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34
Graph Drawing by Forcedirected Placement
, 1991
"... this paper, we introduce an algorithm that attempts to produce aestheticallypleasing, twodimensional pictures of graphs by doing simplified simulations of physical systems. We are concerned with drawing undirected graphs according to some generally accepted aesthetic criteria: 1. Distribute the v ..."
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Cited by 431 (0 self)
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this paper, we introduce an algorithm that attempts to produce aestheticallypleasing, twodimensional pictures of graphs by doing simplified simulations of physical systems. We are concerned with drawing undirected graphs according to some generally accepted aesthetic criteria: 1. Distribute the vertices evenly in the frame. 2. Minimize edge crossings. 3. Make edge lengths uniform. 4. Reflect inherent symmetry. 5. Conform to the frame. Our algorithm does not explicitly strive for these goals, but does well at distributing vertices evenly, making edge lengths uniform, and reflecting symmetry. Our goals for the implementation are speed and simplicity. PREVIOUS WORK Our algorithm for drawing undirected graphs is based on the work of Eades which, in turn, evolved from a VLSI technique called forcedirected placement
A planarreflective symmetry transform for 3d shapes
 ACM Transactions on Graphics (Proc. Siggraph
, 2006
"... Copyright © 2006 by the Association for Computing Machinery, Inc. 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 commercial advantage and that copies bear this notice and ..."
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Cited by 73 (7 self)
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Copyright © 2006 by the Association for Computing Machinery, Inc. 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 commercial advantage and that copies bear this notice and the full citation on the first page. 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, or to redistribute to lists, requires prior specific permission and/or a fee.
Viewpoint Selection using Viewpoint Entropy
, 2001
"... Computation of good viewpoints is important in several fields: computational geometry, visual servoing, robot motion, graph drawing, etc. In addition, selection of good views is rapidly becoming a key issue in computer graphics due to the new techniques of Image Based Rendering. Although there is no ..."
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Cited by 63 (13 self)
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Computation of good viewpoints is important in several fields: computational geometry, visual servoing, robot motion, graph drawing, etc. In addition, selection of good views is rapidly becoming a key issue in computer graphics due to the new techniques of Image Based Rendering. Although there is no consensus about what a good view means in Computer Graphics, the quality of a viewpoint is intuitively related to how much information it gives us about a scene. In this paper we use the theoretical basis provided by Information Theory to define a new measure, viewpoint entropy, that allows us to compute good viewing positions automatically. We also show how it can be used to select a set of N good views of a scene for scene understanding. Finally, we design an algorithm that uses this measure to explore automatically objects or scenes. 1
A FeatureDriven Approach to Locating Optimal Viewpoints for Volume Visualization
 In IEEE Visualization
, 2005
"... Figure 1: Locating optimal viewpoints by individually estimating the visibility quality of each feature subvolume. The value under each image represents its corresponding estimate normalized to [0.0, 1.0]. Optimal viewpoint selection is an important task because it considerably influences the amount ..."
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Cited by 29 (1 self)
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Figure 1: Locating optimal viewpoints by individually estimating the visibility quality of each feature subvolume. The value under each image represents its corresponding estimate normalized to [0.0, 1.0]. Optimal viewpoint selection is an important task because it considerably influences the amount of information contained in the 2D projected images of 3D objects, and thus dominates their first impressions from a psychological point of view. Although several methods have been proposed that calculate the optimal positions of viewpoints especially for 3D surface meshes, none has been done for solid objects such as volumes. This paper presents a new method of locating such optimal viewpoints when visualizing volumes using direct volume rendering. The major idea behind our method is to decompose an entire volume into a set of feature components, and then find a globally optimal viewpoint by finding a compromise between locally optimal viewpoints for the components. As the feature components, the method employs interval volumes and their combinations that characterize the topological transitions of isosurfaces according to the scalar field. Furthermore, opacity transfer functions are also utilized to assign different weights to the decomposed components so that users can emphasize features of specific interest in the volumes. Several examples of volume datasets together with their optimal positions of viewpoints are exhibited in order to demonstrate that the method can effectively guide naive users to find optimal projections of volumes.
