5. Geospatial data visualization www.esri.fi www.sciencedirect.com developers.google.com Geospatial data • Describe objects or events of the real world • Often denoted as geovisualization butdoesitfloat.com Domains of usage • Climate change • Level of unemployment • Level of education • Analysis of customer’s behaviour • Credit card payments • Criminality statistics • … Points, lines, areas • Maps consist of these three basic types of items • Spatial events are divided according to their dimension: – Point events – 0-dimensional – Line events – 1-dimensional – Area events – 2-dimensional – Surface events – 2,5-dimensional Types of maps • Maps of symbols • Point maps wildernessnavigation.blogspot.com www.alignstar.com Types of maps • Land use maps • Choropleth maps mapas.owje.com emilyness16.blogspot.com Types of maps • Line diagrams • Isoline diagrams commons.wikimedia.org pawsomemonkey.blogspot.com Types of maps • Surface maps commons.wikimedia.org Different types of representation • Same data visualized using different types of maps • E.g., cartogram – world population www.esri.com Cartograms Animated cartograms Exploratory geovisualization • Interaction is crucial – Cooperation with the user – Interactive querying • Combinationof maps with: – Statistical visualization – bar charts, line charts – Complex techniques for multidimensional data visualization (e.g., parallel coordinates) Map projection • Mapping of positions on the globe to positions on screen (from sphere to plane) • Defined as: Π: (λ, φ) → (x, y) where λ is longitude in range [-180, 180] φ is latitude in range [-90, 90] Map projections • Conformal projections – Preserve local angles → shapes, the area is not preserved members.shaw.ca Map projections • Equivalent projections, equal area – Show only part of the map, distorts shape and angles http://gis.nic.in/gisprimer/projections1.html Map projections • Equidistant projections – Preserve distance from point or line members.shaw.ca Map projections • Gnomonic projections – Show meridians and parallels of latitude as lines – Preserve the shortest path between two points – We cannot show the whole hemisphere (borders are heading to infinity) Map projections • Azimuthal projections – Preserve the direction from the central point, radially symmetrical www.physics.nyu.edu Map projections • Retroazimuthal projection – Direction from point S to point L corresponds to the direction from S to L on the map commons.wikimedia.org en.wikipedia.org Map projections – classification according to type of surface • Sphere can be projected onto different surfaces: – Cylindrical projection – Planar projection – Cone projection Cylindrical projection • Projecting the sphere surface onto cylinder positioned around the sphere • Shows the whole spherical surface • Conformal projection – preserves local angles commons.wikimedia.org Pseudo-cylindrical projection • Prime meridian and parallels are straight lines, other meridians are distorted www.geowebguru.com Planar projection • Azimuthal projection mapping the sphere surface onto a plane tangential to the sphere • Tangential point correspondsto the center of projection www.mathworks.com Cone projection • Mapping of sphere surface on the tangential cone • Latitude = spheres with centers in the center of projection • Longitude = straight lines from the center of projection en.wikipedia.org Examples of commonly used map projections • Variables used in map projections: ϕ measured degrees of latitudein radians λ measured degrees of longitude in radians x horizontalaxis of the two-dimensionalmap y vertical axis of the two-dimensionalmap ϕ0; λ0 latitudeof the standardparallelresp. meridian measured in radians Different map projections Equirectangular Lambert cylindrical Hammer-Aitoff Mollweide Cosinusodial Albers equal-areaconic Visual variables for spatial data Influence of input data corrections onto the resulting map • Sampling, segmentation, normalization, … can influence the map a lot • Different thresholds → different „borders“→ different results: Influence of input data corrections onto the resulting map • Difference between absolute and relative (here according to population size) mapping Influence of input data corrections onto the resulting map • Different clustering = different maps Geovisualization • Three basic types of objects: – Points – Lines – Areas www.spatialdatamining.org Point data visualization • Discrete, but can describe a continuous phenomenon (e.g., measuring of temperature in a given spot) • From discrete to continuous, from smooth to abrupt Point maps • Quantitative parameter can be mapped onto size or color • Beware of size – correct values for symbol sizes does not mean that we are percieving it correctly!!! • Ebbinghausillusion: diogenesii.wordpress.com Distribution of points • Possible overlaps in areas with dense data Daniel A. Keim, Christian Panse,and MikeSips.“Visual Data Miningof Large Spatial Data Sets.” In Databases in Networked Information Systems, Lecture Notes in Computer Science, 2822,Lecture Notes in Computer Science, 2822, pp. 201–215. Berlin:Springer, 2003. Methods for visualizing dense point maps • 2.5D visualization aggregating data points to regions • Data points visualized as bars PixelMaps • Shifting the overlapping pixels • Recursive algorithm utilizing quad-tree – Dividing into 4 subregions – We divide until the space in the subregion is bigger than the number of pixels in this subregion – Finally we perform the „pixel placement“ algorithm – it places the first data item to its correct position and the subsequent data items are placed to the nearest free positions PixelMaps • Problem – in datasets with high overlaps the positioning depends on the order of the data stored in database 0:00 am (EST) 6:00 am (EST) 10:00 pm (EST) 6:00 pm (EST) Line data visualization • Representation of linear phenomena using line segments between two endpoints defined by their longitude and latitude • Other parameters of data mapped onto line width, pattern, color, labeling www.theatlanticcities.com Flow maps • Eliminating line intersections and deformations of node positions while keeping their relative position • Flow of tourists in Berlin vs. migration from California Kalifornie Flow maps • Edge bundling – highlighting relations, bending of edges Area data visualization • Thematic maps are the most commonly used • Most popular = choropleth maps Area data visualization • Dasymetric maps – if we don’t know the data distributionaccording to regions • Isarhytmic maps – contours of continuous phenomena Area data visualization • Isometric maps – contours derived from real data points (e.g., temperature at a given spot) • Isopleths – data point is considered to be the center of gravity in a given region • Cartograms – scaling of region size in order to visualize statistical information Choropleth maps • Area phenomena visualized as shaded polygons enclosed by a contour • Countries, parcs, … • Problem: – Interesting values in densely populated areas – mostly small polygons ahunsberger.blogspot.com Cartograms • Generalization of thematic maps, tries to avoid problems of choropleth maps • Size of regions is changing according to given input variable associated with the geographic position of input data www.csiss.org Noncontinuous cartograms • Do not preserve topology • Scaled polygons are positioned inside the original polygons • Original size of polygons limits the size of the resulting polygons (especially when enlarging them) Noncontiguous cartograms • Scaling all polygons to their desired size • Polygons do not preserve global topology and neighboring Circular cartograms • Ignore the original shape of input polygons, they are represented by circles • Relaxation of area and topologicallimitations = similar problems as the previous case Continuous cartograms • Preserve the topology of the map • Relaxation of area and shape limitations • From all cartograms, this type preserves the best the topology of the original map Cartograms • Manual creation is complicated, automatic techniques are therefore popular • Preserve shape x preserve area Rectangular cartogram • Approximation of regions by rectangles • Division of the available screen space • Rectangles are positioned as close as possible to the original positions and to the original neighbors • RecMap algorithm RecMap algoritmus Map labeling • Positioning of text or image labels to the proximity of points, lines, and polygons • Set of different algorithms solving this problem, with different efficiency and quality of results • Mostly based on heuristic methods NASA Updates Eyes on Earth Visualization Site • https://eyes.nasa.gov/eyes-on-the-earth.html