Pub Date : 2013-02-01DOI: 10.1109/PacificVis.2013.6596152
Stefan Koch, Alexander Wiebel, Jens Kasten, M. Hlawitschka
Linear approximation plays an important role in many areas employing numerical algorithms. Particularly in the field of vector field visualization, it is the basis of widely used techniques. In this paper, we introduce two methods to extract areas in two- and three-dimensional vector fields that are connected to linear flow behavior. We propose a region-growing algorithm that extracts the linear neighborhood for a certain position. The region is characterized by linear flow behavior up to a user-defined approximation threshold. While this first method computes the size of a region given the mentioned threshold, our second method computes the quality of a linear approximation given a user-defined n-ring neighborhood. The scalar field resulting from the second method is, therefore, called affine linear approximation error. Isosurfaces of this field show regions of close-to-linear and non-linear flow behavior. We demonstrate the expressiveness and discuss the properties of the extracted regions using analytical examples and several datasets from the domain of computational fluid dynamics (CFD).
{"title":"Visualizing linear neighborhoods in non-linear vector fields","authors":"Stefan Koch, Alexander Wiebel, Jens Kasten, M. Hlawitschka","doi":"10.1109/PacificVis.2013.6596152","DOIUrl":"https://doi.org/10.1109/PacificVis.2013.6596152","url":null,"abstract":"Linear approximation plays an important role in many areas employing numerical algorithms. Particularly in the field of vector field visualization, it is the basis of widely used techniques. In this paper, we introduce two methods to extract areas in two- and three-dimensional vector fields that are connected to linear flow behavior. We propose a region-growing algorithm that extracts the linear neighborhood for a certain position. The region is characterized by linear flow behavior up to a user-defined approximation threshold. While this first method computes the size of a region given the mentioned threshold, our second method computes the quality of a linear approximation given a user-defined n-ring neighborhood. The scalar field resulting from the second method is, therefore, called affine linear approximation error. Isosurfaces of this field show regions of close-to-linear and non-linear flow behavior. We demonstrate the expressiveness and discuss the properties of the extracted regions using analytical examples and several datasets from the domain of computational fluid dynamics (CFD).","PeriodicalId":179865,"journal":{"name":"2013 IEEE Pacific Visualization Symposium (PacificVis)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129002641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-02-01DOI: 10.1109/PacificVis.2013.6596148
Anne-Marie Kermarrec, Afshin Moin
We propose FlexGD, a force-directed algorithm for straightline undirected graph drawing. The algorithm strives to draw graph layouts encompassing from uniform vertex distribution to extreme structure abstraction. It is flexible for it is parameterized so that the emphasis can be put on either of the two drawing criteria. The parameter determines how much the edges are shorter than the average distance between vertices. Extending the clustering property of the LinLog model, FlexGD is efficient for cluster visualization in an adjustable level. The energy function of FlexGD is minimized through a multilevel approach, particularly designed to work in contexts where edge length distribution is not uniform. Applying FlexGD on several real datasets, we illustrate both the good quality of the layout on various topologies, and the ability of the algorithm to meet the addressed drawing criteria.
{"title":"FlexGD: A flexible force-directed model for graph drawing","authors":"Anne-Marie Kermarrec, Afshin Moin","doi":"10.1109/PacificVis.2013.6596148","DOIUrl":"https://doi.org/10.1109/PacificVis.2013.6596148","url":null,"abstract":"We propose FlexGD, a force-directed algorithm for straightline undirected graph drawing. The algorithm strives to draw graph layouts encompassing from uniform vertex distribution to extreme structure abstraction. It is flexible for it is parameterized so that the emphasis can be put on either of the two drawing criteria. The parameter determines how much the edges are shorter than the average distance between vertices. Extending the clustering property of the LinLog model, FlexGD is efficient for cluster visualization in an adjustable level. The energy function of FlexGD is minimized through a multilevel approach, particularly designed to work in contexts where edge length distribution is not uniform. Applying FlexGD on several real datasets, we illustrate both the good quality of the layout on various topologies, and the ability of the algorithm to meet the addressed drawing criteria.","PeriodicalId":179865,"journal":{"name":"2013 IEEE Pacific Visualization Symposium (PacificVis)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124395658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-12-20DOI: 10.1109/PacificVis.2013.6596121
Jan-Hinrich Kämper, S. Kobourov, M. Nöllenburg
We present a new circular-arc cartogram model in which countries are drawn as polygons with circular arcs instead of straight-line segments. Given a political map and values associated with each country in the map, a cartogram is a distorted map in which the areas of the countries are proportional to the corresponding values. In the circular-arc cartogram model straight-line segments can be replaced by circular arcs in order to modify the areas of the polygons, while the corners of the polygons remain fixed. The countries in circular-arc cartograms have the aesthetically pleasing appearance of clouds or snowflakes, depending on whether their edges are bent outwards or inwards. This makes it easy to determine whether a country has grown or shrunk, just by its overall shape. We show that determining whether a given map and given area-values can be realized as a circular-arc cartogram is an NP-hard problem. Next we describe a heuristic method for constructing circular-arc cartograms, which uses a max-flow computation on the dual graph of the map, along with a computation of the straight skeleton of the underlying polygonal decomposition. Our method is implemented and produces cartograms that, while not yet perfectly accurate, achieve many of the desired areas in our real-world examples.
{"title":"Circular-arc cartograms","authors":"Jan-Hinrich Kämper, S. Kobourov, M. Nöllenburg","doi":"10.1109/PacificVis.2013.6596121","DOIUrl":"https://doi.org/10.1109/PacificVis.2013.6596121","url":null,"abstract":"We present a new circular-arc cartogram model in which countries are drawn as polygons with circular arcs instead of straight-line segments. Given a political map and values associated with each country in the map, a cartogram is a distorted map in which the areas of the countries are proportional to the corresponding values. In the circular-arc cartogram model straight-line segments can be replaced by circular arcs in order to modify the areas of the polygons, while the corners of the polygons remain fixed. The countries in circular-arc cartograms have the aesthetically pleasing appearance of clouds or snowflakes, depending on whether their edges are bent outwards or inwards. This makes it easy to determine whether a country has grown or shrunk, just by its overall shape. We show that determining whether a given map and given area-values can be realized as a circular-arc cartogram is an NP-hard problem. Next we describe a heuristic method for constructing circular-arc cartograms, which uses a max-flow computation on the dual graph of the map, along with a computation of the straight skeleton of the underlying polygonal decomposition. Our method is implemented and produces cartograms that, while not yet perfectly accurate, achieve many of the desired areas in our real-world examples.","PeriodicalId":179865,"journal":{"name":"2013 IEEE Pacific Visualization Symposium (PacificVis)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131545711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：