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The Contour Spectrum
, 1997
"... We introduce the contour spectrum, a user interface component that improves qualitative user interaction and provides realtime exact quantification in the visualization of isocontours. The contour spectrum is a signature consisting of a variety of scalar data and contour attributes, computed over t ..."
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Cited by 187 (33 self)
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We introduce the contour spectrum, a user interface component that improves qualitative user interaction and provides realtime exact quantification in the visualization of isocontours. The contour spectrum is a signature consisting of a variety of scalar data and contour attributes, computed over the range of scalar values w 2!.We explore the use of surface area, volume, and gradientintegral of the contour that are shown to be univariate Bspline functions of the scalar value w for multidimensional unstructured triangular grids. These quantitative properties are calculated in realtime and presented to the user as a collection of signature graphs (plots of functions of w) to assist in selecting relevant isovalues w 0 for informative visualization. For timevarying data, these quantitative properties can also be computed over time, and displayed using a 2D interface, giving the user an overview of the timevarying function, and allowing interaction in both isovalue and timestep. The effectiveness of the current system and potential extensions are discussed.
OntologyDriven Geographic Information Systems
, 1999
"... This paper introduces a geographic information system architecture based on ontologies. Ontology plays a central role in the definition of all aspects and components of an information system in the socalled ontologydriven information systems. The system presented here uses a container of interoper ..."
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Cited by 173 (22 self)
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This paper introduces a geographic information system architecture based on ontologies. Ontology plays a central role in the definition of all aspects and components of an information system in the socalled ontologydriven information systems. The system presented here uses a container of interoperable geographic objects. The objects are extracted from multiple independent data sources and are derived from a strongly typed mapping of classes from multiple ontologies. This approach provides a great level of interoperability and allows partial integration of information when completeness is impossible.
Computing Contour Trees in All Dimensions
, 1999
"... We show that contour trees can be computed in all dimensions by a simple algorithm that merges two trees. Our algorithm extends, simplifies, and improves work of Tarasov and Vyalyi and of van Kreveld et al. ..."
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Cited by 161 (11 self)
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We show that contour trees can be computed in all dimensions by a simple algorithm that merges two trees. Our algorithm extends, simplifies, and improves work of Tarasov and Vyalyi and of van Kreveld et al.
Competitive Online Routing in Geometric Graphs
 Theoretical Computer Science
, 2001
"... We consider online routing algorithms for finding paths between the vertices of plane graphs. ..."
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Cited by 55 (8 self)
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We consider online routing algorithms for finding paths between the vertices of plane graphs.
Simple Traversal of a Subdivision Without Extra Storage
 International Journal of Geographic Information Systems
, 1996
"... In this paper we show how to traverse a subdivision and to report all cells, edges and vertices, without making use of mark bits in the structure or a stack. We do this by performing a depthfirst search on the subdivision, using local criteria for deciding what is the next cell to visit. Our method ..."
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Cited by 32 (2 self)
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In this paper we show how to traverse a subdivision and to report all cells, edges and vertices, without making use of mark bits in the structure or a stack. We do this by performing a depthfirst search on the subdivision, using local criteria for deciding what is the next cell to visit. Our method is extremely simple and provably correct. The algorithm has applications in the field of Geographic Information Systems (GIS), where traversing subdivisions is a common operation, but modifying the database is unwanted or impossible. We show how to adapt our algorithm to answer related queries, such as windowing queries and reporting connected subsets of cells that have a common attribute. Finally, we show how to extend our algorithm such that it can handle convex 3dimensional subdivisions. Keywords: Subdivisions, traversal algorithms, topological data structure, windowing, three dimensions. 1 Introduction The basic spatial vector data structure in any geographic information system is the...
A OneStep Crust and Skeleton Extraction Algorithm
 Algorithmica
, 2003
"... We wish to extract the topology from scanned maps. In previous work [GNY96] this was done by extracting a skeleton from the Voronoi diagram, but this required vertex labelling and was only useable for polygon maps. We wished to take the crust algorithm of Amenta, Bern and Eppstein [ABE98] and modify ..."
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Cited by 22 (10 self)
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We wish to extract the topology from scanned maps. In previous work [GNY96] this was done by extracting a skeleton from the Voronoi diagram, but this required vertex labelling and was only useable for polygon maps. We wished to take the crust algorithm of Amenta, Bern and Eppstein [ABE98] and modify it to extract the skeleton from unlabelled vertices. We find that by reducing the algorithm to a local test on the original Voronoi diagram we may extract both a crust and a skeleton simultaneously, using a variant of the QuadEdge structure of [GS85]. We show that this crust has the properties of the original, and that the resulting skeleton has many practical uses. We illustrate the usefulness of the combined diagram with various applications.