ThreeDimensional Orthogonal Graph Drawing
, 2000
"... vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . ..."
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Cited by 27 (10 self)
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vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv I Orthogonal Graph Drawing 1 1
Cluster Stability and the Use of Noise in Interpretation of Clustering
, 2001
"... A clustering and ordination algorithm suitable for mining extremely large databases, including those produced by microarray expression studies, is described and analyzed for stability. Data from a yeast cell cycle experiment with 6000 genes and 18 experimental measurements per gene are used to test ..."
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Cited by 22 (9 self)
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A clustering and ordination algorithm suitable for mining extremely large databases, including those produced by microarray expression studies, is described and analyzed for stability. Data from a yeast cell cycle experiment with 6000 genes and 18 experimental measurements per gene are used to test this algorithm under practical conditions. The process of assigning database objects to an X, Y coordinate, ordination, is shown to be stable with respect to random starting conditions, and with respect to minor perturbations in the starting similarity estimates. Careful analysis of the way clusters typically colocate, versus the occasional large displacements under different starting conditions are shown to be useful in interpreting the data. This extra stability information is lost when only a single cluster is reported, which is currently the accepted practice. However, it is believed that the approaches presented here should become a standard part of best practices in analyzing computer clustering of large data collections.
Drawing Nice Projections of Objects in Space
, 1995
"... Given a polygonal object (simple polygon, geometric graph, wireframe, skeleton or more generally a set of line segments) in three dimensional Euclidean space, we consider the problem of computing a variety of "nice" parallel (orthographic) projections of the object. We show that given a general pol ..."
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Cited by 20 (8 self)
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Given a polygonal object (simple polygon, geometric graph, wireframe, skeleton or more generally a set of line segments) in three dimensional Euclidean space, we consider the problem of computing a variety of "nice" parallel (orthographic) projections of the object. We show that given a general polygonal object consisting of n line segments in space, deciding whether it admits a crossingfree projection can be done in O(n 2 log n+k) time and O(n 2 +k) space, where k is the number of edge intersections of forbidden quadrilaterals (i.e. set of directions that admits a crossing) and varies from zero to O(n 4 ). This implies for example that given a simple polygon in 3space we can determine if there exists a plane on which the projection is a simple polygon, within the same complexity. Furthermore, if such a projection does not exist, a minimumcrossing projection can be found in O(n 4 ) time and space. We show that an object always admits a regular projection (of interest to k...
Finding the Best Viewpoints for ThreeDimensional Graph Drawings
 Proc. 5th International Symp. on Graph Drawing (GD ’97
, 1997
"... In this paper we address the problem of finding the best viewpoints for threedimensional straightline graph drawings. We define goodness in terms of preserving the relational structure of the graph, and develop two continuous measures of goodness under orthographic parallel projection. We develop ..."
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Cited by 19 (0 self)
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In this paper we address the problem of finding the best viewpoints for threedimensional straightline graph drawings. We define goodness in terms of preserving the relational structure of the graph, and develop two continuous measures of goodness under orthographic parallel projection. We develop Voronoi variants to find the best viewpoints under these measures, and present results on the complexity of these diagrams.
Camera Control in Computer Graphics
, 2008
"... Recent progress in modelling, animation and rendering means that rich, high fidelity virtual worlds are found in many interactive graphics applications. However, the viewer’s experience of a 3D world is dependent on the nature of the virtual cinematography, in particular, the camera position, orient ..."
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Cited by 17 (2 self)
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Recent progress in modelling, animation and rendering means that rich, high fidelity virtual worlds are found in many interactive graphics applications. However, the viewer’s experience of a 3D world is dependent on the nature of the virtual cinematography, in particular, the camera position, orientation and motion in relation to the elements of the scene and the action. Camera control encompasses viewpoint computation, motion planning and editing. We present a range of computer graphics applications and draw on insights from cinematographic practice in identifying their different requirements with regard to camera control. The nature of the camera control problem varies depending on these requirements, which range from augmented manual control (semiautomatic) in interactive applications, to fully automated approaches. We review the full range of solution techniques from constraintbased to optimizationbased approaches, and conclude with an examination of occlusion management and expressiveness in the context of declarative approaches to camera control.