each node corresponds to a subgraph of G and stores an O(n 1=2+ffl )separator of that subgraph. We demonstrate the utility of such a separator decomposition by showing how it can be used in the design of a parallel algorithm for triangulating a simple polygon deterministically in O(log n) time using O(n= log n) processors on a CRCW PRAM. Keywords: Computational geometry, algorithmic graph theory, planar graphs, planar separators, polygon triangulation, parallel algorithms, PRAM model. 1 Introduction Let G = (V; E) be an nnode graph. An f(n)separator is an f(n)sized subset of V whose removal disconnects G into two subgraphs G 1 and G 2 each...
Using Generic Programming for Designing a Data Structure for Polyhedral Surfaces
 Comput. Geom. Theory Appl
, 1999
"... Appeared in Computational Geometry  Theory and Applications 13, 1999, 6590. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, ..."
Abstract

Cited by 47 (6 self)
 Add to MetaCart
Appeared in Computational Geometry  Theory and Applications 13, 1999, 6590. Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedral surfaces and evaluate edgebased representations with respect to our design goals. A design for polyhedral surfaces in a halfedge data structure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and facebased structures. Key words: Library design; Generic programming; Combinatorial data structure; Polyhedral surface; Halfedge data structure 1 Introduction Combinatorial structures, such as planar maps, are fundamental in computational geometry. In order to be useful in practice, a solid library for compu...
A hybrid approach for computing visual hulls of complex objects
 In Computer Vision and Pattern Recognition
, 2003
"... This paper addresses the problem of computing visual hulls from image contours. We propose a new hybrid approach which overcomes the precisioncomplexity tradeoff inherent to voxel based approaches by taking advantage of surface based approaches. To this aim, we introduce a space discretization whi ..."
Abstract

Cited by 38 (6 self)
 Add to MetaCart
This paper addresses the problem of computing visual hulls from image contours. We propose a new hybrid approach which overcomes the precisioncomplexity tradeoff inherent to voxel based approaches by taking advantage of surface based approaches. To this aim, we introduce a space discretization which does not rely on a regular grid, where most cells are ineffective, but rather on an irregular grid where sample points lie on the surface of the visual hull. Such a grid is composed of tetrahedral cells obtained by applying a Delaunay triangulation on the sample points. These cells are carved afterward according to image silhouette information. The proposed approach keeps the robustness of volumetric approaches while drastically improving their precision and reducing their time and space complexities. It thus allows modeling of objects with complex geometry, and it also makes real time feasible for precise models. Preliminary results with synthetic and real data are presented. 1.
Simplification and Compression of 3D Meshes
 In Proceedings of the European Summer School on Principles of Multiresolution in Geometric Modelling (PRIMUS
, 1998
"... We survey recent developments in compact representations of 3D mesh data. This includes: Methods to reduce the complexity of meshes by simplification, thereby reducing the number of vertices and faces in the mesh; Methods to resample the geometry in order to optimize the vertex distribution; Methods ..."
Abstract

Cited by 31 (5 self)
 Add to MetaCart
We survey recent developments in compact representations of 3D mesh data. This includes: Methods to reduce the complexity of meshes by simplification, thereby reducing the number of vertices and faces in the mesh; Methods to resample the geometry in order to optimize the vertex distribution; Methods to compactly represent the connectivity data (the graph structure defined by the edges) of the mesh; Methods to compactly represent the geometry data (the vertex coordinates) of a mesh.
Designing a Data Structure for Polyhedral Surfaces
 In Proc. 14th Annu. ACM Sympos. Comput. Geom
, 1998
"... Design solutions for a program library are presented for combinatorial data structures in computational geometry, such as planar maps and polyhedral surfaces. Design issues considered are genericity, flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedr ..."
Abstract

Cited by 31 (2 self)
 Add to MetaCart
Design solutions for a program library are presented for combinatorial data structures in computational geometry, such as planar maps and polyhedral surfaces. Design issues considered are genericity, flexibility, time and space efficiency, and easeofuse. We focus on topological aspects of polyhedral surfaces. Edgebased representations for polyhedrons are evaluated with respect to the design goals. A design for polyhedral surfaces in a halfedge data structure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and facebased structures managing holes in facets. 1 Introduction Combinatorial structures, such as planar maps, are fundamental in computational geometry. In order to use computational geometry in practice, a solid library must provide generic and flexible solutions as one of its fundamental cornerstones. Other design criteria are time and space efficiency. Easeofuse is necessar...
FeatureBased Cellular Texturing for Architectural Models
 In Proceedings of ACM SIGGRAPH 2001, ACM
, 2001
"... Cellular patterns are all around us, in masonry, tiling, shingles, and many other materials. Such patterns, especially in architectural settings, are influenced by geometric features of the underlying shape. Bricks turn corners, stones frame windows and doorways, and patterns on disconnected portion ..."
Abstract

Cited by 30 (2 self)
 Add to MetaCart
Cellular patterns are all around us, in masonry, tiling, shingles, and many other materials. Such patterns, especially in architectural settings, are influenced by geometric features of the underlying shape. Bricks turn corners, stones frame windows and doorways, and patterns on disconnected portions of a building align to achieve a particular aesthetic goal. We present a strategy for featurebased cellular texturing, where the resulting texture is derived from both patterns of cells and the geometry to which they are applied. As part of this strategy, we perform texturing operations on features in a welldefined order that simplifies the interdependence between cells of adjacent patterns. Occupancy maps are used to indicate which regions of a feature are already occupied by cells of its neighbors, and which regions remain to be textured. We also introduce the notion of a pattern generator  the cellular texturing analogy of a shader used in local illumination  and show how several can be used together to build complex textures. We present results obtained with an implementation of this strategy and discuss details of some example pattern generators.
Grow & Fold: Compression of Tetrahedral Meshes
, 1998
"... Standard representations of irregular finite element meshes combine vertex data (sample coordinates and node values) and connectivity (tetrahedronvertex incidence). Connectivity specifies how the samples should be interpolated. It may be encoded for each tetrahedron as four vertexreferences, which ..."
Abstract

Cited by 29 (6 self)
 Add to MetaCart
Standard representations of irregular finite element meshes combine vertex data (sample coordinates and node values) and connectivity (tetrahedronvertex incidence). Connectivity specifies how the samples should be interpolated. It may be encoded for each tetrahedron as four vertexreferences, which together occupy 128 bits. Our `Grow&Fold' format reduces the connectivity storage down to 7 bits per tetrahedron: 3 of these are used to encode the presence of children in a tetrahedron spanning tree; the other 4 constrain sequences of `folding' operations, so that they produce the connectivity graph of the original mesh. Additional bits must be used for each handle in the mesh and for each topological `lock' in the tree. However, as our experiments with a prototype implementation show, the increase of the storage cost due to this extra information is typically no more than 12%. By storing vertex data in an order defined by the tree, we avoid the need to store tetrahedronvertex reference...