Topological manipulation of isosurfaces
, 2004
"... In this thesis, I show how to use the topological information encoded in an abstraction called the contour tree to enable interactive manipulation of individual contour surfaces in an isosurface scene, using an interface called the flexible isosurface. Underpinning this interface are several improve ..."
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Cited by 18 (3 self)
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In this thesis, I show how to use the topological information encoded in an abstraction called the contour tree to enable interactive manipulation of individual contour surfaces in an isosurface scene, using an interface called the flexible isosurface. Underpinning this interface are several improvements and extensions to existing work on the contour tree. The first, and most critical, extension, is the path seed: a new method of generating seeds from the contour tree for isosurface extraction. The second extension is to compute geometric information called local spatial measures for contours and store this information in the contour tree. The third extension is to use local spatial measures to simplify both the contour tree and isosurface displays. This simplification can also be used for noise removal. Lastly, this thesis extends work with contour trees from simplicial meshes to arbitrary meshes, interpolants, and tessellation cases. ii Contents ii
Efficient Methods for Isoline Extraction from a Digital Elevation Model based on Triangulated Irregular Networks
 University of Utrecht, the Netherlands
, 1994
"... A data structure is presented to store a triangulated irregular network digital elevation model, from which isolines (contour lines) can be extracted very efficiently. If the network is based on n points, then for any elevation, the isolines can be obtained in O(log n + k) query time, where k is the ..."
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Cited by 17 (0 self)
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A data structure is presented to store a triangulated irregular network digital elevation model, from which isolines (contour lines) can be extracted very efficiently. If the network is based on n points, then for any elevation, the isolines can be obtained in O(log n + k) query time, where k is the number of line segments that form the isolines. This compares favorably with O(n) time by straightforward computation. When a structured representation of the isolines is needed, the same query time applies. For a fully topological representation (with adjacency), the query requires additional O(c log c) or O(c log log n) time, where c is the number of connected components of isolines. In all three cases, the required data structure has only linear size.
An Improved Algorithm for Subdivision Traversal without Extra Storage
, 2000
"... We describe an algorithm for enumerating all vertices, edges and faces of a planar subdivision stored in any of the usual pointerbased representations, while using only a constant amount of memory beyond that required to store the subdivision. The algorithm is a refinement of a method introduced ..."
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Cited by 17 (3 self)
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We describe an algorithm for enumerating all vertices, edges and faces of a planar subdivision stored in any of the usual pointerbased representations, while using only a constant amount of memory beyond that required to store the subdivision. The algorithm is a refinement of a method introduced by de Berg et al (1997), that reduces the worst case running time from O(n²) to O(n log n). We also give experimental results that show that our modified algorithm runs faster not only in the worst case, but also in many realistic cases.
CONSTANTWORKSPACE ALGORITHMS FOR GEOMETRIC PROBLEMS
 JOURNAL OF COMPUTATIONAL GEOMETRY
, 2011
"... Constantworkspace algorithms may use only constantly many cells of storage in addition to their input, which is provided as a readonly array. We show how to construct several geometric structures efficiently in the constantworkspace model. Traditional algorithms process the input into a suitabl ..."
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Cited by 16 (4 self)
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Constantworkspace algorithms may use only constantly many cells of storage in addition to their input, which is provided as a readonly array. We show how to construct several geometric structures efficiently in the constantworkspace model. Traditional algorithms process the input into a suitable data structure (like a doublyconnected edge list) that allows efficient traversal of the structure at hand. In the constantworkspace setting, however, we cannot afford to do this. Instead, we provide operations that compute the desired features on the fly by accessing the input with no extra space. The whole geometric structure can be obtained by using these operations to enumerate all the features. Of course, we must pay for the space savings by slower running times. While the standard data structure allows us to implement traversal operations in constant time, our schemes typically take linear time to read the input data in each step. We begin with two simple problems: triangulating a planar point set and finding the trapezoidal decomposition of a simple polygon. In both cases adjacent features can be enumerated in linear time per step, resulting in total quadratic running time to output the whole structure. Actually, we show that the former result carries over to the Delaunay triangulation, and hence the Voronoi diagram. This also means that we can compute the largest empty circle of a planar point set in quadratic time and constant workspace. As another application, we demonstrate how to enumerate the features of an Euclidean minimum spanning tree (EMST) in quadratic time per step, so that the whole EMST can be found in cubic time using constant workspace. Finally, we describe how to compute a shortest geodesic path between two points in a simple polygon. Although the shortest path problem in general graphs is NLcomplete [18], this constrained problem can be solved in quadratic time using only constant workspace.